The Fourth International Conference on Exotic Nuclei and Atomic Masses: Refereed and Selected Contributions

Società Italiana di Fisica

Carl J. Gross Bldg. 6000, MS-6371 Physics Division Oak Ridge National Laboratory Oak Ridge, TN 37831-6371, USA [email protected]

Witold Nazarewicz Department of Physics and Astronomy 401 Nielsen Physics Building Knoxville, TN 37996-1200, USA [email protected]

Krzysztof P. Rykaczewski Bldg. 6000, MS-6371 Physics Division Oak Ridge National Laboratory Oak Ridge, TN 37831-6371, USA [email protected]

The articles in this book originally appeared on the internet (www.eurphysj.org) as open access publication of the journal The European Physical Journal A – Hadrons and Nuclei Volume 25, Supplement 1 ISSN 1434-601X c SIF and Springer-Verlag Berlin Heidelberg 2005  Cataloging-in-Publication Data applied for Bibliographic information published by Die Deutsche Bibliothek. Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de

ISBN-10 3-540-28441-9 Springer Berlin Heidelberg New York ISBN-13 978-3-540-28441-3 Springer Berlin Heidelberg New York This work is subject to copyright. All rights reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from SIF and Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com c SIF and Springer-Verlag Berlin Heidelberg 2005  Printed in Italy The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting and Cover design: SIF Production Office, Bologna, Italy Printing and Binding: Tipografia Compositori, Bologna, Italy Printed on acid-free paper

SPIN: 11544142 – 5 4 3 2 1 0

ENAM2004 Organization

International Advisory Committee

W. NAZAREWICZ (Chairman) G. AUDI ¨ ¨ J. AYST O P.A. BUTLER J. D’AURIA C.N. DAVIDS G. DE ANGELIS D. GUILLEMAUD-MUELLER D. HABS J.H. HAMILTON J.C. HARDY M. HUYSE B. JONSON H.-J. KLUGE K. LANGANKE M. LEWITOWICZ YU.TS. OGANESSIAN E. ROECKL H. SAGAWA B.M. SHERRILL A.C. SHOTTER I. TANIHATA I.J. THOMPSON M. WIESCHER N. ZELDES E.F. ZGANJAR ˙ J. ZYLICZ

USA France Finland UK Canada USA Italy France Germany USA USA Belgium Sweden Germany Denmark France Russia Germany Japan USA Canada Japan UK USA Israel USA Poland

Local Organizing Committee

C.J. GROSS (Chairman) C. BAKTASH D.W. BARDAYAN J.C. BATCHELDER J.R. BEENE C.R. BINGHAM J.C. BLACKMON H.K. CARTER D.J. DEAN J.F. LIANG P.E. MUELLER D.C. RADFORD K.P. RYKACZEWSKI M.S. SMITH D.W. STRACENER R.L. VARNER C.-H. YU

ORNL ORNL ORNL UNIRIB ORNL University of Tennessee ORNL UNIRIB ORNL ORNL ORNL ORNL ORNL ORNL ORNL ORNL ORNL

ENAM2004 Sponsors

Institutional Supporters Department of Physics and Astronomy, University of Tennessee Department of Physics and Astronomy, Vanderbilt University International Union of Pure and Applied Physics Joint Institute for Heavy Ion Research National Science Foundation Office of Research, University of Tennessee Oak Ridge Associated Universities Oak Ridge National Laboratory Physics Division, Oak Ridge National Laboratory United States Department of Energy University Radioactive Ion Beam Consortium (UNIRIB)

Business Supporters CAEN S.p.A. Canberra European Physical Journal A - Springer IOP - Journal of Physics G Leybold Vacuum MDC Vacuum Products Corp/Insulator Seal Physical Review Letters & Physical Review C Quantar Technology Incorporated RIS (Custom electronics) Saint-Gobain Crystals WIENER Plein & Baus, USA X-ray Instrumentation Associates

The European Physical Journal A Volume 25

 List

•

Supplement 1

•

2005

of participants 33 C. Gu´enaut et al. Is N = 40 magic? An analysis of ISOLTRAP mass measurements

 Preface

1

Masses

35 C. Gu´enaut et al. Extending the mass “backbone” to short-lived nuclides with ISOLTRAP

 1.1 Overview 3 D. Lunney Latest trends in the ever-surprising field of mass measurements 9 A.H. Wapstra Atomic Mass Evaluation 2003

37 M. Sewtz et al. A MISTRAL spectrometer accoutrement for the study of exotic nuclides

41 D. Rodr´ıguez et al. Mass measurement on the rp-process waiting point 72 Kr

 1.2 Mass measurements 17 F. Herfurth et al. Recent high-precision mass measurements with the Penning trap spectrometer ISOLTRAP

23 H. Savajols et al. New mass measurements at the neutron drip-line

27 A. Jokinen et al. Ion manipulation and precision measurements at JYFLTRAP 31 C. Bachelet et al. Mass measurement of short-lived halo nuclides

45 K.S. Sharma et al. Atomic mass ratios for some stable isotopes of platinum relative to 197 Au  1.3 Traps 49 M. Block et al. The ion-trap facility SHIPTRAP Status and perspectives

51 P. Schury et al. Precision experiments with rare isotopes with LEBIT at MSU

VI 53 V.L. Ryjkov et al. TITAN project status report and a proposal for a new cooling method of highly charged ions

2

Radioactivity

 2.1 Neutron-rich nuclei

57 D. Habs et al. Development of a Penning trap system in Munich

83 P.F. Mantica β-decay studies of neutron-rich nuclei

59 R. Ringle et al. The LEBIT 9.4 T Penning trap system

89 R. Grzywacz The structure of nuclei near decay studies

61 T. Sun et al. Commissioning of the ion beam buncher and cooler for LEBIT

93 C. Mazzocchi et al. Beta-delayed γ and neutron emission near the double shell closure at 78 Ni

63 G. Sikler et al. A high-current EBIT for charge-breeding of radionuclides for the TITAN spectrometer

65 C. Weber et al. FT-ICR: A non-destructive detection for on-line mass measurements at SHIPTRAP

67 C. Yazidjian et al. Commissioning and first on-line test of the new ISOLTRAP control system  1.4 Mass modeling 71 S. Goriely et al. Recent progress in mass predictions

75 J.G. Hirsch et al. Bounds on the presence of quantum chaos in nuclear masses

79 J. J¨ anecke and T.W. O’Donnell Symmetry energies and the curvature of the nuclear mass surface

78

Ni from isomer and

95 A.F. Lisetskiy et al. Exotic nuclei near 78 Ni in a shell model approach

97 D.J. Millener Beta decays of 8 He, 9 Li, and 9 C

99 F. Sarazin et al. Halo neutrons and the β-decay of

11

101 V. Tripathi et al. Voyage to the “Island of Inversion”:

105 H. Mach et al. New structure information on

30

111 S. Gr´evy et al. Observation of the 0+ 2 state in

Mg,

44

Li

29

31

Na

Mg and

32

Mg

S

115 C.J. Gross et al. A novel way of doing decay spectroscopy at a radioactive ion beam facility

117 T. Kautzsch et al. Structure of neutron-rich even-even

124,126

Cd

VII 119 S. Rinta-Antila et al. Structure of doubly-even cadmium nuclei studied by β − decay

151 M.N. Tantawy et al. Study of the N = 77 odd-Z isotones near the protondrip line

121 J. Shergur et al. New level information on Z = 51 isotopes, and 134,135 Sb83,84

155 A.P. Robinson et al. Recoil decay tagging study of

111

Sb60

123 A. Korgul et al. On the structure of the anomalously low-lying 5/2+ state of 135 Sb

125 R.S. Chakrawarthy et al. Discovery of a new 2.3 s isomer in neutron-rich 174 Tm  2.2 Proton-rich nuclei

Tm

159 D. Seweryniak et al. Particle-core coupling in the transitional proton emitters 145,146,147 Tm

161 A. Volya and C. Davids Nuclear pairing and Coriolis effects in proton emitters

165 M. Pf¨ utzner Two-proton emission

129 A. Kankainen et al. Beta-delayed gamma and proton spectroscopy near the Z = N line

131 I. Mukha et al. Study of the (21+ ) isomer in

146

94

169 B. Blank et al. First observation of emission

54

Zn and its decay by two-proton

Ag 173 J. Rotureau et al. Microscopic theory of the two-proton radioactivity

135 M. Karny et al. Beta-decay studies near

100

Sn

139 M. Kavatsyuk et al. Beta-decay spectroscopy of

103,105

 2.4 Alpha decay 179 J. Uusitalo et al. Alpha-decay studies using the JYFL gas-filled recoil separator RITU

Sn

 2.3 Proton emitters 145 R. Grzywacz et al. Discovery of the new proton emitter

144

Tm

149 J.C. Batchelder et al. Study of fine structure in the proton radioactivity of 146 Tm

181 H. Kettunen et al. Decay studies of neutron-deficient odd-mass At and Bi isotopes

183 A.-P. Lepp¨ anen et al. Alpha-decay study of closure at Z = 92

218

U; a search for the sub-shell

VIII

3

217 M. Takechi et al. Reaction cross-sections for stable nuclei and nucleon density distribution of proton drip-line nucleus 8 B

Moments and radii

 3.1 Electromagnetic moments 187 J. Billowes Developments in laser spectroscopy at the Jyv¨ askyl¨ a IGISOL

193 M. Kowalska et al. Laser and β-NMR spectroscopy on neutron-rich magnesium isotopes

199 W. N¨ ortersh¨ auser et al. Measurement of the nuclear charge radii of

8,9

Li

The last step towards the determination of the charge radius of 11 Li

201 C. Weber et al. Effects of the pairing energy on nuclear charge radii

221 K. Tanaka et al. Nucleon density distribution of proton drip-line nucleus 17 Ne 223 A. Khouaja et al. Reaction cross-sections and reduced strong absorption radii of nuclei in the vicinity of closed shells N = 20 and N = 28 227 A. L´epine-Szily et al. Anomalous behaviour of matter radii of proton-rich Ga, Ge, As, Se and Br nuclei

4

Reactions

 4.1 Fusion 203 N. Benczer-Koller et al. First g-factor measurement using a radioactive beam

76

Kr

205 N.J. Stone et al. First nuclear moment measurement with radioactive beams by recoil-in-vacuum method: g-factor of the 132 2+ Te 1 state in

209 Y. Utsuno Anomalous magnetic moment of 9 C and shell quenching in exotic nuclei  3.2 Nuclear matter distribution 215 O.A. Kiselev et al. Investigation of nuclear matter distribution of the neutron-rich He isotopes by proton elastic scattering at intermediate energies

233 W. Loveland Fusion studies with RIBs 239 J.F. Liang et al. Sub-barrier fusion induced by neutron-rich radioactive 132 Sn 241 D. Shapira et al. Measurement of evaporation residue cross sections from reactions with radioactive neutron-rich beams  4.2 Direct reactions 245 W.N. Catford et al. First experiments on transfer with radioactive beams using the TIARA array

251 A. Gade et al. Spectroscopic factors in exotic nuclei from nucleonknockout reactions

IX 255 M. Hatano et al. First experiment of 6 He with a polarized proton target

287 E. Pollacco et al. MUST2: A new generation array for direct reaction studies

259 P. Boutachkov et al. Isobaric analog states of neutron-rich nuclei. Doppler shift as a measurement tool for resonance excitation functions

289 M. Romoli et al. The EXODET apparatus: Features and first experimental results  4.5 Theory

261 R. Kanungo et al. A new view to the structure of

19

293 A. Bonaccorso Unbound exotic nuclei studied via projectile fragmentation reactions

C

263 W. Mittig et al. Reactions induced beyond the dripline at low energy by secondary beams

295 F.M. Nunes et al. Progress on reactions with exotic nuclei

267 L. Giot et al. Study of the ground-state wave function of 6 He via the 6 He(p, t)α transfer reaction

299 S. Adhikari et al. Entrance channel dependence in compound nuclear reactions with loosely bound nuclei

 4.3 Reaction mechanism 273 M. Takashina et al. Effect of halo structure on tering

11

Be +

12

C elastic scat-

277 Chinmay Basu et al. Observation of pre-equilibrium alpha particles at extreme backward angles from 28 Si + nat Si and 28 Si + 27 Al reactions at E < 5 MeV/A

279 T.V. Chuvilskaya and A.A. Shirokova Yield of low-lying high-spin states at optimal chargeparticle reactions

5

Clusters and drip lines

 5.1 Clustering 305 Y. Kanada-En’yo et al. Cluster structure in stable and unstable nuclei

311 Fco. Miguel Marqu´es Moreno Multineutron clusters Perspectives to create nuclei 100% neutron-rich

315 G.M. Ter-Akopian et al. New insights into the resonance states of 5 H and 5 He

 4.4 Techniques and detectors  5.2 Halo nuclei 283 K.L. Jones et al. Developing techniques to study A ∼ 132 nuclei with (d, p) reactions in inverse kinematics

323 E. Garrido et al. Borromean nuclei and three-body resonances

X 363 J. Ekman et al. News on mirror nuclei in the sd and fp shells

325 T. Nakamura and N. Fukuda Breakup reactions of halo nuclei

327 R. Kanungo et al. Observation of a two-proton halo in

17

Ne

367 S. Michimasa et al. Study of single-particle states in transfer reaction

23

F using proton

 5.3 Drip lines and beyond 371 J.S. Thomas et al. Single-neutron excitations in neutron-rich N = 51 nuclei

333 M. Thoennessen Remarks about the driplines

335 A. Stolz et al. Discovery of 60 Ge and

64

375 A. Odahara et al. High-spin shape isomers and the nuclear Jahn-Teller effect

Se

339 U. Datta Pramanik et al. Studies of light neutron-rich nuclei near the drip line

343 D. Cortina-Gil et al. One-neutron knockout of

23

377 C.J. McKay et al. Identification of mixed-symmetry states in odd-A 93 Nb  6.2 Coulomb excitation of radioactive ion

O

beams 347 H.J. Ong et al. Inelastic proton scattering on

16

383 D.C. Radford et al. Coulomb excitation and transfer reactions with neutron-rich radioactive beams

C

349 S.D. Pain et al. Experimental evidence of a ν(1d5/ 2 )2 component to the 12 Be ground state

353 K.A. Gridnev et al. Stability island near the neutron-rich

6

40

O isotope

 6.1 Shell structure

100

Sn to

391 R.L. Varner et al. Coulomb excitation measurements of transition strengths in the isotopes 132,134 Sn

395 C.-H. Yu et al. Coulomb excitation of odd-A neutron-rich radioactive beams

Excited states

357 H. Grawe et al. Shell structure from nuclear astrophysics

389 N.V. Zamfir et al. 132 Te and single-particle density-dependent pairing

78

Ni: Implications for

397 H. Scheit et al. Coulomb excitation of neutron-rich beams at REXISOLDE

XI 439 L. Fortunato et al. Soft triaxial rotor in the vicinity of γ = π/6 and its extensions

403 Hiroyoshi Sakurai Spectroscopy on neutron-rich nuclei at RIKEN

409 K. Yamada et al. Reduced transition probabilities for the first 2+ excited state in 46 Cr, 50 Fe, and 54 Ni

415 H. Iwasaki et al. Intermediate-energy Coulomb excitation neutron-rich Ge isotopes around N = 50

of

the

 6.3 Deep inelastic collisions 421 A. Gadea First results of the CLARA-PRISMA setup installed at LNL

427 L. Corradi et al. Multinucleon transfer reactions studied with the heavy-ion magnetic spectrometer PRISMA

429 E. Ideguchi et al. Study of high-spin states in the secondary fusion reactions

48

Ca region by using

431 K.L. Keyes et al. Spectroscopy of Ne and Na isotopes: Preliminary results from a EUROBALL + Binary Reaction Spectrometer experiment

441 T. Grahn et al. RDDS lifetime measurement with JUROGAM + RITU 443 A. Kumar et al. Lifetime measurements and low-lying structure in 112 Sn 447 D. Tonev et al. Check for chirality in real nuclei

449 J. Pakarinen et al. Probing the three shapes in 186 Pb using in-beam γ-ray spectroscopy

451 G. Popa et al. Systematics in the structure of low-lying, non-yrast band-head configurations of strongly deformed nuclei

453 V. Werner et al. A measure for triaxiality from K (shape) invariants

455 V. Werner et al. Alternative interpretation of E0 strengths in transitional regions  6.5 Structure of fission products

 6.4 Collective excitations and shape

coexistence 435 E.A. McCutchan et al. Ground-state properties and phase/shape transitions in the IBA

437 M.S. Fetea et al. Chiral symmetry in odd-odd neutron-deficient Pr nuclei

459 S.J. Zhu et al. Soft chiral vibrations in

106

Mo

463 J.K. Hwang et al. Half-life measurement of excited states in neutronrich nuclei 465 D. Fong et al. Investigations of short half-life states from SF of 252 Cf

XII 467 E.F. Jones et al. Identification of levels in 162,164 Gd and decrease in moment of inertia between N = 98–100

503 N. Michel et al. Effects of the continuum coupling on spin-orbit splitting

469 Y.X. Luo et al. Shape transitions and triaxiality in neutron-rich oddmass Y and Nb isotopes

505 H. Masui et al. Study of drip-line nuclei with a core plus multi-valence nucleon model

471 P.M. Gore et al. Unexpected rapid variations in odd-even level staggering in gamma-vibrational bands

507 T. Papenbrock Wave function factorization of shell-model ground states

7

Nuclear structure theory

509 G. Stoitcheva et al. Shell model analysis of intruder states and high-K isomers in the fp shell

 7.1 Ab initio 475 J.P. Vary et al. Ab initio No-Core Shell Model —Recent results and future prospects

481 P. Navr´ atil et al. Ab initio no-core shell model calculations using realistic two- and three-body interactions

511 J.P. Draayer et al. Extended pairing model revisited

515 V.G. Gueorguiev et al. Application of the extended pairing model to heavy isotopes  7.3 Mean field and beyond

485 M. Wloch et al. Ab initio coupled cluster calculations for nuclei using methods of quantum chemistry

519 M. Bender and P.-H. Heenen Microscopic models for exotic nuclei

489 I. Stetcu et al. Effective operators in the NCSM formalism

525 B.K. Agrawal et al. Breathing mode energy and nuclear matter incompressibility coefficient within relativistic and nonrelativistic models

 7.2 Shell model 493 N. Michel et al. Shell-model description of weakly bound and unbound nuclear states

527 T. Nakatsukasa and K. Yabana Unrestricted TDHF studies of nuclear response in the continuum

499 M. Honma et al. Shell-model description of neutron-rich pf-shell nuclei with a new effective interaction GXPF1

531 N. Paar et al. Self-consistent relativistic QRPA studies of soft modes and spin-isospin resonances in unstable nuclei

XIII 535 H. Sagawa et al. Deformations and electromagnetic moments of light exotic nuclei 539 J. Terasaki et al. Skyrme-QRPA calculations of multipole strength in exotic nuclei 541 J. Dobaczewski et al. On the non-unitarity of the Bogoliubov transformation due to the quasiparticle space truncation

543 A. Blazkiewicz et al. 2-D lattice HFB calculations for neutron-rich zirconium isotopes

545 T. Inakura et al. Soft octupole vibrations on superdeformed states in nuclei around 40 Ca suggested by Skyrme-HF and selfconsistent RPA calculations 547 M. Kobayasi et al. Collective path connecting the oblate and prolate local minima in proton-rich N = Z nuclei around 68 Se

549 H. Ohta et al. Light exotic nuclei studied with the parity-projected Hartree-Fock method 551 W. Satula et al. Using high-spin data to constrain spin-orbit term and spin-fields of Skyrme forces The need to unify the time-odd part of the local energy density functional

553 A.S. Umar and V.E. Oberacker TDHF studies with modern Skyrme forces

555 D. Vretenar et al. Relativistic mean-field models with dependent meson-nucleon couplings

557 K. Yoshida et al. Microscopic structure of negative-parity vibrations built on superdeformed states in sulfur isotopes close to the neutron drip line

559 W. Satula et al. Cranking in isospace Applications to neutron-proton pairing and the nuclear symmetry energy

563 M. Matsuo et al. Di-neutron correlations in medium-mass neutron-rich nuclei near the dripline

567 M.V. Stoitsov et al. Large-scale HFB calculations for deformed nuclei with the exact particle number projection

569 M. Yamagami Collective excitations induced by pairing anti-halo effect 571 N. Tajima Continuum effects on the pairing in neutron drip-line nuclei studied with the canonical-basis HFB method 573 M. Yamagami and Nguyen Van Giai Pairing effects on the collectivity of quadrupole states around 32 Mg

8

Heavy elements

 8.1 Structure and chemistry 577 D. Ackermann Beyond darmstadtium —Status and perspectives of superheavy element research

medium-

583 H.W. G¨ aggeler Chemical properties of transactinides

XIV 629 J.A. Clark et al. Investigating the rp-process with the Canadian Penning trap mass spectrometer

589 Yu.Ts. Oganessian et al. New elements from Dubna

595 M.A. Stoyer et al. Random probability analysis of recent ments

48

Ca experi-

633 K.-L. Kratz et al. r-process isotopes in the

132

Sn region

599 P.T. Greenlees et al. In-beam and decay spectroscopy of transfermium elements

639 H. Schatz et al. The half-life of the doubly-magic r-process nucleus 78 Ni

605 S. Eeckhaudt et al. In-beam gamma-ray spectroscopy of

643 D.W. Bardayan et al. New 19 Ne resonance observed using an exotic beam

254

No

609 K.A. Gridnev et al. Model of binding alpha-particles and applications to superheavy elements

611 A. Baran et al. Ground-state properties of superheavy elements in macroscopic-microscopic models  8.2 Production 615 M. Trotta et al. Fusion hindrance and quasi-fission in actions

18

645 L. Barr´ on-Palos et al. 12 C + 12 C cross-section measurements at low energies

647 N.C. Summers and F.M. Nunes 7 Be breakup on heavy and light targets

649 A. Tumino et al. Quasi-free 6 Li(n, α)3 H reaction at low energy from 2 H break-up 48

Ca induced re-

Implications for super-heavy element production

619 V.Yu. Denisov Entrance-channel potentials for hot fusion reactions

 9.2 Theory 653 S. Goriely Global microscopic models for r-process calculations

659 G. Mart´ınez-Pinedo Shell-model applications in supernova physics 9

F

Nuclear astrophysics

 9.1 Experiment 623 A.E. Champagne Amazing developments in nuclear astrophysics

665 S. Typel The Trojan-Horse method for nuclear astrophysics

669 D.G. Yakovlev et al. Pycnonuclear reactions in dense stellar matter

XV 673 E. Ter´ an and C.W. Johnson A statistical spectroscopy approach for calculating nuclear level densities

 11

Radioactive ion beam production and applications  11.1 Facilities and beams

 10

Fundamental symmetries

677 K. Jungmann Fundamental symmetries and interactions —Some aspects

685 J.A. Behr et al. Weak interaction symmetries with atom traps

691 J. Engel Time-reversal violation in heavy octupole-deformed nuclei

695 J.C. Hardy and I.S. Towner Superallowed 0+ → 0+ β decay and CKM unitarity: A new overview including more exotic nuclei

699 T.V. Chuvilskaya et al. Search for P-odd time reversal noninvariance in nuclear processes

703 B.S. Nara Singh et al. Parity non-conservation in the γ-decay of polarized 17/2− isomers in 93 Tc

713 G. Savard Ion manipulation with cooled and bunched beams

719 F. Becker et al. Status of the RISING project at GSI

723 L.M. Fraile Recent highlights from ISOLDE@CERN

729 U. K¨ oster et al. ISOL beams of neutron-rich oxygen isotopes

733 R. Lichtenth¨ aler et al. Radioactive Ion beams in Brazil (RIBRAS)

737 W. Mittig and A.C.C. Villari GANIL and the SPIRAL2 project

739 P. Delahaye et al. Recent developments of the radioactive beam preparation at REX-ISOLDE

743 I. Podadera et al. Preparation of cooled and bunched ion beams at ISOLDE-CERN

705 D. Rodr´ıguez et al. The LPCTrap for the measurement of the β-ν correlation in 6 He

745 H. Penttil¨ a et al. Performance of IGISOL 3

709 T. Sumikama et al. Alignment correlation term in mass A = 8 system and G-parity irregular term

749 K. Per¨ aj¨ arvi et al. Production of beams of neutron-rich nuclei between Ca and Ni using the ion-guide technique

XVI 751 O.B. Tarasov LISE++ development: Application to projectile fission at relativistic energies

 Conference

summary

 12.1 Neutron-rich nuclei 753 A. Bonaccorso Exotic nuclei within the INFN-PI32 network

¨ o 767 J. Ayst¨ Concluding remarks of the ENAM’04 Conference

 11.2 Applications  Erratum 757 J. Benlliure Spallation reactions for nuclear waste transmutation and production of radioactive nuclear beams

763 O. Tengblad et al. TARGISOL: An ISOL-database on the web

773 C.J. McKay et al. Identification of mixed-symmetry states in odd-A 93 Nb

 Author

index

List of participants Dieter Ackermann GSI & Johannes Gutenberg-University Mainz Planckstr. 1 Darmstadt, D-64291 Germany [email protected]

Bijay Agrawal Texas A&M University Cyclotron Institute College Station, TX 77843 USA [email protected]

Matthew Amthor Michigan State University NSCL, 1 Cyclotron Michigan State University East Lansing, MI 48824-1321 USA [email protected] Corina Andreoiu University of Guelph Department of Physics MacNaughton Building Gordon Street Guelph, Ontario N1G 2W1 Canada [email protected] Ani Aprahamian University of Notre Dame Department of Physics 225 Nieuwland Science Hall Notre Dame, IN 46556 USA [email protected]

Lagy Baby Florida State University Physics Department Tallahassee, FL 32306 USA [email protected] Cyril Bachelet CSNSM Bˆatiment 108 Orsay Campus, F-91405 France [email protected] Cyrus Baktash Oak Ridge National Laboratory Physics Division, MS-6371 P.O. Box 2008 Oak Ridge, TN 37831-6371 USA [email protected] Dan Bardayan Oak Ridge National Laboratory Physics Division, Bldg. 6025, MS-6354 P.O. Box 2008 Oak Ridge, TN 37831-6354 USA [email protected] Libertad Barron Palos Universidad Nacional Autonoma de M´exico Instituto de F´ısica Apartado Postal 20-364 Ciudad Universitaria, M´exico, D.F. 01000 M´exico libertad@fisica.unam.mx

Georges Audi CSNSM Bˆ atiment 108 Orsay Campus, F-91405 France [email protected]

Jon Batchelder UNIRIB/ORAU Oak Ridge National Laboratory Bldg. 6008, MS-6374 P.O. Box 2008 Oak Ridge, TN 37831-6374 USA [email protected]

¨ o Juha Ayst¨ University of J¨askyl¨a Department of Physics Survontie 9 Jyv¨ askyl¨a, FIN-40351 Finland [email protected].fi

Marcus Beck Katholieke Universiteit Leuven Instituut voor Kern- en Stralingsfysika Celestijnenlaan 200 D Leuven, B-3001 Belgium [email protected]

XVIII

The European Physical Journal A

Frank Becker GSI Darmstadt Planckstr. 1 Darmstadt, D-64291 Germany [email protected]

Bertram Blank CEN Bordeaux-Gradignan Le Haut-Vigneau Gradignan, F-33175 France [email protected]

Jim Beene Oak Ridge National Laboratory Bldg. 6000, MS-6368 P.O. Box 2008 Oak Ridge, TN 37831-6368 USA [email protected]

Artur Blazkiewicz Vanderbilt University Physics and Astronomy Department Box 1807 - Station B Nashville, TN 37235 USA [email protected]

John Behr TRIUMF 4004 Wesbrook Mall Vancouver, BC V6T 2A3 Canada [email protected] Michael Bender Institute for Nuclear Theory University of Washington Box 351550 Seattle, WA 98195-1550 USA [email protected] Jose Benlliure University of Santiago de Compostela Facultad de F´ısica, Campus Sur Santiago de Compostela, E-15706 Spain [email protected] Jon Billowes University of Manchester Department of Physics and Astronomy Manchester, M13 9PL UK [email protected] Carrol Bingham University of Tennessee 401 Nielsen Physics Building University of Tennessee Knoxville, TN 37996-1200 USA [email protected] Jeff Blackmon Oak Ridge National Laboratory Bldg. 6025, MS-6354 P.O. Box 2008 Oak Ridge, TN 37831-6354 USA [email protected]

Michael Block GSI Darmstadt Planckstr. 1 Darmstadt, D-64291 Germany [email protected] Georg Bollen Michigan State University NSCL, South Shaw Lane East Lansing, MI 48823 USA [email protected] Angela Bonaccorso INFN - Sezione di Pisa Via F. Buonarroti, 2 Pisa, I-56127 Italy [email protected] Carmen Bonomo INFN - Laboratori Nazionali del Sud Via S. Sofia, 62 Catania, I-95123 Italy [email protected] Piotr Borycki University of Tennessee 401 Nielsen Physics Building Knoxville, TN 37996-1200 USA [email protected] Plamen Boutachkov University of Notre Dame Department of Physics Notre Dame, IN 46556 USA [email protected]

List of participants

XIX

Karlheinz Burkard GSI Darmstadt Planckstr. 1 Darmstadt, D-64291 Germany [email protected]

Yunxian Chu X-Ray Instrumentation Associates 8450 Central Avenue Newark, CA 94560 USA [email protected]

Peter Butler CERN PH-ISOLDE Gen`eva 23, CH-1211 Switzerland [email protected]

Tatjana V. Chuvilskaya Moscow State University Institute of Nuclear Physics Moscow 119899 Russia [email protected]

Chris Caron Springer Heidelberg Tiergartenstr. 17 Heidelberg, D-69121 Germany [email protected]

Yurii Chuvilskiy Skobeltsyn Institute of Nuclear Physics Moscow State University Vorob’evy Gory Moscow, 119992 Russia [email protected]

Ken Carter Oak Ridge Associated Universities Bldg. 6008, MS-6374 P.O. Box 2008 Oak Ridge, TN 37831-6374 USA [email protected]

Jason Clark Argonne National Laboratory/University of Manitoba Physics Division (Building 203) 9700 South Cass Avenue Argonne, IL 60439 USA [email protected]

Rick Casten Yale University Physics Department - WNSL 272 Whitney Avenue, P.O. Box 208124 New Haven, CT 06520-8124 USA [email protected]

Lorenzo Corradi INFN - Laboratori Nazionali di Legnaro Via Romea, 4 Legnaro (Padova), I-35020 Italy [email protected]

Wilton Catford University of Surrey Stag Hill Guildford, Surrey GU2 7SH UK [email protected]

Dolores Cortina Universidad de Santiago de Compostela Facultad de F´ısica Departamento F´ısica de Particulas Santiago de Compostela, E-15786 Spain [email protected]

Art Champagne University of North Carolina Department of Physics and Astronomy Phillips Hall, CB 3255 Chapel Hill, NC 27599 USA [email protected]

John D’Auria Simon Fraser University Chemistry Burnaby, BC V5A 1S6 Canada [email protected]

Bob Chapman University of Paisley High Street Paisley, Renfrewshire PA1 2BE UK [email protected]

Ushasi Datta Pramanik Saha Institute of Nuclear Physics Nuclear and Atomic Physics Division 1/AF Bidhannagar Kolkata, W.B. 700064 India [email protected]

XX

Barry Davids TRIUMF 4004 Wesbrook Mall Vancouver, BC V6T 2A3 Canada [email protected] Cary Davids Argonne National Laboratory Physics Division 9700 South Cass Avenue Argonne, IL 60439 USA [email protected] Giacomo de Angelis INFN - Laboratori Nazionali di Legnaro Viale dell’Universit`a, 2 Legnaro (Padova), I-35020 Italy [email protected] David Dean Oak Ridge National Laboratory Bldg. 6025, MS-6373 P.O. Box 2008 Oak Ridge, TN 37831-6373 USA [email protected]

The European Physical Journal A

Jerry Draayer Louisiana State University Physics and Astronomy Nicholson Hall Baton Rouge, LA 70803-4001 USA [email protected] Sarah Eeckhaudt askyl¨a University of Jyv¨ Department of Physics P.O. Box 35 (YFL) Jyv¨ askyl¨a, FIN-40014 Finland [email protected].fi Jorgen Ekman Lund University Department of Physics, Professorsgatan 1 Box 118 Lund, SE-22100 Sweden [email protected] Jonathan Engel University of North Carolina Department of Physics and Astronomy, CB 3255 Chapel Hill, NC 27599-3255 USA [email protected]

Pierre Delahaye CERN-ISOLDE Division PH-UIS route de Meyrin Gen`eva, CH-1211 Switzerland [email protected]

Dmitri Fedorov Aarhus University Department of Physics and Astronomy Ny Munkegade Aarhus, DK-8000 Denmark [email protected]

Vitali Denysov GSI/KINR Theory Department Planckstr. 1 Darmstadt, D-64291 Germany [email protected]

Mirela Fetea University of Richmond Physics Department 23 Westhampton Way Richmond, VA 23173 USA [email protected]

Jens Dilling TRIUMF 4004 Wesbrook Mall Vancouver, BC V6T 2A3 Canada [email protected]

Angela Fincher Oak Ridge National Laboratory Bldg. 1060COM, MS-6481 P.O. Box 2008 Oak Ridge, TN 37831-6481 USA fi[email protected]

Jacek Dobaczewski Warsaw University/Oak Ridge National Laboratory Bldg. 6025, MS-6373 P.O. Box 2008 Oak Ridge, TN 37831-6373 USA [email protected]

Dennis Fong Vanderbilt University 6301 Stevenson Center Box 1807 - Station B Nashville, TN 37235 USA [email protected]

List of participants

XXI

Lorenzo Fortunato Instituut voor Nucleaire Wetenschappen Vakgroep Subatomaire en stralingsfysica Proeftuinstraat,86 Ghent, B-9000 Belgium [email protected]

Philip Gore Vanderbilt University Department of Physics and Astronomy VU Station B 351807 Nashville, TN 37235 USA [email protected]

Luis M. Fraile CERN-ISOLDE PH Department Gen`eva, CH-1211 Switzerland [email protected]

Stephane Goriely Universite Libre de Bruxelles Institut d’Astronomie et d’Astrophysique Campus de la Plaine - CP 226 Brussels, B-1050 Belgium [email protected]

Alexandra Gade Michigan State University NSCL, 1 Cyclotron East Lansing, MI 48824-1321 USA [email protected] Andres Gadea INFN - Laboratori Nazionali di Legnaro Viale dell’Universit` a, 2 Legnaro (Padova), I-35020 Italy [email protected] Heinz Gaeggeler Paul Scherrer Institut Laboratory for Radio- and Environmental Chemistry Villigen PSI, CH-5232 Switzerland [email protected] Alfredo Galindo-Uribarri Oak Ridge National Laboratory Bldg. 6000, MS-6368 P.O. Box 2008 Oak Ridge, TN 37831 USA [email protected] Leandro Gasques University of Notre Dame 225 Nieuwland Science Hall South Bend, IN 46556 USA [email protected] Chris Goodin Vanderbilt University Physics Department 6301 Stevenson Center Nashville, TN 38235 USA [email protected]

Tuomas Grahn askyl¨a University of Jyv¨ Department of Physics P.O. Box 35 Jyv¨ askyl¨a, FIN-40014 Finland [email protected].fi Hubert Grawe GSI Darmstadt Planckstr. 1 Darmstadt, D-64291 Germany [email protected] Paul Greenlees askyl¨a University of Jyv¨ P.O. Box 35 (YFL) Jyv¨ askyl¨a, FIN-40014 Finland [email protected].fi Carl J. Gross Oak Ridge National Laboratory Physics Division, Bldg. 6000, MS-6371 P.O. Box 2008 Oak Ridge, TN 37831-6371 USA [email protected] Robert Grzywacz University of Tennessee 401 Nielsen Physics Building Knoxville, TN 37996 USA [email protected] C´eline Gu´enaut CSNSM Bˆatiment 108 Orsay Campus, F-91405 France [email protected]

XXII

The European Physical Journal A

Vesselin Gueorguiev Louisiana State University 3650 Nicholson Drive Apt. 2171 Baton Rouge, LA 70802 USA [email protected]

Alexander Herlert University of Greifswald Institute of Physics Greifswald, D-17487 Germany [email protected]

Dieter Habs University of Munich Sektion Physik Am Coulombwall 1 Garching, D-85748 Germany [email protected]

Jorge Hirsch Universidad Nacional Autonoma de M´exico Instituto de Ciencias Nucleares A.P. 70-543 M´exico, D.F. 04510 M´exico [email protected]

Joseph Hamilton Vanderbilt University Department of Physics Box 1807 - Station B Nashville, TN 37235 USA [email protected] John Hardy Texas A&M University Cyclotron Institute College Station, TX 77843-3366 USA [email protected] Paul Hausladen Oak Ridge National Laboratory Bldg. 3500, MS-6010 P.O. Box 2008 Oak Ridge, TN 37831-6010 USA [email protected] Adam Hecht University of Maryland Department of Chemistry College Park, MD 20742 USA [email protected] Stefan Hennrich Institut f¨ ur Kernchemie Fritz-Strassmann Weg 2 Mainz, D-55128 Germany [email protected] Frank Herfurth GSI Darmstadt Planckstr. 1 Darmstadt, D-64291 Germany [email protected]

Michio Honma University of Aizu Center for Mathematical Sciences Tsururga, Ikki-machi Aizu-Wakamatsu, Fukushima 965-0001 Japan [email protected] Nathan Hoteling University of Maryland Department of Chemistry College Park, MD 20740 USA [email protected] Jae-Kwang Hwang Vanderbilt University Department of Physics Box 1807 - Station B Nashville, TN 37235 USA [email protected] Eiji Ideguchi University of Tokyo Center for Nuclear Study 2-1 Hirosawa Wako, Saitama 351-0198 Japan [email protected] Sergy Ilyushkin Mississippi State University Department of Physics & Astronomy P.O. Box 5167 Mississippi State, MS 39762-5167 USA [email protected] Tsunenori Inakura Niigata University Graduate school of Science and Technology 8050, Ikarashi Ninomachi Niigata, 650-2181 Japan [email protected]

List of participants

Hiro Iwasaki University of Tokyo Department of Physics, Faculty of Science Bldg. 1, Room 305 7-3-1 Hongo, Bunkyo Tokyo, 113-0033 Japan [email protected]

Joachim Janecke University of Michigan Department of Physics 500 East University Ann Arbor, MI 48109-1120 USA [email protected]

Micah Johnson Oak Ridge Associated Universities Bldg. 6025, MS-6354 P.O. Box 2008 Oak Ridge, TN 37831 USA [email protected]

James Johnson Jr. Enviro-Vac Systems/Leybold Vacuum USA P.O Box 10205 Knoxville, TN 37939 USA [email protected]

Ari Jokinen askyl¨a University of Jyv¨ Department of Physics P.O. Box 35 Jyv¨ askyl¨a, FIN-40014 Finland [email protected].fi

Elizabeth Jones Vanderbilt University Department of Physics and Astronomy Station B 351807 Nashville, TN 37235 USA [email protected]

Kate Jones Rutgers University/Oak Ridge National Laboratory Bldg. 6025, MS-6354 P.O. Box 2008 Oak Ridge, TN 37831-6354 USA [email protected]

XXIII

Klaus Jungmann Rijksuniversiteit Groningen, KVI Zernikelaan 25 Groningen, 9747 AA The Netherlands [email protected] Y. Kanada-En’yo High Energy Accelerator Research Organization (KEK) Oho 1-1 Tsukuba, 305-0801 Japan [email protected] Anu Kankainen University of Jyv¨ askyl¨a Department of Physics Survontie 9, P.O. Box 35 Jyv¨ askyl¨a, FIN-40014 Finland [email protected].fi Rituparna Kanungo RIKEN 2-1 Hirosawa Wako, Saitama 351-0198 Japan [email protected] Marek Karny Warsaw University Institute of Experimental Physics ul. Ho˙za 69 Warsaw, PL-00-681 Poland [email protected] Myroslav Kavatsyuk GSI Darmstadt Planckstr. 1 Darmstadt, D-64291 Germany [email protected] Heikki Kettunen University of Jyv¨ askyl¨a Department of Physics Jyv¨ askyl¨a, FIN-40014 Finland [email protected].fi Kirstine Keyes University of Paisley Institute of Physical Research, Office J123 High Street Paisley, PA1 2BE UK [email protected]

XXIV

The European Physical Journal A

Mark Kibilko SE Technical Sales, Inc. P.O. Box 2760 Windermere, FL 34786-2760 USA [email protected]

Noemie Koller Rutgers University Department of Physics and Astronomy New Brunswick, NJ 08903 USA [email protected]

Rob Kiefl University of British Columbia Department of Physics and Astronomy 6224 Agricultural Road Vancouver, BC V6T1Z1 Canada kiefl@triumf.ca

Agnieszka Korgul Warsaw University Institute of Experimental Physics ul. Ho˙za 69 Warszawa, PL-00-681 Poland [email protected]

Michael Kirson Weizmann Institute of Science Department of Particle Physics Rehovot, 76100 Israel [email protected] Oleg Kiselev Mainz University Institute of Nuclear Chemistry Fritz-Strassmann-Weg 2 Mainz, D-55128 Germany [email protected] Juergen Kluge GSI Darmstadt Atomic Physics Division Planckstr. 1 Darmstadt, D-64291 Germany [email protected] Masato Kobayashi Kyoto University Department of Physics, Graduate School of Science Kitashirakawa Kyoto, Kyoto 606-8502 Japan [email protected] Sissy Koerner NuPECC James-Franck-Str. 1 Garching, D-85748 Germany [email protected] Ulli K¨oster CERN PH Department Gen`eva 23, CH-1211 Switzerland [email protected]

Magdalena Kowalska CERN ISOLDE Gen`eva, CH-1211 Switzerland [email protected] Reiner Kr¨ ucken Technische Universit¨ at M¨ unchen Physik-Department E12 James-Franck-Str. Garching, D-85748 Germany [email protected] Karl-Ludwig Kratz University of Mainz Institut f¨ ur Kernchemie Fritz-Strassmann-Weg 2 Mainz, D-55128 Germany [email protected] Andreas Kronenberg Oak Ridge Associated Universities Bldg. 6008, MS-6374 P.O. Box 2008 Oak Ridge, TN 37831-6374 USA [email protected] Ashok Kumar University of Kentucky Department of Physics and Astronomy Lexington, KY 40506 USA [email protected] Sherry Lamb University of Tennessee JIHIR Bldg. 6008, MS-6374 P.O. Box 2008 Oak Ridge, TN 37831 USA [email protected]

List of participants

Karlheinz Langanke University of Aarhus Institute for Physics and Astronomy Ny Munkegade Bld 520 Aarhus, DK-8000 Denmark [email protected]

XXV

Rubens Lichtenth¨ aler Universidade de S˜ ao Paulo Instituto de F´ısica, Departamento de F´ısica Nuclear ao, 187 Travessa R da Rua do Mat˜ S˜ ao Paulo, SP 05508-900 Brazil [email protected]

Mary Ruth Lay Oak Ridge National Laboratory Physics Department, Bldg. 6000, MS-6371 P.O. Box 2008 Oak Ridge, TN 37831-6371 USA [email protected]

Alexander Lisetskiy Michigan State University NSCL, 1 Cyclotron Laboratory East Lansing, MI 48824 USA [email protected]

Alinka Lepine-Szily University of S˜ ao Paulo Institute of Physics Travessa R da Rua do Mat˜ ao 187 S˜ ao Paulo, SP 05508-900 Brazil [email protected]

Walt Loveland Oregon State University 100 Radiation Center Corvallis, OR 97331 USA [email protected]

Ari Lepp¨ anen University of Jyv¨ askyl¨a Department of Physics Survontie 9 Jyv¨ askyl¨a, FIN-40014 Finland [email protected].fi

David Lunney CSNSM-IN2P3/CNRS Universit´e de Paris Sud Orsay, F-91405 France [email protected]

Marek Lewitowicz GANIL BP 55027 Caen, F-14076 France [email protected]

Yixiao Luo Lawrence Berkeley National Laboratory Nuclear Science Division MS-70-319 Berkeley, CA 94720 USA [email protected]

Ke Li Vanderbilt University Department of Physics Box 1807 - Station B Nashville, TN 37235 USA [email protected]

Henryk Mach Uppsala University ISV, Studsvik Laboratory Nykoping, SE-61182 Sweden [email protected]

Felix Liang Oak Ridge National Laboratory Physics Division, Bldg. 6000, MS-6368 P.O. Box 2008 Oak Ridge, TN 37831 USA [email protected]

Piotr Magierski Warsaw University of Technology Faculty of Physics ul. Koszykowa 75 Warsaw, PL-00-662 Poland [email protected]

Xiaoying Liang University of Paisley EEP High street Paisley, PA1 2BE UK [email protected]

Paul Mantica Michigan State University NSCL, 1 Cyclotron Road East Lansing, MI 48824 USA [email protected]

XXVI

Miguel Marques LPC-Caen 6 Boulevard du Marechal Juin Caen, F-14050 France [email protected] Gabriel Martinez Pinedo Institut d’Estudis Espacials de Catalunya Edifici Nexus 201, Gran Capit`a 2 Barcelona, E-08034 Spain [email protected] Hiroshi Masui RIKEN Heavy Ion Nuclear Physics Laboratory 2-1 Hirosawa Wako, Saitama 351-0198 Japan [email protected] Masayuki Matsuo Niigata University Graduate School of Science and Technology Ikarashi Ninocho 8050 Niigata, 950-2181 Japan [email protected] Ken Matsuyanagi Kyoto University Department of Physics, Graduate School of Science Kitashirakawa Kyoto, 606-8502 Japan [email protected] Chiara Mazzocchi University of Tennessee Department of Physics and Astronomy 401 Nielsen Physics Building Knoxville, TN 37996 USA [email protected]

The European Physical Journal A

Nicolas Michel Oak Ridge National Laboratory Bldg. 6025, MS-6373 P.O. Box 2008 Oak Ridge, TN 37831-6373 USA [email protected] S. Michimasa RIKEN 2-1 Hirosawa Wako, Saitama 351-0198 Japan [email protected] John Millener Brookhaven National Laboratory 510A Upton, NY 11973 USA [email protected] Wolfgang Mittig GANIL B.P.55027 Caen Cedex, F-14076 France [email protected] Brian Moazen Tennessee Technological University Department of Physics Cookeville, TN 38505 USA [email protected] Michael Momayezi X-Ray Instrumentation Associates 8450 Central Avenue Newark, CA 94560 USA [email protected]

Ann McCoy Oak Ridge National Laboratory Bldg. 6000, MS-6368 P.O. Box 2008 Oak Ridge, TN 37831-6368 USA [email protected]

Tohru Motobayashi RIKEN 2-1 Hirosawa Wako, Saitama 351-0198 Japan [email protected]

Deseree Meyer Yale University WNSL 272 Whitney Avenue New Haven, CT 06520 USA [email protected]

Peter Mueller Argonne National Laboratory 9700 South Cass Avenue Argonne, IL 60439 USA [email protected]

List of participants

Takashi Nakamura Tokyo Institute of Technology Department of Physics 2-12-1 O-Okayama Meguro, Tokyo 152-8551 Japan [email protected] Takashi Nakatsukasa University of Tsukuba Institute of Physics, University of Tsukuba Tsukuba, 305-8571 Japan [email protected]

XXVII

Atsuko Odahara Nishinippon Institute of Technology Aratsu 1-11 Kanda-tyo, Miyako-gun, Fukuoka-ken 800-0394 Japan [email protected] Hirofumi Ohta University of Tsukuba 1-1-1 Tennodai Tsukuba, Ibaraki 305-8571 Japan [email protected]

Petr Navratil LLNL L-414, P.O. Box 808 Livermore, CA 94551 USA [email protected]

H. Jin Ong University of Tokyo Sakurai Laboratory, Department of Physics Graduate School of Science 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 Japan [email protected]

Witek Nazarewicz University of Tennessee/ORNL Department of Physics and Astronomy 401 Nielsen Physics Building Knoxville, TN 37996 USA [email protected]

Nico Orce University of Kentucky Department of Physics & Astronomy Lexington, KY 40506 USA [email protected]

Caroline Nesaraja Oak Ridge National Laboratory Bldg. 6025, MS-6354 P.O. Box 2008 Oak Ridge, TN 37831-6354 USA [email protected]

Nils Paar University of Zagreb Physics Department Bijenicka 32 Zagreb, 10000 Croatia [email protected]

Rainer Neugart Universitaet Mainz Institut fuer Physik Staudingerweg 7 Mainz, D-55099 Germany [email protected]

Steve Pain Rutgers University/ORNL Bldg. 6025, MS-6354 P.O. Box 2008 Oak Ridge, TN 37831-6354 USA [email protected]

Gerda Neyens Katholieke Universiteit Leuven Instituut voor Kern- en Stralingsfysica Celestijnenlaan 200 D Leuven, B-3001 Belgium [email protected]

Janne Pakarinen University of Jyv¨ askyl¨a Department of Physics P.O. Box 35, Jyv¨ askyl¨a, FIN-40351 Finland [email protected].fi

Wilfried N¨ortersh¨ auser GSI Darmstadt Planckstr. 1 Darmstadt, D-64291 Germany [email protected]

Andre Papenberg University of Paisley Institue of Physical Research High Street Paisley, Renfrewshire PA1 2BE Scotland [email protected]

XXVIII

Thomas Papenbrock Oak Ridge National Laboratory/University of Tennessee ORNL Physics Division, Bldg. 6025, MS-6373 Oak Ridge, TN 37831-6373 USA [email protected] John Pavan Oak Ridge National Laboratory Bldg. 6000, MS-6371 P.O. Box 2008 Oak Ridge, TN 37831-6371 USA [email protected] Joe Pavasko Leybold Vacuum 5700 Mellon Road Export, PA 15632 USA [email protected] Heikki Penttil¨a Univeristy of Jyv¨ askyl¨a Department of Physics P.O. Box 35 YFL Jyv¨ askyl¨a, FIN-40014 Finland [email protected].fi Kari Perajarvi Lawrence Berkeley National Laboratory Nuclear Science Division One Cyclotron Rd., MS 88RO192 Berkeley, CA 94720-8101 USA [email protected] Marek Pf¨ utzner Warsaw University Institute of Experimental Physics ul. Ho˙za 69 Warszawa, PL-00-681 Poland [email protected] Andreas Piechaczek Louisiana State University 202 Nicholson Hall Department of Physics & Astronomy Baton Rouge, LA 70803 USA [email protected] Piotr Piecuch Michigan State University Department of Chemistry East Lansing, MI 48824 USA [email protected]

The European Physical Journal A

Steven C. Pieper Argonne National Laboratory Physics, Bldg. 203 Argonne, IL 60439 USA [email protected] Marek Ploszajczak GANIL BP 55027 Caen, F-14076 France [email protected] Ivan Podadera Aliseda CERN-ISOLDE Rue de Meyrin, 23 Gen`eve, CH-1211 Switzerland [email protected] Gabriela Popa University of Notre Dame Department of Physics 225 Nieuwland Science Hall Notre Dame, IN 46556-5670 USA [email protected] Riccardo Raabe Katholieke Universiteit Leuven Instituut voor Kern- en Straslingsfysica Celestijnenlaan 200 D Leuven, B-3001 Belgium [email protected] David Radford Oak Ridge National Laboratory Physics Division, Bldg. 6000, MS-6371 P.O. Box 2008 Oak Ridge, TN 37831-6371 USA [email protected] Chakrawarthy Ravuri TRIUMF Science Div., 4004 Wesbrook Mall Vancouver, BC V6T 2A3 Canada [email protected] Lee Riedinger Oak Ridge National Laboratory Office of Laboratory Director P.O. Box 2008, Bldg. 4500N Oak Ridge, TN 37831-6263 USA [email protected]

List of participants

Ryan Ringle Michigan State University NSCL, 1 Cyclotron East Lansing, MI 48824-1321 USA [email protected] Sami Rinta-Antila University of Jyv¨ askyl¨a Department of Physics P.O. Box 35 (YFL) Jyv¨ askyl¨a, FIN-40014 Finland [email protected].fi Andrew Robinson Univerity of Edinburgh Room 4420, School of Physics JCMB, The King’s Buildings, Mayfield Rd. Edinburgh, EH9 3JZ UK [email protected] Daniel Rodr´ıguez LPC-ENSICAEN 6 Boulevard du Marechal Juin Caen Cedex, F-14050 France [email protected]

XXIX

Csaba Rozsa Saint-Gobain Crystals 12345 Kinsman Road Newbury, OH 44065 USA [email protected] Krzysztof P. Rykaczewski Oak Ridge National Laboratory Physics Division, Bldg. 6000, MS-6371 P.O. Box 2008 Oak Ridge, TN 37831-6371 USA [email protected] Hiro Sagawa University of Aizu Center of Mathematical Sciences ITsuruga kki-machi Aizu Wakamatsu, Fukushima 965-8580 Japan [email protected] Hide Sakai University of Tokyo Department of Physics Hongo 7-3-1 Bunkyo Tokyo, 113-0033 Japan [email protected]

Ernst Roeckl GSI Darmstadt/Warsaw University Planckstr. 1 Darmstadt, D-64291 Germany [email protected]

Hiro Sakurai University of Tokyo Department of Physics 7-3-1 Hongo Bunkyo-ku, Tokyo 113-0033 Japan [email protected]

Mauro Romoli Istituto Nazionale di Fisica Nucleare Complesso Universitario MSA, Via Cintia Napoli, I-80125 Italy [email protected]

Fred Sarazin Colorado School of Mines Department of Physics 1523 Illinois Street Golden, CO 80401 USA [email protected]

Jimmy Rotureau GANIL Boulevard Henri Becquerel, BP 55027 Caen Cedex 5, F-14076 France [email protected]

Wojtek Satula Warsaw University Institute of Theoretical Physics ul. Ho˙za 69 Warszawa, PL-00-681 Poland [email protected]

Patricia Roussel-Chomaz GANIL Boulevard Henri Becquerel, BP 55027 Caen Cedex 5, F-14076 France [email protected]

Herve Savajols GANIL Boulevard Henri Becquerel, BP 55027 Caen Cedex, F-14470 France [email protected]

XXX

The European Physical Journal A

Guy Savard Argonne National Laboratory & University of Chicago 9700 South Cass Avenue Argonne, IL 60439 USA [email protected]

Hariprakash Sharma University of Manitoba ANL Physics Division 9700 South Cass Avenue Argonne, IL 60439 USA [email protected]

Hendrik Schatz Michigan State University NSCL, 1 Cyclotron Laboratory East Lansing, MI 48824 USA [email protected]

Kumar Sharma University of Manitoba Department of Physics and Astronomy 301 Allen Building Winnipeg, Manitoba R3T 2N2 Canada [email protected]

Heiko Scheit Max-Planck-Insitut f¨ ur Kernphysik Saupfercheckweg 1 Heidelberg, D-69117 Germany [email protected] Peter Schury Michigan State University NSCL, 1 Cyclotron East Lansing, MI 48824 USA [email protected] Stefan Schwarz Michigan State University NSCL, South Shaw Lane East Lansing, MI 48824 USA [email protected] Lutz Schweikhard Inst. of Physics University of Greifswald Domstr. 10a Greifswald, D-17487 Germany [email protected]

Brad Sherrill Michigan State University South Shaw Lane East Lansing, MI 48824 USA [email protected] Alan Shotter TRIUMF 4004 Wesbrook Mall Vancouver, BC V6T 2A3 Canada [email protected] Tanuja Shringare Texas A&M University Cyclotron Institute College Station, TX 77840 USA tanu17@rediffmail.com Kamila Sieja Maria Curie-Sklodowska University Department of Theoretical Physics Radziszewskiego 10 Lublin, PL-20-031 Poland [email protected]

Darek Seweryniak Argonne National Laboratory Physics Division 9700 South Cass Avenue Argonne, IL 60439 USA [email protected]

Gunther Sikler Max-Planck-Insitut f¨ ur Kernphysik Saupfercheckweg 1 Heidelberg, D-69117 Germany [email protected]

Dan Shapira Oak Ridge National Laboratory Physics Division, Bldg. 6000, MS-6368 P.O. Box 2008 Oak Ridge, TN 37830 USA [email protected]

Margaret Smith Institute of Physics Publishing 150 S. Independence Mall West Public Ledger Building - 929 Philadelphia, PA 19106 USA [email protected]

List of participants

Mathew Smith TRIUMF/UBC 4004 Wesbrook Mall Vancouver, BC V6T 2A3 Canada [email protected] Ionel Stetcu University of Arizona Department of Physics 1118 E 4th St. Tucson, AZ 85721 USA [email protected] Gergana Stoitcheva Oak Ridge National Laboratory Physics Division, Bldg. 6025, MS-6373 P.O. Box 2008 Oak Ridge, TN 37831 USA [email protected] Mario Stoitsov Oak Ridge National Laboratory Physics Division, Bldg. 6025, MS-6373 P.O. Box 2008 Knoxville, TN 37919 USA [email protected] Andreas Stolz Michigan State University NSCL, 1 Cyclotron East Lansing, MI 48824 USA [email protected]

XXXI

Toshiyuki Sumikama RIKEN Heavy Ion Nuclear Physics Laboratory 2-1 Hirosawa Wako, Saitama 351-0198 Japan [email protected] Neil Summers Michigan State University NSCL, 1 Cyclotron Laboratory East Lansing, MI 48824 USA [email protected] Tao Sun Michigan State University NSCL, 1 Cyclotron Laboratory East Lansing, MI 48824-1321 USA [email protected] Sam Tabor Florida State University Physics Department Talllahassee, FL 32306 USA [email protected] Naoki Tajima Fukui University Department of Applied Physics Bunkyo 3-9-1 Fukui, 910-8507 Japan [email protected]

Nick Stone Oxford University Clarendon Laboratory Parks Road, Oxford, OX1 3PU UK [email protected]

Masaaki Takashina RIKEN Heavy Ion Nuclear Physics Laboratory 2-1 Hirosawa Wako, Saitama 351-0198 Japan [email protected]

Mark Stoyer Lawrence Livermore National Laboratory L-236 7000 East Avenue Livermore, CA 94550 USA [email protected]

Kanenobu Tanaka RIKEN Heavy Ion Nuclear Physics Laboratory 2-1 Hirosawa Wako, Saitama 351-0198 Japan [email protected]

Dan Stracener Oak Ridge National Laboratory Bldg. 6000, MS-6368 P.O. Box 2008 Oak Ridge, TN 37831 USA [email protected]

Isao Tanihata Argonne National Laboratory Physics, Bldg. 203, Room F173 9700 South Cass Avenue Argonne, IL 60439 USA [email protected]

XXXII

The European Physical Journal A

Noor Tantawy University of Tennessee 401 Nielsen Physics Building Knoxville, TN 37996-1200 USA [email protected]

Vandana Tripathi Florida State University Physics Department Tallahassee, FL 32306 US [email protected]

Oleg Tarasov Michigan State University NSCL, South Shaw Lane 164 East Lansing, MI 48824-1321 USA [email protected]

Monica Trotta INFN - Sezione di Napoli Complesso Universitario MSA, Via Cintia, Ed. G Napoli, I-80126 Italy [email protected]

Gurgen Ter-Akopian Joint Institute for Nuclear Research Flerov Laboratory of Nuclear Reactions Dubna, 141980 Russia [email protected]

Stefan Typel GSI Darmstadt Planckstr. 1 Darmstadt, D-64291 Germany [email protected]

Edgar Teran San Diego State University 5500 Campanile Dr San Diego, CA 92182-1233 USA [email protected]

Sait Umar Vanderbilt University Physics and Astronomy 6301 Stevenson Center Nashville, TN 37235 USA [email protected]

Jun Terasaki University of North Carolina at Chapel Hill Department of Physics and Astronomy Phillips Hall Chapel Hill, NC 27599 USA [email protected]

Yutaka Utsuno Japan Atomic Energy Research Institute 2-4 Shirakata-Shirane, Tokai, Naka-gun Ibaraki, 319-1195 Japan [email protected]

Michael Thoennessen Michigan State University NSCL, 1 Cyclotron East Lansing, MI 48824 USA [email protected]

Vladimir Utyonkov Joint Institute for Nuclear Research Joliot-Curie 6 Dubna, Moscow region, 141980 Russia [email protected]

Jeff Thomas Rutgers University Department of Physics and Astronomy 136 Frelinghuysen Rd. Piscataway, NJ 08854-8019 USA jeff[email protected]

Juha Uusitalo University of Jyv¨ askyl¨a Department of Physics Survontie 9 Jyv¨ askyl¨a, FIN-40500 Finland [email protected].fi

Dick Todd RIS Corp. 5905 Weisbrook Lane Suite 101 Knoxville, TN 37909 USA [email protected]

Piet Van Duppen Katholieke Universiteit Leuven Instuut voor Kern- en Stralingsfysica Celestijnenlaan 200 D Leuven, B-3001 Belgium [email protected]

List of participants

Carlos Vargas Universidad Veracruzana Sebastian Camacho No. 5 Centro, CP 91000 Xalapa, Ver., 91000 M´exico [email protected]

XXXIII

Yuyan Wang University of Manitoba & Argonne National Laboratory Physics Division (Building 203) 9700 South Cass Avenue Argonne, IL 60439 USA [email protected]

Robert Varner Oak Ridge National Laboratory Bldg. 6000, MS-6368 P.O. Box 2008 Oak Ridge, TN 37831-6368 USA [email protected]

Aaldert Wapstra NIKHEF P.O. Box 41882 Amsterdam, 1009DB The Netherlands [email protected]

James Vary Iowa State University Physics Room 12 Ames, IA 50011 USA [email protected]

Roger Ward Keele University School of Chemistry and Physics Keele, Staffordshire ST5 5BG UK [email protected]

Joseph Vaz TRIUMF 4004 Wesbrook Mall Vancouver, BC V6T 2A3 Canada [email protected]

Christine Weber GSI Darmstadt Planckstr. 1 Darmstadt, D-64291 Germany [email protected]

Antonio Villari GANIL B.P. 55027 Caen, F-14000 France [email protected]

Volker Werner University of Cologne Institute for Nuclear Physics Zuelpicher Str. 77 Cologne, D-50937 Germany [email protected]

Alexander Volya Florida State University Keen 208, Department of Physics Tallahassee, FL 32306-4350 USA [email protected]

Chris Wesselborg American Physical Society Editorial Office 1 Research Road Ridge, NY 11961 USA [email protected]

Dario Vretenar University of Zagreb Physics Department Bijenicka 32 Zagreb, 10000 Croatia [email protected]

Ingo Wiedenhoever Florida State University 217 Keen Building Tallahassee, FL 32306-4350 USA [email protected]

Bill Walters University of Maryland Department of Chemistry Chemistry and Biochemistry College Park, MD 20742 USA [email protected]

Jeff Winger Mississippi State University P.O. Box 5167 Department of Physics and Astronomy Mississippi State, MS 39762-5167 USA [email protected]

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Andreas Woehr University of Notre Dame Physics Department 225 Nieuwland Science Hall Notre Dame, IN 46556 USA [email protected] Dima Yakovlev Ioffe Physical Technical Institute Politekhnicheskaya Street 26 St.-Petersburg, 194021 Russia [email protected]ffe.ru Kazunari Yamada RIKEN Heavy Ion Physics Laboratory 2-1 Hirosawa Wako, Saitama 351-0198 Japan [email protected] Masayuki Yamagami RIKEN Heavy Ion Nuclear Physics Laboratory 2-1 Hirosawa Wako, Saitama 351-0198 Japan [email protected] Chabouh Yazidjian CERN Physics Departement PHIS Gen`eva 23, CH-1211 Switzerland [email protected] Kenichi Yoshida Kyoto University Department of Physics Graduate School of Science Kitashirakawa Kyoto, 606-8502 Japan [email protected]

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Glenn Young Oak Ridge National Laboratory Physics Division, Bldg. 6025, MS-6369 P.O. Box 2008 Oak Ridge, TN 37831-6369 USA [email protected]

Chang-Hong Yu Oak Ridge National Laboratory Physics Division, Bldg. 6000, MS-6371 P.O. Box 2008 Oak Ridge, TN 37831 USA [email protected]

Nissan Zeldes The Hebrew University of Jerusalem The Racah Institute of Physics Jerusalem, 91904 Israel [email protected]

Ed Zganjar Louisiana State University Department of Physics and Astronomy Nicholson Hall Baton Rouge, LA 70803 USA [email protected]

˙ Jan Zylicz Warsaw University Institute of Experimental Physics ul. Ho˙za 69 Warsaw, PL-00-681 Warszawa Poland [email protected]

Eur. Phys. J. A 25, s01, XXXV–XXXVI (2005) DOI: 10.1140/epjad/i2005-06-102-5

EPJ A direct electronic only

Preface

The Fourth International Conference on Exotic Nuclei and Atomic Masses (ENAM’04) was held on September 12-16, 2004 at the Southern Pine Conference Center of Callaway Gardens in Pine Mountain, GA, USA and was organized by the Physics Division at Oak Ridge National Laboratory (ORNL). The conference has gained the status of the premier meeting for the physics of nuclei far from stability. The measurements and modelling of atomic masses, as well as the studies using radioactive beams are creating a substantial part of the scientific program. The ENAM conference series began after the joint meeting of the Nuclei Far from Stability (NFFS) and on Atomic Masses and Fundamental Constants (AMCO) series in 1992. Previous conferences were held in 2001 (H¨ameenlinna, Finland), 1998 (Bellaire, MI, USA), and 1995 (Arles, France). ENAM’04 welcomed 280 participants from 23 countries. Over 280 abstracts were submitted and considered by the International Advisory Committee. More than 125 oral presentations were made including 38 invited, 49 contributed and 43 short “poster advertising” talks. Over 160 posters were on display during the meeting. Many thanks go to all contributors whose work illustrates the tremendous progress in the field of exotic nuclei and atomic masses achieved ¨ o of the during last three years. The organizers would like to express their particularly warm thanks to Juha Ayst¨ University of Jyv¨askyl¨a for his summary talk, which is included here, and to the many colleagues who served as referees to this volume. The papers in this volume are published in EPJ A direct and are accessible free of charge on the internet (www.eurphysj.org). A bound and printed volume can be ordered from Springer. The conference site, Callaway Gardens, offered a professionally equipped conference center with pleasant surroundings and leisure opportunities which contributed to a successful meeting. The staff of Callaway Gardens, lead by Pam Sanners, was extremely helpful and responded quickly to all requests. Even Hurricane Ivan (see fig. 1) respected the scientific part of the meeting by waiting one hour after Juha’s summary to deliver a power failure. Two music performances made our evenings more enjoyable. The Tennessee Schmaltz featuring Dan Shapira of ORNL welcomed the participants on Sunday and inspired the dancers among us with the Klezmer-style Tennessee Schmaltz Waltz. George Carere’s Dixieland Stompers and Riverboat Drifters, enhanced by trumpeter Cary Davids

ENAM'04

Fig. 1. Many thanks to Carl Gross’ brother Jim who provided daily updates on Ivan’s path from the National Hurricane Center in Miami, FL. Photo courtesy of NOAA.

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of Argonne National Laboratory, entertained us during the banquet. Peter Butler of CERN/University of Liverpool offered a few comments and jokes and Aaldert Wapstra received a SUNAMCO medal for his work on atomic masses. We thank our Institutional and Business Supporters, listed on the following pages, for their financial support as well as their products which we use every day in our research. Generous support from our Institutional Supporters permitted us to offer financial assistance to 67 participants most of whom were students and postdocs. In fact, the average age of a conference attendee was only 42. Finally, we acknowledge the long hours of work by the Local Organizing Committee and especially to Ann McCoy, Robert Varner, Felix Liang, Sherry Lamb, and Mary Ruth Lay. Without you, this conference could not succeed. We all look forward to the next ENAM conference which will be organized in Poland, and we wish its chairman, Marek Pf¨ utzner, the very best.

Carl Gross Witek Nazarewicz Krzysztof Rykaczewski The Editors Thomas Walcher Editor-in-Chief

1 Masses 1.1 Overview

Eur. Phys. J. A 25, s01, 3–8 (2005) DOI: 10.1140/epjad/i2005-06-119-8

EPJ A direct electronic only

Latest trends in the ever-surprising field of mass measurements D. Lunneya Centre de Spectrom´etrie Nucl´eaire et de Spectrom´etrie de Masse (CSNSM), IN2P3/CNRS-Universit´e de Paris Sud, Bˆ atiment 108, F-91405 Orsay, France Received: 25 March 2005 / c Societ` Published online: 27 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The binding energy of the nucleus, from its mass, continues to be of importance —not only for various aspects of nuclear physics itself, but for other branches of physics such as weak-interaction studies and stellar nucleosynthesis. The number of dedicated programs is increasing worldwide with recent results reflecting experimental achievements worthy of admiration. A brief description is offered of the modern experimental techniques dedicated to the particularly challenging task of measuring the mass of exotic nuclides and detailed comparisons are made in order to present future projects in a critical perspective. PACS. 21.10.Dr Binding energies and masses

1 Introduction Mass measurements have a noble (and Nobel) tradition thanks to the pioneering work of Francis Aston. The link between the nuclear binding energy and stellar nuclear synthesis (forged by Eddington, among others) also dates from this ´epoque. It is difficult for new results from such a well-established field to be regarded as “hot topics” in the (popular) scientific literature. A recent headline heralded “Attogram mass measurements,” performed by solid-state physicists at Cornell [1], who fabricated a nanometer-scale cantilever and measured its vibration frequency when loaded with a cluster of gold atoms. The achievement was qualified with an interesting statement: “To get any better measurement of mass you would have to vaporize the particle and shoot its constituent molecules through a mass spectrometer.” [2] —exactly how our community makes it living1 ! By “our community” is meant nuclear physics where the bulk of atomic mass measurements is done principally because of our interest in exotic nuclei for which the binding energy gives us so much information about nuclear structure and decay modes. Masses of radionuclides are also very important in the interdisciplinary fields of weak interactions [4] and astrophysics [5]. Since there are so many more radioactive nuclides than stable ones and we still cannot really predict their masses, our community continues to prosper. Measurements of the mass are among the most precise performed, as described by a recent article in the journal Science by a group at MIT [6]. In addition to the weigha

e-mail: [email protected] Note that the goal of their work is to weigh viruses [3] —things we would never dare ionize and post-accelerate! 1

ing of chemical bonds, a principal motivation of this work is an alternate determination of the fine-structure constant, α2 . Such metrology often begs the question: what’s the point? Apart from efforts at redefining the kilogram —the only fundamental standard still represented by an artifact [7]— recent astronomical observations [8] indicate a possible variation of α over time, something that no metric theory of gravity (including general relativity) allows. Theories aiming at the unification of quantum mechanics and gravity (such as string theory) in some cases predict such variation so that experimental limits should provide important constraints (see [9, 10] for the latest on precision measurements and α’s purported variation). Even the best theory of all, QED, needs to be tested and binding energies from precision mass measurements are starting to allow us to do that [11]. One idea that has considerably stirred our community is that chaos might prevent us from ever providing accurate mass predictions [12]. While this may seem like more of a question for theorists, it seems that models are still insufficiently accurate to establish a real limit (see contribution of Hirsch et al. [13]) so that measurements are still required to improve them to the point where this assertion can be verified. The organizers asked for a review of the achievements regarding experimental mass measurements since the last ENAM conference in 2001 [14]. Having published a review article [15] on the subject in 2003, you would think that it was easy. As it turns out, the prolific activity in the field has conspired to make it a challenge with many new 2

D. Pritchard recently donated the MIT trap to Florida State University where this work will continue under the responsibility of E. Meyers.

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results in only the last 1-2 years. Only a brief description of the different techniques will be offered here, in the same spirit as [15] to which the reader is referred (as well as the recent proceedings of APAC2000 [16]) for an exhaustive bibliography. Some detailed comparisons are made using the different methods and for examining performance and complementarity. (Near) future projects are then cast in their (exciting) perspective.

2 Measurement programs and context Traditionally, we speak of two categories of mass measurements: so-called indirect techniques —reactions and decays— that produce Q-values, or energy differences; and direct (or inertial) methods of mass spectrometry where time-of-flight or cyclotron-frequency measurements of the exotic species are combined with those of wellknown reference masses, ultimately linking them to 12 C (from which the mass unit is defined). The two canonical radioactive-beam production methods, fragmentation (or fusion-evaporation) of thin targets with in-flight separation (FIFS) and thick-target, isotope separation on-line (ISOL), previously offered a clear separation between the mass measurement techniques, namely time-of-flight for the former and cyclotron frequency for the latter. Also, while the in-flight approach is generally more sensitive, the ISOL-based method is generally more accurate. Thanks to the advent of gas cells and RFQ coolers, the best of both worlds is now possible. The high precision brought by holding an ion at rest in a Penning trap can now equally be brought to bear on ions born in fragmentation at relativistic speeds (as explained in [17]). Mass measurement programs have been underway for many years at GANIL, GSI and ISOLDE. Very recently, ANL, MSU and JYFL have made their first measurements and realization is well underway at MAFF and TRIUMF. With TOFI (LANL) gone, SPEG at GANIL is now the senior program —and still very active. With fragmented projectiles, measurements of time-of-flight and rigidity are combined to determine the mass. Although the resolving power is modest, the tremendous sensitivity of their method allows them to reach the drip line for many light species. So SPEG is in an excellent position to study the migration of magic numbers [18]. Attempts have been made to improve time-of-flight measurements by lengthening the flight path using the many turns that result from injection of fusionevaporation products into the CSS2 cyclotron [19]. Some difficulties were experienced initially but recently the technique (and corresponding analysis) has been improved and the newly-measured results and revised errors now provide good agreement in all cases (see discussion below). The same idea of lengthening the time of flight can be realized in a storage ring, as with the ESR at GSI. Relativistic fragments are filtered through a mass separator and injected into the ring operated with a given rigidity where their masses can be measured two ways [20]. One is by detecting the so-called Shottky signal of a charged particle each time it passes an electrode and obtaining the

revolution frequency from the Fourier transform. Since the fragmented beam has a relatively large velocity spread, it must be cooled. This is done with an electron cooler but the process requires several seconds [21]. The second method, used to measure short-lived species, requires operating the ring in isochronous mode where the revolution frequency is (to first order) independent of the velocity spread. In this case the ions are monitored in-beam with a thin-foil detector the the revolution frequency is derived from matching successive time signals [22]. An enormous volume of mass data has been produced by the ESR, spanning a sizeable portion of the nuclear chart. In 2002, they used the fragmentation of U to produce neutron-rich species that were measured with the two techniques [23, 24]. Recently, their 1997 data was reanalyzed using all the time-correlation information available over the duration of the stored beam. The large mass harvest of heavy proton-rich nuclei out to the drip line was consequently extended and improved (thanks additionally to important α-decay links) [21]. The very drip line itself is a question of binding energy (or rather, its disappearance). We also know that for light, neutron-rich nuclides, halos manifest themselves at the dripline. The mass is a critical input parameter for halo models and due to the extremely small binding energies and very short half-lives, special techniques must be used. MISTRAL is a good example of such a technique. As a transmission, time-of-flight spectrometer using a radiofrequency “clock”, its measurement technique is very fast and as it determines the ion cyclotron frequency, it is very accurate [25]. In 2003 MISTRAL measured the mass of 11 Li (a “superlarge” nuclide —see [26]) with an accuracy of 5 keV. What is interesting is that the halo binding energy has changed by more than 20% [27]. MISTRAL is located at the end of the mother of all ISOL facilities: ISOLDE, where a few meters of beamline separate it from ISOLTRAP, the mother of all on-line Penning trap installations [28]. ISOLTRAP has pioneered most of the methods now being used (mostly) for radioactive species elsewhere3 . Starting with a gas-filled, linear RFQ trap, low-energy ion bunches are injected into a large-volume, cylindrical Penning trap for isobaric purification. The isobar of interest is retained and sent to the precision Penning trap where its cyclotron frequency is determined by measurement of its time of flight after excitation and ejection. During 2003, ISOLTRAP measured several masses of neutron-rich Ni, Cu, and Ga isotopes in an attempt to answer the question: is N = 40 magic? (for the answer, see [29]). In the course of those measurements, the triple-decker isomer 70 Cu was encountered, whose β-decaying branches had complicated spectroscopy efforts. By bringing the enormous reserve of resolving power to bear, ISOLTRAP was able to weigh each laser-selected isomeric state separately, resulting in unambiguous identification [30]. 3 Note that the original use of the Penning trap for precision measurements earned H. Dehmelt a share of the 1989 Nobel prize and that Penning traps had already been developed for mass measurements of stable species (see, e.g., [6]).

D. Lunney: Latest trends in the ever-surprising field of mass measurements

Due to its superior precision, ISOLTRAP is able to contribute to the fascinating field of weak interaction physics. The comparative half-life (or F t value) of a super-allowed beta transition gives us almost unhindered access to the weak vector coupling constant (one leg of Vud , the up-down quark element of the CKM matrix). To determine F t, the decay Q-value is needed (along with the half-life and branching ratio as well as nuclear corrections and the rate function, f ). Nine such decays are sufficiently known to contribute to CVC and unitarity tests and ISOLTRAP has recently provided the masses so that two new points [31, 32] can be added to this figure (see also [28]). The superior performance of the versatile Penning trap has naturally triggered new experimental programs. The first “clone” of ISOLTRAP was SMILETRAP located at the Manne Siegbahn Laboratory in Stockholm, generally dedicated to stable species but in high charge states. The next project was the Canadian Penning trap and after a difficult early life with its excommunication from Canada, is now in full-fledged operation [33,34]. It is the first instrument of its kind making use of “the best of both worlds”; the advantages of high energy reactions and low energy precision apparatus —linked by a gas cell (see [17]). Their first success was 68 Se, established as a waiting point of the putative rapid proton-capture process, thought to power X-ray bursts [35]. askyl¨a, a twoThe newest arrival is JYFLTRAP in Jyv¨ in-one design meaning that the isobaric separator trap and precision hyperbolic trap are located in the same magnet (inspired by SHIPTRAP, see below). The great advantage of JYFLTRAP is the host of neutron-rich refractory elements made available by the IGISOL technique, insuring a chasse gard´ee. In the course of commissioning the isobaric cooler part of JYFLTRAP, new masses of Rh [36], Ru [37] and Zr [38] nuclides were measured (some for the first time). Now the precision trap has been brought into the battle with impressive results (see [39]). Also reporting exciting prelminary results at ENAM04 were the LEBIT facility at MSU [40] and SHIPTRAP at GSI [41]. Both are new-generation instruments reaching for the best of both worlds by trapping species that issue forth from a gas cell with LEBIT trapping the products of fragmentation reactions and SHIPTRAP, those of particularly heavy-ion fusion-evaporation (eventually seeking trans-uranium elements). Finally, MAFFTRAP [42] will enjoy the copious production rates of neutron-rich species offered by thermal neutron-induced fission using the FRM-2 reactor, now operating near Garching and TITAN [43], a Penning trap system being built at TRIUMF in Vancouver, will be the first installation to use high-charge states of radioactive species (bred in an EBIT) to achieve higher accuracy (i.e., higher cyclotron frequencies) with shorter trapping times.

3 Comparisons To compare the performance of the various techniques a composite plot of experimental uncertainty vs. (weighted)

5

isobaric distance from stability was offered in [15]. The same figure is presented here (fig. 1) (the same axes and definitions are used for the sake of direct comparison with fig. 6 in [15]) for results published only since [15] went to press. The number of measurements (217) that have appeared in the last 1-2 years is remarkable. Overall, the results show that most of the various techniques have been improved in that lower uncertainty (and in some cases, better sensitivity) has been achieved. While offering only modest uncertainty, SPEG does offer the mass values that go farthest from stability. The newest SPEG results [18], though they did not reach further than [44] (those data included in fig. 6 of [15]), have seen their precision —and very likely, their accuracy— improved. The new results conform to the systematic extrapolations of the recent Atomic Mass Evaluation [45] whereas the earlier results did not, a faux pas that resulted in their exclusion from that work. The same is true for the CSS2 values that now, although having lost a little on the precision axis, now provide reliable results (see below). The ESR97 data were analyzed using time dependence —an important consequence of the storage ring technique that offers a dynamic profile of the beam. Not only could more mass values be derived but the precision was considerably improved —up to a factor of five in many cases (Note that although hundreds of masses were measured, the values shown here correspond to only the 75 new masses not produced from α-links.) A smattering of proton-rich masses measured using the IMS technique were recently published [22]. Though more modest in uncertainty, the masses in question were farther from stability. A larger IMS data set, of fission products obtained from fragmentation of a U beam, has appeared since [23]. Though not shown here, these preliminary results show a relative uncertainty of roughly 10−6 and are of particular interest in light of mass-model predictions for neutronrich nuclides. New on this figure for MISTRAL is the result for the very short-lived, drip-line nuclide 11 Li [27]. This light nuclide is one of the extreme points on the isobaric axis and the excellent precision offered by MISTRAL makes it a valuable tool in the overall quest for mass data. There are two newcomers to this figure —both from the North: the Canadian Penning Trap (now at Argonne) and the Finnish Penning Trap in Jyv¨ askyl¨a4 . Measured 68 back in 2001, the CPT Se mass was only recently published [35] due to the obligations of long consistency and error checks. The achieved uncertainty has already improved with more measurements [46]. The JYFL trap results come from on-line tests mentioned above, using the cooler trap [36,37, 38] and not the precision trap, however mass measurements using both traps have now been made [39]. The power of traps is nicely illustrated here with the latest cooler trap results showing a similar precision with those of cooled ions in the storage ring. Last (and least —in terms of experimental uncertainty), ISOLTRAP. Not only has there been an impressive harvest in the past 18 months (77 values here, in4

Both also have a common ancestor in ISOLTRAP.

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Fig. 1. Experimental uncertainty vs. (weighted) isobaric distance from stability (as in fig. 6 of [15]) of new mass results published in only the last two years. Data from SPEG: [18]; CSS2: [47]; ESR-IMS: [22]; ESR-SMS: [21]; MISTRAL: [27]; CPT: [35, 46]; ISOLTRAP: [28, 29, 31, 32, 48].

cluding some improved masses even for stable nuclides), but thanks to the pioneering error survey using carbon cluster ions [49] the uncertainty is routinely at the 10−8 level. Here, even stable nuclide masses can often be improved. Comparison with fig. 6 in [15] is striking since the majority of those earlier ISOLTRAP measurements sat at the 10−7 level, corresponding to the overly conservative systematic error addition. The enviable sensitivity of ISOLTRAP —only a few hundred ions per second are necessary to achieve such an uncertainty— combined with the enormous reserve of resolving power, enable the measurement of masses very far from stability. For details and references of these measurements, see [28]. Like any type of measurement, masses can be determined inaccurately, meaning they are wrong —even if repeated determinations with the same apparatus give the same results (i.e., high precision). Due to the high accuracy inherently required for masses, they are particularly prone to systematic errors. Aside from making detailed error surveys and consistency checks, an excellent test comes when comparing results for like masses from different techniques. In [15], several such comparisons were offered and on the whole, the various methods were quite consistent. One exception was CSS2 for which three deviating results had been published [19]. The reason for citing this example is by no means to castigate the CSS2 collaboration but simply to show that their story has a happy ending: mea-

surements with other techniques enabled a re-evaluation and improvement of their technique, deriving a more realistic experimental uncertainty [47]. Shown in fig. 2, the recent measurements of 68 Se and 80 Y are now in complete agreement with those in the literature. Also shown in fig. 2 are the very recent cases of 94–95 Kr from ISOLTRAP [50] and the ESR [23] as well as 22 Mg and 22 Na from CPT [46] and ISOLTRAP [32]. Note that the latter are perhaps the most accurate on-line measurements ever made with radioactive nuclides (note the mass difference scale over a thousand times smaller than the first case). It is worth mentioning again that all methods rely on the availability of reference masses. This gives an inherent complementarity to all of the techniques described here in that the more accurate measurements calibrate the ones that are farther from stability. In many cases for example, MISTRAL and ISOLTRAP results have been used to calibrate ESR and SPEG measurements.

4 On (and beyond) the horizon We have looked at the established mass measurement programs and what they have spawned. The Penning trap has had an enormous influence in the field. Dominating most of the performance categories, it has also proved versatile

D. Lunney: Latest trends in the ever-surprising field of mass measurements

7

Fig. 2. Comparisons of the masses of different nuclides determined by different techniques. Note the change of overall scale from 3 MeV to 2 keV. Respective data points for 68 Se from [35, 51, 52, 19, 47]; 80 Y from [19, 53, 54, 47, 55]; 94–95 Kr from [50, 23]; and 22 Mg and 22 Na from [32, 46].

enough to be found at the heart of practically every new measurement program. After the Penning trap, is there room for another type of mass spectrometer? The answer is yes. The trivial reason is that there are so many nuclides for which masses will need to be measured that a veritable battery of techniques is necessary. For the moment, the only weakness of the Penning trap is in the serial time-of-flight scheme currently utilized which is somewhat inefficient (even impossible for such cases as superheavy nuclides) so that large areas (i.e., spanning several Z values) require a lot of effort. Already this is being remedied with the development of the Fourier Transform (FT-ICR) technique that is non-destructive so that a complete measurement is possible with only one rarely produced ion (see [56]). Two other techniques are worthy of mention here: the use of electrostatic mirrors [57] and so-called “household appliances” [58]. These schemes offer an attractive alternative: masses of nuclides far from stability (i.e., short half-lives) with decent accuracy and moderate cost and effort. Of course, nothing associated with exotic nuclides comes cheap and easy but the impressive feats of the Penning trap came only with vigorous effort, sustained over many years. Amongst the myriad applications of mass measurements, perhaps the most demanding is that of nuclear astrophysics. There, the need is for masses as far as possible from stability, almost regardless of the attained precision.

Even a rudimentary mass value —provided it is accurate within the associated uncertainty— can give significant insight into the associated nuclear structure. But the key point is that these values far from stability not only provide the greatest test for nuclear mass models but are also used as diagnostics for their improvement and evolution (see [5]). The enormous harvest of masses from the ESR has proved particularly valuable in this regard. For this reason (and for nuclear structure itself) the future plans of the FAIR facility at GSI are important to mention [59]. In addition to a low energy branch (which will, naturally, include a Penning trap) new storage rings are planned, one for Schottky-type measurements (with another for faster, stochastic pre-cooling) and one for isochronous measurements. The production rates at this facility indicate that new masses will number in the thousands! Though tremendous improvements in experimental sensitivity and production techniques appear promising, the masses of many exotic nuclei of interest will certainly remain unmeasured for many years to come, leaving no choice but to resort to theory. Thus, the interplay between theory and experiment is crucial and new measurements far from stability are now used as diagnostics in the development of new microscopic mass models. If extrapolation to the drip lines remains an existential issue, at least a veritable articulation now exists between theory and experiment.

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I thank my fellow mass measurers for having produced so much new data in the short time since [15] and making me sweat profusely trying to present it all.

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Eur. Phys. J. A 25, s01, 9–13 (2005) DOI: 10.1140/epjad/i2005-06-198-5

EPJ A direct electronic only

Atomic Mass Evaluation 2003 A.H. Wapstraa National Institute of Nuclear Physics and High-Energy Physics, NIKHEF, P.O. Box 41882, 1009DB Amsterdam, The Netherlands Received: 12 September 2004 / c Societ` Published online: 15 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The new collection of atomic masses, AME, published in December 2003, comprises evaluated experimental masses and estimates for several unknown ones. PACS. 21.10.Dr Binding energies and masses

1 Mass spectroscopy and reaction and decay energies Several times in the past, most recently last year [1], we published what we thought were best values for atomic masses of nuclear ground states from experimental data. They were derived from measurements of atomic masses, and those of nuclear reactions and decays. Experimentalists invented recently three ways to make this task more complicated: A. Mass measurements are now often made for rather far unstable nuclides. Nice! But not rarely the resolution was not sufficient to separate isomers. We therefore had to develop methods to derive valuable information on ground-state masses from such measurements. B. Some groups, sometimes without saying so, used a definition for reaction energies different from the conventional one. They did accept Q as the conventional relation between the masses of initial and final nuclides (including those of the bombarding particle and the one leaving the final nuclide): Q = M i − Mf + Mp − Ms but took M to be masses of bare nuclei, not those of neutral atoms. They called it “Q corrected for screening”. Confusion resulted; even so much that in a certain paper investigating two reactions they gave, for the two reaction energies, values according to different definitions! And since our purpose is to calculate masses of neutral atoms, our input values have to be the ones according to the conventional definition. We therefore are sorry that even the Nuclear Data Group, in an issue on proton decay energies [2], used the unconventional definition! C. Groups fail sometimes to realize that the data they give are insufficient for using them in an adequate way, a

e-mail: [email protected]

Table 1. Example of overdetermined input data (all keV). 163

Re

m

Q(α) = 6568(5)

m

← 167 Ir

→

Eexc = 115.1(4.0) 163

Re

Q(α) = 6507(5)

Q(p) = 1246(7) Eexc = 175.3(2.2)

← 167 Ir →

Q(p) = 1071(6)

anyhow for our purpose. I want to mention a curious example. Some very proton-rich nuclides decay by both proton and α emission, and have isomers that do the same. And the properties of proton decays then allow to derive a value for the isomeric excitation energy. If now, as not rarely occurs, one of the two α-decays feeds a ground state, the other its isomer, they then derive too a value for the excitation energy of that isomer. The values that they give for the four differences between four different states evidently form an overdetermined set. I will consider an example (see table 1) [3]. The excitation energy of 167 Irm “has been determined from the measured proton energy difference, using the peak centroids and the energy dispersion”. Evidently, they are correlated: the error in their difference is much smaller than follows from the separate errors. Use of all four data in our least squares evaluation would unduly decrease errors in the two Q(α)’s, which must also be correlated: they yield a value for the difference in the two Eexc ’s with an error of only (4.02 −2.22 )0.5 = 3.3. No exact solution for this problem can be derived from these experimental data. As best solution, we omit one of the four data and manipulate values and errors of the remaining three to yield final values differing not too much from those given by the authors.

2 Backbone If desired in energy units, we used in our earlier atomic mass evaluations an unit based on accepting a standard constant in the Josephson relation between energy and

10

The European Physical Journal A Table 2. Conversion of mass units to energy ones.

was

1 u = 931 493 860 (70) eV90

[4]

1 u = 931 494 009.0 (7.1) eV90

was

1 eV90 = 1.000 000 006 (63) eV

[4]

1 eV90 = 1.000 000 004 (39) eV

Table 3. Proton-neutron capture gamma-ray energy values.

[6]

2224 589.0 (2.2) eV90 = 2388 176.8 (2.4) nu

[5]

2224 566.0 (0.4) eV90 = 2388 169.95 (0.42) nu

frequency. For our 2003 mass evaluation we considered whether this was still useful. As a point of departure we used the recent evaluation of natural constants by Mohr and Taylor [4] (see table 2). The resulting differences with earlier data are important only in very few cases. On the other hand, a relatively larger difference was caused when a remeasurement of the γ-rays emitted in the H(n, γ) reaction [5] revealed an error in the earlier results [6] (see table 3). The difference has a consequence for all reported (n, γ) reactions; among them for the 14 N(n, γ)15 N one. But in this case, new mass spectroscopic measurements for 14 N and 15 N also gave new results not quite agreeing with earlier ones. This is important since 14 N(n, γ)15 N is often used for calibrating (n, γ) results. Even though for several of them the differences are not large, they add up along the line of stability, the “back-bone”. For that reason we made the necessary correction in many cases. Unfortunately, lack of time and of the neccessary information prevented us doing so for a large number of new measurements presented to us, in preliminary shape, by Firestone et al. [7]. We hope that their final report will allow us to treat them in the way they deserve. Use of Penning traps resulted in better values for several light elements. Among them were the measurements on 14 N and 15 N just mentioned. Checks showed that the new results were very dependable. Yet following difficulty remains. The new mass measurements for the stable helium isotopes differ somewhat more from the previous ones than their error estimates. And especially for measurements on 3 He, discussions with the authors [8] indicated that the claimed errors must be considered optimistic. It is hoped that new measurements will clear the situation.

3 The TOFI mass values Measurements in Los Alamos, using flight time measurements on reaction products, were mentioned at ENAM1998 [9]. The authors were so kind to give us a list of resulting useful mass values of nuclides from 44 Sc to 77 Zn, with precisions of the order of a few times 100 keV. It is a pity that no discussion of them has yet appeared in the open literature. We accepted the data as reported, but feel that at least some results should be checked with newer instruments.

4 Mass values from the Isobaric Multiplet Mass Equation In the region A < 60 several atomic mass values have been reported that were derived with help of data on delayed proton decays. Such measurements may give mass values of isobaric analogues of ground-states of proton-rich nuclides. Use of a quadratic Isobaric Multiplet Mass Equation, combining such results with those for other isobaric analogues, then yield a value for that proton-rich nuclide. It was reported [10] that for A = 33 the IMME gave a wrong result. But later work showed that the discrepancy disappeared when one of the other measurements involved was repeated. Yet, we decided that we would use such results only as indication for a value chosen for that mass but reported by us as derived from systematics. Mass values derived from symmetry relations were treated in a similar way. Another source of usefull information were measurements on proton decays. Even if the ground-state decay energy could not be determined, measurement of the halflives allowed to get estimates for the decay energies, as shown, e.g., by Janas et al. [11].

5 Mass values from Penning traps The measurements on very light isotopes are not the only valuable new results using Penning traps. Many results have been reported, both near stability but also far removed, even up to very proton-rich ones. As an example I want to mention the new 133 Cs results [12]. It is now known with a precision of 22 eV - but the new value is 5 keV higher than the one we gave in our earlier evaluation, to which an error of 3 keV was assigned. Very precise values have now also been reported for 23 Na, 85 Rb, 87 Rb [12], 36 Ar [13] and 76 Ge and 76 Se [14]. For early mass spectroscopic results, which mostly formed overdetermined sets, we found in their least-squares evaluations that, as a rule, the assigned errors were underestimated by, mostly, some 50%. We took this into account in our evaluations of their combinations with one another and with reaction and decay energy results. The just-mentioned Penning trap results also form an overdetermined set. We were pleased to find, that for them the consistency factor did not differ significantly from unity. The ISOLTRAP group continued their measurements with a Penning trap. New data, with a precision only slightly worse than 10 keV, became available for nuclides from 114 Xe to 154 Dy [15,16]; and from 182 Hg to 203 At [17].

6 Other new mass measurements. The problem with isomers In Darmstadt [18], measurements were started with, essentially, the same technique as TOFI, but using a far larger instrument. Data were given for nuclides from 79 Kr up to 208 Po. The claimed precision was, in some cases, as good as a few tens of keV’s. The new measurements

A.H. Wapstra: Atomic Mass Evaluation 2003

were made with resolutions insufficient to separate isomers, with a few exceptions. And in checking this feature, the authors found some surprises. In measurements with a time resolution of some 8 seconds, one does not expect to see isomers with ten times smaller half-lives. Yet, the GSI group [18] observed the isomers in 149 Dy and 151 Er, with reported half-lives of about 1/2 s! (The excitation energies were about 2.5 MeV.) But these half-lives refer to neutral atoms. The measurements, however, were made on fully stripped nuclei. And because of the large conversion coefficients of the relevant isomeric transitions, these isomeric nuclei in their stripped states live long enough! As decided seven years ago, we collected data on decay properties of nuclei in ground- and isomeric states and published these. An updated version of this work is contained in the 2003 Atomic Mass Evaluation [1]. It should be realized that the half-lives given there refer to neutral atoms. A least squares evaluation of a combination of these new mass spectroscopic results with decay energies, discussed below, did not indicate a necessity for correction to their errors as mentioned above. The total result of these measurements is, that mass values for proton-rich nuclides are much better known than earlier.

7 The old mercury difficulty As shown in fig. 1 on page 193 of our 1985 mass evaluation [19] (see there for early references), mass spectroscopic data near mass numbers A = 160, 180, 190, 190 and 235 turned out to suggest 20–40 keV more stability than their combination with the Winnipeg data for mercury isotopes [20] and available connecting reaction and decay energies. But an adjustment of them not using the mercury data gave acceptable results; except of course for those mercury results which then came out some 20 keV high. But also the data for odd-A Hg isotopes deviated some 4 keV more than those for even-A ones. The latter were obtained in comparison with ions containing the rare 13 C isotope. This suggested that an intensity dependence might have affected these results, which we therefore did not accept. It is a pleasure to report that new Winnipeg results [21] on 183 W, 199 Hg and their combination, and also new Stockholm results [22] agree now very well with another. They also agree reasonably with the mentioned earlier accepted data. Towards lower masses, the situation is much improved due to those new Winnipeg data. Towards higher masses the situation is also better than before. Yet the earlier mass determinations of 232 Th, 235 U and 238 U together suggest more stability. A new, precise measurement in this region would be quite interesting!

8 New data on trans-uranics Somewhat unfortunately, names of most elements with Z = 104–109 earlier proposed, and accepted in the 1995 update of our 1993 evaluation were changed in 1997 [23]. Table 4 presents the differences. It also shows names and symbols for elements 110 and 111 that were proposed when the data of Darmstadt on element 110 [24] and

11

Table 4. Element names Z > 103.

Z

104 105 106 107 108 109 110 111

1995 evaluation

Dubnium Joliotium Rutherfordium Bohrium Hahnium Meitnerium No name yet No name yet

Db Jl Rf Bh Hn Mt – –

2003 evaluation

Rutherfordium Dubnium Seaborgium unchanged Hassium unchanged Darmstadtium Roentgenium

Rf Db Sg Bh Hs Mt Ds Rg

Table 5. Characteristics reported for element 112 and its daughters.

A

Z

Ref. [27]

277 273 269 265 261

112 110 108 106 104

257

102

700 μs 11.3 MeV 210 μs 11.1 MeV 21 s 9.2 MeV 13 s 8.7 MeV 11 s 8.5 MeV one case SF 15 s 8.3 MeV

Ref. [28]

10 s 2s one 56 s

9.0 MeV 8.7 MeV 8.5 MeV case SF 8.2 MeV

111 [25] were accepted recently as being a convincing discovery of these elements. Until recently, the reports [26, 27] on element 112 were not accepted as sufficiently convincing. But recently it was confirmed [28] that the (supposed) daughters [27] showed compatible decay characteristics, see table 5. And chemistry confirmed [28] that the claimed grand-daughter belongs indeed to element 108. A Dubna group reported [29, 30, 31] results interpreted as belonging to elements 114 and 116. This has not been accepted as sufficiently convincing. Indeed, Armbruster [32] expressed serious doubts in their correctness. It may be hard to interpret them otherwise. But care is necessary, as showed by the fact that an earlier claim for discovery of an isotope of element 118 by a Berkeley group had to be withdrawn [33]. Very shortly after closing the inputs for our 2003 mass adjustment, a Dubna- Livermore group [34] reported synthesis of isotopes of the new elements 115 and 113, the latter as α-decay daughters of the former. In the three observed 288 115 chains and the one of 287 115, α-decay daughters were observed down to isotopes of Z = 105 which decayed by spontaneous fission. I do not see reasons to doubt the observations; but no earlier information on the claimed daughters is available. The Dubna group strengthens their claim by remarking that the observed α-decay energies for the, supposedly, Z = 109 and 107 daughters agree well with theoretical results. But, on the other hand, those for their Z = 111, 113 and 115 ancestors are several hundreds of keV lower. They explain this by assuming that for them the observed α-rays feed excited levels. Even more recently [35] it came to our attention, that a DubnaLivermore group found evidence for element 118. With deep interest, we await future developments in this region.

12

The European Physical Journal A

The author thanks the institute NIKHEF for permission to use their facilities, and especially Mr K. Huyser for his indispensable and always prompt help.

18. 19.

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A.H. Wapstra: Atomic Mass Evaluation 2003 33. V. Ninov, K.E. Gregorich, W. Loveland, A. Ghiorso, D.C. Hoffman, D.M. Lee, H. Nitsche, W.J. Swiatecki, U.W. Kirbach, C.A. Laue, J.L. Adams, J.B. Patin, D.A. Shaughnessy, D.A. Strellis, P.A. Wilk, Phys. Rev. Lett. 89, 39901 (2002). 34. Yu.Ts. Oganessian, V.K. Utyonkov, Yu.V. Lobanov, F.Sh. Abdullin, A.N. Polyakov, I.V. Shirokovsky, Yu.S. Tsyganov, G.G. Gulbekian, S.L. Bogomolov, A.N. Mezentsev, S. Iliev, V.G. Subbotin, A.M. Sukov, A.A. Voinov, G.V. Buklanov, K. Subotic, V.I. Zagrebaev, M.G. Itkis, J.B. Patin, K.J. Moody, J.F. Wild, M.A. Stoyer, D.A.

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Shaughnessy, J.M. Kenneally, R.W. Lougheed, Phys. Rev. C 69, 021601 (2004). 35. Yu.Ts. Oganessian, V.K. Utyonkov, Yu.V. Lobanov, F.Sh. Abdullin, A.N. Polyakov, I.V. Shirokovsky, Yu.S. Tsyganov, G.G. Gulbekian, S.L. Bogomolov, B.N. Gikal, A.N. Mezentsev, S. Iliev, V.G. Subbotin, A.M. Sukov, A.A. Voinov, G.V. Buklanov, K. Subotic, V.I. Zagrebaev, M.G. Itkis, J.B. Patin, K.J. Moody, J.F. Wild, M.A. Stoyer, N.J. Stoyer, D.A. Shaughnessy, J.M. Kenneally, R.W. Lougheed, Nucl. Phys. A 734, 109 (2004).

1 Masses 1.2 Mass measurements

Eur. Phys. J. A 25, s01, 17–21 (2005) DOI: 10.1140/epjad/i2005-06-031-3

EPJ A direct electronic only

Recent high-precision mass measurements with the Penning trap spectrometer ISOLTRAP F. Herfurth1,a , G. Audi2 , D. Beck1 , K. Blaum1,3 , G. Bollen4 , P. Delahaye5 , S. George3 , C. Gu´enaut2 , A. Herlert6 , A. Kellerbauer5 , H.-J. Kluge1 , D. Lunney2 , M. Mukherjee1 , S. Rahaman1 , S. Schwarz4 , L. Schweikhard6 , C. Weber1,3 , and C. Yazidjian1 1 2 3 4 5 6

GSI, Planckstraße 1, 64291 Darmstadt, Germany CSNSM-IN2P3-CNRS, 91405 Orsay-Campus, France Institute of Physics, Johannes Gutenberg-University, 55099 Mainz, Germany NSCL, Michigan State University, East Lansing MI 48824-1321, USA CERN, 1211 Geneva 23, Switzerland Institute of Physics, Ernst-Moritz-Arndt-University, 17487 Greifswald, Germany Received: 22 October 2004 / Revised version: 11 February 2005 / c Societ` Published online: 25 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The Penning trap mass spectrometer ISOLTRAP has to date been used for the determination of close to 300 masses of radionuclides. A relative mass uncertainty of 10 −8 can now be reached. Recent highlights were measurements of rp-process nuclides as for instance 72–74 Kr or superallowed β emitters like 22 Mg, 74 Rb and 34 Ar. The heaviest nuclides measured so far with ISOLTRAP are neutron-rich radium and francium isotopes. An overview of ISOLTRAP mass measurements and details about the recent experiment on 229–232 Ra and 230 Fr are presented. PACS. 21.10.Dr Binding energies and masses – 82.80.Qx Ion cyclotron resonance mass spectrometry

1 Introduction High-precision atomic mass measurements are important for many areas of science. For nuclear physics in general it is presently sufficient to determine the mass of a large number of nuclei with a relative uncertainty of roughly 10−6 since a few 100 keV is the current uncertainty level of global theoretical models [1]. Nevertheless, there are many cases where a lower experimental uncertainty and also a high resolving power is asked for. As an example, low-lying isomeric states may spoil the measurements and hence need to be resolved [2]. Furthermore, it is not always possible to assign the levels unambiguously from decay spectroscopy alone [3]. In such cases, high-resolution mass spectroscopy as performed with ISOLTRAP can be used to clarify and to discover yet unmeasured long-lived isomers [4]. Nuclear reaction rates, which scale with the Q-value, the mass difference between initial and final state, are important input parameters for nuclear astrophysics calculations. For two processes of nucleosynthesis, the r- and the rp-process there are especially important nuclei, socalled waiting points, that determine the path as well as a

Conference presenter; e-mail: [email protected]

the timescale of the process. In the neighborhood of these nuclei mass measurements are needed with a relative uncertainty of about 10−7 [5,6,7,8]. Beta-decaying nuclei can be used as a laboratory to investigate the weak interaction and the mass is a very important parameter in this context. According to the conserved-vector-current (CVC) hypothesis the weak force should not be affected by the strong force in the nuclear environment. A test is the comparison of superallowed 0+ → 0+ decays. After application of some theoretical corrections the comparative half-life F t of these decays should be constant. Besides the decay half-life and branching ratio, the decay energy or Q-value is one of the experimentally accessible input parameters. However, since the statistical rate function f depends on Q5 the required relative mass uncertainty is 10−8 and smaller [9,10, 11, 12]. During the last years the precision of ISOLTRAP mass measurements and the applicability to very short-lived and very rare nuclei has been improved considerably. It is now possible to reach a relative mass uncertainty better than 10−8 and to investigate nuclei that are produced at a rate of only 100 ions per second. The half-life limit for a nuclide subjected to precise mass measurements is well below 100 ms [11]. This gives new insights into nuclear

18

The European Physical Journal A MCP detector Penning trap: - precision mass measurements - isomeric separation

B 5.9 T

3

Penning trap: - cooling - isobaric cleaning

B 4.7 T

2 Linear RFQ trap - stopping - accumulation - cooling

ISOLDE 1 beam (DC) 60 keV HV platform

ion bunches ~ 2.5 keV

Fig. 1. Experimental setup of the ISOLTRAP Penning trap mass spectrometer. The three main parts are: 1) a gas-filled linear radio-frequency quadrupole (RFQ) trap for retardation of ions, accumulation, cooling and bunched ejection at low energy, 2) a gas-filled cylindrical Penning trap for further cooling and isobaric separation, and 3) an ultra-high-vacuum hyperboloidal Penning trap for the mass measurement. For this, the cyclotron frequency is determined by a measurement of the time of flight of the ions ejected out of the Penning trap to a micro-channel-plate (MCP) detector.

physics with a precision that has before only been possible for stable nuclei. Additionally, the very high resolving power of up to 10 million gives access to further interesting questions of physics [13, 14, 15].

quadrupole (RFQ) trap, a gas-filled cylindrical Penning trap, and a high-vacuum hyperboloidal Penning trap. The radioactive ion beam delivered from ISOLDE is accumulated, cooled, and bunched in the linear RFQ trap. The main task of this device is to transform the 60 keV continuous ISOLDE beam into ion bunches at low energy (2–3 keV) and low emittance (≤ 10 π mm mrad) [17]. These bunches can be efficiently transported to and captured in the first, cylindrical Penning trap, where a massselective buffer-gas cooling technique is employed. It allows the trap to operate as an isobar separator with a resolving power of up to m/Δm = 105 for ions with mass number A ≈ 140 [18]. The ions are then transported to the second, hyperboloidal Penning trap [19]. This is the high-precision trap used for the mass measurements of the ions. It can also be used as an isomer separator with a resolving power of up to m/Δm = 107 [20]. The actual mass measurement is carried out via a determination of the cyclotron frequency νc = qB/(2πm) of an ion with mass m and charge q in a magnetic field of strength B. For this, an azimuthal radio-frequency field is applied to excite the ion motion. The duration TRF of the excitation determines the mass resolving power R = m/δm = ν/δν, δν ≈ 1/TRF . The energy gained from the excitation is detected by the corresponding decrease in time of flight when the ions are ejected from the trap to a detector. B is determined by measuring νc of a reference ion with a well-known mass [14]. The main contributions to the uncertainty of the frequency ratio r = νcref /νc between the frequency of the reference ion νcref and that of the ion of interest νc are unnoticed magnetic-field changes and different orbits in the trap for reference ion and radioactive ion due to their mass difference. The magnitudes of these uncertainties have been investigated in a large number of carbon-cluster ions cross-reference measurements [14]. A residual deviation of only δr/r = 8 · 10−9 was found during these investigations [14]. The measured frequency ratio r = νcref /νc is converted into the atomic mass value m for the measured nuclide by m = r · (mref − me ) + me

2 The ISOLTRAP mass spectrometer ISOLTRAP is a triple-trap mass-spectrometer setup at the on-line mass separator ISOLDE [16]. Radioactive nuclides are produced by bombarding a thick target with 1 or 1.4 GeV proton pulses with an average intensity of 2 μA. The produced atoms diffuse out of the target and are ionized either by a plasma discharge, surface ionization, or resonant laser ionization. The ions are accelerated to 60 keV and mass separated by a magnetic sector field of resolving power R = m/Δm of up to 8000. The ion beam is transported to the ISOLTRAP setup where it is efficiently stopped and cleaned from possibly remaining isobaric and isomeric contaminants before the mass of a radioactive nuclide can be measured. To this end the ISOLTRAP spectrometer consists of three main parts as shown in fig. 1: a gas-filled linear radio-frequency

(1)

with the electron mass me and the atomic mass of the reference nuclide mref .

3 ISOLTRAP mass measurements 3.1 Overview and recent highlights ISOLTRAP mass measurements span the whole range of physics presented in the introduction. Since they started in the late 1980s [21, 22] close to 300 nuclides have been investigated as listed in table 1. In the beginning, the technique of collecting the radioactive beam on a foil and releasing it by heating gave access only to surface ionizable elements. A large number of measurements of isotopes of alkali elements originate

F. Herfurth et al.: Recent high-precision mass measurements with the Penning trap spectrometer ISOLTRAP Table 1. List of short-lived nuclei whose mass was measured with ISOLTRAP.

Element Ne Ne Na Mg K Ar

Cr Mn Ni Cu Ga Se Br Kr

Rb

Sr

Ag Sn Xe Cs

Ba Ce Pr Nd Pm Sm Eu Dy Ho Tm Yb Hg Tl Pb Bi Po At Fr

Ra

Mass number 17 18, 19, 23, 24 21, 22 22 35 . . . 38, 43 . . . 46 33, 34, 42, 43 34 32, 44, 45, 46 56, 57 56, 57 57, 65 . . . 69 66 . . . 74, 76 63 . . . 65, 70, 72 . . . 78 70 . . . 73 72 . . . 74 74 . . . 78 72 . . . 74 87 . . . 95 75 . . . 84, 86, 88 . . . 94 74 82m 78 . . . 83, 87, 91 . . . 95 76, 77 92 98 . . . 101, 103 128 . . . 132 114 . . . 123 117 . . . 132, 134 . . . 142 124, 127 145, 147 123 . . . 128, 131, 139 . . . 144 130 132 . . . 134 133 . . . 137 130, 132, 134 . . . 138 136 . . . 141, 143 136 . . . 143 139, 141 . . . 149, 151, 153 148, 149, 154 150 165 158 . . . 164 179 . . . 195, 197 181, 183, 186m, 187, 196m 196, 198 187, 197m 197 190 . . . 196, 215, 216 198 203 209 . . . 212, 221, 222 203, 205, 229 230 214, 229, 230 226, 230 229 . . . 232

(a ) Measured in 2002, to be published. (b ) Measured in 2004, to be published.

Reference (b)

[23] [12] [12] (b)

[24] [13] [25] [26] [26] [27] [27] [27] (a) (a)

[13, 11] [8] (b)

[28, 29] [13, 11] [26] [28, 29] [30] [26] (a)

[30] [31] [32] [26] [33] [32, 34] [26] [35] [34] [34] [34] [34] [34, 35] [34, 35] [34] [35] [35] [4] [33] [4] [33] [4, 33] [33] [4] [4] [36] [33] this work [33] [36, 32] this work

19

from this time [28, 32,36]. The first important improvement was obtained when the first Penning trap was reconstructed and decoupled from the collection foil. This new trap could be used to purify the ISOLDE ion beam from isobaric contaminations very efficiently. This led to successful measurements in the rare-earths region of the chart of nuclei [34]. The next important step was the replacement of the collector foil by a large cylindrical Paul trap. This buffer-gas filled trap made it possible to stop and accumulate all elements produced at ISOLDE. A long chain of mercury isotopes and some heavier bismuth, polonium and astatine isotopes [4] have been measured after the installation of this device. The impact on the mass surface was considerable since there where many alphadecay chains linked to the measured mercury isotopes. The main challenge was the resolution of low-lying, long-lived isomeric states in order to identify the ground state unambiguously. Later, to improve the efficiency, the large Paul trap has been replaced by a linear radio-frequency structure that is presently used [17]. The boost in efficiency enabled measurements on even more exotic nuclei as for instance the very short-lived 33 Ar [37]. Since then a large number of nuclides has been investigated and measured with ISOLTRAP (table 1). A recent highlight is the measurement of the mass of 22 Mg and its reaction partners with unprecedented precision. These studies are motivated by both, nuclear astrophysics and a standard model test. Ten independent frequency ratios between 22,24 Mg, 21–23 Na, and 37,39 K were measured with a relative uncertainty of 10−8 . A leastsquares adjustment with input data from the Atomic Mass Evaluation 2003 [38] for 24 Mg, 23 Na, and 37,39 K determined the mass and β-decay Q values with an uncertainty of about 250 eV [12]. This allowed, together with the branching ratio and half-life measurements from [39] as well as the theoretical corrections from [40], to obtain a corrected F t-value that is almost comparable to nine decays previously studied with high precision [41]. The uncertainty in F t is still about 2.5 times higher than for the best cases but it is now mainly due to the branching-ratio uncertainty [41]. With the mass measurements of 74 Rb [11], the shortest-lived nucleus ever investigated in a Penning trap (T1/2 = 65 ms), that of its daughter 74 Kr, and that of 34 Ar it became possible to add three nuclides to the investigation of superallowed β decays. Due to the recent ISOLTRAP experiments the precision of the comparative half-life F t for these three decays is no longer limited by the mass uncertainty. Another highlight shows the need of further mass measurements in the context of nuclear astrophysics, in particular of the rp-process above Z = 32. The mass of 72 Kr and other krypton isotopes has been measured with a relative uncertainty close to 10−7 [8]. Using these precise new mass values, the mass of rubidium and strontium nuclei (and hence the proton separation energies) could be determined via Coulomb energies with a rather high precision of about 100 keV. In combination with proton-capture rates, photo-disintegration rates and β-decay half-lives the

20

The European Physical Journal A

Table 2. Frequency ratios and mass excess values (ME) for radium and francium isotopes. 133 Cs was used for calibration of the magnetic field of the Penning trap. Literature values MElit are from [38]. The last column gives the difference between literature and ISOLTRAP values Δ = ME∗exp − MElit .

Nuclide 229 Ra 230 Ra 231 Ra 232 Ra 230 Fr ∗

T1/2 4.0 min 93 min 103 s 250 s 19.1 s

freq. ratio 1.723 295 1.730 835 1.738 389 1.745 932 1.730 875

νcref /νc 23(20) 33(16) 50(16) 03(10) 61(24)

ME∗exp (keV) 32542(24) 34513(19) 38226(19) 40498(12) 39500(29)

MElit (keV) 32563(19) 34518(12) 38400(300) # 40650(280)# 39600(450)#

Δ (keV) 21 5 174 152 100

m(133 Cs) = 132.905 451 933(24) u [38];

1 u = 931.4940090(71) MeV/c2 [42]. #

Value from extrapolation using experimental data trends [38].

16000

Pu

Two-neutron separation energy (keV)

Np 15000 14000 13000 12000

Es Fm Md No

Ac Ra Fr Rn At

10000

Po Bi Pb Tl

8000 128

Bk Cf

U Pa Th

11000

9000

Am Cm

130

132

134

136

138

140

142

144

146

148

150

152

154

156

Neutron number Fig. 2. Two-neutron separation energy plotted as a function of the neutron number. Full circles mark experimental values as cited in the Atomic Mass Evaluation 2003 [38]. Open circles result from an extrapolation [38]. Data that include one of the radium or francium nuclides presented in this work and in [33] are marked with diamonds and connected with a solid line. The error bars of these new data points are smaller than the symbols.

mass values allowed to perform detailed calculations in the vicinity of this possible waiting point. The result is the effective lifetime of 72 Kr in the stellar environment. It can be concluded that 72 Kr may indeed be a waiting point nucleus. However, the proton separation energy of 74 Sr changed due to the new mass values and consequently the rate of the 73 Rb(p, γ)74 Sr reaction has increased influence on the effective lifetime of 72 Kr. In particular a resonant state in 74 Sr close to the proton threshold could change the present picture considerably [8]. 3.2 The masses of radium and francium isotopes The masses of neutron-rich radium and francium nuclei, the heaviest masses investigated yet at ISOLTRAP, have been measured during a recent experiment. For the production of the radionuclides a uranium carbide target

was bombarded about each second with approximately 3 · 1013 protons per pulse at 1.4 GeV. After their diffusion out of the hot (≈ 2000 K) target container the atoms were surface-ionized in a tungsten ionizer cavity. The ions were accelerated to 60 keV, mass-separated by the highresolution mass separator HRS at ISOLDE [16] and transferred to ISOLTRAP where the ratio of their cyclotron frequency was measured with respect to the cyclotron frequency of 133 Cs ions. Ions of different mass (contaminations) simultaneously present in the precision trap would influence the cyclotron frequency of the ions of interest. Therefore, all measured cyclotron frequencies were evaluated as a function of the number of detected ions in each experimental cycle. This procedure allows an extrapolation to only a single ion stored in the trap. The extrapolation uncertainty can be considered as a reflection of possible, but unobserved contaminations [14].

F. Herfurth et al.: Recent high-precision mass measurements with the Penning trap spectrometer ISOLTRAP

The results of the mass measurements of very neutronrich radium and francium nuclei are summarized in table 2. For comparison the mass excess values as given in the Atomic Mass Evaluation (AME) 2003 [38] have been added. The AME2003 values for 229 Ra and 230 Ra are based on previous ISOLTRAP measurements [33] and have been reproduced very well in the present measurements. The mass of three nuclides has been measured for the first time. To visualize the effect of the new results on the mass landscape the two-neutron separation energy is plotted as a function of the neutron number before and after our measurements (fig. 2). The considerably lower uncertainty as well as the first ever measurement of 230 Fr mark a clear change in the trend of the two-neutron separation energy. While the extrapolation naturally delivered a smooth behavior, the experimental values do not follow this trend. A significant drop in the S2n value is observed between N = 144 and 145 for radium and for francium between N = 143 and 144. Further investigations of the impact of these new and more precise mass values will follow in a detailed publication [33].

4 Summary and outlook The wide range of physics interest in precise nuclear masses has triggered the development of many mass spectrometers. Penning trap spectrometers provide the most precise and reliable mass values. As an example the heaviest short-lived nuclides studied with ISOLTRAP have been presented —the neutron-rich radium and francium isotopes 229–232 Ra and 230 Fr, three of which have been measured for the first time. While the masses of close to 300 radioactive nuclides have already been determined with ISOLTRAP, the recent developments at this triple-trap mass spectrometer mark the present limit of measurements of short-lived radioactive nuclides. The relative mass uncertainty has reached 10−8 as verified by cross-reference measurements on carbon clusters. New experimental techniques are currently implemented that will improve the stability of the magnetic field, the sensitivity and give access to nuclides of elements not produced at ISOLDE [43]. Thus the range for possible applications will be further extended. We would like to thank the ISOLDE collaboration and the ISOLDE technical staff for their continuous support. This work was supported by the German Ministry for Education and Research (BMBF) under contract Nos. 06MZ962I, 06GF151 and 06LM968, the European Commission under contracts HPRICT-2001-50034 (NIPNET), HPRI-CT-1998-00018 (LSF) and HPMT-CT-2000-00197 (Marie Curie Fellowship) and by the Helmholtz association of national research centres (HGF) under contract No. VH-NG-03.

21

References 1. D. Lunney, J.M. Pearson, C. Thibault, Rev. Mod. Phys. 75, 1021 (2003). 2. G. Bollen et al., Phys. Rev. C 46, R2140 (1992). 3. J. Van Roosbroeck et al., Phys. Rev. Lett. 92, 112501 (2004). 4. S. Schwarz et al., Nucl. Phys. A 693, 533 (2001). 5. G. Wallerstein et al., Rev. Mod. Phys. 69, 995 (2002). 6. K.L. Kratz et al., Hyperfine Interact. 129, 185 (2000). 7. H. Schatz et al., Phys. Rep. 294, 167 (1998). 8. D. Rodr´ıguez et al., Phys. Rev. Lett. 93, 161104 (2004). 9. J.C. Hardy, I.S. Towner, Hyperfine Interact. 132, 115 (2001). 10. I.S. Towner, J.C. Hardy, J. Phys. G 29, 197 (2003). 11. A. Kellerbauer et al., Phys. Rev. Lett. 93, 072502 (2004). 12. M. Mukherjee et al., Phys. Rev. Lett. 93, 150801 (2004). 13. F. Herfurth et al., Eur. Phys. J. A 15, 17 (2002). 14. A. Kellerbauer et al., Eur. Phys. J. D 22, 53 (2003). 15. K. Blaum et al., J. Phys. B 36, 921 (2003). 16. E. Kugler, Hyperfine Interact. 129, 23 (2000). 17. F. Herfurth et al., Nucl. Instrum. Methods A 469, 254 (2001). 18. H. Raimbault-Hartmann et al., Nucl. Instrum. Methods B 126, 378 (1997). 19. G. Bollen et al., Nucl. Instrum. Methods A 368, 675 (1996). 20. K. Blaum et al., Europhys. Lett. 67, 586 (2004). 21. G. Bollen et al., Hyperfine. Interact. 38, 793 (1987). 22. H. Stolzenberg et al., Phys. Rev. Lett. 65, 3104 (1990). 23. K. Blaum et al., Nucl. Phys. A 746, 305 (2004). 24. F. Herfurth et al., Phys. Rev. Lett. 87, 142501 (2001). 25. K. Blaum et al., Phys. Rev. Lett. 91, 260801 (2003). 26. C. Gu´enaut et al., these proceedings. 27. C. Gu´enaut et al., to be published. 28. T. Otto et al., Nucl. Phys. A 567, 281 (1994). 29. H. Raimbault-Hartmann et al., Nucl. Phys. A 706, 3 (2002). 30. G. Sikler et al., Proceedings of the 3rd International Conference on Exotic Nuclei and Masses, H¨ ameenlinna, Fin¨ o (Springer Verlag, 2002), mass land 2001, edited by J. Ayst¨ values to be published, p. 48. 31. J. Dilling et al., Eur. Phys. J. A 22, 163 (2004). 32. F. Ames et al., Nucl. Phys. A 651, 3 (1999). 33. C. Weber et al., to be published. 34. D. Beck et al., Eur. Phys. J. A 8, 307 (2000). 35. G. Bollen et al., Hyperfine Interact. 132, 215 (2001). 36. G. Bollen et al., J. Mod. Optics 39, 257 (1992). 37. F. Herfurth et al., Phys. Rev. Lett. 87, 142501 (2001). 38. G. Audi, A.H. Wapstra, C. Thibault, Nucl. Phys. A 729, 337 (2003). 39. J.C. Hardy et al., Phys. Rev. Lett. 91, 082501 (2003). 40. I.S. Towner, J.C. Hardy, Phys. Rev. C 66, 035501 (2002). 41. J.C. Hardy et al., these proceedings. 42. P.J. Mohr, B.N. Taylor, Rev. Mod. Phys. 72, 351 (2000), 1998 CODATA values. 43. A. Herlert et al., New. J. Phys. 7, 44 (2005).

Eur. Phys. J. A 25, s01, 23–26 (2005) DOI: 10.1140/epjad/i2005-06-189-6

EPJ A direct electronic only

New mass measurements at the neutron drip-line H. Savajols1,a , B. Jurado1 , W. Mittig1 , D. Baiborodin2 , W. Catford3 , M. Chartier4 , C.E. Demonchy1,4 , Z. Dlouhy2 , A. Gillibert5 , L. Giot1,6 , A. Khouaja1,10,12 , A. L´epine-Szily8 S. Lukyanov9 , J. Mrazek2 , N. Orr6 , Y. Penionzhkevich9 , S. Pita1,11 , M. Rousseau1,7 , P. Roussel-Chomaz1 , and A.C.C. Villari1,13 1 2 3 4 5 6 7 8 9 10 11 12 13

GANIL, BP 55027, F-14075 Caen Cedex 5, France Nuclear Physics Institute ASCR, 25068, Rez, Czech Republic University of Surrey, Nuclear Physics Department, Guilford, GU27XH, UK University of Liverpool, Department of Physics, Liverpool, L69 7ZE, UK CEA/DSM/DAPNIA/SPHN, CEN Saclay, F-91191 Gif-sur Yvette, France LPC - ISMRA and University of Caen, F-6704 Caen, France IReS - Strasbourg, 23 rue du loess, BP 28, F-67037 Strasbourg, France University of S˜ ao Paulo IFUSP, C.P. 66318, 05315-970 S˜ ao Paulo, Brazil FLNR, JINR Dubna, P.O. Box 79, 101000 Moscow, Russia LNS-INFN, 44 S. Sofia, I-95129 Catania, Italy Coll`ege de France, 11 Place Marcelin Berthelot, F-75231 Paris Cedex 05, France LPTN Faculty of Sciences, El Jadida BP 20, 24000 El Jadida, Morocco Physics Division, Argonne National Laboratory, 9700 S. Cass Av., Argonne, IL 60439, USA Received: 5 May 2005 / c Societ` Published online: 11 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A new SPEG mass measurement experiment has been performed to determine masses closer to the neutron drip-line in the mass region A ∼ 10–50. The precision of 37 masses has been improved and 8 masses were measured for the first time. The region covered was motivated by the study of shell structure and of shape coexistence in the region of closed shells N = 20 and N = 28. The evolution of the two neutron separation energies and the shell correction energy have been studied as a function of the neutron number. The results thus obtained provide a means of identifying, in exotic nuclei, new nuclear structure effects that are well illustrated by the changes of the conventional magic structure. PACS. 21.10.Gv Mass and neutron distributions – 21.10.Dr Binding energies and masses

1 Introduction The extension of known experimental properties up to very neutron rich nuclei is of fundamental interest particularly for nuclear theory models which have been mainly derived based on properties observed close to stability. New experimental data deepens our understanding of nuclear structure evolution towards large fluid asymmetries. The structure of neutron-rich nuclei is today the focus of many theoretical and experimental efforts. Deformations, shape coexistence or variations in the spin-orbit strength emerging with the evolution of the neutron-to-proton ratio can provoke the existence of magic numbers different from those observed near stability. Such behaviour has also been proven to be important in other domains. As seen, for example, in nucleo-synthesis, where a quenching of shell effects, and consequently of spin orbit splitting, can provide for a better agreement between model calculations and observed abundances [1]. a

Conference presenter; e-mail: [email protected]

In this context, the measurement of masses (or binding energy) of nuclei far from stability is of fundamental interest for our understanding of nuclear structure. Their knowledge over a broad range of the nuclear chart is an excellent and severe test of nuclear models. This is why considerable experimental and theoretical efforts have been and are invested in this domain. In this contribution, we present new mass measurements for neutron-rich nuclei in the region defined by (5 < N < 28 ; 7 < Z < 18) obtained with the spectrometer SPEG at GANIL. These data correspond to the most exotic nuclei presently attainable in this region and provide first indications of new regions of deformation or shell closures very far from stability.

2 Experimental set-up The method used is a direct time of flight combined with rigidity analysis technique (see fig. 1). The exotic nuclides are produced by bombarding a 181 Ta production target

24

The European Physical Journal A

(Si telescope)

) SISSI Target

flight path ~ 82m

(Drift chamber)

Fig. 1. Experimental set-up.

with an intense 48 Ca primary beam (6 × 1011 pps) at intermediate energy, 60 A · MeV. The dominant mechanism at this energy is projectile fragmentation, after which the forward-directed fragments are selected in flight by the α-shaped spectrometer and transported to the highresolution spectrometer SPEG [2]. The very broad elemental and isotopic distributions resulting from such reactions combined with the fast in-flight electromagnetic selection can provide the mapping of an entire region of the nuclear mass surface in a single measurement. The 181 Ta production target, placed between the two superconducting solenoids (SISSI) of GANIL [3], rotated at 2000 rpm, was composed of three different sectors with thickness of 550 mg/cm2 (89%), 450 mg/cm2 (10%) and 250 mg/cm2 (1%). This ensured a sufficient production of both very and less exotic nuclei, allowing to measure a broad range of reference masses from which unknown masses are derived. The mass is deduced from the relation γm0 v , Bρ = q

where Bρ is the magnetic rigidity of a particle of rest mass m0 , charge q and velocity v and γ the Lorentz factor. This technique requires only a precise determination of the magnetic rigidity and the velocity of the ion, which is determined from a time-of-flight measurement. The time of flight (ToF) is measured using a pair of microchannel plate detector systems located near the production target (start signal) and at the final focal plane of SPEG (stop signal). The flight times are typically of the order of 1 μs for a path 82 m long. The intrinsic resolution of the start and stop detectors are of the order of 100–200 ps (FWHM) leading to a time-of-flight resolution of Δt/t ∼ 2 · 10−4 . The magnetic rigidity, δ, of each ion is derived from two horizontal position measurements. The first measurement is performed by a thin position-sensitive microchannel plate system located at the dispersive image planes of the analysing magnet, i.e. at the conventional target chamber where the dispersion in momentum is large (10 cm/%). The second is made by two drift chambers used after the spectrometer. Thus reconstruction of the trajectories of each ion is possible and we accurately determine the value of the magnetic rigidity independantly of the object size. A momentum resolution of 10−4 is commonly achieved. The identification of each ion arriving at the focal plane of SPEG is achieved by the measured ToF and the

Fig. 2. Experimental S2n values as a function of the neutron number N in the region of N = 20 and N = 28 shell closures .

energy loss and total energy signals from a detector telescope. As a check that deduced masses are not affected by the existence of isomers, the present mass measurement are combined with a detection of delayed γ rays by a 4π NaI array surrounding the telescope. A mass resolution corresponding typically to ± 3 MeV of the mass excess can be obtained from the combination of the time-of-flight and the magnetic rigidity measurement. For a nucleus A = 40, the final uncertainties range from 100 keV for thousands of events (nuclei relatively close to stability) to 1 MeV for tens of events (nuclei approaching the ends of isotopic chains).

3 Results of mass measurements From this experiment and its subsequent analysis, the masses of 80 neutron-rich nuclei have been measured. The precision of 37 masses has been significantly improved while 8 masses were measured for the first time. Details of the analysis technique can be found in already published papers [4, 5]. The separation energy of the 2 last neutrons corresponding to a derivative of the mass surface, S2n , derived from the current and previous measurements are displayed in fig. 2. A more direct way to see shell effects on nuclear masses is to subtract from the mass excesses the contribution of the macroscopic properties of the nuclei. Here we have used the finite range liquid drop model of [6]. The difference —the microscopic or Shell Correction Energy (SCE)— is plotted in fig. 3 for Z = 14 to Z = 20 isotopes and fig. 4 for Z = 8 to Z = 13 isotopes. As can be seen for both observables, i.e. experimental S2n and SCE, the Ca isotopes (Z = 20) show the typical behavior of the filling of shells with the two shell closures at N = 20 and N = 28; sharp decrease of the S2n at N = 20 and a slow decrease of S2n as the 1f7/2 shell is filled and SCE minima at N = 20 and N = 28. In the rest of the article, the standard behavior represented by the Ca chain will be taken as reference.

H. Savajols et al.: New mass measurements at the neutron drip-line

Fig. 3. Shell corrections as defined in the text of the mass of Si, P, S, Cl, Ar and Ca isotopes.

3.1 The N = 28 region Contrary to the Ar and K isotopes, both S2n and SCE values of the Cl, S, P and Si isotopic chains differ around N = 28 from the standard behavior represented by the Ca chain. A discontinuity in the S2n slope when filling the ν1f7/2 shell (from N = 20 to N = 28) is strongly pronounced for the Cl, S and P isotopes. This trend is attenuated for the Si and Al chains. This overbinding, already observed in our previous mass measurement experiment [7], but with large uncertainties, was attributed to deformed ground state configurations. The observation, in the same experiment, of a low excited isomeric state in 43 S [7], confirmed the analysis of the masses and constituted the first shape coexistence in that region. More detailed informations have been obtained for these nuclei by other experimental probes, i.e. Coulomb excitation measurement for the S isotopes [8,9] and in beam gamma spectroscopy experiment [10]; both conclude for deformed ground state configurations. Beyond N = 28, the isotopic P and S isotopic chains show a clear increase of the S2n , this is an indication for the vanishing of this shell closure for these very neutronrich nuclei. The standard behavior represented by the Ca chain seems to reappear slowly when moving to the chains of Cl and Ar. In order to determine the origin of the increase of S2n for 44 P and 45 S, the present results should be compared with model calculations. For the neutron-rich nucleus 42 Si, the protons confined in the πd5/2 orbital (Z = 14 sub-shell gap) and the N = 28 gap together, could favor spherical configuration. Indeed, our result for the mass excess of 42 Si is around 3 MeV

25

Fig. 4. Shell corrections as defined in the text of the mass of O, F, Ne, Na, Mg, Al and Ca isotopes.

smaller than the extrapolation of the mass table [11]. This indicates that this nucleus is much more bound than what one would obtain if the Si isotopic chain would follow the standard trend of the Ca chain. This could possibly be an indication of the strong deformation of 42 Si. Different theoretical approaches exist. On one hand, shell model calculations performed by Retamosa et al. [12], indicate that 42 Si has the characteristics of a doubly magic nucleus such as 48 Ca. More recently, the interaction has been adjusted to reproduce single-particle states in 35 Si [13] and the shell gap 1f7/2 -2p3/2 is steadily reduced from its initial value of 2 MeV at Z = 20 until almost zero at Z = 8. Therefore the closed-shell configuration becomes vulnerable and at some point it becomes energetically favorable to promote neutrons across the gap, recovering the cost in single-particle energies by the gain in neutron proton quadrupole correlation energy. Moreover, those calculations lead to a deformed 43 S ground state with spin 3/2− while the spherical single-hole state 7/2− would be the first-excited state, in good agreement with experimental data. On the other hand, the calculations performed by Lalazissis et al. [14] (relativistic Hartree Bogoliubov) predict the breaking of the N = 28 shell gap below 48 Ca with a large deformed configuration for 42 Si. 3.2 The N = 20 region The value obtained for 23 N mass excess is considerably smaller (∼ 1.5 MeV ) than the extrapolation of the mass evaluation 2003 value given by Audi et al. [11], which is obtained assuming a regular behaviour of S2n . This indicates that 23 N with 16 neutrons is more bound than

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The European Physical Journal A

expected. This might be an indication for the existence of a shell closure at N = 16 for very neutron-rich nuclei. Also the value for the mass excess that we obtain for 24 O with 16 neutrons is lower than the value given in the mass table, which again indicates that 24 O is more bound than what was thought previously. For the Ne and the Na isotopic chains the two-neutron separation energies decrease much more steeply after N = 16 than after N = 20, which is again an indication for the existence of the shell closure N = 16 for this very neutron-rich nuclei. Moreover, the absence of the steep decrease after N = 20 for the Mg and Al chains confirms the vanishing of this spherical shell closure. Shell closure N = 20 starts to reappear for the less neutron-rich isotopes of the Al and Si chains. Beyond N = 20, for the Ne, Na and Mg isotopes, a rapid decrease of S2n indicates that those isotopes may become unbound rapidly with respect to the neutron emissions. If we add one proton in the πd5/2 from the oxygen configuration, the picture for the fluorine isotopes changes drastically. The S2n values decrease continuously to almost zero for 29 F. Only strong shell effects could bind the heaviest known fluorine isotope, 31 F. The shell correction energies from fig. 4 nicely show the shell effect evolution in that region and confirm the previous discussion on the experimental S2n values. If we start from the O isotopes, we clearly observe two N = 8 and N = 16 minima with a rather high, 5 MeV, difference in magnitude between them (O with N > 16 do not exist as bound nuclei). The gap at N = 16 still persists when we add a proton in the πd5/2 shell, but the amplitude decreases smoothly up to 29 Al. Moreover, the SCE confirm the vanishing of the shell closure at N = 20, SCE are maximized at N = 20 for the F, Ne, Na and Mg isotopes. More recent shell model calculations [15] interpret this disappearance of the magic number N = 20 by the inversion of the order of the shells due to the dependence of the neutron-proton interaction on the combination of their spin in the nucleus (nucleon-nucleon spin-isospin Vστ interaction). In that region, the basic mechanism of this change is the strongly attractive interaction between spin-orbit partners πd5/2 and νd3/2 . As Z increases from 8 to 14, valence protons are added into the πd5/2 orbit. Due to the strong attraction between a proton in πd5/2 and a neutron in νd3/2 , as more protons are put in πd5/2 , a neutron in νd3/2 is more strongly bound. The magic number N = 20 should be therefore replaced by N = 16 for the nuclei in this region very far from stability, and that this

phenomenon should occur over all the chart of the nuclei. In particular, the non-observance of 28 O, a doubly magic nucleus in theory, could also be explained by this modification of its shell structure.

4 Conclusions The direct time-of-flight method with SPEG is a powerful method for measuring masses up to the neutron drip-line in the mass region A ∼ 10–50. This paper presents preliminary results of 8 new masses and 37 masses measured with a better precision than previously. The final result will be published in a future publication. The experimental shell corrections and the two neutron separation energies have been calculated. The results thus obtained provide a means of identifying new nuclear structure effects that are well illustrated by this work in the N = 16, N = 20 and N = 28 region. ACCV acknowledges his partial support by the U.S. Department of Energy, Office of Nuclear Physics, under contract W31-109-ENG-38. This work was particularly supported by the INTAS-00-00463, by the Russian Foundation for Fundamental Research (RFFR) and PICS (IN2P3) No. 1171.

References 1. B. Pfeiffer et al., Z. Phys. A 357, 235 (1997). 2. L. Bianchi et al., Nucl. Instrum. Methods Phys. Res. A 276, 509 (1989). 3. R. Anne, Nucl. Instrum. Methods Phys. Res. B 126, 279 (1997). 4. F. Sarazin, Thesis GANIL T 99 03 (1999). 5. H. Savajols, Hyperfine Interact. 132, 245 2001. 6. P. Moller, J.R. Nix, At. Data Nucl. Data Tables 59, 185 (1995). 7. F. Sarazin et al., Phys. Rev. Lett. 84, 5062 (2000). 8. H. Scheit et al., Phys. Rev. Lett. 77, 3967 (1996). 9. T. Glasmacher et al., Phys. Lett. B 395, 163 (1997). 10. D. Sohler et al., Phys. Rev. C 66, 054302 (2002). 11. G. Audi et al., Nucl. Phys. A 729, 2003 3. 12. J. Retamosa et al., Phys. Rev. C 55, 1266 (1997). 13. S. Nummela et al., Phys. Rev. C 63, 044316 (2001). 14. G.A. Lalazissis et al., Phys. Rev. C 60, 014310 (1999). 15. T. Otsuka et al., Phys. Rev. Lett. 87, 082502 (2001).

Eur. Phys. J. A 25, s01, 27–30 (2005) DOI: 10.1140/epjad/i2005-06-180-3

EPJ A direct electronic only

Ion manipulation and precision measurements at JYFLTRAP ¨ o1 A. Jokinen1,a , T. Eronen1 , U. Hager1 , J. Hakala1 , S. Kopecky1 , A. Nieminen2 , S. Rinta-Antila1 , and J. Ayst¨ 1 2

Department of Physics, P.O. Box 35 (YFL), FIN-40014 University of Jyv¨ askyl¨ a, Jyv¨ askyl¨ a, Finland University of Manchester Nuclear Physics Group, Schuster Laboratory, Manchester, UK Received: 15 January 2005 / c Societ` Published online: 11 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Various ion manipulation tools based on ion trapping technologies have been implemented at the IGISOL-facility in JYFL. An RFQ ion cooler and buncher is used to enhance the sensitivity of collinear laser spectroscopy and as an injector to the Penning trap. Penning traps are utilized both in nuclear spectroscopy and for precision mass measurements, as explained in the paper. Atomic masses of neutronrich Zr, Mo and Sr isotopes were found to be in disagreement with the Atomic-Mass Evaluation and two-neutron separation energies imply strong nuclear structure effects at the neutron number N = 60. PACS. 07.75.+h Mass spectrometers – 21.10.Dr Nuclear structure: Binding energies and masses – 27.60.+j Properties of specific nuclei listed by mass ranges: 90 ≤ A ≤ 149

1 Introduction The mass of the ground state of a nucleus results from the structure of a complex quantum system. Therefore, an accurate determination of the nuclear mass surface can provide additional information compared to those obtained from excited states, such as the underlying symmetries and microscopic features like charge symmetry of nuclear interaction, shell effects, coexisting structures, pairing effects, spin-orbit interaction, and so forth. For this to be successful, measurements and theory have to be able to probe fluctuations in the order of 1 to 100 keV. Global correlations are typically variations due to closed shells and broad areas of deformation where the required accuracies in mass measurements are typically of the order of 100 keV. However, detection of local correlations such as those due to the presence of closed shell discontinuities, the local zones of deformation or those due to configuration mixing or shape mixing require mass accuracies preferably of the order of 10 keV [1]. Among neutron-rich nuclei, the binding energy data comes usually from beta endpoint measurements, since application of reaction studies is limited, although an advent of new radioactive ion beam facilities will partly change the situation. It is therefore of importance to perform direct mass measurements on neutron-rich side of the nuclide chart. In this paper we report on mass measurements applying ion trapping technologies in the Department of Physics in the University of Jyv¨askyl¨a (JYFL). a

Conference presenter; e-mail: [email protected]

2 Ion manipulation in JYFLTRAP An Ion Guide Isotope Separator On-Line (IGISOL) technique was developed more than twenty years ago at JYFL. Since then it has been applied in variety of spectroscopic studies both in Jyv¨askyl¨a but also in different laboratories all over the world. For comprehensive compilation of past studies see [2]. In this study we have employed the fission reaction of 238 U induced by 30 MeV protons with typical intensity of a few μA. Due to its symmetric mass division, a protoninduced fission is well suited for the production of medium mass neutron-rich nuclei in the transitional Zr-Pd region. Refractory elements are considered to be difficult cases for conventional ion sources. In the IGISOL-technique neither chemical nor physical properties affect the ionization efficiency. All reaction products recoiling out from the target are stopped in noble buffer gas, where they end up as singly-charged ions after numerous charge-exchange processes. Neutral buffer gas and singly-charged ions are rapidly transported out from the stopping volume through a small exit hole. An immediate differential pumping section with stepwise acceleration removes neutral atoms while ions are accelerated to 30 keV energy. For recent developments in the IGISOL-separator at JYFL see [3]. 2.1 Radiofrequency ion cooler and buncher Due to the rather large energy spread and the modest emittance of the ion beam extracted from the ion guide, a gas-filled radiofrequency quadrupole (RFQ) was introduced in to the beam line system [4]. Its main task is

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The European Physical Journal A

Fig. 1. Isobaric separation in the purification trap.

to provide cooled and bunched beams for all experiments requiring improved ion optical properties. It has remarkably increased the sensitivity of the collinear laser spectroscopy by reducing Doppler broadening of optical resonances due to the smaller energy spread and by increasing signal-to-noise ratio due to the bunched structure of the ion beam [5]. The former leaves the resonance line shape dominated by the natural atomic line width and the latter allows gated photon detection synchronized by the arrival of the ion bunch suppressing the non-resonant background by a factor of ∼ 104 . The RFQ is also an ideal tool for bunched injection to the Penning trap system [6].

Fig. 2. Beta-gated gamma spectra obtained at A = 104 with mass purification favoring 104 Nb (an upper graph) or 104 Zr (lower graph). Shaded areas illustrate gamma-transition belonging to the beta decay of 104 Zr. Arrows point to gammalines belonging to the beta decay of high-spin isomer of 104 Nb.

2.2 Tandem Penning trap The ion trap installation at JYFL combines two Penning traps installed inside the warm bore of a single superconducting solenoid with a magnetic field of 7T. The magnet has been shimmed to provide two trapping sections, the first with magnetic homogeneity ΔB/B ∼ 10−6 in one cm3 and another with ΔB/B ∼ 10−7 . These regions are located in the center of the magnet 20 cm apart from each other. The first region is used for the isobaric purification and the second one for precision measurements [7].

2.3 Purification trap An example of the scanning of the quadrupole excitation frequency over wide range is shown in fig. 1. By fixing the radial excitation frequency it is possible to remove other ions while the wanted ones are centered in the trap and transported to the precision trap [8]. The typical mass resolving power in the purification trap is M/ΔM ∼ 105 . A possibility to isobarically clean the ion sample provides an additional tool for conventional nuclear spectroscopy. In a recent decay study we have applied an isobaric purification in the decay study of 100,102,104 Zr. An example of mass purified γ-spectra obtained at A = 104 and in coincidence with β’s is shown in fig. 2.

Fig. 3. A time-of-flight resonance obtained with the stable 129 Xe ions from the cross beam ion source.

2.4 Precision trap In the precision trap, ions are first moved out from the center of the trap to larger radius and then resonantly excited with a quadrupole field. As a result, ions in resonance with the excitation frequency gain radial energy. While the ions are moving out from the magnetic field, the radial energy is transferred to axial energy in the field gradient. Thus the resonantly excited ions gain more axial energy and correspondingly their time of flight from the ion trap to the detection setup outside of the trap is shorter [8]. A reduction in the time of flight can be seen in the resonance curve, which is exemplified in fig. 3 for 129 Xe ions.

3 Mass measurements of refractory fission products After the successful commissioning of the full trapping facility, we have performed systematical studies to characterize the optimum experimental conditions as well as to

A. Jokinen et al.: Ion manipulation and precision measurements at JYFLTRAP

29

learn about systematic uncertainties. Most of these studies have been performed with an ion beam from a cross beam ion source or by using nuclides with well-known mass produced on-line. Such a preparatory work is needed for a reliable evaluation of the data obtained in on-line mass measurements in unexplored regions of the nuclide chart. Our first mass measurements of exotic nuclei were performed for isotopic chains of Zr, Mo and Sr isotopes produced in fission. During these measurements, the reference ion 97 Zr was obtained from fission in conditions similar to those for the unknown masses. The statistical uncertainties related to these measurements were of the order of a few keV at maximum and systematic errors taken into account in similar manner than described in [9]. Systematic errors considered in the analysis were the following. – The uncertainty of the mass excess of 97 Zr, which was chosen as a reference for all measurements, was taken from the Atomic-Mass Evaluation table AME03 [10], M E(97 Zr) = (−82946.6 ± 2.8) keV. This uncertainty does not affect the uncertainty of the frequency ratio ωc,ref , but only that of the mass excess. x = ωc,meas – The uncertainty related to magnetic field fluctuations was deduced using all measurements of 97 Zr done during the run. From this, the fluctuation of the cyclotron frequency due to magnetic field variations could be estimated to result in an uncertainty of about 4 · 10−8 of the frequency ratio x, corresponding to about ±4 keV in this mass region. – A large number of ions in the precision trap can cause the measured cyclotron frequency to shift due to ionion-interactions in the trap. In order to reduce this effect, it was attempted to keep the countrate below 20 ions per bunch after purification. When necessary, the beam intensity was reduced by inserting slits of variable opening before the RFQ. The countrate effect had been examined during a previous online run using 58 Ni. For the countrates used in this experiment, it was found to give an uncertainty of ±0.1 Hz on the measured frequency. In a separate measurement for 99 Sr, the countrate was lower resulting in an estimated uncertainty of ±0.05 Hz. – Another possible source for errors is the mass difference between the measured ion and the reference ion. An estimation for the mass dependent uncertainty could be obtained during an offline measurement by comparing the measured frequencies for 132 Xe and O2 -molecules. The uncertainty was found to be xexp −xAME = 7 · 10−10 (m − mref ), with xAME being the xAME frequency ratio calculated from mass table values.

3.1 Systematic errors

Fig. 4. TOF-resonance for reference ion 97 Zr and for measured ions 108 Mo and 104 Zr.

The mass excess data obtained in this measurement will be given in more detail in [11], but in this paper we show the comparison to AME2003 [10] for Zr isotopes, see fig. 5. It clearly shows a good agreement in less exotic nuclei where tabulated values originate from reactions and are rather precisely known already. Another observation is a noticeable deviation of the measured masses from the tabulated ones when moving further from the stability. There the old values are based on the long chains of beta endpoint measurements. Apart from the mass excess it is of interest to derive the two neutron separation energies S2n . The two-neutron separation energy is a useful quantity to extract information on local correlations of the binding energy surface. In fig. 6 we show two-neutron separation energies for Zr isotopes. This plot reflects clearly the change of deformation on S2n at N = 58–60.

3.2 Preliminary results

4 Conclusions In fig. 4 we show a typical resonance curve obtained for the reference ion and examples of resonance curves obtained for ions whose masses have been measured for the first time in this experiment.

Our first set of precision measurements in neutron-rich nuclei illustrates two facts. Firstly, the old data found in the literature and entering to AME, can often be

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Fig. 5. Comparison of the experimental mass excesses and AME2003 [10] values for Zr isotopes. Error bars in the baseline corresponds to uncertainty of AME2003 values. Solid circles are tabulated values based on the experimental data and open circles corresponds to those isotopes, whose AME2003 value is based on the extrapolation as described in AME2003 [10].

those obtained with laser spectroscopy studies and comparing to modern theoretical models, the observed correlations can be traced to nuclear deformation effects. The IGISOL facility has been upgraded recently and we have inititated a project to construct a laser ion source based on the ion guide method. With these improvements together with an optimization of the trap, precise mass measurements have a promising future at the IGISOL facility in coming years. With an easy access to neutron-rich nuclei, also for refractory elements, we will extend these studies to selected areas in the element range of Z = 28–50, i.e. between two closed proton shells. In addition to systematical mapping of the mass surface, these studies will shed light on many nuclear physics questions, like binding in the vicinity of the doubly magic 78 Ni, nuclear structure effects at N = 60, possible magicity of 110 Zr and shell-quenching while approaching N = 82. This work has been supported by the European Union within the NIPNET RTD project under Contract No. HPRI-CT-200150034 and by the Academy of Finland under the Finnish Centre of Excellence Programme 2000-2005 (Project No. 44875). A.J. is indebted to financial support from the Academy of Finland.

References 1. 2. 3. 4.

Fig. 6. Two-neutron separation energies for Zr isotopes. Errors of individual points are of the size of the symbol.

5. 6. 7. 8.

erroneous. Secondly, by taking a closer look at the mass surface around 100 Zr, we have observed a clear indication of nuclear structure correlation. By combining new data to

9. 10. 11.

D. Lunney et al., Rev. Mod. Phys. 75, 1021 (2003). ¨ o, Nucl. Phys. A 693, 477 (2001). J. Ayst¨ H. Penttil¨ a et al., these proceedings. A. Nieminen et al., Nucl. Instrum. Methods A 469, 244 (2001). A. Nieminen et al., Phys Rev. Lett. 88, 094801 (2002). ¨ o, A. Jokinen, J. Phys. B 36, 573 (2003). J. Ayst¨ V. Kolhinen et al., Nucl. Instrum. Methods A 528, 776 (2004). M. K¨ onig et al., Int. J. Mass. Spectrom. Ion Processes 142, 95 (1995). A. Kellerbauer et al., Eur. Phys. J. D 22, 53 (2003). G. Audi et al., Nucl. Phys. A 729, 3 (2003). U. Hager et al., submitted to Phys. Rev. Lett. (2005).

Eur. Phys. J. A 25, s01, 31–32 (2005) DOI: 10.1140/epjad/i2005-06-005-5

EPJ A direct electronic only

Mass measurement of short-lived halo nuclides C. Bachelet1,a , G. Audi1 , C. Gaulard1 , C. Gu´enaut1 , F. Herfurth2 , D. Lunney1 , M. De Saint Simon1 , C. Thibault1 , and the ISOLDE Collaboration3 1 2 3

CSNSM-IN2P3-CNRS, F-91405 Orsay-Campus, France GSI Planckstraße 1, 64291 Darmstadt, Germany CERN, CH-1211 Geneva 23, Switzerland Received: 23 November 2004 / c Societ` Published online: 12 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A direct mass measurement of the very-short-lived halo nuclide 11 Li (T1/2 = 8.7 ms) has been performed with the transmission mass spectrometer MISTRAL. The preliminary result for the two-neutron separation energy is S2n = 376 ± 5 keV, improving the precision seven times with an increase of 20% compared to the previous value. In order to confirm this value, the mass excess of 11 Be has also been measured, M E = 20171 ± 4 keV, in good agreement with the previous value. PACS. 21.10.Dr Binding energies and masses – 21.45.+v Few-body systems

a

e-mail: [email protected]

18.02 / 17 χ2 / ndf 9.961 ± 2.66 p0 -385.3 ± 25.89 p1

Calibration Law -7

Relative Mass Difference with Evaluation (10 )

The 11 Li is a two-neutron halo nuclide, consisting of a Li core and two neutrons with a large spatial extension. The nuclide has a radius far beyond the droplet approximation [1], and has a very weak binding energy [2]. It is a Borromean three-body system, since the constituents cannot form bound two-body systems (i.e. 10 Li or the dineutron). This particular configuration represents a good test for theory to reproduce the three-body effect and to understand the neutron-neutron interaction. The two-neutron separation energy, derived from the mass, is a critical input parameter to modern three-body models, and gives a better idea of the weight of the s and p-wave groundstate configuration of the two valence neutrons. It also constrains calculations based on the resonance energy of the unbound 10 Li. The MISTRAL experiment (Mass measurements at ISOLDE/CERN with a Transmission RAdiofrequency spectrometer on Line), determines the mass of short-lived nuclides by measuring their cyclotron frequency in a homogeneous magnetic field [3]. The ISOLDE beam is injected directely in the spectrometer alternately with an offline stable boron reference beam used to measure the magnetic field from its cyclotron frequency. With a resolving power up to 105 , we can reach a relative mass uncertainty of a few 10−7 for a production rate of 1000 ions/s. The accessible half-life is only limited by the time-of-flight of the ions through the beamline. The rapidity of this on-line method allows us to measure nuclides with ms half-lives. 11 Li was provided by a tantalum thin-foil target and surface ionized [4] while the Laser Ion Source of the ISOLDE facility was used for Be beams. 9

40 20

10

B- 10Be

0 10

-20 10

-40 -60

B-9Be

9

B- Li 11

B- 9Be

11

B-11Li 11

-80

B- 9Li

-100 -0.1 -0.05 0 0.05 0.1 0.15 0.2 Relative Energy Difference between MISTRAL-ISOLDE beams

Fig. 1. Calibration law for the 11 Li run. The spectrometer was calibrated with 3 nuclei provided by ISOLDE target (9,10 Be and 9 Li), in comparison with 10,11 B from the MISTRAL reference source. We used five combinations of these nuclides to determine the calibration law. Moreover, 11 Li measurements were added to show the difference.

In order to transmit the ISOLDE beam and the reference beam with the same magnetic field, the energy of the reference ions is adjusted in proportion. A deviation of the measurement with the mass from the AME −mAME ), proportional to the relative difference ( mMISTRAL mAME −ERef ) required a calibration of the beam energies ( EISOLDE E 11 law to correct the Li measurement (see fig. 1) [5].

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Table 1. Summary of the different measurements of the mass.

Reference

Method

S2n (keV)

Thibault et al. [6] Wouters et al. [7] Kobayashi et al. [8] Young et al. [9] MISTRAL03

Mass Spec. TOF 11 B(π − , π + )11 Li 14 C(11 B, 11 Li)14 O Mass Spec.

170 ± 80 320 ± 120 340 ± 50 295 ± 35 376 ± 5

Table 2. Summary of the different measurements of the mass.

Reference

Method

Pullen et al. [10] Gooseman et al. [11] MISTRAL03

9

11

Li

Be

Mass excess (keV)

11

Be(t, p) Be Be(d, p)11 Be Mass Spec.

10

20175 ± 15 20174 ± 7 20171 ± 4

Table 3. Different calculations of the neutron-neutron rms radii for 11 Li [12, 13], with respectively S2n = 0.29 MeV and S2n = 0.37 MeV, as a function of the 10 Li virtual state energy. To compare the experimental value [14].

(11 Li) S2n (MeV)

(10 Li) Sn (keV)

0.29

0 −50 0 −50

0.37



2 rnn  (fm)

9.7 8.5 8.6 7.7



2 rnn exp (fm)

6.6 ± 1.5 6.6 ± 1.5

With the seven corrected measurements of 11 Li, we have a preliminary measured value in comparison with the mass of AME95, mMISTRAL − mAME95 = −75 ± 5 keV. The new measurement of 11 Li is seven times more precise than the value of Young et al. [9], having the dominant weight in the 1995 mass evaluation. Moreover, we find the mass more bound by 75 keV compared to this value, with the 14 C(11 B, 11 Li)14 O reaction (table 1). Though small, this represents a sizable shift in the twoneutron separation of more than 20%. To make us sure of the value found, the mass of the 11 Be has been measured and be found nearly equal with the past one. Its precision has been improved by a factor near of two: mMISTRAL − mAME95 = −4 ± 4 keV (table 2). Yamashita et al. [12] have developed a zero-range interaction model in which the two-neutron separation energy

is an input parameter to calculate the neutron-neutron distance in core-n-n halo nuclei as a function of the resonant energy of the core-n unbound nuclei. This model reproduced well the experimental value of 6 He and 14 Be but not the one of 11 Li with the previous S2n . Calculations have been done with the new preliminary value [13] and the results are reported in table 3. The results are now in better agreement with the experimental value of Marqu´es et al. [14], and also for the 50 keV 10 Li resonant energy measured by Thoennessen et al. [15]. Recent results using nuclear field theory that include core polarization give ground state binding energies for 11 Be and 12 Be within a few percent [16]. For 11 Li, their result (S2n = 360 keV [17]) was higher than that given by other models. As it turns out, their calculation is in excellent agreement with our higher S2n . The MISTRAL measurement program on short-lived halo nuclides will be continued at ISOLDE for the cases of 12,14 Be and 19 C. An upgrade to the spectrometer is in program to improve the sensitivity in order to match the extremely low production rates of these exotic nuclides [18].

References 1. I. Tanihata et al., Phys. Rev. Lett. 55, 2676 (1985). 2. G. Audi, A. Wapstra, C. Thibault, Nucl. Phys. A 279, 545 (2003). 3. D. Lunney et al., Phys. Rev. C 64, 054311 (2001). 4. J.R.J. Bennett et al., Nucl. Instrum. Methods Phys. Res. B 204, 215 (2003). 5. C. Bachelet, PhD Thesis, Universit´e Paris XI (2004). 6. C. Thibault et al., Phys. Rev. C 12, 644 (1975). 7. J.M. Wouters et al., Z. Phys. A 331, 229 (1988). 8. T. Kobayashi et al., KEK Report 91-22 (1991). 9. B.M. Young et al., Phys. Rev. Lett. 71, 4124 (1993). 10. D. Pullen et al., Nucl. Phys. 36, 1 (1962). 11. D. Gooseman, R. Kavanagh, Phys. Rev. C 1, 1939 (1970). 12. M.T. Yamashita, L. Tomio, T. Frederico, Nucl. Phys. A 735, 40 (2004). 13. M.T. Yamashita, L. Tomio, T. Frederico, private communication (2004). 14. F.M. Marqu´es et al., Phys. Rev. C 64, 061301 (2001). 15. M. Thoennessen et al., Phys. Rev. C 59, 111 (1999). 16. G. Gori et al., Phys. Rev. C 69, 041302 (2004). 17. R.A. Broglia et al., Proceedings of the International Nuclear Physics Conference 2001 (American Institute of Physics, 2002) p. 746. 18. M. Sewtz et al., to be published in Nucl. Instrum. Methods Phys. Res. B.

Eur. Phys. J. A 25, s01, 33–34 (2005) DOI: 10.1140/epjad/i2005-06-029-9

EPJ A direct electronic only

Is N = 40 magic? An analysis of ISOLTRAP mass measurements C. Gu´enaut1,a , G. Audi1 , D. Beck2 , K. Blaum2,3 , G. Bollen4 , P. Delahaye5 , F. Herfurth2 , A. Kellerbauer5 , H.-J. Kluge2 , D. Lunney1 , S. Schwarz4 , L. Schweikhard6 , and C. Yazidjian2 1 2 3 4 5 6

CSNSM-IN2P3-CNRS, 91405 Orsay-Campus, France GSI, Planckstraße 1, 64291 Darmstadt, Germany Institute of Physics, Johannes Gutenberg-University, 55099 Mainz, Germany NSCL, Michigan State University, East Lansing, MI 48824-1321, USA CERN, Physics Department, 1211 Gen`eve 23, Switzerland Institute of Physics, Ernst-Moritz-Arndt-University, 17487 Greifswald, Germany Received: 8 November 2004 / c Societ` Published online: 20 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Recently high-precision mass measurements were performed on Ni, Cu, and Ga isotopes at the triple-trap mass spectrometer ISOLTRAP at ISOLDE/CERN. The relative uncertainty was of the order of 10−8 . Data indicate a competition between the sub-shell closure N = 40 and the mid-shell region N = 39 between the well-known magic numbers N = 28 and N = 50. PACS. 21.10.Dr Binding energies and masses – 21.60.Cs Shell model – 32.10.Bi Atomic masses, mass spectra, abundances, and isotopes

Shell closures are fundamental characteristics on which nuclear structure is based but which we now know to erode as we explore extreme isospin systems. The first so-called “magic” number to disappear was the N = 20 shell closure around Na and Mg and now N = 8 [1,2] and N = 28 [3] appear to succumb as well. Like a good magic act, shell closures, having disappeared, can also reappear as attested by the cases N = 16 [1] and N = 32 [4,5,6]. Different observables can be used for the analysis of this “magic number migration”: first excitation energies in even-even nuclei, nuclear level densities, interaction crosssections and, in the grandest tradition, nucleon separation energies. The latter are particularly sensitive to pairing correlations in the context of superfluidity [7], especially for the case of semi-magic nuclei. Using the ISOLTRAP mass spectrometer [8], we have made precision mass measurements around N = 40 for Ni, Cu, and Ga isotopes (fig. 1) in order to finely map the mass surface in this region. The accuracy of the ISOLTRAP mass measurements also permits us to map out the fine structure of the neutron pairing energy which we have analyzed for correlations and signatures of closed or open shells. ISOLTRAP is a high-precision mass spectrometer located at ISOLDE [9], CERN. It consists of three main parts. First a radiofrequency quadrupole (RFQ) ion beam cooler delivers low energy (2.7 keV) ion bunches with a a

Conference presenter; e-mail: [email protected]

sharp time structure. Then a cylindrical preparation Penning trap is used for accumulation, cooling, and isobaric purification. Finally a high-precision, hyperbolic Penning trap is used for the measurement of the cyclotron frequency of the stored ions with charge to mass ratio q/m. The mass value can be determined by measuring the cyclotron frequency νc = qB/(2πm) with respect to a wellknown reference mass. Most of the nuclides in this study were measured with a precision of 10−8 . Particularly high resolving power was necessary for the separation of isomeric states in 68 Cu [10] and 70 Cu [11]. The difference between experimental mass values and values predicted by the Bethe-Weizs¨acker mass formula can provide a neutral indication for shell closures. The Bethe-Weizs¨acker formula is given by: Enuc = avol A + asf A−1/3 3e2 2 −4/3 Z A + 5r0   + asym + ass A−1/3 I 2   (−1)Z + (−1)N + ap A−y−1 2

(1)

with I = (N − Z)/A. The coefficients used for the calculations are from J.M. Pearson [12]: avol = −15.65 MeV, asf = 17.63 MeV, ass = −25.60 MeV, asym = 27.72 MeV,

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The European Physical Journal A

Fig. 1. Section of the nuclear chart where the nuclides measured at ISOLTRAP are shown in striped boxes. Black squares mark stable nuclides. The two frames indicate the N = 50, neutron magic number and the N = 40, our region of interest. 4

2

M(exp) - M(B&W) (MeV)

However, around N = 40 a small indentation is apparent for Ni and Ga, which could be an indication of magicity or simply the indication of a sub-shell closure. This analysis indicates a barely perceptible imprint of N = 40 sub-shell binding on the dominant N = 39 midshell comportment of binding-energy derivatives. More detailed studies of this question using the shell gap (difference of S2n values) and pairing energy are addressed in a forthcoming publication [15]. Note that detection of such fine structure effects on the mass surface requires mass values with relative uncertainties below 1·10−7 , which can be accomplished with Penning trap mass spectrometers such as ISOLTRAP.

Ni Z = 28 Cu Z = 29 Ga Z = 31

0

-2

-4

-6

-8 25

30

35

40

45

50

Neutron number N

Fig. 2. Difference between the predicted masses by the BetheWeizs¨ acker formula (eq. (1)) and the experimental values as a function of N for Z = 28, 29, and 31. Data are from this work and complemented by [13].

and r0 = 1.233 fm. We also added a pairing term from J.M. Fletcher [14], with ap = −7 MeV and y = 0.4. The residuals show especially strong effects (∼ 15 MeV) for nuclides with N = 50 and N = 82. Figure 2 shows the mass difference between experimental values and theoretical predictions of eq. (1) for the three isotopic chains of Cu, Ni, and Ga between the known shell closures at N = 28 and N = 50. The difference is less for N = 28 but still above 7 MeV. Between the shell closures the mass differences follow a smooth inverted parabola.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

A. Ozawa et al., Phys. Rev. Lett. 84, 5493 (2000). S. Shimoura et al., Phys. Lett. B 560, 31 (2003). F. Sarazin et al., Phys. Rev. Lett. 84, 5062 (2000). J.I. Prisciandaro et al., Phys. Lett. B 510, 17 (2001). P.F. Mantica et al., Phys. Rev. C 67, 014311 (2003). P.F. Mantica et al., Phys. Rev. C 68, 044311 (2003). P. Van Isacker, C. R. Phys. 4, 529 (2003). F. Herfurth et al., J. Phys. B 36, 931 (2003). E. Kugler, Hyperfine Interact. 129, 23 (2000). K. Blaum et al., Europhys. Lett. 67, 586 (2004). J. Van Roosbroeck et al., Phys. Rev. Lett. 92, 112501 (2004). J.M. Pearson, Hyperfine Interact. 132, 59 (2001). G. Audi, A.-H. Wapstra, C. Thibault, Nucl. Phys. A 729, 337 (2003). J.M. Fletcher, MSc Thesis, University of Surrey (2003). C. Gu´enaut et al., to be published in Phys. Rev. C (2005).

Eur. Phys. J. A 25, s01, 35–36 (2005) DOI: 10.1140/epjad/i2005-06-030-4

EPJ A direct electronic only

Extending the mass “backbone” to short-lived nuclides with ISOLTRAP C. Gu´enaut1,a , G. Audi1 , D. Beck2 , K. Blaum2,3 , G. Bollen4 , P. Delahaye5 , F. Herfurth2 , A. Kellerbauer5 , H.-J. Kluge2 , D. Lunney1 , S. Schwarz4 , L. Schweikhard6 , and C. Yazidjian2 1 2 3 4 5 6

CSNSM-IN2P3-CNRS, Universit´e de Paris Sud, 91405 Orsay-Campus, France GSI, Planckstrasse 1, 64291 Darmstadt, Germany Institute of Physics, Johannes Gutenberg-University, 55099 Mainz, Germany NSCL, Michigan State University, East Lansing, MI 48824-1321, USA CERN, Physics Department, 1211 Gen`eve 23, Switzerland Institute of Physics, Ernst-Moritz-Arndt-University, 17487 Greifswald, Germany Received: 9 November 2004 / c Societ` Published online: 20 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. New measurements performed with the Penning trap mass spectrometer ISOLTRAP extend the backbone to short-lived species. Recently obtained mass results are presented. PACS. 21.10.Dr Binding energies and masses – 32.10.Bi Atomic masses, mass spectra, abundances, and isotopes

In the Atomic Mass Evaluation [1], a backbone of very well known nuclides is distinguished (see fig. 1). For these nuclides the atomic-mass values are known with exceptionally high precision: their accuracy is below 1 keV. The precision now achieved with Penning traps allows also to improve the precision in our knowledge of atomic mass values of short-lived nuclides to extend the backbone. ISOLTRAP [2] is a Penning trap mass spectrometer at the on-line mass separator ISOLDE, located at CERN, Geneva. It was designed for high-precision mass measurements of short-lived nuclides, based on the determination of the cyclotron frequency of ions stored in a Penning trap. The present relative mass uncertainty limit of ISOLTRAP is 8 · 10−9 [3]. In an effort to extend the backbone, the masses of seven (six of them short-lived) nuclides were investigated (see table 1), almost all of them with an accuracy below than 4 keV. These high-precision mass values were included in the new Atomic Mass Evaluation 2003 [1]. All of them are in good agreement with the value recorded in the previous table [4] (see fig. 2). The Atomic Mass Evaluation (AME) results from an evaluation of all available experimental data on mass measurements including decay and reaction energies, forming a linked network. The evaluation takes into account all measurements and achieved accuracy to produce a mass table. The new mean value can replace all the old ones and become the only one used, or the new one can be combined with old values to decrease the uncertainty. The a

Conference presenter; e-mail: [email protected]

Fig. 1. Nuclear chart, where nuclides in black constitute the backbone. Their accuracy is below 1 keV (created by NUCLEUS-AMDC) [5]. Table 1. Comparison between previous [4], ISOLTRAP and new mass excess values [1]. All values are given in keV. Isotopes

Previous Mass Excess

ISOLTRAP Mass Excess

Mn (2.6h) Mn (85.4s) Rbm (6.5h) 92 Sr (2.7h) 124 Cs (30.9s) 127 Cs (6.2h) 130 Ba (Stable)

−56905.6 (1.4) −57485 (3) −76121.1 (1.5) −82875 (7) −81743 (12) −86240 (9) −87271 (7)

−56910.3 (1.4) −57486.4 (2.2) −76118.8 (2.6) −82865.2 (4.0) −81745.5 (14.2) −86244.0 (7.2) −87260.2 (3.2)

56

57

82

New value from AME2003 table

−56909.7 −57486.8 −76119.1 −82868 −81731 −86240 −87261.6

(0.7) (1.8) (2.4) (3) (8) (6) (2.8)

36

The European Physical Journal A 8 7

10

6

5

5

N-Z

Δ (ISOLTRAP - AME1995 ) (keV)

15

0

1

-15

ISOLTRAP AME1995

-20

57Mn 82mRb 92Sr

92

Mass Excess (keV)

92

92

Rb(β-) Sr

-82820 92

Sr

92

Sr(β-) Y

ISOLTRAP02

-82860

ISOLTRAP03

-82880 92

92

Rb(β-) Sr

-82900

92

92

Rb(β-) Sr

-82920

92

92

Sr(β-) Y 93

-

AME1995 AME2003

92

Rb(β n) Sr

-82940 1

2

3

4

5

6

7

8

Measurement

Fig. 3. 92 Sr measurements done with 92 Sr(β − )92 Y [6, 7], 92 Rb(β − )92 Sr [7, 8, 9], 93 Rb(β − n)92 Sr [10], the resulting value recorded in the AME 1995 [4], and ISOLTRAP values [11]. The final value in the AME 2003 table [1] has an uncertainty two times lower.

case of 92 Sr can be taken as an example (see fig. 3). Six decay measurements were taken into account in the AME95 table [4]: 92 Sr(β − )92 Y [6,7], 92 Rb(β − )92 Sr [7, 8, 9] and 93 Rb(β − n)92 Sr [10]. Since then, two measurements were done by ISOLTRAP: one in 2002 [11], and the other one presented in this work. The final precision of the mass value is increased by a factor of two, thanks to ISOLTRAP’s measurements, but all the values are still taken into account: 88.64% from ISOLTRAP, 7.28% from 92 Rb(β − )92 Sr, 2.89% from 92 Sr(β − )92 Y, and 7.28% from 93 Rb(β − n)92 Sr, according to the relative accuracy. The linked network formed by the evaluation has an important role in the mass world. Links are built from measurements, but they also have an influence on measurements. For example, the SPEG [12] experiment needs calibration masses to deduce their mass of interest and has to add an extrapolation error. With a stronger, more accurate backbone, this error is decreased. The links between atomic mass values improved the accuracy of more than

Co

Mass measured at ISOLTRAP

Co

Related masses

54

55

56

57

58

59

60

A

124Cs 127Cs 130Ba

Fig. 2. Deviation of the ISOLTRAP measurements from the AME 1995 values [4].

Co

Co

53

56Mn

Co Co

Fe

Fe

0

-25

Fe Fe

Fe

Co

Fe

Mn

Mn

Fe

Mn Mn

Mn

2

-10

-82840

Cr

4 3

-5

Cr Cr

Fig. 4. Nuclides linked to the two manganese isotopes measured by ISOLTRAP.

20 nuclides of Cr, Mn, Fe, and Co, thanks to our highprecision measurements on manganese (see fig. 4). Some of these nuclides are now known with an accuracy below 1 keV, extending the backbone from the valley of stability. In conclusion, a strong backbone is needed to increase our overall knowledge on atomic masses. The backbone is now extended by recent ISOLTRAP mass measurements as well as the ESR [13]. Further measurements also at other facilities are under progress [14,15,16, 17] or planned for the near future [18].

References 1. 2. 3. 4. 5. 6. 7. 8.

9. 10.

11. 12. 13. 14. 15. 16. 17. 18.

G. Audi et al., Nucl. Phys. A 729, No. 1 (2003). F. Herfurth et al., J. Phys. B 36, 931 (2003). A. Kellerbauer et al., Eur. Phys. J. D 22, 53 (2003). G. Audi, A.H. Wapstra, Nucl. Phys. A 595, 409 (1995). http://www-csnsm.in2p3.fr/amdc/. F.K. Wohn, W.L. Talbert jr., Phys. Rev. C 18, 2328 (1978). R. Iafigliola et al., Can. J. Chem. 61, 694 (1983). M. Groß et al., in Proceedings of the 6th Interantional Conference on Nuclei Far from Stability (NFFS-6) jointly with the 9th International Conference on Atomic Masses and Fundamental Constants (AMCO-9), Bernkastel-Kues, Germany, 19-25 July 1992 (IOP Publ. Ltd., Bristol, 1992) p. 77. M. Przewloka et al., Z. Phys. 342, 23 (1992). K.-L. Kratz et al., in Proceedings of the 7th International Conference on Atomic Masses and Fundamental Constants (AMCO-7), Darmstadt-Seeheim, Germany, 3-7 September 1984 (Lehrdruckerei, Darmstadt, 1984) p. 127. H. Raimbault-Hartmann et al., Nucl. Phys. A 706, 3 (2002). H. Savajols, Hyperfine Interact. 132, 245 (2001). Yu.A. Litvinov et al., Nucl. Phys. A 734, 473 (2004). G. Savard et al., Nucl. Phys. A 626, 353 (1997). J. Szerypo et al., Nucl. Phys. A 701, 588 (2002). I. Bergstr¨ om et al., Nucl. Instrum. Methods Phys. Res. A 487, 618 (2002). J. Sch¨ onfelder et al., Nucl. Phys. A 701, 579 (2002). J. Dilling et al., Nucl. Instrum. Methods Phys. Res. B 204, 492 (2003).

Eur. Phys. J. A 25, s01, 37–39 (2005) DOI: 10.1140/epjad/i2005-06-070-8

EPJ A direct electronic only

A MISTRAL spectrometer accoutrement for the study of exotic nuclides M. Sewtza , C. Bachelet, C. Gu´enaut, J.F. K´epinski, E. Leccia, D. Le Du, N. Chauvin, and D. Lunney b CSNSM-IN2P3/CNRS, Universit´e de Paris Sud, F-91405 Orsay, France Received: 20 December 2004 / c Societ` Published online: 17 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. An ion beam cooler has been constructed to adapt the emittance of the ISOLDE rare isotope beam to the acceptance of the mass spectrometer MISTRAL at CERN. Using 20,22 Ne+ beams with an energy of Ebeam = 45 keV the transmission through the cooler was measured to be T = 0.25. An analytical model to describe the transmission as a function of the trapping potential is discussed. By fitting this model to the data, the lateral energy distribution of the radially confined ions was determined to be centered at E0 = 1.3(1) eV and to have a width of σE = 1.6(1) eV. PACS. 29.27.Eg Beam handling; beam transport – 21.10.Dr Binding energies and masses

1 Introduction The investigation of the nuclear properties of halo nuclei, especially the determination of their binding energies, is a real challenge. The two-neutron halo nucleus 14 Be for example can be produced by nuclear reactions at ISOLDE with a rate of only 10/s [1]. This results in a need for ultimate efficiency of any experimental setup. Several years ago the first attempts to adapt the emittance and time structure of an exotic ion beam to the acceptance of the experiments by deceleration and subsequent cooling of the incoming beam were elaborated [2] and are now operational, e.g. at ISOLDE [3] and Jyv¨ askyl¨a [4]. To reduce the emittance of an ion beam, a non-conservative interaction is needed. Beam momentum can be dissipated by low-energy collisions with a light, inert buffer gas at background pressures of typically 0.01 mbar. To avoid any loss of the exotic beam particles, linear Paul traps [5] are used for radial confinement.

2 Setup Even though its short half-life of 4.4 ms renders 14 Be inaccessible for investigations at ISOLTRAP [6] it poses no such problem for the mass spectrometer MISTRAL [7,8] at ISOLDE. This transmission, radiofrequency mass spectrometer allows for direct mass measurements of nuclides with half-lives of less than 100 μs and is therefore best suited for very short-lived exotic nuclei. Its acceptance a b

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amounts to 3 π mm mrad in the horizontal and vertical directions which results presently in the poor transmission of TM ≈ 10−4 for the ISOLDE rare isotope beam having an emittance of ε0 = 30 π mm mrad. Therefore, a dedicated 60 keV beam cooler (described in detail elsewhere [9]) is being developed for MISTRAL. First, in order to preserve the initial energy Ebeam = 60 keV, the beam is decelerated to Ekin ≤ 50 eV by gaining the potential energy Epot = eUHV with the high voltage UHV of the cooler. Subsequently the ions are injected into a He-buffer-gas filled, linear Paul trap [5]. At a buffer gas pressure of 10−2 mbar, light ions are stopped during one pass through the radio frequency quadrupole (RFQ) of 504 mm length. The quadrupole rods each consist of 15 electrically isolated segments. Using dc-offsets of typically 1 V between two neighboring segments, a mean axial electric field of 0.25 V/cm can be created which allows for an extraction of the injected ions within 40 μs. In the last part the ions are re-accelerated to the energy Ebeam = eUHV ≈ 59.95 keV.

3 Measurements First tests of the cooler were performed at low beam energies. It was shown [10] that a 6 keV Na+ beam could be extracted with a beam emittance of ε = 8 π mm mrad. This corresponds to ε = 2.5 π mm mrad at 60 keV and will improve the transmission T through the mass spectrometer MISTRAL by three orders of magnitude [9]. However, a crucial part is the deceleration of the 60 keV ISOLDE beam. Therefore, a new deceleration system has been installed and successfully tested [9] behind

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20

Ne Experiment Ne Simulation 22 Ne Experiment

20

(b)

T(q)

0.10

0.05 (a) (c)

0.00 0.0

0.2

0.4

0.6

0.8

1.0

q (m=20 u) Fig. 1. Transmission T = ICF2 /ICF1 as function of q (m = 20 u). Amplitudes of experimental curves were multiplied by a factor 0.7 for better comparison. The full line is a best fit to the data, see text.

the mass separator SIDONIE [11] at Orsay. To determine the transmission T , the currents of 20,22 Ne+ beams have been measured with Faraday cups before (ICF1 ) and behind the cooler (ICF2 ). To avoid the charging of insulators by scattered and deflected ions, the ion current IS = 3 μA delivered from the separator was reduced with slits to ICF1 = 400 pA. The gas flow of the He-buffer gas amounted to 0.6 mbar l/s and corresponds to a calculated mean gas pressure of p = 0.01 mbar. Figure 1 shows T (q) 4eARF as a function of the Mathieu parameter q = m(r 2 [5] 0 ω) which is plotted for the mass m = 20 u, the RF angular frequency ω = 5 × 106 /s and the inner radius r0 = 7 mm of the rod system. The elementary charge is denoted by e. The parameter q was varied by selecting the RF amplitude ARF . To obtain q = 0.9 at the end of the transmission curve of 20 Ne due to the instability of the trajectories [5], the measured ARF was multiplied by a factor 1.3. This correction is necessary since ARF decreases during its measurement using a capacity probe of an oscilloscope.

4 Results and conclusion For q < 0.5 the potential energy of the trapped  2 ions can be approximated by E(q) = cq 2 rr0 , c = m(r0 ω)2 16

[4,12]. The maximal transversal energy of the ions Emax = E0 + 2σE must thus be smaller than E(q) and limits the transmission of the ions. If we assume a Gaussian for the transversal energy distribution I(E) with the center E0 and the width σE , T (q) can be calculated for r = r0 : T (q) = (E (q )−E(q ))2 E(q) q 1 − 0 2σ 2 √ E 2cq  dq  . A 0 I(E)dE = A 0 2πσ e E The constant A = 1.3(1) was used to fit the experimental data; see fig. 1. This fit yields E0 = 1.3(1) eV and σE = 1.6(1) eV. The model describes the experimental

data very well up to q ≈ 0.55. Beyond this value the transmission decreases due to RF-heating and subsequent destabilization of the trajectories [2]. At q = 0.55 the trapping potential amounts to E(q = 0.55) = 4.8 eV and coincides with the deduced maximal transversal energy of the ions Emax = 4.5(2) eV. This leads to the assumption that the transmission T ≈ 0.11 is limited by the trapping potential. Simulations using the software package SIMION7 [13] confirm this interpretation. The absolute transmission, as well as the shape of the curve are well reproduced by the simulation; see fig. 1. Collisions in the region of the fringing field at the entrance of the quadrupole can provoke losses of ions. This may explain the onset of the transmission at higher q values (a) with respect to the simulations in which the buffer gas interaction was omitted. This may also explain why the step in the transmission function of the 20 Ne ions at q = 0.86 (c) appears in the simulation already at q = 0.8 (b). This step may be explained by the radius of the macro motion in front of the exit cone which varies with q [14] and may exceed the radius of the latter. By increasing the angular frequency to ω = 1.3 × 107 /s, the trapping potential amounts to E(q = 0.55) = 32 eV and the simulations yield a transmission of T = 0.3. This was confirmed in a test experiment using ω = 0.9 × 107 /s where a transmission of T = 0.25 was observed. An unambiguous identification of the ions was possible by recording the transmission curves for different isotopes; see fig. 1. The transmission curve of 22 Ne is displaced with respect to 20 Ne by Δq/q = 0.1 corresponding exactly to 2 mass units, as expected, and therefore excludes the observation of ionized buffer gas impurities. To increase the transmission, a reduction of the quadrupole capacitance is planned which will allow for a higher amplitude ARF = 235 V at ω = 1.3 × 107 /s and thus E(q = 0.55) = 32 eV. After final emittance measurements of the extracted beam, the set up will be installed at ISOLDE. This work has been supported by the French IN2P3 and the EU-network NIPNET under contract HPRI-CT-2001-50034.

References 1. U. K¨ oster et al., ENAM’98, AIP Conf. Proc. 455, 989 (1998). 2. M.D. Lunney, R.B. Moore, Int. J. Mass Spectrom. 190/191, 153 (1999). 3. F. Herfurth et al., Nucl. Instrum. Methods Phys. Res. A 469, 254 (2001). 4. A. Nieminen et al., Nucl. Instrum. Methods Phys. Res. A 469, 244 (2001). 5. W. Paul, H.P. Reinhard, U. von Zahn, Z. Phys. 152, 143 (1958). 6. F. Herfurth et al., J. Phys. B 36, 931 (2003). 7. A. Coc et al., Nucl. Instrum. Methods Phys. Res. A 271, 512 (1988). 8. D. Lunney et al., Phys. Rev. C 64, 054311 (2001).

M. Sewtz et al.: A MISTRAL spectrometer accoutrement for the study of exotic nuclides 9. M. Sewtz et al., Nucl. Instrum. Methods Phys. Res. B (in press). 10. S. Henry et al., in Exotic Nuclei and Atomic Masses, ¨ o, P. Dendooven, A. Jokinen, M. Leino, edited by J. Ayst¨ (Springer, Berlin, 2001) p. 490.

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11. N. Chauvin, F. Dayras, D. Le Du, R. Meunier. Nucl. Instrum. Methods Phys. Res. A 521, 149 (2004). 12. K. Okuno, J. Phys. Soc. Jpn. 55, 1504 (1986). 13. D.A. Dahl, SIMION 3D, INEEL-95/0403, 2000. 14. S. Henry, PhD Thesis, University of Strasbourg, 2001.

Eur. Phys. J. A 25, s01, 41–43 (2005) DOI: 10.1140/epjad/i2005-06-164-3

EPJ A direct electronic only

Mass measurement on the rp-process waiting point

72

Kr

¨ o2 , D. Beck1 , K. Blaum1,4 , G. Bollen5 , F. Herfurth1 , A. Jokinen2 , D. Rodr´ıguez1,a , V.S. Kolhinen2,b , G. Audi3 , J. Ayst¨ A. Kellerbauer6 , H.-J. Kluge1 , M. Oinonen7 , H. Schatz5,8 , E. Sauvan6,c , and S. Schwarz5 1 2 3 4 5 6 7 8

GSI, Planckstraße 1, 64291 Darmstadt, Germany University of Jyv¨ askyl¨ a, P.O. Box 35, 40351 Jyv¨ askyl¨ a, Finland CSNSM-IN2P3-CNRS, 91405 Orsay-Campus, France Institute of Physics, University of Mainz, Staudingerweg 7, 55128 Mainz, Germany NSCL, Michigan State University, East Lansing, MI 48824-1321, USA CERN, Physics Department, 1211 Geneva 23, Switzerland Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, 00014 Helsinki, Finland Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824-1321, USA Received: 13 January 2005 / c Societ` Published online: 1 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. With the aim of improving nucleosynthesis calculations, we performed for the first time, a direct high-precision mass measurement on the waiting point in the astrophysical rp-process 72 Kr. We used the ISOLTRAP Penning trap mass spectrometer located at ISOLDE/CERN. The measurement yielded a relative mass uncertainty of δm/m = 1.2 × 10−7 . In addition, the masses of 73 Kr and 74 Kr were measured directly with relative mass uncertainties of 1.0 × 10−7 and 3 × 10−8 , respectively. We analyzed the role of 72 Kr in the rp-process during X-ray bursts using the ISOLTRAP and previous mass values of 72–74 Kr. PACS. 07.75.+h Mass spectrometers – 21.10.Dr Binding energies and masses – 26.30.+k Nucleosynthesis in novae, supernovae and other explosive

1 Introduction Very precise mass values of elements formed along the rapid proton capture process (rp-process) are crucial for reliable calculations of X-ray burst light curves [1]. An Xray burst is a thermonuclear explosion on the surface of a neutron star accreting hydrogen and helium rich matter from a companion star in a binary system. The extreme temperature and density conditions in this scenario can lead to the formation of elements up to Te (Z = 52) within 10–100 s. They are formed by continuous rapid proton captures, interrupted at the so-called waiting points by β + -decays. Waiting point nuclei come on stage when (p, γ) proton capture is hindered by (γ, p) photodisintegration of weakly proton bound or unbound nuclei. This causes a delay in the X-ray burst duration and consequently, affects the X-ray burst light curve and the nucleosynthesis. This delay is the time for a certain abundance to drop to 1/e and is referred to as effective lifetime. The effective lifetime a

Conference presenter; Present address: IN2P3, LPCENSICAEN 6, Boulevard du Mar´echal Juin, 14050, Caen Cedex, France; e-mail: [email protected] b Present address: LMU M¨ unchen, Am Coulombwall 1, 85748 Garching, Germany. c Present address: IN2P3, CPPM, 13288 Marseille, France.

depends exponentially on the mass difference between the waiting point nucleus, here 72 Kr, and the possibly formed nucleus 73 Rb (or as the temperature increases 74 Sr). This calls for mass values of 72 Kr, 73 Rb, and 74 Sr with relative mass uncertainties δm/m of the order of 10−7 . We measured directly the mass of 72 Kr at ISOLTRAP [2]. Since 73 Rb and 74 Sr are difficult to access experimentally, we determined their masses from the masses of their mirror nuclei 73 Kr and 74 Kr, also measured directly in the experiment reported here.

2 Experimental setup and method The ISOLTRAP facility [3, 4,5] is located at ISOLDE/CERN [6] in Geneva (Switzerland). The system is shown in fig. 1. It consists of three different traps: A gas-filled linear Paul trap [4], a gas-filled cylindrical Penning trap [7] and a hyperbolic Penning trap in ultra-high vacuum [3]. The 60 keV krypton beam from ISOLDE is electrostatically retarded to about 10–20 eV and thermalized in the buffer-gas-filled linear Paul trap. After an accumulation time of up to a few tens of milliseconds, the cooled ion bunch is ejected with a temporal width of less than

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The European Physical Journal A

Table 1. Mass excess values for 72,73,74 Kr, 73 Rb, and 74 Sr from ISOLTRAP [2] compared to previous results [12]. Note that the mass values of 73 Rb and 74 Sr are obtained through the mass values of their mirror nuclei 73 Kr and 74 Kr using the calculated Coulomb shifts from Brown et al. [13].

Nuclide

(1)

where B is the strength of the homogeneous magnetic field in the center of the precision Penning trap (∼ 5.9 T), and e is the atomic unit of charge. The cyclotron frequency is determined using a resonant time-of-flight technique [8]. The magnetic field B in eq. (1) is deduced from the measurement of the cyclotron frequency of ions with well-known mass, here 85 Rb+ (δm/m = 2 × 10−10 [9]). This is performed before and after the measurement of the cyclotron frequency of each ion of interest. The value adopted for B is the result of the linear interpolation of both measurements to the center of the time interval during which the cyclotron frequency of the ion of interest was measured. In that way, possible drifts of the magnetic field are accounted for. The final relative mass uncertainty includes effects like the long term drifts of the magnetic field and the presence of contaminating ions, among the mass dependant uncertainty and the systematics uncertainty of the apparatus (δm/m = 8 × 10−9 ) [10].

3 Results and discussion The mass excess D of a nucleus is given by D = m − A · u,

DISOLTRAP /keV

72

Kr

17.2 s

−54110(270)

−53940.6(8.0)

Kr

27.0(1.2) s

−56890(140)

−56551.7(6.6)

74

Kr

11.5(1) min

−62170(60)

−62332.0(2.1)

73

Rb

< 24 ns

−46270(170)

−45940(100)

74

Sr

50 ms

−40670(120)

−40830(100)

30

Effective lifetime /s

1 μs. The ion bunches are transported with an energy of 2.8 keV and after retardation captured in the purification Penning trap for isobaric cleaning. Thereafter, the ions are ejected and transferred to the precision Penning trap where the mass measurement is carried out. The mass m of singly charged ions is determined by a measurement of the cyclotron frequency νc employing the relationship 1 e · B, · 2π m

Dpre /keV

73

Fig. 1. Sketch of the ISOLTRAP setup.

νc =

T1/2

10

AME 95 ISOLTRAP

1

Fig. 2. Effective lifetime for 72 Kr at 1.3 GK. The solid line marks the lowest limit due to the non-observation of 73 Rb, and the dotted line gives the β-decay lifetime.

the mass excess values of 72,73,74 Kr, 73 Rb, and 74 Sr from ISOLTRAP [2] compared to those given in the literature prior to our measurements [12]. With the mass excess values given in table 1 we calculated the effective lifetime for 72 Kr. We took into account proton capture on 72 Kr and 73 Rb, photodisintegration on 73 Rb, and 74 Sr, and β + -decay of 72 Kr, 73 Rb, and 74 Sr. Proton capture rates are as in Schatz et al. [14]. Figure 2 shows the minimum effective lifetime (T = 1.3 GK, ρ = 106 g/cm3 , Yp = 0.88) using the ISOLTRAP mass values and the previous results. Our result shows that 72 Kr is a strong waiting point in the rp-process [2]. It delays the X-ray burst by at least 20.8(3.4) s. This reduces considerably the uncertainty in the delay obtained using the previous mass values (2–24.8 s). However, the effective lifetime depends linearly on the 73 Rb(p, γ)74 Sr reaction rate and for this reaction rate, uncertainties of a few orders of magnitude cannot be excluded. This implies the necessity to measure this rate experimentally.

(2)

where m is the atomic mass, A the atomic mass number, and u the atomic mass unit [11]. Table 1 shows

This work was supported by funds from EU, NSF, and the Alfred P. Sloan Foundation.

D. Rodr´ıguez et al.: Mass measurement on the rp-process waiting point

References 1. H. Schatz et al., Phys. Rep. 294, 167 (1998). 2. D. Rodr´ıguez et al., Phys. Rev. Lett. 93, 161104 (2004). 3. G. Bollen et al., Nucl. Instrum. Methods A 368, 675 (1996). 4. F. Herfurth et al., Nucl. Instrum. Methods A 469, 254 (2001). 5. K. Blaum et al., Nucl. Instrum. Methods B 204, 478 (2003).

72

Kr

43

6. E. Kugler, Hyperfine Interact. 129, 23 (2000). 7. H. Raimbault-Hartmann et al., Nucl. Instrum. Methods B 126, 378 (1997). 8. G. Gr¨ aff et al., Z. Phys. A 297, 35 (1980). 9. M.P. Bradley et al., Phys. Rev. Lett. 83, 4510 (1999). 10. A. Kellerbauer et al., Eur. Phys. J. D 22, 53 (2003). 11. G. Audi, Hyperfine Interact. 132, 7 (2001). 12. G. Audi, A.H. Wapstra, Nucl. Phys. A 595, 409 (1995). 13. B.A. Brown et al., Phys. Rev. C 65, 045902 (2002). 14. H. Schatz et al., Phys. Rev. Lett. 86, 3471 (2001).

Eur. Phys. J. A 25, s01, 45–46 (2005) DOI: 10.1140/epjad/i2005-06-191-0

EPJ A direct electronic only

Atomic mass ratios for some stable isotopes of platinum relative to 197Au K.S. Sharma1,a , J. Vaz1 , R.C. Barber1 , F. Buchinger2 , J.A. Clark1 , J.E. Crawford2 , H. Fukutani1 , J.P. Greene3 , S. Gulick2 , A. Heinz3 , J.K.P. Lee2 , G. Savard3 , Z. Zhou3 , and J.C. Wang1 1 2 3

Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB R3T 2N2, Canada Department of Physics, McGill University, Montreal, QC H3A 2T8, Canada Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA Received: 15 January 2005 / c Societ` Published online: 11 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The Canadian Penning Trap mass spectrometer was designed to determine precisely the masses of stable and unstable isotopes. To date, such measurements have been carried out on approximately 60 short-lived species. A laser ablation ion source is also available to produce ions of stable isotopes, intended for use in calibrations, checks for systematic effects and for measurements involving stable isotopes. Mass ratios for the isotopes 194,195,196,198 Pt relative to 197 Au have been determined to a precision of better than 3 × 10−8 . These measurements were motivated, in part, by the long-standing discrepancy between earlier mass measurements and the Atomic Mass Evaluations in the mercury region. The results also demonstrate the stability of the measurement system and set limits on the magnitude of systematic effects. No significant deviations from accepted values were found. PACS. 21.10.Dr Binding energies and masses – 27.80.+w Properties of specific nuclei listed by mass ranges: 190 ≤ A ≤ 219 – 32.10.Bi Atomic masses, mass spectra, abundances, and isotopes

The Canadian Penning Trap (CPT) mass spectrometer [1] is a unique instrument that was designed to extend precise atomic mass measurements, from the region of beta-stability where they were traditionally grounded, to the nuclides at the limits of stability. Our measurements are concentrated on improving our knowledge of the atomic masses of the well-known masses close to stability, proton and neutron-rich nuclei of astrophysical interest and nuclear masses that play a key role in the testing of symmetries in nuclear and particle physics. The instrument combines the high accuracy and extreme sensitivity of Penning ion traps with a unique gas catcher, which allows the direct capture of products from nuclear reactions without first stopping the activities in a solid material [2, 3]. Over 60 masses among proton-rich species produced with beams from ATLAS, and neutronrich species produced by a 252 Cf fission source, have been measured so far with accuracies ranging from 10−6 to 10−8 of the mass. Here we report the results of our measurements with platinum and gold ions produced by a laser ablation ion source. This source is used to produce ions of stable isotopes intended for use in calibrations, checks for systema

Conference presenter; e-mail: [email protected]

Table 1. Measured mass ratios for platinum isotopes. The masses for the isotopes before and after the application of the systematic correction are also shown.

194

Pt Pt 196 Pt 198 Pt 195

(a )

Mass ratio for ions

Uncorrected mass(a) (μu)

Corrected mass(a) (μu)

0.984749172(16) 0.989836899(16) 0.994914788(15) 1.005083758(15)

193962673.9(3.1) 194964783.1(3.2) 195964954.7(2.9) 197967896.3(2.9)

193962674.7(4.4) 194964783.7(4.4) 195964955.0(4.3) 197967896.1(4.3)

Using the mass for

197

Au from AME03.

atic effects and determinations of their mass. We were motivated by the long-standing discrepancy between earlier mass measurements and previous Atomic Mass Evaluations [4] in the mercury region. This discrepancy was recently resolved [5, 6, 7] but some inconsistencies still exist between Ir and Pt isotopes. Mass ratios for the isotopes 194,195,196,198 Pt relative to 197 Au have been determined to a precision of 1.6 × 10−8 . In addition, the data demonstrate the stability of the measurement system and set limits on the magnitude of systematic effects. The measurements were carried out over the period of two weeks. Each isotope was measured every day with

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0.08

10

0.06 Difference (μu)

Frequency - 459134.807 (Hz)

5

0.04 0.02 0.00 -0.02

0 -5 -10

-0.04 -0.06

-15 194Pt

-0.08

-0.12 -10

40

90

140

190

240

290

Time (hrs)

Fig. 1. Variation of the cyclotron frequency for gold ions over the period of the experiment. Only data where the number of ions detected were less than or equal to 9 were included.

50 40

Frequency shift (mHz)

195Pt

196Pt

198Pt

Nuclide

-0.10

30 20

197Au 194Pt 195Pt 196Pt 198Pt

10 0 -10 -20 -30 -40 -50 0 to 9

10 to 19

20 to 29

30 to 39

40 to 49

Number of ions

Fig. 2. The variation of the measured cyclotron frequency with the number of ions detected.

scans over the calibration nuclide, 197 Au, carried out at the beginning and end of each day. The measured cyclotron frequencies were combined in a weighted average and used to generate the mass ratios shown in table 1. The magnetic field of the spectrometer is very stable with time. Figure 1 shows the variation in the cyclotron frequency (directly linked to the magnetic field) for gold ions plotted as a function of time over the 250-hour period of these measurements. The standard deviation of the field values are less than 4 parts in 108 over this period and the frequencies determined for the other species show a similar stability. Accordingly, no corrections were applied for field drifts. Slight misalignments of the axis of the trap with the magnetic field can contribute a mass dependent systematic shift [8]. Based on the comparison of the measured cyclotron frequencies of 197 Au to those of lighter ions near A = 50, we determined that a correction of 1.3 × 10−9 of the mass for every mass unit of separation between the reference mass and unknown in this region was needed.

Fig. 3. Differences between the measured masses and the AME03. The thick dark-gray (red on-line) lines indicate the uncertainties in output of the AME03, while the error bars show the precision achieved in this work.

Such a correction was applied to our results even though it was much smaller than our quoted uncertainties. The number of ions loaded into the trap is known to affect the measured frequencies. Figure 2 shows that the effect of ion number on the measured cyclotron frequency is at the level of 1.5 mHz per ion. Because the effect of this shift on the measured mass ratios is negligible if a similar number of ions is used for scans over both calibrant and unknown masses, we only accepted data when the number of ions detected was between 0 to 9 ions. Based on the variations shown in fig. 2, we inflated the uncertainty in the mass values by 1.6 × 10−8 of the mass. Table 1 gives the measured masses for the platinum isotopes before and after these corrections were applied to the data. The differences between our results and the values from AME03 [5] are shown in fig. 3. The results are consistent with the AME03 within the precision attained. However, only in the case of 198 Pt is the precision high enough to influence future mass evaluations. These measurements confirm the validity of our measurement technique and the applied corrections and have paved the way to more accurate measurements with the CPT. This work was supported by the Natural Sciences and Engineering Research Council of Canada and by the U.S. Department of Energy, Office of Nuclear Physics, under Contract No. W-31-109-ENG-38.

References 1. 2. 3. 4. 5. 6. 7.

G. Savard et al., Nucl. Phys. A 626, 353 (1997). J.A. Clark et al., these proceedings. G. Savard et al., these proceedings. G. Audi, A.H. Wapstra, Nucl. Phys. A 565, 1 (1993). G. Audi et al., Nucl. Phys. A 729, 337 (2003). D.K. Barillari et al., Phys. Rev. C 67, 064316 (2003). I. Bergstr¨ om et al., Nucl. Instrum. Methods Phys. Res. A 487, 618 (2002). 8. G. Bollen et al., J. Appl. Phys. 68, 4355 (1990).

1 Masses 1.3 Traps

Eur. Phys. J. A 25, s01, 49–50 (2005) DOI: 10.1140/epjad/i2005-06-013-5

EPJ A direct electronic only

The ion-trap facility SHIPTRAP Status and perspectives M. Block1,a , D. Ackermann1 , D. Beck1 , K. Blaum1,2 , M. Breitenfeldt3 , A. Chauduri3 , A. Doemer4 , S. Eliseev1 , D. Habs5 , S. Heinz5 , F. Herfurth1 , F.P. Heßberger1 , S. Hofmann1 , H. Geissel1,6 , H.-J. Kluge1 , V. Kolhinen5 , G. Marx3 , J.B. Neumayr5 , M. Mukherjee1 , M. Petrick6 , W. Plass6 , W. Quint1 , S. Rahaman1 , C. Rauth1 , D. Rodr´ıguez7 , C. Scheidenberger1,6 , L. Schweikhard3 , M. Suhonen8 , P.G. Thirolf5 , Z. Wang6 , C. Weber1 , and the SHIPTRAP Collaboration 1 2 3 4 5 6 7 8

Gesellschaft f¨ ur Schwerionenforschung mbH, Planckstrasse 1, D-64291 Darmstadt, Germany Institut f¨ ur Physik, Johannes-Gutenberg-Universit¨ at Mainz, Staudingerweg 7, 55128 Mainz, Germany Institut f¨ ur Physik, Ernst-Moritz-Arndt-Universit¨ at, Domstrasse 10a, 17489 Greifswald, Germany Department of Physics & Astronomy, Michigan State University, South Shaw Lane, East Lansing, MI 48823, USA Sektion Physik, Ludwig-Maximilians-Universit¨ at M¨ unchen, Am Coulombwall 1, 85748 Garching, Germany II. Physikalisches Institut, Justus-Liebig-Universit¨ at, Heinrich-Buff-Ring 16, 35392 Gießen, Germany LPC, ENSICAEN, 6 Bd. Marechal Juin, 14050 Caen Cedex, France Atomic Physics, Stockholm University, Alba Nova University Centrum, S-106 91, Stockholm, Sweden Received: 14 January 2005 / c Societ` Published online: 18 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The Penning-trap mass spectrometer at the ion trap facility SHIPTRAP is in the final stage of commissioning. First on-line mass measurements of neutron-deficient radionuclides in the rare-earth region around A = 147 were performed in July 2004. Systematic investigations in order to determine systematic errors are ongoing. Further improvements of the efficiency of the system are in preparation, e.g. improved detection schemes and further optimization of the stopping cell. SHIPTRAP will then address exotic nuclides produced in fusion-evaporation reactions at the velocity filter SHIP. This production technique will give access to nuclei not available at ISOL facilities, especially in the transuranium region. PACS. 07.75.+h Mass spectrometers – 21.10.Dr Binding energies and masses

The ion-trap facility SHIPTRAP [1] at GSI Darmstadt was set up to enable various precision experiments on heavy elements produced in fusion-evaporation reactions at the velocity filter SHIP [2]. In the first stage SHIPTRAP focuses on precision mass measurements of nuclei not available at ISOL or fragmentation facilities with a Penning-trap mass spectrometer. In this respect the region of the elements heavier than uranium is most attractive since the majority of masses in this region is only known from extrapolations to a few hundred keV precision [3]. In addition, the extrapolated mass values are linked to only few α-decay chains [3]. From the measured mass values the nuclear binding energy can be deduced which is an important parameter for nuclear structure theories. Systematic measurements along isotopic or isotonic chains covering shell closures are planned. For the elements heavier than uranium the very low production rates, dropping to only a few ions per week in the extreme case of Z = 112, are very challenging. In the second stage atomic and nuclear structure studies by means of trap-assisted or in-trap nuclear speca

Conference presenter; e-mail: [email protected]

troscopy and by laser spectroscopy are envisaged. Isobarically purified low-emittance beams at low energy with the option of pure isomeric beams could be delivered to dedicated spectroscopy set-ups. The advantage of a point-like source could be exploited for instance for X-ray or conversion electron spectroscopy. The laser spectroscopic studies could comprise for instance isotope-shift measurements to determine nuclear charge radii. A schematic drawing of the setup is shown in fig. 1. The reaction products from SHIP with energies in the order of a few 100 keV/u are stopped in a buffer-gas-filled stopping cell with an overall efficiency, including the extraction RFQ, of about 5–8% as described in [4]. To improve the beam quality of the ion beam extracted from the stopping cell for an efficient injection into the Penning trap an RFQ cooler and buncher is utilized. In this buffer-gasfilled four-rod structure the ions are cooled within a few milliseconds and extracted as a low-emittance bunched beam. Ions from the stopping cell can also be stacked in the RFQ. A system of two cylindrical Penning traps in one superconducting magnet of 7 T field strength allows for high-precision mass measurements. The first trap with

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The European Physical Journal A 320 300

Mean TOF [ms]

280 260 240 220 200 -15

a mass resolving power of about 85000 for 133 Cs is used for isobaric purification. In the second trap mass measurements are performed by the time-of-flight ion cyclotron resonance method [5]. A mass resolving power of 106 is routinely achieved. This allows for the identification of isomeric states and hence an unambiguous mass determination of the ground state. Extensive off-line tests were carried out in order to characterize all individual components. In addition, online experiments at GSI and tests with radioactive ions at the Maier-Leibnitz Laboratory in Garching were carried out to optimize the stopping process in the gas cell. The overall efficiency of SHIPTRAP of currently about 0.5% is limited by the total efficiency of the gas cell of 5–8% and the detection efficiency of the micro-channel plate detectors of 10–30%. While further improvements are being prepared first mass measurements of radionuclides in the rare-earth region with production rates of some thousand ions per second in front of the stopping cell are already feasible. This was demonstrated with radionuclides around A = 147 in July 2004. In this beam time the first on-line mass measurements at SHIPTRAP were performed. Holmium and erbium radionuclides produced in the reaction 92 Mo(58 Ni, xpxn) at SHIP were studied. The primary beam energy was chosen to be 4.36 MeV/u yielding the highest production rate in the 3p evaporation channel for 147 Ho. The area close to 147 Ho is interesting because of the phenomenon of ground-state proton radioactivity, which was discovered at SHIP [6] several years ago. The key parameter is the proton separation energy, which can be derived from atomic masses. Furthermore, important data for nuclear structure studies is obtained allowing for the calculation of two neutron separation energies around the neutron shell closure at N = 82. At present, many masses in this region are experimentally unknown. In the run in July 2004 the masses of 147 Ho, 147 Er and 148 Er were measured. The mass of the two erbium nuclides was experimentally determined for the first time. The data analysis is ongoing and the results will be presented elsewhere. As an example a time-of-flight resonance of 147 Ho is shown in fig. 2 with a Fourier-limited resolution. After first on-line mass measurements in July 2004 the systematic errors of the system have to be determined and the overall efficiency has to be improved. A carbon cluster ion source which will enable cross-reference mea-

-10

-5

0

5

10

15

20

Excitation frequency - 732227 [Hz]

Fig. 1. A schematic overview of the SHIPTRAP facility.

Fig. 2. Time-of-flight resonance of excitation time of 200 ms.

147

Ho+ obtained with an

surements as described in [7] is being tested. This will not only allow for the determination of the systematic error, but also for absolute mass measurements since the atomic mass standard is defined via the mass of 12 C. An improvement of the overall efficiency of the the stopping cell may be possible e.g. by an increase of the pressure from 40 to about 100 mbar. This will result in a narrower distribution of the stopped ions and hence more ions will be stopped within the extraction volume. In addition, an efficiency increase of the system is expected by using a detector with an extra conversion-electrode combined with a micro-channel plate (MCP) e.g. of Daley type [8] instead of the presently used MCP detectors. This will allow for an increased detection efficiency by a factor of 2–3. In the long-term future a cryogenic trap system utilizing the non-destructive Fourier transform ion cyclotron resonance (FT-ICR) detection will replace the current trap system. This will enhance the sensitivity especially for long-lived nuclides with lowest production rates allowing for a mass measurement even with a single ion. A more detailed description of this cryogenic trap system is given in [9]. With all the improvements implemented SHIPTRAP will start a mass measurement program focussed on neutron-deficient heavy ions. We acknowledge financial support by the EU within the networks NIPNET (contract HPRI-CT-2001-50034) and Ion Catcher (contract HPRI-CT-2001-50022).

References 1. J. Dilling et al., Hyperfine Interact. 127, 491 (2000). 2. S. Hofmann, G. M¨ unzenberg, Rev. Mod. Phys. 72, 733 (2000). 3. G. Audi, A.H. Wapstra, C. Thibault, Nucl. Phys. A 729, 337 (2003). 4. J. Neumayr, PhD Thesis, LMU M¨ unchen (2004). 5. G. Gr¨ aff, H. Kalinowski, J. Traut, Z. Phys. A 297, 35 (1980). 6. S. Hofmann et al., Z. Phys. A 305, 111 (1982). 7. A. Kellerbauer et al., Eur. Phys. J. D 22, 53 (2003). 8. N.R. Daley, Rev. Sci. Instrum. 31, 264 (1960). 9. C. Weber, PhD Thesis, Heidelberg (2003); C. Weber et al., these proceedings.

Eur. Phys. J. A 25, s01, 51–52 (2005) DOI: 10.1140/epjad/i2005-06-131-0

EPJ A direct electronic only

Precision experiments with rare isotopes with LEBIT at MSU P. Schury1,2,a , G. Bollen1,2,b , D.A. Davies1,3 , A. Doemer2 , D. Lawton1 , D.J. Morrissey1,3 , J. Ottarson1 , A. Prinke2 , R. Ringle1,2 , T. Sun1,2 , S. Schwarz1 , and L. Weissman1 1 2 3

National Superconducting Cyclotron Laboratory, East Lansing, MI, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA Department of Chemistry, Michigan State University, East Lansing, MI, USA Received: 14 January 2005 / c Societ` Published online: 10 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The Low-Energy Beam and Ion Trap facility LEBIT at the NSCL is in the final phase of commissioning. Gas stopping of fast fragment beams and modern ion manipulation techniques are used to provide beams for high-precision mass measurements and other experiments. The status of the facility and the result of first test mass measurements on stable krypton isotopes are presented. PACS. 21.10.Dr Binding energies and masses – 34.50.Bw Energy loss and stopping power – 41.85.Ja Beam transport – 29.25.Rm Sources of radioactive nuclei

1 Introduction The Low-Energy beam and Ion Trap facility LEBIT opens the door to a new class of experiments with projectile fragment beams. The Coupled Cyclotron Facility at the NSCL delivers a large range of rare isotopes with high intensities, produced by the in-flight separation method. LEBIT converts these beams into low-energy beams with excellent quality by using gas stopping and advanced ion guiding, cooling, and bunching techniques. Penning trap mass measurements are the first experiments to be carried out with LEBIT, but in the future other experiments may profit from low-energy beams at the NSCL as well.

2 The LEBIT facility Figure 1 shows a schematic view of the LEBIT facility. The main components are a gas stopping station, an ion beam cooler and buncher, and a Penning trap system for high-precision mass measurements. The system has been designed to be expandable. Stations for decay studies and laser spectroscopy are indicated as examples of future experimental opportunities. 2.1 The gas stopping station The gas stopping station converts the fast fragment beams coming from the A1900 fragment separator into lowa b

Conference presenter; e-mail: [email protected] e-mail: [email protected]

g a s c e ll a n d io n g u id e s y s te m

b e a m fro m

d e c a y s tu d ie s

R F Q io n tr a p fo r b e a m a c c u m u la tio n c o o lin g a n d b u n c h in g

te s t b e a m io n s o u rc e

la s e r s p e c tro s c o p y

9 .4 T tr a p m a s m e a s

P e n n in g sy ste m s u re m e n ts

A 1 9 0 0

Fig. 1. Layout of the LEBIT facility at the NSCL/MSU.

energy beams. A set of flat and wedged glass degraders, a Be entrance window and high-purity helium gas at a pressure of up to 1 bar are employed to slow down, stop, and thermalize the high-energy beam. A combination of DC electric fields, created by a set of focusing electrodes inside the gas cell, and gas flow through an extraction nozzle is used to transport ions out of the gas cell. An RFQ-ion guide system transfers the ions into high vacuum and forms a continuous low-energy ion beam. A number of tests have been performed to investigate the stopping and extraction performance of this system. They include range measurements [1,2] in the gas cell employing energy bunching [3] by means of a wedged degrader, and ion stopping and extraction of the rare isotopes [4, 5]. As an example, for a mixed 38 Ca/37 K beam a stopping efficiency of 50% was observed. Extraction efficiencies up to 8% were measured for beam rates up to 100 pps and found to decrease for increasing beam rates.

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2.2 The ion cooler and buncher The ion accumulator and buncher in the LEBIT project has the task to convert the continuous 5-keV ion beam from the gas cell or from an off-line test ion source into cold ion pulses with excellent ion optical properties. The system is based on an advanced linear RFQ trap concept. It has been designed as a cryogenic two-stage system in order to optimize the cooling and extraction processes: A high-pressure part allows for fast cooling whereas in a low-pressure trapping region ion bunches with low energyspread are formed. The two sections are separated by a miniature RFQ providing differential pumping. Both the cooler and the trap section have been built as cryogenic devices and can be cooled with LN2 . Such a cooling should increase the acceptance of the system, decrease the cooling time and significantly reduce the emittance of the resulting pulse compared to an operation at room temperature. The cooler-buncher has been extensively tested and provides an overall efficiency of 30% in pulsed mode and 80% if operated as a continuous beam cooler. For a detailed discussion of the LEBIT cooler-buncher system, see [6].

Fig. 2. Difference between the mass values measured with LEBIT for different krypton isotopes and the results of the most recent mass evaluation [8].

This together with the observed small deviation translated into a limit for mass dependent systematic effects which is smaller than 1 · 10−9 /u.

2.3 The Penning trap The first experimental program to benefit from the lowenergy beams produced will be high-accuracy mass measurements on very short-lived isotopes. These measurements will be carried out with a 9.4 T Penning trap system. Compared to the usual 6-7 T systems, the main advantage of the 9.4 T system is a reduction of the measurement time for obtaining a given statistical uncertainty by a factor of roughly two. The LEBIT Penning trap has undergone extensive testing with stable beams from the test ion source or the gas cell. The details of the design of the system and its performance are given in [7]. Here we present the result of first test mass measurements on stable krypton isotopes. Singly-charged krypton and 40 Ar ions were provided from the test ion source. They were cooled and bunched and captured in-flight in the high-precision trap. Here their cyclotron frequency ωc was measured. Simultaneously captured ions of undesired isotopes were removed from the trap by selective excitation of their motion prior to the cyclotron frequency measurement. The cyclotron frequency of 40 Ar was used to calibrate the magnetic field required for the mass determination. Figure 2 shows the result of this mass determination as the difference between the mass values measured for the krypton isotopes and values from the most recent mass evaluation [8]. Within the measurement uncertainty of about 6 · 10−8 very good agreement is observed for 78,80,82,86 Kr, isotopes for which the previous mass values are determined predominately by other Penning trap results. 83 Kr and 84 Kr have not yet been determined by a direct technique and the large deviation from our results could be an indication that their mass values are wrong. The observed averaged relative deviation from the literature values is less than 2 · 10−8 , if 83,84 Kr are excluded. The mass of the reference ion 40 Ar is about 40 mass units away from the measured candidates.

3 Summary and outlook The LEBIT facility at the NSCL is undergoing final commissioning. The gas stopping cell has been shown to efficiently stop relativistic ions and convert them into a low energy continuous beam. The cooler-buncher shows excellent performance in converting such beams into brilliant pulses. Still under commissioning, the Penning trap system already provides a very good mass accuracy. The experimental program of LEBIT will start with high-precision mass measurements on nuclides along the N = Z line and on neutron-rich isotopes in the vicinity of N = 28. Other experiments envisaged are in-trap decay studies. Provisions are made for a future extension of the experimental activities towards laser spectroscopy and towards post-accelerated beams.

References 1. L. Weissman et al., Nucl. Instrum. Methods A 522, 212 (2004). 2. L. Weissman et al., Nucl. Instrum. Methods A 531, 416 (2004). 3. H. Weick et al., Nucl. Instrum. Methods B 164-165, 168 (2000). 4. L. Weissman et al., Nucl. Phys. A 746, 655c (2004). 5. L. Weissman et al., Nucl. Instrum. Methods A 540, 245 (2005). 6. T. Sun et al., Commissioning of the ion beam buncher and cooler for LEBIT, these proceedings. 7. R. Ringle et al., The LEBIT 9.4 T Penning trap system, these proceedings. 8. G. Audi et al., Nucl. Phys. A 729, 337 (2003).

Eur. Phys. J. A 25, s01, 53–56 (2005) DOI: 10.1140/epjad/i2005-06-122-1

EPJ A direct electronic only

TITAN project status report and a proposal for a new cooling method of highly charged ions V.L. Ryjkov1,a , L. Blomeley4 , M. Brodeur2 , P. Grothkopp1 , M. Smith2 , P. Bricault1 , F. Buchinger4 , J. Crawford4 , G. Gwinner3 , J. Lee4 , J. Vaz1 , G. Werth5 , J. Dilling1,b , and the TITAN Collaboration 1 2 3 4 5

TRIUMF National Laboratory, Vancouver, BC, Canada Department of Physics, University of British Columbia, Vancouver, BC, Canada University of Manitoba, Winnipeg, MB, Canada Department of Physics, McGill University, Montreal, QC, Canada Department of Physics, University of Mainz, Mainz, Germany Received: 11 March 2005 / Revised version: 14 March 2005 / c Societ` Published online: 26 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The TITAN facility for precision mass measurements of short-lived isotopes is currently being constructed at the ISAC radioactive beam facility at TRIUMF, Vancouver, Canada. Current status and developments in the project are reported. A new method for cooling of highly charged ions (HCI) with singly charged ions in a Penning trap, critically needed for precision measurements, is presented. Estimates show that the technique is promising and can be applied to cooling of highly charged short-lived isotope ions without recombination losses. PACS. 07.75.+h Mass spectrometers – 21.10.Dr Binding energies and masses – 32.10.Bi Atomic masses, mass spectra, abundances, and isotopes – 52.27.Jt Nonneutral plasmas

1 Introduction Determination of the nuclear masses remains one of the fundamental and important quests of nuclear physics. As the focus of the research shifts further away from stability, going to extreme isospin, hence short life-time, it becomes more important to reduce measurement time further and further, while maintaining high accuracy. One way to achieve this goal is to apply high precision Penning trap measurement methods, but reduce the necessary measurement time by using the highly charged ions (HCI). The resolving power of the Penning trap, whose inverse can be interpreted as the precision of a single mass measurement, can be written as   q B Trf , (1) R ≈ νc Trf = m 2π

where Trf is the time of a single TOF measurement, νc is the cyclotron frequency, B is the strength of the magnetic field, q and m is the charge and the mass of the measured ion. The short lived isotopes require short measurement times, which reduces the possible resolving power. This limiting factor can be offset by increasing the charge of the measured ion. a b

e-mail: [email protected] Conference presenter; e-mail: [email protected]

HCI mass measurements on stable, heavy isotopes were first explored at the SMILETRAP facility [1] and are a part of an extensive HCI measurement program for the planned HITRAP facility at GSI [2]. The TITAN facility [3] at TRIUMF is the first experimental facility that will exploit this advantage to measure the masses of shortlived isotopes with a planned precision of δm/m ≤ 10−8 . It should be noted that the precision of a series of N mass measurements is better than the precision of a single mea√ surement by the statistical factor N . In addition to mass measurements, the modular structure of the TITAN facility that includes an RFQ buncher, an EBIT charge breeder and a Penning trap, will allow for a wide spectrum of experiments on trapped highly and singly charged ions produced at ISAC (Isotope Separator and Accelerator) and off-line. One of the challenges of HCI studies is cooling thereof. The electron stripping methods used to produce the HCI in the EBIT [4,5] invariably increase the energy spread and emittance of the produced ions. For precision measurements it is necessary to reduce the energy spread of these ions. The buffer gas cooling method used for singly charged ions in RFQs and Penning traps is not applicable to the HCI, since they would rapidly recombine. Other methods include resistive cooling [6], and electron/positron cooling [7]. In this article we describe a proposal for using the singly charged ions (SCI) to cool highly charged ions.

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to other experiments

EBIT charge breeder ISAC beam

Surface ion source

RFQ cooler and buncher

Wien mass/ charge state selector

Penning trap mass spectrometer

Plasma ion source Fig. 1. Block diagram of the TITAN setup.

2 TITAN setup The overall diagram of the TITAN facility is presented in fig. 1. The radioactive isotopes are delivered from the ISAC ion source by the low energy (30–60 keV) transport beamline. They are first directed into the RFQ cooler and buncher. A pulsed cool beam is sent out of the RFQ either directly into the Penning trap mass spectrometer for experiments with SCIs, or to the EBIT for charge breeding. The second option is a big advantage of this setup. After the charge breeding the HCI can be either studied in the EBIT, or sent to the Penning trap for mass measurements. On the way the HCI are selected according to their chargeto-mass ratio using a Wien filter. There is a capability to add other experiments to the TITAN facility that will be able to accept ions from either the RFQ or the EBIT. For test purposes we have two different ion sources incorporated into the setup. The RFQ can be loaded with alkaline ions from a 60 keV surface ion source, and also a plasma ion source that can produce a wide variety of different ions at 5 keV energy for tests of the Penning trap mass spectrometer.

2.2 The EBIT charge breeder The EBIT will accept the radioactive isotope ions from the RFQ and strip them of most of the electrons. In EBIT, an intense high energy electron beam is compressed in the center of the trap by a strong magnetic field. The electron beam pulls the ions towards the center radially. Along the axial direction the ions are confined by a DC potential well. The major difference of the TITAN EBIT from the previously commissioned EBITs [4,5] is the increase in the electron beam current up to 5 A, compared to typical values of 0.3–0.5 A. This will allow for a faster production of the HCI, which is of high importance when operating with short-lived isotopes. The TITAN EBIT’s 6 T split pair superconducting magnet has been delivered and tested. The 5 A electron gun construction is finished and its comprehensive tests are to be commenced shortly.

2.3 Penning trap mass spectrometer 2.1 The RFQ cooler and buncher The first task of the TITAN setup is to accept the radioactive isotope beam (RIB) from ISAC. For that purpose, an RFQ cooler and buncher [8, 9] has been designed and built. It improves the beam quality by cooling it with helium buffer gas. The beam is decelerated electrostatically to an energy of a few eV. It is pulled through the area filled with helium buffer gas by a gradient of the DC potentials applied to the RFQ segments. The exit side of the RFQ structure can be closed for beam accumulation, and opened for emission of the bunched beam. A special cicuit has been designed at TRIUMF, based on fast FET swithes, that can supply square wave rf signal with frequencies up to 3 MHz and amplitudes up to 1 kV, making it suitable for optimal transmission of ions in a large mass range. The construction of the RFQ is now complete. It is fully integrated into the ISAC standard EPIX computer control system and is currently tested with the surface ion source.

The Penning trap mass spectrometer system is designed to operate using the well established [1,10] TOF technique [11,12]. The resolving power of such system is given by eq. (1). For unstable isotopes, Trf is limited by the halflife of the ion. The increase of resolving power due to larger magnetic fields is limited by the magnet technology. However, one can immediately see that an increase in resolving power by an order to two orders of magnitude is possible if one is to use HCI. A 4 T high homogeneity superconducting magnet system has been ordered and the design of the various components of the mass spectrometer is underway. An important issue for the operation of the Penning trap mass spectrometer is the emittance and the energy spread of the ions from the EBIT. It directly translates into signal-to-noise ratio of the TOF spectra. Little is known about the effects that influence emittance of the EBIT, therefore the reduction of the phase space (cooling) of the ions coming out of the EBIT before injecting them into the Penning trap is desired.

V.L. Ryjkov et al.: TITAN project status report and a proposal for a new cooling method of highly charged ions

3 Cooling of highly charged ions The ions coming out of EBIT could have the energy spread of up to 50 eV per charge state. For the proper operation of the Penning trap mass spectrometer we need to achieve the energy spread lower than 1 eV per charge. In this section we discuss the known cooling solutions that can be applied to the HCI and propose a new method that is foreseen for the TITAN facility.

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a) b) c)

3.1 Available methods The well developed technique of buffer gas cooling is not applicable to the HCI since they will capture the electrons from the buffer gas. One option is to use electrons or positrons in the Penning trap. These light particles will cool themselves to the environment temperature through synchrotron radiation and cool the HCI via Coulomb interaction. The use of positrons is excluded due to the need for a strong positron source. The electron cooling has been experimentally investigated [7] and is has been evaluated [13] for the HITRAP [2] facility. However, it is only applicable at energies of the HCI higher than 100 eV/q, because at lower energy the recombination rate becomes too high. The other well developed method is resistive cooling of ions in a Penning trap [6]. The cooling time of this method decreases when the charge state q is increased. However, the requirement to capture the ions with a high energy spread requires the use of a larger catcher trap, and the cooling time increases with the square of the trap size. Additionally, the trap system is currently not cryogenically cold, and therefore prohibits the use of the high quality cryogenic resonant circuits, which further increases the cooling time. 3.2 Proposed ion-ion cooling method Due to the unique constraints posed by the HCI and the required cooling times, the well-developed methods are not suitable for our purpose at this point. Much like electron and positron cooling methods, our proposed method is based on mixing the HCI into the thermal bath of other charged particles inside a special cooling Penning trap, allowing for energy transfer via Coulomb interaction. In our case we plan to use cold ions (protons) as the bath ions. Unlike electrons and positrons though, synchrotron self-cooling of protons is too slow, and can be disregarded. The protons are to come from the plasma ion source, that can typically produce up to 10 μA of ion beams. We expect a proton beam of at least 10 nA out of this source. The few eV energy spread of the beam will allow the temperature of the proton bath prepared in the first step to be about 1 eV. The proposed cooling method is schematically illustrated in fig. 2. The DC potential along the catcher/cooler trap axis is envisioned to be a combination of two wells. The bigger well is to contain the bath ions. The smaller well is to

d) e) Fig. 2. The step-by-step diagram of the proton cooling method. a) Injection of the proton beam into the cooler trap; b) injection of the hot HCI; c) thermalization of the HCI and bath ions; d) separation of the bath ions/evaporative cooling; e) ejection of the HCI into the measurement trap.

accumulate the HCI as they cool down. The catcher trap is initially loaded with protons from the plasma source, while the depth of the main potential well is gradually increased to accomodate larger space charge. The hot HCI are then injected into the trap. They thermalize through Coulomb interaction with the dense proton plasma in the trap and achieve approximately the same temperature as the bath ions. Since the depth of the small accumulator well is proportinal to charge of the ions, it is much more likely to find an HCI ion inside that region than a proton. After the thermalization period the protons will be released from the trap by gradually lowering the trap depth. This way the hottest protons will escape first, effectively cooling the remaining protons and HCIs in the trap (evaporative cooling). Finally, the HCIs are ejected. It is possible that some amount of the coldest protons will be present together with the HCIs in the small potential well. They will be separated in flight by the Wien filter before injection into the measurement Penning trap. The cooling time of any method applied to short-lived isotopes is of extreme importance. Here we estimate the cooling times that can be reached with this method, based on the Coulomb pair collision picture. It was used by Rolston and Gabrielse [14] to calculate the cooling of (anti) protons by electrons, and, more recently, it was used to calculate the cooling of HCIs by electrons [13]. Here we apply it to the cooling of HCIs by protons. Spitzer has derived a widely used relation giving the thermalization time constant for a two-component plasma of hot (h) and field (b) ions [15]: 3mh mb c3 τhb = √ 8 2πnb Zh2 Zb2 e4 ln Λ



kTb kTh + mb c2 mh c2

 32

,

(2)

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Fig. 3. Time evolution of energy per charge for 104 Kr36+ ions being cooled down by a cloud of 107 protons of 1 eV temperature.

where mh,b , Zh,b , Th,b is respectively mass, charge, and temperature of hot and bath ions; nb is the density of bath ions (which should be higher than the density of the hot ions for the expression to be accurate). ln Λ is the Coulomb logarithm, which is the logarithm of the ratio of the smallest and the largest collision impact parameters to be considered. We have employed the same form for the Coulomb logarithm as in ref. [13]. We have calculated the time evolution of the temperatures of bath protons and the injected HCIs, which is governed by the system of two nonlinear differential equations:

1 dTh (Th − Tb ) , =− τhb (Th , Tb ) dt

(3)

1 Nh dTb (Th − Tb ) , = Nb τhb (Th , Tb ) dt

(4)

of the proton plasma stored in the trap is increased. Rotating wall technique allows to reach ion densities close to a fraction of the Brillouin limit (in our case the proton Brillouin density limit is approximately 4 × 1010 cm−3 ), and it should be possible to achieve proton densities higher than 107 cm−3 . In addition, it has been pointed out [16] that expression (2) is not accurate in the case of dense magnetized plasmas. It underestimates the thermalization rate, often by an order of magnitude or more, because in that case the energy is transferred much more efficiently through interaction with the collective plasma modes of the dense plasma. Each of the above factors has the potential to increase the thermalization rate by at least an order of magnitude, which would extend the applicability of this cooling method to the lightest of HCIs and the short-lived isotopes with half-lives of 20 ms or even less.

4 Summary In this article we have outlined the progress in design and construction of the new TITAN facility at the TRIUMF national laboratory. The components of the TITAN setup are at various stages of completion and the last one (Penning trap) should be operational by the end of 2005. We have also proposed a new cooling technique for preparing hot HCIs for the mass measurement in a Penning trap. The preliminary theoretical estimates show that the proposed method is very promising for many HCI ions, and it will be implemented and studied further. Support of this project under NSERC grant is gratefully acknowledged by the authors.

References

where Nh,b are the numbers of hot and bath ions in the trap. Figure 3 shows the time dependence for one of the middle range HCI. The number of the HCIs injected into the trap Nh = 104 is our estimate for a typical number of HCIs in a desired charge state produced by the EBIT. The values of proton density nb = 107 cm−3 , and the total number of protons Nb = 107 used in the calculation are attainable in a Penning trap. The calculation shows that the HCIs reach the target temperature of 1 eV per charge in under 70 ms, and reach equilibrium temperature of 2.8 eV (0.08 eV/q) in about 100 ms. This example shows that easily achievable densities, numbers, and temperatures of the bath protons are already sufficient to achieve cooling speed fast enough for cooling of HCIs of many short-lived isotopes for precision measurements in the Penning trap. Since the thermalization time scales approximately as mh /Zh2 , this method would seem not as powerful for cooling of lighter ions as it is for heavier ones. However, we can easily cool those ions in under 100 ms if the density

1. I. Bergstrom et al., Nucl. Instrum. Methods A 487, 618 (2002). 2. W. Quint et al., Hyperfine Interact. 132, 457 (2001). 3. J. Dilling et al., Nucl. Instrum. Methods B 204, 492 (2003). 4. J.R. Crespo Lopez-Urrutia et al., Phys. Rev. Lett. 77, 826 (1996). 5. F. Wenander, Nucl. Phys. A 701, 528 (2002). 6. H.G. Dehmelt et al., Phys. Rev. Lett. 21, 127 (1968). 7. D.S. Hall et al., Phys. Rev. Lett. 77, 1962 (1996). 8. F. Herfurth et al., Nucl. Instrum. Methods A 469, 254 (2001). 9. A. Nieminen et al., Nucl. Instrum. Methods A 469, 244 (2001). 10. K. Blaum et al., Nucl. Instrum. Methods B 204, 478 (2003). 11. G. Gr¨ aff et al., Z. Phys. A 297, 35 (1980). 12. G. Bollen et al., J. Appl. Phys. 68, 4355 (1990). 13. J. Bernard et al., Nucl. Instrum. Methods A 532, 224 (2004). 14. S.L. Rolston et al., Hyperfine Interact. 44, 233 (1989). 15. L. Spitzer, Physics of Fully Ionized Gases (Interscience, New York, 1956). 16. E.M. Hollmann et al., Phys. Rev. Lett. 82, 4839 (1999).

Eur. Phys. J. A 25, s01, 57–58 (2005) DOI: 10.1140/epjad/i2005-06-196-7

EPJ A direct electronic only

Development of a Penning trap system in Munich D. Habs1,a , M. Gross1 , S. Heinz1 , O. Kester1 , V.S. Kolhinen1 , J. Neumayr1 , U. Schramm1 , T. Sch¨ atz1 , J. Szerypo1 , P. Thirolf1 , and C. Weber2 1 2

Department of Physics, University of Munich (LMU), D-85748 Garching, Germany Institute of Physics, University of Mainz, D-55099 Mainz, Germany Received: 9 December 2004 / Revised version: 6 May 2005 / c Societ` Published online: 15 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The MLLTRAP (Maier-Leibnitz-Laboratory TRAP) Penning trap system at the FRM-II research reactor in Munich is presented. Its planned developments to reach very high “relative atomic mass” measurement precision (e.g., below 10−10 for stable ions) are described. PACS. 07.75.+h Mass spectrometers – 39.10.+j Atomic and molecular beam sources and techniques

The MAFF facility (Munich Accelerator for Fission Fragments) —planned at the new research reactor FRM-II in Munich— is dedicated to produce, cool, and accelerate high-intensity beams of fission fragments of up to 1014 /s. Recently a significant progress was achieved: the FRM-II reactor has reached its final power of 20 MW. Within one year we expect a building permit from the German technical supervision for MAFF itself. The experimental hall for both low- and high-energy beams of MAFF is in a final planning stage and should be available by the end of 2006. The experimental activities at MAFF will focus on nuclear spectroscopy studies and nuclear mass measurements. One of the experimental devices serving this purpose will be the Penning trap system MLLTRAP [1]. Its main tasks are to decelerate, cool, bunch, and purify the radioactive beam delivered by the MAFF facility and to perform high-precision mass measurements. In order to achieve that, very exotic n-rich, or superheavy, nuclei resulting from fusion reactions are mass-selected and separated from the beam (about 6 MeV/u) by the recoil mass separator MORRIS. Furthermore, they are decelerated to low (eV range) energies in a gas stopping chamber [2], extracted with an RFQ ion guide system, transferred to the EBIS charge-breeder to create high charge states, sympathetically cooled in a bath of singly charged Mg ions and finally injected into the Penning trap system for the precise nuclear mass measurements. The latter is possible also for the primary, low-energy (30 keV), fission product beam. The challenges of present-day physics impose high requirements on the nuclear mass measurements. On the one hand, a more precise determination of the hyperfine structure constant, or a microscopic definition of the mass unit, demand uncertainties at 10−10 in the mass determination for stable nuclei. On the other hand, weak interaca

Conference presenter; e-mail: [email protected]

tion studies (e.g., the unitarity of CKM matrix, or testing the CVC hypothesis) must be supplied with data on nuclei far from stability measured with relative precision better than 10−8 . With the new trap set-up, two main goals are envisaged: – High-precision (Δm/m ≤ 10−10 ) mass measurements of stable nuclei, as well as fusion residua from (HI, xn) reactions, at the MLL. As an example, the presently existing Penning trap system for stable, higly charged nuclei SMILETRAP [3] has a mass measurement accuracy between 10−9 and 10−10 . – Precise (Δm/m ≈ 10−9 ) mass measurements of shortlived exotic nuclei produced at MAFF. At present, the existing Penning trap systems for mass measurements on radioactive nuclei (ISOLTRAP, CPT, SHIPTRAP, JYFLTRAP, LEBIT, see these proceedings) work with singly charged ions. The most advanced system, ISOLTRAP at CERN, has reached a residual systematic uncertainty of 8 × 10−9 [4]. In order to achieve these goals, several developments are foreseen, combining three technologies: 1) The use of a cryogenic FT-ICR (Fourier Transform Ion Cyclotron Resonance) technique with a single ion stored in a Penning trap. This non-destructive detection method should allow for very sensitive mass measurements [5]. 2) Using a charge breeder —Electron Beam Ion Source EBIS (I = 3 A, U = 6 kV)— to convert the radioactive ions of interest into highly charged ones (HCI), in order to improve both the mass measurement precision and the signal-to-noise (S/N) ratio, thus the measurement sensitivity. This technique is already applied in case of stable ions [3]. In this way an S/N improvement by more than an order of magnitude is expected. 3) Sympathetic cooling of highly charged ions of interest with laser-cooled Mg+ ions. Sympathetic cooling reduces

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Fig. 2. Electrode structure of the double-Penning-trap system. Fig. 1. The 7 T superconducting magnet with two homogeneous field centers for the operation of the double-Penning-trap system.

the ion energy from an initial value after the EBIS of about 100 eV/q down to the Doppler limit of about 10−6 eV (temperature of about 10 mK). As a container for both HCI and Mg+ ions, it is planned to use a linear RFQ trap, with the trap for Mg+ ions nested inside the trap for HCI. By sweeping the storage potential for Mg+ ion with respect to the one for HCI a fast sympathetic cooling of the latter ions is possible. An effective rejection of Mg+ ions from the ions of interest during extraction will be achieved by placing the latter ones in a potential well at the RFQ end. Subsequent ejection through the narrow diaphragm and TOF separation of both ion species should allow for an injection of the practically clean highly charged ion sample into the Penning trap. There is a long-term experience at the LMU in laser cooling of Mg+ ions [6]. A recently developed, much more compact laser system, based on Erfiber laser and frequency quadrupling, will be used. Apart from the developments mentioned above, in order to reach high-precision additional precautions will be needed, like temperature stabilization inside the magnet bore and pressure stabilization in the liquid helium tank. At present, there are other planned Penning trap systems, like for example HITRAP [7], TITAN [8], MATS/FAIR [9], where using HCI, FTICR and HCI cooling are also foreseen. As the present status of MLLTRAP is concerned, a superconducting B = 7 T magnet (Magnex Scientific) was installed already at MLL in Garching, see fig. 1. It was energized and shimmed to reach maximum field inhomo-

geneity of 3 × 10−7 within 1 ccm in two places lying 20 cm apart on the B-field axis. These two places may host two Penning traps for precise mass measurements. In a first step, it is planned to build the MLLTRAP in a conventional way and to work with singly charged ions. The system will consist of a cooling/purification Penning trap, using the mass-selective buffer gas cooling scheme for rejection of isobaric contaminants [10], and a precision Penning trap, where the main mass measurement, involving the TOF technique, is performed. The corresponding electrode structure was machined in the LMU workshop and is shown in fig. 2. Other parts of both vacuum system and electronics are being completed. First tests of the set-up are foreseen at the end of 2005. Subsequently, an upgrade is planned aiming at including the components mentioned in points 1)–3).

References 1. J. Szerypo et al., Nucl. Instrum. Methods B 204, 512 (2003). 2. J. Neumayr, PhD Thesis, LMU Munich, 2004. 3. T. Fritioff et al., Nucl. Phys. A 723, 3 (2003). 4. A. Kellerbauer et al., Eur. Phys. J. D 22, 53 (2003). 5. C. Weber, PhD Thesis, University of Heidelberg, 2004. 6. U. Schramm et al., Prog. Part. Nucl. Phys. 53, 583 (2004). 7. W. Quint et al., Hyperfine Interact 132, 457 (2001). 8. J. Dilling et al., Nucl. Instrum. Methods B 204, 492 (2003). 9. K. Blaum et al., MATS Technical Proposal, University of Mainz (2005). 10. G. Savard et al., Phys. Lett. A 158, 247 (1991).

Eur. Phys. J. A 25, s01, 59–60 (2005) DOI: 10.1140/epjad/i2005-06-132-y

EPJ A direct electronic only

The LEBIT 9.4 T Penning trap system R. Ringle1,2,a , G. Bollen1,2 , D. Lawton1 , P. Schury1,2 , S. Schwarz1 , and T. Sun1,2 1 2

National Superconducting Cyclotron Laboratory, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA Received: 21 January 2005 / Revised version: 14 March 2005 / c Societ` Published online: 5 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The initial experimental program with the Low-Energy Beam and Ion Trap Facility, or LEBIT, will concentrate on Penning trap mass measurements of rare isotopes, delivered by the Coupled Cyclotron Facility (CCF) of the NSCL. The LEBIT Penning trap system has been optimized for high-accuracy mass measurements of very short-lived isotopes. PACS. 21.10.Dr Binding energies and masses – 32.10.Bi Atomic masses, mass spectra, abundances, and isotopes – 07.75.+h Mass spectrometers

1 Introduction The primary experimental goal of the LEBIT project is to make high-precision mass measurements of rare isotopes produced by projectile fragmentation. For this purpose, relativistic rare isotope beams are converted into low-energy beams with excellent quality by using gas stopping and advanced ion guiding, cooling, and bunching techniques, as discussed in more detail in [1]. For the mass measurements a high-performance Penning trap mass spectrometer has been designed and built.

2 The LEBIT 9.4 T Penning trap system 2.1 Experimental setup Figure 1 shows the layout of the experimental setup of the LEBIT Penning trap mass spectrometer. The magnetic field is provided by an actively-shielded persistent superconducting magnet (Cryomagnetics). The magnet system has been upgraded by additional external-field compensation coils, which reduce the effect of external field changes, as they occur in an accelerator environment. The employment of a 9.4 T field, as compared to ∼ 6 T which is typical of current systems, has the advantage that a given precision can be achieved in about half the measurement time. A precisely machined vacuum tube, mounted inside the room-temperature bore of the magnet, serves as an ion optical bench for optics components and the trap electrode a

Conference presenter; e-mail: [email protected]

E in z e l le n s

Io n D e te c to r (D a ly )

Io n D e te c to r

P e n n in g T r a p

P u m p

9 .4 T M a g n e t

Fig. 1. Schematic layout of the LEBIT Penning trap system.

system. Two ion-optical packages, one containing the injection optics and Penning trap and the other containing the ejection optics, are inserted into opposite ends of this bore tube. The ion trap and optics elements in its vicinity can be cooled with the help of a cryogenic shield. This aids the creation of an ultra-high vacuum in the center of the bore tube, which is pumped by two turbomolecular pumps located on either end of the magnet. Ion bunches that are delivered by the LEBIT buncher/cooler [2] are focused and injected into the magnetic field and captured in the Penning trap. For the mass determination via cyclotron frequency determination the ions are driven by a radiofrequency (RF) field, ejected out of the trap and their time of flight to a detector is measured. Currently a micro channel plate detector located down-stream of the trap is used. In the near future it is planned to eject the ions upstream and to use a Daly detector, mounted perpendicular to the beam axis, as indicated in fig. 1. This would free the back side of the ion trap, allowing for example detectors for in-trap decay studies to be installed.

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1 1 .3 0

T O F [m s]

9 .6 0 7 .9 0 6 .2 0 4 .5 0

Fig. 2. The LEBIT high-precision Penning trap with the endcap electrode removed.

10 9 8 7 6

8 7 6 5 4

3 7 .4

3 1 .4

n

R F

4 3 .4

4 9 .4

5 5 .4

[H z ] - 1 7 6 0 7 0 0

Fig. 4. Cyclotron resonance curve of 82 Kr+ ions with a fit of the theoretical line shape. An excitation time of 200 ms has been used in this measurement [4].

12 11

2.3 The Lorentz steerer

TOF [μs]

TOF [μs]

12 11 10 9

2 5 .4

20

40

60

80

νRF [Hz] - 3607500

100

5 4

20

40

60

80

100

νRF [Hz] - 3607500

Fig. 3. Two resonance curves obtained with dipole excitation at the reduced cyclotron frequency. Optimized correction voltages (left) and incorrect values (right). The same scale is used in both panels. Lines are to guide the eye only and not a fit.

2.2 Penning trap design The LEBIT Penning trap’s electrodes (see fig. 2) are constructed of high-conductivity copper and plated with gold. The insulators are made of aluminum oxide. The ring electrode is eightfold segmented. This allows not only for the creation of a quadrupole RF field, as required for the excitation of the ion motion at the ion’s cyclotron frequency ωc , but also the application of an octupole RF field. Such a field should allow one to drive the ion motion at 2ωc and provide a higher resolving power. This new excitation mode is presently under study at LEBIT. Extensive numerical calculations have been performed for the minimization of electric and magnetic imperfections and the optimization of the trap design. To avoid introducing systematic errors in mass measurements both the electric quadrupole and magnetic dipole field inside the trap must be free of imperfections. Magnetic field imperfections introduced by the susceptibility of the chosen materials can be strongly minimized by using thin electrodes and by optimizing the material distribution. Deviations from the electric quadrupole field are due to finite electrodes, and holes and segments in the electrodes. Two pairs of correction electrodes are used to provide efficient compensation of these effects. The importance of using such correction electrodes and appropriate voltages applied to them is illustrated in fig. 3. Poorly chosen correction voltages lead to frequency shifts and broadened and asymmetric shapes of the resonance curves. Most sensitive for these tests are resonances of the reduced cyclotron motion, which can be excited with dipole RF fields and which have been used in the example shown here.

Mass measurements using the LEBIT Penning trap system are based on a cyclotron frequency determination achieved via the excitation of the ion motion with an azimuthal quadrupole RF field [3]. In this scheme the ions must be prepared to perform a magnetron motion prior to this excitation. The usual method involves driving the ions resonantly at their magnetron frequency. To eliminate this step, thus saving time, we have developed a new technique. A cylindrical tube which has been segmented into four pieces is located in front of the trap in the high-field region. This arrangement is used to create an electric field perpendicular to the magnetic field. Passing through this field combination the ions perform an E × B drift motion, leading to an off-axis capture of the ions inside the Penning trap and resulting in the desired magnetron motion.

3 System performance The LEBIT Penning trap has been commissioned with stable beams. Already after a few month of system tuning very good performance is observed. For the transfer of ions from the buncher into the Penning trap an efficiency of ∼ 50–70% is typically achieved. Excellent line shapes and high resolving powers are obtained. A sample cyclotron resonance curve with R ∼ 450000 for a 200 ms excitation time is shown in fig. 4. Perfect agreement is observed between the data points and the fit with the theoretical line shape [4]. The highest resolving power observed so far is about 3000000 for a 1 s excitation time. Test measurements have also been performed to assess the achievable accuracy. Already in the first mass comparisons between stable krypton and argon isotopes a mass accuracy of better than 10−7 has been verified [1].

References 1. P. Schury et al., Precision experiments with rare isotopes with LEBIT at MSU, these proceedings. 2. T. Sun et al., Commissioning of the ion beam buncher and cooler for LEBIT, these proceedings. 3. G. Bollen et al., J. Appl. Phys. 68, 4355 (1990). 4. M. K¨ onig et al., Int. J. Mass Spectrum. Ion. Processes 142, 95 (1995).

Eur. Phys. J. A 25, s01, 61–62 (2005) DOI: 10.1140/epjad/i2005-06-126-9

EPJ A direct electronic only

Commissioning of the ion beam buncher and cooler for LEBIT T. Sun1,2,a , S. Schwarz1 , G. Bollen1,2 , D. Lawton1 , R. Ringle1,2 , and P. Schury1,2 1 2

NSCL/Michigan State University, East Lansing, MI 48824-1321, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824-2320, USA Received: 20 December 2004 / c Societ` Published online: 9 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A radiofrequency-quadrupole ion accumulator and buncher has been set-up for the low-energybeam and ion-trap (LEBIT) facility, which is in its final commissioning phase at the NSCL/MSU. The buncher is a cryogenic system with separated cooling and accumulation stages, optimized for excellent beam quality and high performance. The completed set-up of the LEBIT ion buncher is presented as well as first experimental results on pulse forming and beam properties. PACS. 41.85.Ja Beam transport – 29.25.Rm Sources of radioactive nuclei

1 Introduction The goal of the low-energy-beam and ion-trap (LEBIT) project is to convert the high-energy exotic beams produced at NSCL/MSU into low-energy low-emittance pulsed beams for ISOL-type high-precision experiments. The necessary beam manipulation is done in two steps. First a high-pressure gas stopping cell reduces the beam energy from ≈ 100–150 MeV/u to about 5 keV. A radiofrequency quadrupole (RFQ) ion buncher then accumulates and cools the beam before it ejects the ions as pulses. These pulses are then sent to a 9.4 T Penning trap mass spectrometer for high-precision mass determination. Details on the LEBIT project, its status and the gas stopping cell can be found in separate contributions to this conference [1, 2].

2 Concept of the LEBIT ion beam buncher The ion accumulator and buncher in the LEBIT project is a linear Paul trap system that accepts the 5 keV DC beam from the gas cell and converts it into low-energy low-emittance pulsed beams. The cooler and buncher has been designed as a two-stage system in order to separately optimize the cooling and extraction processes: A high-pressure part allows for fast cooling whereas in a low-pressure trapping region ion bunches with low energyspread are formed. The two sections are separated by a miniature RFQ providing sufficient differential pumping. Both the cooler and the trap section have been built as cryogenic devices and can be cooled with LN2 . This measure is to increase the acceptance of the system, to dea

Conference presenter; e-mail: [email protected]

Fig. 1. Photographs of the cooler section (left) and the trap section (right).

crease the cooling time and to significantly reduce the emittance of the resulting pulse compared to an operation at room temperature. A third feature distinguishing the LEBIT buncher from RFQ ion bunchers used at ISOL facilities elsewhere is the novel electrode design which allows the electric force in the cooling section to be created without the need for segmented rods. Figure 1 shows the fully assembled sections before insertion into their cryogenic chambers. More details of the design of the buncher system can be found in [3].

3 Experimental results A series of systematic investigations has been launched to characterize the performance of the buncher, some exemplary results are presented here. In order to illustrate the damping of the axial ion motion in the buncher, short ion pulses have been injected into the buncher. The DC voltages of the buncher

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D C e ffic ie n c y

N [a u ]

4 0

2 0

0 0

1 0 0

2 0 0

3 0 0

0 .6 0 .4 0 .2 0 .0

4 0 0

0 .1

T O F [m s] Fig. 2. Temporal shape of an ion pulse produced by a 3 μs beam gate after passing through the buncher. The experimental result (solid curve) is compared with that of corresponding simulations (square dots).

N [a u ]

1 5 0 0 1 0 0 0 0 .7 2 m s

5 0 0 0

3 0

3 1

3 2

3 3

3 4

T O F [m s] Fig. 3. Time-of-flight distribution of ions accumulated in the buncher and extracted as pulses measured with an MCP detector. The experimental result (solid curve) is compared with that of corresponding simulations (square dots). The latter is corrected for a 0.4 μs electronic time delay.

section were permanently set to ejection mode, so that the ions were directly accelerated to a micro-channel plate (MCP) detector after a single passage through the system. Figure 2 shows the temporal shape of an ion pulse produced by a 3 μs beam gate after passing through the cooler/buncher for a buffer gas pressure of p = 5 · 10−3 mbar. The ion pulse is delayed and considerably broadened compared to its initial width of 3 μs. The results of corresponding microscopic ion-trajectory calculations (also shown in fig. 2) reproduce the temporal profile nicely ascribing it to multiple scattering of the ions with the He buffer gas molecules. Proper timing is essential for the efficient transfer of ion pulses from the buncher to the subsequent Penning trap. For this reason time-of-flight distributions are routinely measured with an MCP detector downstream the buncher. Figure 3 shows such a distribution of Ar ions accumulated in the buncher and extracted as pulses together with the result of accompanying ion-trajectory calculations. The calculations reproduce the shape of the distribution well except for a shift of about 0.4 μs, which can be assigned to electronic effects.

1

I

1 0

in

[n A ]

1 0 0

Fig. 4. Transmission efficiency for continuous beam as a function of the incoming beam current. The solid line is to guide the eye.

After having found initial good operation parameters the efficiency of the system was determined. The ingoing current was recorded at a Faraday cup located before the buncher, where a movable phosphorus screen was used to confirm that all of the ingoing beam entered the Faraday cup. To check the efficiency of the buncher as a DC beam cooler the DC voltages of the buncher section were again set to ejection mode and the beam coming out of the buncher was detected with another Faraday cup. Figure 4 shows the transmission efficiency for continuous beam as a function of the incoming beam current. The efficiency is about 70% for currents up to 10 nA. This range covers well typical beam intensities at current rare-isotope facilities. The efficiency then drops to about 10% for 500 nA of ingoing beam. Preliminary simulations indicate that this drop occurs at the space-charge limit of the miniature RFQ. First attempts to cool the cooler with LN2 resulted in an efficiency increase to ≈ 80% for low beam current, however due to temporary technical reasons, the temperature could only be lowered to about T ≤ 234 K. In pulsed-mode the efficiency for the buncher and Penning trap combination was measured to be ≥ 10–15% for incoming beams currents of a few pA.

4 Summary An RFQ ion accumulator and buncher has been commissioned as part of NSCL’s effort to provide exotic nuclei produced in fragmentation reactions as a low-energy lowemittance ion beam for high-precision experiments. Initial tests of the buncher show good pulse-forming capability and high efficiency for both continuous and pulsed beam extraction.

References 1. P. Schury et al., Precision experiments with rare isotopes with LEBIT at MSU, these proceedings. 2. R. Ringle et al., The LEBIT 9.4 T Penning trap system, these proceedings. 3. S. Schwarz et al., Nucl. Instrum. Methods B 204, 474 (2003).

Eur. Phys. J. A 25, s01, 63–64 (2005) DOI: 10.1140/epjad/i2005-06-072-6

EPJ A direct electronic only

A high-current EBIT for charge-breeding of radionuclides for the TITAN spectrometer G. Sikler1,a , J.R. Crespo L´ opez-Urrutia2 , J. Dilling1 , S. Epp2 , C.J. Osborne2 , and J. Ullrich2 1 2

TRIUMF, 4004 Wesbrook Mall, Vancouver BC, V6T 2A3, Canada Max-Planck-Institut f¨ ur Kernphysik, Saupfercheckweg 1, D-69117, Heidelberg, Germany Received: 7 December 2004 / c Societ` Published online: 3 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The TITAN (Triumf’s Ion Trap for Atomic and Nuclear science) Penning trap mass spectrometer will be located at ISAC/TRIUMF in Vancouver, Canada. It is designed for conducting high-precision mass measurements on radionuclides via the determination of the cyclotron frequency of the ions confined within the Penning trap. An essential component of the setup will be an electron beam ion trap (EBIT) which will allow charge breeding of the radionuclides prior to the actual mass measurement. Compared to singly charged ions, the investigation of highly charged ions (HCIs) yields higher accuracies and enables access to radionuclides with half-lives considerably shorter than 100 ms. The working principle of an EBIT as well as the design of the TITAN-EBIT in particular will be described. PACS. 34.80.Kw Electron-ion scattering; excitation and ionization – 32.10.Bi Atomic masses, mass spectra, abundances, and isotopes – 07.75.+h Mass spectrometers

1 Introduction The atomic mass of ions can be measured with very high accuracy using Penning trap mass spectrometry (as described in, e.g., [1]). While the ions are spatially confined by means of a strong homogeneous magnetic field and a weak electrostatic field they perform a characteristic gyration around the magnetic field lines: the cyclotron motion. The cyclotron frequency of an ion with charge q and mass m trapped in a magnetic field B is given by νc = (q ·B)/(2π ·m). One way to determine this frequency, and the mass for a given q and B, is to excite the cyclotron motion of the ions resonantly. The accuracy Δνc depends on the number of ions N that contribute to the spectrum and the width of the resonance being defined by the excitation time Tex . The relative accuracy is proportional to

m Δν √ . ∝ ν Tex qB N

Increasing q (or B) enhances the relative accuracy of the mass determination. On the other hand, to reach a desired accuracy the excitation times (usually limited by the nuclear half-life of the ions under investigation) can be shorter and the required count rates can be smaller when the charge of the ions is larger. Both the number of ions a

Conference presenter; Present address: Max-PlanckInstitut f¨ ur Kernphysik, Saupfercheckweg 1, D-69117, Heidelberg, Germany; e-mail: [email protected]

Fig. 1. Principle of an electron beam ion trap. An intense electron beam is compressed by a strong magnetic field. The high space charge potential provides confinement in the radial degrees of freedom, while the ions are trapped axially by external potentials applied to the trap electrodes.

and their nuclear half-life are limiting factors in investigating radionuclides very far from the valley of stability. Therefore the TITAN mass spectrometer [2] will employ an electron beam ion trap to enhance the charge state of the radionuclides considerably prior to the actual mass determination.

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insulators

trap

injection and extraction

insulators

collector magnet

e-gun head

Fig. 2. Schematic overview of the TITAN-EBIT. A superconducting 6 T magnet with cold bore houses the actual trap setup. Both the electron gun head and the electron collector unit are adjustable with respect to the magnetic field and relative to each other to provide an optimal electron beam performance. The electron gun and the collector are floating on negative high voltage, whereas the trap is held at ground potential.

2 Electron beam ion trap The electron beam of an EBIT is produced with a thermionic cathode and then electrostatically accelerated and injected into a strong magnetic field (see fig. 1). Here the electrons are radially confined by the Lorentz force, and the beam is compressed as the magnetic field strength increases. A general description of EBIT can be found in [3]. For the TITAN-EBIT the magnetic field strength will be 6 T. The acceleration voltage which gives the maximum kinetic energy of the electrons will be variable up to 80 kV and a beam current of 5 A is envisaged. With these parameters a compression of the electron beam down to 150 μm is expected. The confinement of such an amount of negative electric charge provides a space charge potential, which is more than 5 kV deep. This space charge potential allows radial confinement of the ions. Axial confinement is accomplished by applying external potentials to the trap electrodes. Whilst trapped in the dense electron beam the ions undergo further ionization through successive electron impact processes. To obtain highly charged ions in charge states such as, e.g., Xe44+ , typical ionization times are in the order of 10 to 50 ms. Figure 2 shows a rendered design drawing of the TITAN-EBIT. The radionuclides enter the EBIT as cooled

bunches of singly charged ions, in the figure from the left side through the collector. The extraction after charge breeding takes place along the same path but in the opposite direction. The extraction and the transport to the Penning trap will be accomplished by means of floatable drift tubes and pulsed cavities (not drawn in the figure). The design of all parts of the TITAN-EBIT is completed and the device is currently being assembled. Stable operation at high electron beam currents is foreseen for the year 2005, as well as first off-line tests of injecting and extracting ions. We thank our collaboration partners, the Heidelberg-EBIT group, for the outstanding support, the many advices and the friendly hospitality, that we experienced during the design and construction phase of the TITAN-EBIT.

References 1. P.K. Ghosh, Ion Traps (Oxford University Press, Oxford, 1995). 2. J. Dilling et al., Nucl. Instrum. Methods B 204, 492 (2003). 3. F.J. Currell, The Physics of Multiply and Highly Charged Ions, Vol. 1: Sources, Applications and Fundamental Processes (Kluwer Academic Publishers, Dordrecht, 2003).

Eur. Phys. J. A 25, s01, 65–66 (2005) DOI: 10.1140/epjad/i2005-06-167-0

EPJ A direct electronic only

FT-ICR: A non-destructive detection for on-line mass measurements at SHIPTRAP C. Weber1,2,a , K. Blaum1,2 , M. Block1 , R. Ferrer2 , F. Herfurth1 , H.-J. Kluge1 , C. Kozhuharov1 , G. Marx3 , M. Mukherjee1 , W. Quint1 , S. Rahaman1 , S. Stahl2 , and the SHIPTRAP Collaboration 1 2 3

GSI, Planckstr. 1, D-64291 Darmstadt, Germany Institute of Physics, Johannes Gutenberg-University, D-55099 Mainz, Germany Department of Physics, Ernst-Moritz-Arndt-University, D-17487 Greifswald, Germany Received: 14 January 2005 / c Societ` Published online: 7 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The SHIPTRAP facility is set up behind the velocity filter SHIP at GSI. One of the main physics goals is the direct mass determination of trans-uranium nuclides by Penning trap mass spectrometry. In this contribution the applicability of the non-destructive Fourier Transform-Ion Cyclotron Resonance (FT-ICR) detection technique to mass spectrometry of short-lived nuclides is discussed. PACS. 07.75.+h Mass spectrometers – 27.90.+b 220 ≤ A

The SHIPTRAP facility [1,2, 3] is designed to provide clean and cooled beams of singly charged radioactive ions produced in a fusion-evaporation reaction and separated by the velocity filter SHIP [4]. The scientific program comprises mass spectrometry, atomic and nuclear spectroscopy, and chemistry of elements with Z > 92, which are not available at ISOL- or fragmentation facilities. Since predicted mass values in this region often vary by about 1 MeV, direct experimental values serve as a test of theoretical models. Furthermore, they allow for the calculation of shell corrections in the stabilized, deformed region around Z = 108, as well as at the shell closure of the superheavy elements. The mass m of an ion with charge q stored inside a Penning trap is determined via a measurement of its cyclotron frequency νc = qB/(2πm), where B denotes the magnetic field strength. For unstable nuclides this is up to now only achieved with the destructive time-of-flightICR detection method [5]. One of the main limitations to the experimental investigations is the low production rate of most of these exotic superheavy nuclides, in many cases less than one per minute. However, several nuclides in the trans-uranium region exhibit particular long halflives. There are 173 known nuclides above uranium with a half-life longer than one minute, and beyond fermium 37 nuclides fulfill this requirement. This allows for comparatively long observation times, enabling an increased precision in the frequency determination. Here, a sensitive and non-destructive method, like the Fourier TransformICR [6] technique, is ideally suited for the identification and characterization of these species. The induced image a

Conference presenter; e-mail: [email protected]

currents of charged particles stored in a Penning trap with segmented electrodes are picked up and Fourier analyzed. This mass spectroscopic technique is applied throughout in the field of analytical chemistry and is routinely achieving an accuracy at the sub-ppm level for different elemental compositions in a wide mass range [7]. The FT-ICR setup at SHIPTRAP is especially optimized for the sensitive detection of single, short-lived ions with A > 200. The main characteristics are: Ions are stored in an orthogonalized hyperbolic Penning trap [8] and their signals are detected with a narrow-band tuned circuit. With FT-ICR the complete frequency spectrum is obtained after loading the trap only once, whereas in TOFICR a minimum number of ions Nion > 500 is required. In order to √ reach a relative mass uncertainty δm/m ∝ 1/(νc · T · Nion ) [9] the loss in ion statistics Nion of rare species from SHIP is overcome by a prolonged observation time T due to longer half-lives and the possibility of multiple measurements due to the non-destructive character of the method. The signal-to-noise ratio of one singly charged ion detected with a standard room temperature setup is estimated: An ion with mass A = 250 revealing a reduced cyclotron frequency ν+ of about 420 kHz (B = 7 T, U = 10 V) is expected to give S/N ≈ 0.9 which lies below the detection limit. For any given  ion species Q/(T C). q/m the S/N is proportional to the factor Here Q denotes the quality factor of the tuned circuit, T the temperature, and C the capacitance of the overall detection system. Changing the technology of the tuned circuit from resistive to superconducting material leads to an estimated increase in S/N by a factor of 3.2. A reduction of the temperature from 300 K to for example 77 K results in a factor of 2.0. The capacitance C is given by

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7 T - MAGNET - WITH TWO HOMOGENEOUS CENTERS

4K

IONS FROM RFQ-BUNCHER

300 K

LN 2RESERVOIR 77 K

L

77 K

MCPDETECTOR

drift tubes

PURIFICATION TRAP

PRECISION TRAP

ISOLATION VACUUM

TRAP VACUUM

1.94 m

Fig. 1. Schematic of the SHIPTRAP cryogenic trap setup [10]. Two Penning traps are placed inside a vacuum tube that is cooled by a liquid N2 flow. The ion motion is detected with a superconducting, tuned circuit L in an external liquid He dewar. A flexible bellow (right side) is used in order to compensate the length contraction of the vacuum chamber during initial cooling down. The drift tubes and the microchannel plate (MCP) allow for an ejection of ions and a subsequent time-of-flight determination.

the distance of the tuned circuit to the trap and therefore defined by the design. The drawback in the reduced bandwidth of this detection scheme is that only a limited mass range of A ≈ ±10 u is accessible, else the tuned circuit has to be modified and exchanged. Hence, the FT-ICR detection will be exclusively dedicated to the nuclides (T1/2 > 1 s) that are produced in rare amounts at SHIP. Nevertheless fusion products with higher production cross-sections can be alternatively studied with the destructive time-of-flight method. In addition the delivery of purified, rare nuclides from SHIPTRAP to subsequent experimental setups is envisaged in the future. Hence, the trap system had to be kept open at the exit side which determined the position of the detection inductivity and the design of the setup inside the warm bore of the superconducting magnet. The cryogenic Penning trap system that has been built [10] is schematically shown in fig. 1. The double trap setup, consisting of a cylindrical purification trap for isobaric cleaning and a hyperbolic precision trap for the frequency determination is kept at liquid nitrogen temperature. The precision trap (see fig. 2) is made of hyperbolically shaped electrodes, which guarantees a high harmonicity of the storage potential across a large volume. Even in the case of exciting the ion motion to a large radius in order to detect with sufficiently high signal-to-noise ratio, the ion will experience an harmonic electrostatic potential and a narrow resonance linewidth Δνion can be achieved. This resonance signal is picked up with a tuned, superconducting inductivity L made from NbTi which is placed in an external liquid helium dewar (4.2 K). By this means the signal-to-noise ratio in the cryogenic setup with combined liquid N2 - and He-cooling will be improved by at least a factor of seven compared to a room temperature setup. This implies an increase in sensitivity which enables the detection of a single ion as well as successive measurements with the same ion. Further-

Fig. 2. Precision trap with hyperbolic electrodes. The characteristic trap dimensions are ρ0 = 6.38 mm as the minimum radius and z0 = 5.5 mm as the minimum distance from the trap center to the endcaps. Electrodes are isolated via customized sapphire pieces. The ring electrode is azimuthally segmented into an electrode pair for excitation (2 × 40◦ ) and detection (2 × 140◦ ).

more, the improved background pressure inside the precision trap guarantees a longer coherence time of the ion motion during the detection period. In contrast to a TOF-ICR measurement, where the true cyclotron frequency νc is determined, here the trap eigenmotion with the reduced cyclotron frequency ν+ is monitored. Using the expansion ν+ ≈ νc − V0 /(2π2d2 B), for the characteristic trap dimension d (d2 = (1/2)(z02 + ρ20 /2)), the true cyclotron frequency can be deduced from few measurements at different storage potentials V0 and an extrapolation to zero. In order to calibrate the strength of the magnetic field B, reference ions with precisely known mass values will be studied in alternate measurements. For this purpose singly ionized carbon clusters (12 C+ n , 1 ≤ n ≤ 23) provide the ideal tool for absolute mass calibration. The advantages in conjunction with a FT-ICR detection at SHIPTRAP are twofold: In the first place, reference masses covering the entire nuclear chart are obtained [11]. Hence, systematic effects can be studied and since the calibration mass is at most six mass units different from the mass to be determined, the resulting mass-dependent frequency shifts are reduced [12]. In the second place, the short time needed for a complete frequency determination with FT-ICR permits more frequent calibration measurements and reduces the effect of the temporal magnetic-field drift.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

J. Dilling et al., Hyperfine Interact. 127, 491 (2000). G. Marx et al., Hyperfine Interact. 146/147, 245 (2003). M. Block et al., these proceedings. S. Hofmann, G. M¨ unzenberg, Rev. Mod. Phys. 72, 733 (2000). G. Gr¨ aff et al., Z. Phys. A. 297, 35 (1980). M.B. Comisarow, A.G. Marshall, Chem. Phys. Lett. 25, 282 (1974). A.G. Marshall, Int. J. Mass Spectrom. 200, 331 (2000). G. Gabrielse, Phys. Rev. A 27, 2277 (1983). G. Bollen, Nucl. Phys. A 693, 3 (2001). C. Weber, PhD Thesis, University of Heidelberg, 2003. K. Blaum et al., Eur. Phys. J. D 15, 245 (2002). A. Kellerbauer et al., Eur. Phys. J. D 22, 53 (2003).

Eur. Phys. J. A 25, s01, 67–68 (2005) DOI: 10.1140/epjad/i2005-06-096-x

EPJ A direct electronic only

Commissioning and first on-line test of the new ISOLTRAP control system C. Yazidjian1,a , D. Beck1 , K. Blaum1,2 , H. Brand1 , F. Herfurth1 , and S. Schwarz3 1 2 3

GSI-Darmstadt, Planckstraße 1, 64291 Darmstadt, Germany Institut f¨ ur Physik, Johannes Gutenberg-Universit¨ at, Staudingerweg 7, 55128 Mainz, Germany NSCL, Michigan State University, East Lansing, MI 48824-1321, USA Received: 12 December 2004 / c Societ` Published online: 17 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 r based control system has been developed and implemented at Abstract. A new versatile LabVIEW the ISOLTRAP experiment. This enhances the ease of use as well as the flexibility and reliability for ISOLTRAP and is flexible enough to be used for other trap experiments as well. PACS. 07.05.Dz Control systems – 07.05.Hd Data acquisition: hardware and software – 21.10.Dr Binding energies and masses – 82.80.Qx Ion cyclotron resonance mass spectrometry

2 The ISOLTRAP experiment

1 Introduction The tandem Penning trap mass spectrometer ISOLTRAP [1, 2], installed at the on-line isotope separator ISOLDE [3] at CERN (Geneva) is a facility dedicated to high-precision mass measurements on short-lived radionuclides. The mass measurement is based on the determination of the cyclotron frequency νc of ions manipulated by use of radiofrequency (rf) fields in Penning traps. With a charge to mass ratio q/m and a magnetic field B the relation is νc =

1 q · B. · 2π m

(1)

A relative mass uncertainty of δm/m ≈ 10−8 is routinely reached with ISOLTRAP. These high-precision mass measurements contribute to fundamental tests like the unitarity of the Cabibbo-Kobayashi-Maskawa mixing matrix [4,5,6]. ISOLTRAP is a versatile experiment. It can manipulate and measure the mass the majority of radioactive ions produced at ISOLDE. The manipulation of the stored ions requires a reliable and fast control system, especially in case of short-lived nuclides with half-lives in the millisecond range. From the new general control system framework, CS, developed at DVEE/GSI, a dedicated control system for ISOLTRAP has been derived and implemented by adding experiment specific add-ons to the framework [7]. a

e-mail: [email protected]

The ISOLTRAP spectrometer is composed of three parts: 1) A linear radio-frequency quadrupole (RFQ) ion trap which has the task to stop, accumulate, cool, and bunch the 60 keV ISOLDE beam for an efficient transfer into the preparation trap. 2) A cylindrical preparation Penning trap filled with helium gas to prepare and mass separate [8] (resolving power R = m/Δm up to 105 ) the ions coming from the RFQ and to bunch them for an efficient delivery to the second Penning trap where the mass measurement is performed. 3) A hyperbolical precision Penning trap to determine the cyclotron frequency νc (eq. (1)) of the ion of interest and of the reference ion. In the precision trap, the experimental procedure for a mass measurement requires a scan of the frequency of the rf-field to excite the ion motion around νc . The duration of each frequency step varies from 0.3 to 1.5 s depending on the half-life of the ion of interest.

3 Design of the control system 3.1 Motivation The old control system was based on a VME bus crate controlled via a Motorola processor E6 CPU using OS9. For more than a decade, it was successfully used, but the hardware has become outdated and not reliable any longer

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since no support was available. ISOLTRAP needs to remotely control more than 100 voltages (ion optics, trapping electrodes, etc.), the regulation of the buffer gas pressures, as well as 8 delay times and up to 10 different frequencies. The complex timing scheme, especially for short lived-ions needs the different steps to be synchronized with a precision of better than a 1 μs. Thus a modular control system with the ability to follow the growth of the experimental set-up in size and complexity was required.

Control Control and and on-line on-line analysis analysis GUI GUI

ISOLTRAP ISOLTRAP Sequencer Sequencer CycleControl

Timing Timing

3.2 The CS framework The old VME based system was used to control the hardware devices and the measurement procedure. A Graphical User Interface (GUI) was operated from a PC connected to the VME-bus via TCP/IP to setup the measurement and display the on-line data. In spring 2003 a new control system has been implemented and commissioned. The GUI is reused as well as practically all existing hardware devices of ISOLTRAP whereas the VME-bus is replaced by a PC. Instead of trying to port the old system from VME to the new PC platform, the all-new objectoriented CS framework has been implemented [7] in about nine man months. It does not only replace the old system but provides more functionality that enhances the experimental capabilities of ISOLTRAP. Figure 1 shows a simplified overview of the control system hierarchy. The hardware devices (rounded boxes) are represented by objects (boxes) which are organized in a corresponding package (shadowed boxes). The hardware devices, with number of modules used at ISOLTRAP in brackets, are addressed either by GPIB or OPC interfaces (not shown in fig. 1). In the Function Generator package, two different kinds of hardware are shown: DS345 from Stanford Research Systems and AG33250A from Agilent. Following the same principle, SR430 is a multichannel analyzer for data acquisition and Data Collector which collects and buffers data from acquisition devices. DF94011 is a programable delay box. The highlighted part with a darker grey box is experiment specific. The Sequencer (with the CycleControl and MassMeas) is the conductor of the control system. Once the user starts a measurement from the GUI, the Sequencer takes over the control of the experiment. It communicates with the other objects via events. The arrows show the communication paths between the objects (for better understanding the arrows target the package, but not the objects themselves). Thanks to this object-oriented structure, a broken hardware device can be easily replaced by another one belonging to the same package. The only change in the CS is the one of the object associated to the hardware part. As an example of its flexibility, a DS345 function generator can be exchanged by a AG33250A in a few minutes without shutting down the CS nor the whole experiment.

4 Commissioning of the control system The new control system was put into operation by late summer 2003, and after extensive off-line tests all the on-

GUI PC

Acquisition Acquisition Data Collector

MassMeas

Multi Channel Analyzer

Function Function Generator Generator

Delay Gate Generator

Stanford Research Systems

Agilent

DF94011

DS345

AG33250A

SR430

(x6)

(x10)

(x2)

(x1)

Control PC

Fig. 1. Simplified sketch of the ISOLTRAP control system. Shadowed boxes represent a package of software modules (depicted by boxes) attached to their hardware component (rounded boxes). Arrows indicate the communication path. For more details see text.

line radioactive beam experiments in 2004 were performed with it. In full operation, about 80 objects are required simultaneously for controlling the hardware. The control system runs stable for at least one week of operation. With such a versatile concept, the easy maintenance of the new control system is one more advantage to add to those that allow higher stability and flexibility. Also enhanced is the comfortable handling by having a quick parameter setup feature for the requirement of high-precision mass measurements, especially for short-lived nuclides.

5 Conclusion The high-precision mass spectrometer ISOLTRAP needed a reliable and more convenient control system for its experimental data acquisitions. The new flexible CS framework fulfilled the requirement of this versatile apparatus and enhances the experimental capabilities of ISOLTRAP. During on-line runs the CS framework has shown its numerous advantages and its new powerful features. Meanwhile, this control system is also in operation at the Penning trap mass spectrometers SHIPTRAP [9] and LEBIT [10].

References 1. G. Bollen et al., Nucl. Instrum. Methods A 368, 675 (1996). 2. F. Herfurth et al., Nucl. Instrum. Methods A 469, 254 (2001). 3. E. Kugler et al., Nucl. Instrum. Methods B 70, 41 (1992). 4. K. Blaum et al., Phys. Rev. Lett. 91, 260801 (2003). 5. M. Mukherjee et al., Phys. Rev. Lett. 93, 150801 (2004). 6. A. Kellerbauer et al., Phys. Rev. Lett. 93, 072502 (2004). 7. D. Beck et al., Nucl. Instrum. Methods A 527, 567 (2004). 8. G. Savard et al., Phys. Lett. A 158, 247 (1991). 9. J. Dilling et al., Hyperfine Interact. 127, 491 (2000). 10. S. Schwarz et al., Nucl. Instrum. Methods B 204, 507 (2003).

1 Masses 1.4 Mass modeling

Eur. Phys. J. A 25, s01, 71–74 (2005) DOI: 10.1140/epjad/i2005-06-022-4

EPJ A direct electronic only

Recent progress in mass predictions S. Goriely1,a , M. Samyn1 , J.M. Pearson2 , and E. Khan3 1 2 3

Institut d’Astronomie et d’Astrophysique, Universit´e Libre de Bruxelles, CP 226, 1050 Brussels, Belgium D´eptartement de Physique, Universit´e de Montr´eal, Montr´eal (QC) H3C 3J7, Canada Institut de Physique Nucl´eaire, IN2P3-CNRS, 91406 Orsay, France Received: 13 October 2004 / c Societ` Published online: 18 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We review the latest efforts devoted to the global prediction of atomic masses. Special attention is paid to the new developments made within the Hartree-Fock-Bogolyubov framework. So far, 9 HFB mass tables based on different parametrizations of the effective interactions in the Hartree-Fock and pairing channels have been published. We analyze their ability to reproduce experimental masses as well as nuclearmatter and giant-resonance properties. The possibility to derive within the HFB framework a universal effective interaction that can describe all known properties of the nuclei (including their masses) and of asymmetric nuclear matter is critically discussed. PACS. 21.30.Fe Forces in hadronic systems and effective interactions – 21.60.Jz Hartree-Fock and randomphase approximations

1 Introduction Attempts to develop formulas estimating the nuclear masses of nuclei go back to the 1935 “semi-empirical mass formula” of von Weizs¨ acker [1]. Improvements have been brought little by little to the original liquid-drop mass formula, leading to the development of macroscopicmicroscopic mass formulas, where microscopic corrections to the liquid drop part are introduced in a phenomenological way (for a review, see [2]). In this framework, the macroscopic and microscopic features are treated independently, both parts being connected exclusively by a parameter fit to experimental masses. Later developments included in the macroscopic part properties of infinite and semi-infinite nuclear matter and the finite-range character of nuclear forces. Until recently the atomic masses were calculated on the basis of one form or another of the liquid-drop model, the most sophisticated version being the FRDM model [3]. Despite the great empirical success of this formula (it fits the 2149 Z ≥ 8 measured masses [4] with an r.m.s. error of 0.656 MeV), it suffers from major shortcomings, such as the incoherent link between the macroscopic part and the microscopic correction, the instability of the mass prediction to different parameter sets, or the instability of the shell correction. The quality of the mass models available is traditionally estimated by the r.m.s. error obtained in the fit to experimental data and the associated number of free parameters. However, this overall accuracy does not imply a reliable extrapolation far away from the experimentally known region in view of the a

Conference presenter; e-mail: [email protected]

possible shortcomings linked to the physics theory underlying the model. The reliability of the mass extrapolation is a second criterion of first importance when dealing with specific applications such as astrophysics, but also more generally for the predictions of experimentally unknown ground- and excited-state properties. Generally speaking, the more microscopically grounded is a mass formula, the better one would expect its predictive power to be. In the present paper, we describe the latest developments made to estimate nuclear masses on the basis of global meanfield models and the ability of such models to reproduce some nuclear-matter and giant-resonance properties.

2 The Hartree-Fock mass formulas It was demonstrated recently [5] that Hartree-Fock (HF) calculations in which a Skyrme force is fitted to essentially all the mass data are not only feasible, but can also compete with the most accurate droplet-like formulas available nowadays. Such HF calculations are based on the conventional Skyrme force of the form vij = t0 (1 + x0 Pσ )δ(rij )  1

+ t1 (1 + x1 Pσ ) 2 p2ij δ(rij ) + h.c. 2¯h 1 + t2 (1 + x2 Pσ ) 2 pij · δ(rij )pij h ¯ 1 + t3 (1 + x3 Pσ )ργ δ(rij ) 6 i + 2 W0 (σ i + σ j ) · pij × δ(rij )pij , h ¯

(1)

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and a δ-function pairing force acting between like nucleons,  α ρ δ(rij ), (2) vpair (rij ) = Vπq 1 − η ρ0

where ρ is the density and ρ0 the saturation value of ρ. The strength parameter Vπq is allowed to be different for neutrons and protons, and also to be stronger for an odd − + ) than for an even number (Vπq ). number of nucleons (Vπq The HF formula adds to the energy corresponding to the above forces the Coulomb energy and a phenomenological Wigner term of the form ⎧  2 ⎫ ⎨ N −Z ⎬ (3) EW = VW exp −λ ⎭ ⎩ A ⎧   ⎫ 2 ⎬ ⎨ A  . (4) + VW |N − Z| exp − ⎩ A0 ⎭

A completely microscopic HF mass formula, known as HFBCS-1, was constructed for the first time in [5]. It consists of a tabulation of the masses of all nuclei lying between the drip lines over the range Z, N ≥ 8 and Z ≤ 120, calculated by the HF method with a Skyrmetype force, together with a BCS treatment of pairing. In order to improve the description of highly neutron-rich nuclei, the BCS approach was later replaced by the full HFBogoliubov (HFB) calculation [6]. These two mass formulas give comparable fits (typically with a r.m.s. deviation of about 0.75 MeV) to the 1888 measured masses of nuclei with N, Z ≥ 8 that appear in the 1995 compilation [7]. A comparison between HFB and HFBCS masses shows that the HFBCS model is a very good approximation to the HFB theory provided both models are fitted to experimental masses. The extrapolated masses never differ by more than 2 MeV below Z ≤ 110. The reliability of the HFB predictions far away from the experimentally known region, and in particular towards the neutron drip line, is however increased thanks to the improved Bogoliubov treatment of the pairing correlations. The new data made available in 2001 [8] (with 382 “new” nuclei out of which only 45 are neutron rich) revealed significant limitations in both the HFBCS-1 and HFB-1 models. This defiency was cured in the subsequent HFB-2 mass formula [9], where considerable improvement was obtained by modifying the prescription for the cutoff of the spectrum of s.p. states over which the pairing force acts. The r.m.s. error with respect to the measured masses of all the 2149 nuclei included in the latest 2003 atomic mass evaluation [4] with Z, N ≥ 8 is 0.659 MeV [9]. Despite the success of the HFB-2 mass formula, it was not regarded as definitive, in particular in relation to the large and uncertain parameter space made by the coefficient of the Skyrme and pairing interactions. For this reason, a series of studies of possible modifications to the basic force model and to the method of calculation were initiated all within the HFB framework [10,11,12,13]. The most obvious reason for making such modifications would be to improve the data fit, but there is also a considerable interest

in being able to generate different mass formulas even if no significant improvement in the data fit is obtained, since, in the first place, it is by no means guaranteed that mass formulas giving equivalent data fits will extrapolate in the same way out to the neutron drip line: the closer that such mass formulas do agree in their extrapolations the greater will be our confidence in their reliability. But there is another reason to study different HFB mass models, and that concerns the fact that masses are not the only property of highly unstable nuclei that one might wish to determine by extrapolation from measured nuclei. An understanding of the r-process nucleosynthesis, in particular, requires also a knowledge of the nuclear-matter equation of state, as well as fission barriers, β-decay strength functions, giant dipole resonances, nuclear level densities and neutron optical potential of highly unstable nuclei. It may be that different models that are equivalent from the standpoint of masses may still give different results for other properties. Our intention to develop different HFB mass models is thus motivated also by the quest for a universal framework within which all the different nuclear aspects can be estimated. For this reason, a set of additional 7 new mass tables, referred to as HFB-3 to HFB-9, and the corresponding effective forces, known as BSk3 to BSk9, respectively, were designed and the sensitivity of the mass fit and extrapolations towards the neutron drip line analysed. These new tables consider modified parametrizations of the effective interaction. In particular HFB-3, 5, 7 [10, 11] are obtained with a density dependence of the pairing force as inferred from the calculations of the pairing gap in infinite nuclear matter at different densities [14] using a “bare” or “realistic” nucleon-nucleon interaction (corresponding to η = 0.45 and α = 0.47 in eq. (2)). For the mass tables HFB-4, 5 (HFB-6, 7) [11], a low isoscalar effective mass Ms∗ = 0.92 (Ms∗ = 0.8) is adopted as prescribed by microscopic (Extended Br¨ uckner-Hartree-Fock) nuclearmatter calculations [15]. The improvement considered in the HFB-8 and HFB-9 models restores the particle number symmetry by applying the projection-after-variation technique to the HFB wave function [12]. Finally, while in all calculations prior to the HFB-9, the nuclear-matter symmetry coefficient J was kept to the lowest acceptable value (i.e. J = 28 MeV) to avoid the collapse of neutron matter at densities above saturation, in the HFB-9 paramterization [13], J is constrained to the value of 30 MeV to conform with realistic calculation of neutron matter at high densities (see below). All new mass tables reproduce the 2149 experimental masses [4] with a high level of accuracy, i.e. with a r.m.s. error of about 0.65 MeV, except in the case of HFB-9, for which the constraint on J = 30 MeV rises the r.m.s. value to 0.73 MeV. The HFB r.m.s. charge radii as well as the radial charge density distributions are also in excellent agreement with experimental data [12]. More specifically, the deviation between the theoretical HFB-9 and experimental r.m.s. charge radii for the 782 nuclei with Z, N ≥ 8 listed in the 2004 compilation [16] amounts to only 0.027 fm. The Skyrme forces were also tested on their ability to reproduce excited state properties. In particular, the giant

S. Goriely et al.: Recent progress in mass predictions 20

22

Si

E(ISGQR) [MeV]

20 27

Al

18 24

32

Exp BSk2 (M*=1.04) BSk4 (M*=0.92) BSk9 (M*=0.80)

S Ar 40 Ca

40

54

Fe

120

Sn

12

209 208

10 0

50

100

150

250

energy/nucleon [MeV]

70 Friedman, Pandharipande (1981)

BSk8 (J=28MeV)

BSk9 (J=30MeV)

40 30 20 10 0

0

0.1

0.2

-10 0

50

100

150

N

Fig. 1. Comparison of experimental and HFB+QRPA ISGQR energies for spherical nuclei. The HFB + QRPA results are shown for 3 forces (BSk2, BSk4 and BSk9) characterized by different nucleon effective mass M ∗ .

50

0 -5

A

60

5

Bi

Pb 200

0.3

-3

0.4

M(FRDM)-M(HFB-9)

10

Mg

14

8

M(HFB-2)-M(HFB-9) 15

ΔM [MeV]

28

16

73

0.5

density [fm ] Fig. 2. Energy per nucleon as a function of density of neutron matter for the forces BSk8 and BSk9, and for the calculations of ref. [24].

dipole resonance properties obtained within the HFB plus Quasi-particle Random Phase Approximation (QRPA) framework with the BSk2-7 forces were found to agree satisfactorily with experiments [17]. As far as isoscalar giant quadrupole resonance (ISGQR) is concerned, a comparison with experiments provides a stringent test for the adopted values of the nucleon effective mass (Ms∗ ). Figure 1 compares the experimental [18,19,20, 21,22,23] and theoretical ISGQR excitation energies obtained in the framework of the HFB+QRPA for 3 of our forces, namely BSk2 (Ms∗ = 1.04), BSk4 (Ms∗ = 0.92) and BSk9 (Ms∗ = 0.80). The agreement is seen to be excellent for the BSk9 force characterized by the low effective mass Ms∗ = 0.80, as also inferred from realistic nuclear-matter calculations. All our original HFB forces lead to a neutron matter that was a little softer than the prediction of realistic neutron matter calculations, as, for example, in the work of Friedman and Pandharipande [24]. The situation is well represented in fig. 2 by the case of BSk8; all our earlier forces lead to essentially the same curves. In fact, there

200

0

50

100

150

200

N

Fig. 3. Differences between the HFB-2 masses and the HFB-9 (left panel) or FRDM (right panel) masses as a function of the neuton number N for all nuclei with 8 ≤ Z ≤ 110 lying between the proton and neutron drip lines.

was a general tendency in our mass fits for neutron matter to be still softer, with an optimal mass fit leading to an unphysical collapse of neutron matter at sub-nuclear densities. We were able to avoid this contradiction with the known stability of neutron stars by imposing a nuclearmatter symmetry coefficient J = 28 MeV. To conform with the calculations of neutron matter at high densities [24], the latest BSk9 force was constrained in such a way that J = 30 MeV. As seen in fig. 2, this constraints leads to a neutron matter energy per nucleon in excellent agreement with the Friedman and Pandharipande curve. As explained above, this constraint inevitably rises the r.m.s. error. This compromise on the mass accuracy is however essential for a correct description of the transition from nuclear matter to nuclei, as required in particular during the decompression of nuclear matter composing the inner crust of neutron stars [13, 25]. Future accurate measurements of the neutron skin thickness of finite nuclei will hopefully help in further constraining the value of J (for more details, see [13]).

3 Extrapolations Globally the extrapolations out to the neutron drip line of all these different HFB mass formulas are, so far, essentially equivalent. Figure 3 compares the HFB-2 and HFB-9 masses for all nuclei with 8 ≤ Z ≤ 110 lying between the proton and neutron drip lines. Although HFB-2 and HFB-9 masses are obtained from significantly different Skyrme forces, deviations not larger than 5 MeV are obtained for all nuclei with Z ≤ 110. In contrast, higher deviations are seen between HFB-9 and FRDM masses (fig. 3), especially for the heaviest nuclei. For lighter species, the mass differences remain below 5 MeV, but locally the shell and deformation effects can differ significantly. Most interestingly, the HFB mass formulas show a weaker (though not totally vanishing) neutron shell closure close to the neutron drip line with respect to droplet-like models as FRDM (e.g. [10,11]).

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More fundamentally, mean-field models still need to be studied coherently and confronted to all possible observables (such as giant resonances, nuclear-matter properties, fission barriers, . . . ) on the basis of one unique effective force. These various nuclear aspects are extremely complicate to reconcile within one unique framework and this quest towards universality will most certainly be an important challenge for future fundamental nuclear-physics research.

M(HFB-9cc) - M(HFB-9)

ΔM [MeV]

10

5

0

References

-5 50

100

150

N

200

15

10

5

0

S [MeV] n

Fig. 4. Differences between the HFB-9cc and HFB-9 masses as a function of N (left panel) and the neutron separation energy Sn (right panel) for all nuclei with 8 ≤ Z ≤ 110 lying between the proton and neutron drip lines.

Although complete mass tables have now been derived within the HFB approach, further developments that could have an impact on mass extrapolations towards the neutron drip line need to be studied. Most particularly, all HFB mass fits show a strong pairing effect that most probably accounts in part for extra correlations that have not been explicitly included in our calculation of the total binding energy (note, however, that the good mass fits shows that these correlations are included implicitly in a way or another through the adjustement of the force parameter). In particular, our HFB calculation should also explicitly include the correction for vibrational zero-point motion. To the best of our knowledge, there exists no strategy to estimate the vibrational correction properly and at the same time include them in a global mass fit as ours with current computing resources. Finally, some specific effects still need to be worked out in detail. In particular, the interplay between the Coulomb and strong interactions was shown [26] to lead to an enhancement of the Coulomb energy in the nuclear surface that could solve the Nolen-Schiffer anomaly, i.e. the systematic reduction in the estimated binding energy differences between mirror nuclei with respect to experiment. This Coulomb correlation effect could in fact significantly affect the nuclearmass predictions close to the neutron drip line. To analyse its impact, we have refitted the BSk9 Skyrme force excluding the contribution from the Coulomb exchange energy, since, as shown by [26], in a good approximation the Coulomb correlation energy cancels the Coulomb exchange energy. The final force leads to an r.m.s. error on all the 2149 experimental masses of 0.73 MeV, i.e. a value identical to the HFB-9 one. The resulting HFB-9cc masses are seen in fig. 4 to differ by more than 10 MeV from the HFB-9 masses close to the neutron drip line. This effect is actually larger than the one studied so far (see fig. 3) and will need to be further scrutinized.

1. C.F. von Weizs¨ acker, Z. Phys. 99, 431 (1935). 2. D. Lunney, J.M. Pearson, C. Thibault, Rev. Mod. Phys. 75, 1021 (2003). 3. P. M¨ oller, J.R. Nix, W.D. Myers, W.J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995). 4. G. Audi, A.H. Wapstra, C. Thibault, Nucl. Phys. A 729, 337 (2003). 5. S. Goriely, F. Tondeur, J.M. Pearson, At. Data Nucl. Data Tables 77, 311 (2001). 6. M. Samyn, S. Goriely, P.-H. Heenen, J.M. Pearson, F. Tondeur, Nucl. Phys. A 700, 142 (2002). 7. G. Audi, A.H. Wapstra, Nucl. Phys. A 595, 409 (1995). 8. G. Audi, A.H. Wapstra, private communication (2001). 9. S. Goriely, M. Samyn, P.-H. Heenen, J.M. Pearson, F. Tondeur, Phys. Rev. C 66, 024326 (2002). 10. M. Samyn, S. Goriely, J.M. Pearson, Nucl. Phys. A 725, 69 (2003). 11. S. Goriely, M. Samyn, M. Bender, J.M. Pearson, Phys. Rev. C 68, 054325 (2003). 12. M. Samyn, S. Goriely, M. Bender, J.M. Pearson, Phys. Rev. C 70, 044309 (2004). 13. S. Goriely, M. Samyn, J.M. Pearson, M. Onsi, Nucl. Phys. A 750, 425 (2005). 14. E. Garrido, P. Sarriguren, E. Moya de Guerra, P. Schuck, Phys. Rev. C 60, 064312 (1999). 15. W. Zuo, I. Bombaci, U. Lombardo, Phys. Rev. C 60, 024605 (1999). 16. I. Angeli, At. Data Nucl. Data Tables 87, 185 (2004). 17. S. Goriely, E. Khan, M. Samyn, Nucl. Phys. A 739, 331 (2004). 18. M.B. Lewis, F.E. Bertrand, Nucl. Phys. A 196, 337 (1972). 19. M. Nagao, Y. Torizuka, Phys. Rev. Lett. 30, 1068 (1973). 20. J.M. Moss, C.M. Rozsa, D.H. Youngblood, J.D. Bronson, A.D. Bacher, Phys. Rev. Lett. 34, 748 (1975). 21. R. Pitthan, F.R. Buskirk, J.N. Dyer, E.E. Hunter, G. Pozinsky, Phys. Rev. C 19, 299 (1979). 22. D.H. Youngblood, Y.-W. Lui, H.L. Clark, Phys. Rev. C 60, 014304 (1999). 23. D.H. Youngblood, Y.-W. Lui, H.L. Clark, Phys. Rev. C 63, 067301 (2001). 24. B. Friedman, V.R. Pandharipande, Nucl. Phys. A 361, 502 (1981). 25. S. Goriely, P. Demetriou, H.-J. Janka, J.M. Pearson, M. Samyn, to be published in Nucl. Phys. A. 26. A. Bulgac, V.R. Shaginyan, Phys. Lett. B 469, 1 (1999).

Eur. Phys. J. A 25, s01, 75–78 (2005) DOI: 10.1140/epjad/i2005-06-050-0

EPJ A direct electronic only

Bounds on the presence of quantum chaos in nuclear masses  J.G. Hirsch1,a , A. Frank1 , J. Barea1 , P. Van Isacker2 , and V. Vel´azquez3 1 2 3

Instituto de Ciencias Nucleares, Universidad Nacional Aut´ onoma de M´exico, AP 70-543, 04510 M´exico DF, Mexico GANIL, BP 55027, F-14076 Caen Cedex 5, France Departamento de F´ısica, Facultad de Ciencias, Universidad Nacional Aut´ onoma de M´exico, AP 70-348, 04511 M´exico DF, Mexico Received: 14 January 2005 / Revised version: 25 February 2005 / c Societ` Published online: 20 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Differences between measured nuclear masses and those calculated using the Finite-Range Droplet Model are analyzed. It is shown that they have a well defined, clearly correlated oscillatory component as a function of the proton and neutron numbers. At the same time, they exhibit in their power spectrum the presence of chaos. Comparison with other mass calculations strongly suggest that this chaotic component arises from many body effects not included in the mass formula, and that they do not impose limits in the precision of mass calculations. PACS. 21.10.Dr Binding energies and masses – 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion – 24.60.Lz Chaos in nuclear systems – 05.45.Tp Time series analysis

1 Introduction It has been recently proposed that there might be an inherent limit to the accuracy with which nuclear masses can be calculated [1], due to the presence of chaotic motion inside the atomic nucleus [2]. This suggestion could have important consequences in the fields of nuclear physics and astrophysics, because the knowledge of nuclear masses is of fundamental importance for a complete understanding of the nuclear processes that power the Sun and for the synthesis and relative abundances of the elements [3]. Though great progress has been made in the challenging task of measuring the mass of exotic nuclei, theoretical models are necessary to predict their mass in regions far from stability [4]. The simplest one is that of the LiquidDrop Model (LDM). It incorporates the essential macroscopic terms, which means that the nucleus is pictured as a very dense, charged liquid drop. The Finite-Range Droplet Model (FRDM) [5], which combines the macroscopic effects with microscopic shell and pairing corrections, has become the de facto standard for mass formulas. A microscopically inspired model has been introduced by Duflo and Zuker (DZ) [6] with good results. Finally, among the mean-field methods it is also worth mentioning the Skyrme-Hartree-Fock approach [7]. Besides the “global” formulas of which the FDRM method has become the standard, there are a number of 

This work was supported in part by the Conacyt, Mexico, and DGAPA-UNAM. a Conference presenter; e-mail: [email protected]

“local” mass formulas. These local methods are usually effective when we require the calculation of the mass of a nucleus, or a set of nuclei, which are fairly close to a number of other nuclei of known mass, exploiting the relative smoothness of the masses M (Z, N ) as a function of proton (Z) and neutron (N ) numbers to deduce systematic trends. Among these methods there are a set of algebraic relations for neighboring nuclei, known as the Garvey-Kelson (GK) relations [8]. These relations do not have any free parameters and can be derived from an independent particle picture. They are based on a clever idea. The combinations are such that the number of neutron-neutron, neutron-proton and proton-proton interactions cancel. In addition to having the correct number of interactions, the single-particle energies and the residual interactions within each level, to a first approximation, cancel too [8]. In order to understand the nature of the errors, in [9] a systematic study of nuclear masses was carried out using the shell model. This was achieved by employing realistic Hamiltonians with a small random component. In [10, 11] we have analyzed in detail the error distribution for the mass formulas of M¨ oller et al. [5] and found a conspicuous long range regularity that manifests itself as a double peak in the distribution of mass differences [10]. This striking non-Gaussian distribution was found to be robust under a variety of criteria. By assuming a simple sinusoidal correlation, we could empirically substract these correlations and made the average deviation diminish by nearly 15% [11].

The European Physical Journal A

ΔM

2 Mapping the mass errors

| Fk | 2

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N

In fig. 1 we show a gray tone (color-coded on line) depiction of the distribution of mass deviations in the LiquidDrop Model, in the FRDM, in the DZ calculations, and in GK calculations, in the proton number (N ) - neutron number (Z) space. We can see large domains with a similar error (each tone is associated to the magnitude of the error). The shell closures are clearly seen in the LDM, It is remarkable that very well defined correlated areas of the same gray tone exist for the errors in the FRDM, and to a lesser extent in the DZ calculations, which are a clear indication of remaining systematics and correlation. In the GK calculations the errors are around 100 keV. Although the latter calculations do not allow reliable extrapolations, they exhibit the calculability of nuclear masses when enough local information (masses of neighbor nuclei or shell model realistic interactions) is available. In order to measure and quantify the oscillatory patterns in the FRDM observed in fig. 1, different cuts were performed along selected directions on the N -Z plane. Given the large number of chains which can be studied, we have selected those with the largest number of nuclei with measured mass. For each cut a Fourier analysis was performed, and the squared amplitudes are plotted as a function of the frequencies on the right-hand side of each figure. We start our analysis for fixed N or Z, i.e. we selected different chains of isotopes or isotones. Those isotopic chains with 20 or more nuclei with measured masses

0.1

Fig. 2. Mass errors in the isotope chains Z = 46 to 56, and their Fourier analysis.

ΔM

In the present contribution we analyze the mass deviations in the Finite-Range Droplet Model (FRDM) of M¨ oller et al. [5], and in the microscopically motivated mass formula of DZ [6], and those obtained using the GarveyKelson relations [11]. The presence of strong correlations between mass errors in neighboring nuclei is clearly exhibited, as well as the existence of a well defined chaotic signal in its power spectrum, when their correlations are analyzed as time series [12,13]. It is also shown that the intrinsic average mass error is smaller that 100 keV.

Z = 46

50 55 60 65 70 75 80 85 90 N

Δ M [MeV]

Fig. 1. Mass differences from the LDM, FRDM, DZ and our GK studies, in MeV, as functions of N and Z.

2 0 -2 0 -2 0 -2 0 -2 0 -2 0 -2 0 -2 0 -2 0 -2 0 -2 0 -2

| Fk |2

[MeV]

ΔM

[MeV]

76

0.1

0.3 0.2 frequency

0.4

0.5

Fig. 3. Mass errors in the isotope chains with Z = 30, 36, 37, 38, 40, 87, 89, 91, and their Fourier analysis.

are presented in figs. 2 and 3. Until 1995, the element which had most isotopes with measured masses was Cs (Z = 55), with 34. Figure 2 displays the mass errors for the isotope chains Z = 46 to 56, and their Fourier analysis, nearly all exhibiting a prominent peak around the low frequency f ≈ 1/20 = 0.05. Figure 3 displays the mass errors for the isotope chains Z = 30, 36, 37, 38, 40, 87, 89, 91, and their Fourier analysis. When the squared Fourier amplitudes are plotted as functions of the frequency ω = k/N using a log-log scale, the corresponding spectral distributions can then be fitted to a power law of the form |F (ω)|2 ∼ ω m . For the 18 chains listed, the fitted slopes m are (1)

mFRDM = −1.18 ± 0.17,

(1)

mDZ = −0.67 ± 0.16. (1)

They give values close to −1.2 in the FRDM data and around −0.7 for the deviations found by DZ. The former is consistent with a frequency dependence of f −1 characteristic of quantum chaos [14], while the latter suggest a tendency towards a more random behavior characteristic of white noise.

J.G. Hirsch et al.: Bounds on the presence of quantum chaos in nuclear masses 4 2

1

log(|Fk|2)

Δ M [MeV]

2

0 -1 -2

0

-2 -4

100

80

60 Z

40

20

0

-6

Moller et al, m= -0.91

2

2 1

2

log(|Fk| 2)

Δ M [MeV]

77

0 -1 -2

0

200

400

600

1000

800

1200

1400

1600

0 -2 -4

-6

Duflo & Zuker, m= -0.51

i

-7

Δ M [MeV]

2

-6

-5

1 0 -1 -2

0

20

40

60

100

80

120

140

-4 Log(k/N)

-3

-2

-1

Fig. 5. Log-log plot of the squared amplitudes of the Fourier transforms of the mass differences, as functions of the order parameter (top). Data from FRDM (top) and from Duflo and Zucker (bottom).

N

Fig. 4. Mass differences plotted as function of Z (top), N (bottom), and of an ordered list (middle).

tudes are presented in fig. 5. The slopes are (2)

mFRDM = −0.91 ± 0.05,

3 The boustrophedon line Plotting the mass differences for different Z, fig. 4 top, and for different N , fig. 4 bottom, is very common in mass calculations. Both plots exhibit some degree of structure. In this way we obtain a plot of mass differences as a function of Z, with all the isotopes plotted along the same vertical line, see fig. 4. The difficulty in quantifying these regularities lies in the simple fact that there are many nuclei with a given N or Z. For this reason in [10] we have analyzed the data using different cuts. Another way to organize the FRDM mass errors for the 1654 nuclei with measured masses is to order them in a single list, numbered in increasing order. To avoid jumps, we have ordered the isotopes along a βoυτ ρoφηδ´ oν (boustrophedon) line [11], which literally means “in the way the ox ploughs”. Nuclei were ordered in increasing mass order. For a given even A, they were accommodated following the increase in N -Z, and those nuclei with odd A starting from the largest value of N -Z, and going on in decreasing order. The middle panel exhibits the same mass differences plotted against the order number, from 1 to 1654, providing an univalued function, The presence of strong correlations in the M¨ oller et al. mass differences is apparent from the plot. Regions with large positive or negative errors are clearly seen. In contrast, the distribution of errors for the data of Duflo and Zuker (not shown, see ref. [12]) is closer to the horizontal axis, and the correlations are less pronounced, although not completely absent. The ordering provides a single-valued function, whose Fourier transform can be calculated. The squared ampli-

(2)

mDZ = −0.51 ± 0.05,

(2)

for the FRDM and DZ mass differences. While this ordering is quite different from the chains along N and Z, the slopes are very similar. To understand the possible origin of these spectral distributions, it is worth recalling that, while the FRDM calculations involve a liquid-droplet model plus meanfield corrections, including deformed single-particle energies through the Strutinsky method and pairing [5], the DZ calculations depend on the number of valence proton and neutron particles and holes, including quadratic terms motivated by the microscopic Hamiltonian [6].

4 Local analysis of the differences between measured and calculated masses We apply the GK procedure to all nuclei in the 2003 compilation [15] where at least one of the relations −M (N +1, Z −2)+M (N +1, Z)−M (N +2, Z −1) + M (N +2, Z −2)−M (N, Z)+M (N, Z −1) = 0, (3) M (N +2, Z)−M (N, Z −2)+M (N +1, Z −2) − M (N +2, Z −1)+M (N, Z −1)−M (N +1, Z) = 0 (4) is applicable. These simple equations are based on the independentparticle shell model and, furthermore, constructed such that neutron-neutron, neutron-proton, and proton-proton interactions cancel. Both GK relations provide an estimate for the mass of a given nucleus in terms of five of its neighbors. This calculation can be done in six different forms,

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Table 1. σr.m.s. mass differences, in keV for the LDM, FRDM, DZ and GK calculations, and for different GK calculations.

Model σr.m.s.

LDM 3447

FRDM 669

DZ 346

GK 189

GK relations A ≥ 16 A ≥ 60

1-12 189 123

4-12 162 102

7-12 117 87

10-12 95 81

12 86 80

as we can choose any of the six terms in the formula to be evaluated from the others. Using both formulas, we can have a maximum of 12 estimates for the mass of a given nucleus, if the masses of all the required neighboring nuclei are known. Of course, there are cases where only 11 evaluations are possible, and so on. About half of all nuclei with measured masses [15] can be estimated in 12 different ways and, in all cases, our estimate corresponds to the average value. To our knowledge, the systematic application of GK relations in this extended fashion [13] is new. Using the GK procedure we obtain a very specific prediction, determined by that of its neighbors. In this procedure there are no free parameters and there is no fit to the data, just a prediction of nuclear masses arising from those of its neighbors. In what follows we compare the mass deviations found in three of the global methods (LDM, FRDM, DZ) and our GK studies. The corresponding σr.m.s. deviations, defined as 

σr.m.s.

N  1  i i 2 Mexp − Mth = N i=1

1/2 (5)

are displayed in table 1, where we also include the smaller samples GK-n which involve the application of n or more GK relations, for which the average deviation is also quoted. Note the systematic decrease in the errors as a consequence of a better determination of the masses, proportional to the number of GK relations applied, for each of the four methods employed. In our best scenario, that of GK-12, we find an r.m.s. deviation of 80 keV, almost an order of magnitude smaller than the FDRM one.

5 Conclusions In summary, a careful use of several global mass formulas and a systematic application of the Garvey-Kelson relations imply that there is no evidence that nuclear masses cannot be calculated with an average accuracy of better than 100 keV. While mass errors in mean-field calculations like the FRDM behave in a manner akin to quantum chaos, with a slope in the power spectrum close to −1, microscopic models’ results correspond to smaller slopes.

Finally, for the local GK relations the remaining mass deviations behave very much like white noise. These results seem to confirm that the chaotic behavior in the fluctuations arises from neglected many-body effects. In other words, the chaoticity discussed in [2], according to the criteria put forward in [14], seems indeed to be present in the deviations induced by calculations using the M¨ oller et al. liquid-droplet mass formula, while it tends to diminish in the microscopically motivated calculations of Duflo and Zucker. While for the liquid-droplet model plus shell corrections a quantum chaotic behavior m ≈ 1 is found, errors in the microscopic mass formula have m ≈ 0.5, closer to white noise. Given that both models attempt to describe the same set of experimental masses, our analysis suggests that quantum fluctuations in the mass differences arising from substraction of the regular behavior provided by the liquid-droplet model plus shell corrections, may have their origin in an incomplete consideration of many body quantum correlations, which are partially included in the calculations of Duflo and Zuker.

References 1. S. ˚ Aberg, Nature 417, 499 (2002). 2. O. Bohigas, P. Leboeuf, Phys. Rev. Lett. 88, 92502 (2002). 3. C.E. Rolfs, W.S. Rodney, Cauldrons in the Cosmos (University of Chicago Press, 1988). 4. D. Lunney, J.M. Pearson, C. Thibault, Rev. Mod. Phys. 75, 1021 (2003). 5. P. M¨ oller, J.R. Nix, W.D. Myers, W.J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995). 6. J. Duflo, Nucl. Phys. A 576, 29 (1994); J. Duflo, A.P. Zuker, Phys. Rev. C 52, R23 (1995). 7. S. Goriely, F. Tondeur, J.M. Pearson, At. Data Nucl. Data Tables 77, 311 (2001); M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, S. Pittel, D.J. Dean, Phys. Rev. C 68, 054312 (2003). 8. G.T. Garvey, I. Kelson, Phys. Rev. Lett. 16, 197 (1966); G.T. Garvey, W.J. Gerace, R.L. Jaffe, I. Talmi, I. Kelson, Rev. Mod. Phys. 41, S1 (1969). 9. V´ıctor Vel´ azquez, Jorge G. Hirsch, Alejandro Frank, Rev. Mex. F´ıs. 49, Suppl. 4, 34 (2003). 10. J.G. Hirsch, A. Frank, V. Vel´ azquez, Phys. Rev. C 69, 37304 (2004). 11. J.G. Hirsch, V. Vel´ azquez, A. Frank, Rev. Mex. F´ıs. 50, Suppl. 2, 40 (2004). 12. J.G. Hirsch, V. Vel´ azquez, A. Frank, Phys. Lett. B 595, 231 (2004). 13. J. Barea, A. Frank, J.G. Hirsch, P. van Isacker, Phys. Rev. Lett. 94, 102501 (2005), arXiv:nucl-th/0502038. 14. A. Rela˜ no, J.M.G. G´ omez, R.A. Molina, J. Retamosa, E. Faleiro, Phys. Rev. Lett. 89, 244102 (2002). 15. G. Audi, A.H. Wapstra, C. Thibault, Nucl. Phys. A 729, 337 (2003).

Eur. Phys. J. A 25, s01, 79–80 (2005) DOI: 10.1140/epjad/i2005-06-034-0

EPJ A direct electronic only

Symmetry energies and the curvature of the nuclear mass surface J. J¨anecke1,a and T.W. O’Donnell2 1 2

Department of Physics, University of Michigan, Ann Arbor, MI 48109-1120, USA Michigan Center for Theoretical Physics and Science, Technology and Society Program, Residential College, University of Michigan, Ann Arbor, MI 48109-1245, USA Received: 24 November 2004 / Revised version: 16 February 2005 / c Societ` Published online: 20 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A global study of the symmetry energies reflects upon the curvature of the mass surface. Special attention is given to the region from 56 Ni to 100 Sn. Isospin inversion is indicated for odd-odd self-conjugate nuclei. Coexistence of isoscalar and isovector n-p interactions in the localized region N ≈ Z, A = 76–96 is suggested by the isospin dependence of the symmetry energy. Experimental symmetry energies and values extracted from nine mass equations are compared. Overall agreement exists, but some distinct differences are also observed. PACS. 21.10.Dr Binding energies and masses – 21.60.-n Nuclear structure models and methods

1 Introduction Symmetry energies Esym (A, T ) depend strongly on isospin T and also on nucleon number A. They influence the curvatures of the experimental nuclear mass surface as well as the mass surfaces obtained from mass equations. The goodness of mass equations can therefore be tested by comparing the calculated and experimental values.

2 Symmetry energies Excitation energy differences between isobaric analog states with isospins T  and T in nuclei with nucleon number A are denoted by ΔT  ,T (A). While many such energies have been measured directly, a set including all known nuclei was used in the present work. It was deduced from Coulomb-energy-corrected differences of all available experimental masses for neighboring isobars. The energies ΔT  ,T (A) can furthermore be expressed as differences between symmetry and pairing energies [1,2]. An expression for the symmetry energies has been introduced as a(A, T ) T (T + 1). (1) Esym (A, T ) = A The factor a(A, T ) is an operationally defined symmetry energy coefficient. Symmetry energies Esym (A, T ) and the coefficients a(A, T ) were deduced globally over the entire bregion of experimentally known nuclei from

a(A, T ) = a

A ΔT +2,T (A) 4T + 6

e-mail: [email protected]

for A = even and odd

(2)

which is valid for both odd-A and even-A nuclei. The energies ΔT +2,T (A) were obtained with the use of the new updated atomic mass evaluation Ame2003 [3].

3 Results Results were discussed earlier [1, 2]. The symmetry energy coefficients a(A, T ) are nearly constant over wide ranges of nuclei where the shell model dominates in the description of the symmetry energies. Systematic deviations from a constant value are observed, though, particularly for shell regions where neutrons and protons occupy different shellmodel orbits. Furthermore, an interesting effect was observed locally for nuclei with N ≈ Z in the region A = 76 to 96 [4]. The quantity a(A, T ) displays an essentially smooth dependence on A for most of the fpg shell containing the p1/2 p3/2 f5/2 g9/2 shell-model orbitals. The nuclei with N = Z display a particularly interesting behavior. Here, the even-even self-conjugate nuclei from A = 58 to 98 follow a smooth dependence on mass number A. These nuclei have T = 0 ground states. For the odd-odd nuclei with N = Z with ground states of T = 0 or T = 1, however, anomalies are observed for A = 62, 66, 70, and 74 suggesting isospin inversion in agreement with experiment. The departures from the smooth T = 0 curve make it possible to estimate the excitation energies for the lowest T = 0 states [4]. The symmetry energies of most nuclei in the fpg shell with Z > 28 and N < 50 follow a T (T + 1) dependence on isospin as expected for the shell model. Distinct local deviations in the heavier region near N = Z from

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MeV

MeV

MeV

MeV

MeV

MeV

MeV

MeV

MeV

MeV

Fig. 1. Symmetry-energy coefficients a(A, T ) as a function of neutron and proton numbers N and Z deduced from experimental mass data and from mass equations or algorithms: (a) ref. [5], (b) ref. [6], (c) ref. [7], (d) ref. [8], (e) ref. [9], (f) ref. [10], (g) ref. [11], (h) ref. [12], (i) ref. [13].

A = 76 to 96 and centered at A ≈ 86 are observed. Here, the symmetry energies display a T (T + 4) dependence on isospin. Such a behavior is compatible with the Wigner supermultiplet model [14], and contributions from the isovector and isoscalar n-p interactions are thus indicated. However, spin-isospin symmetry is known to be broken in heavier nuclei contrary to an interpretation in terms of SU (4) spin-isospin symmetry. Lunney, Pearson, and Thibault [15] pointed out that the isoscalar n-p interaction appears to provide a more direct description of this localized effect. The intense interest in the T = 0 n-p interaction is reflected in the numerous theoretical approaches reported in the literature (see, e.g., references cited in ref. [4]). The origin of the above effect is not entirely understood.

4 Mass equations Replacing the experimental mass data by available theoretical mass predictions as basis for the above procedures to extract symmetry energies makes it possible to directly

compare theoretical and experimental quantities, particularly the symmetry energy coefficients a(A, T ). Such a comparison reflects upon the goodness or possible shortcomings of the respective mass equation. A study of so far nine mass equations or procedures for reproducing experimental masses and extrapolating into regions of unknown nuclei is in progress [16]. While approximate agreement exists, as seen in fig. 1, distinct discrepancies between theoretical and experimental quantities are observed particularly in regions of neutron-rich and proton-rich nuclei. The unusual behavior of the mass surface characterized by the T (T + 4) dependence of the symmetry energy in the upper fpg shell near N ≈ Z is apparently not reproduced except, it seems, for mass equation (g). Interestingly, some mass equations appear to predict a similar behavior for nuclei approaching N = Z for the next higher shell from A = 100 to A = 164. Mass equation (h) gives poor extrapolations for heavier very poton-rich and neutron-rich nuclei. Mass equation (i) displays no shell effects for both, the symmetry energy coefficients a(A, T ) and the pairing energies P (A, T ). Many additional details become apparent from the comparison of the curvature of the experimental and theoretical mass surfaces, both, in the region of nuclei which overlaps with the experimentally known masses and for the extrapolated regions. These effects become more apparent by displaying (not shown) the differences between the theoretical and experimental values.

References 1. J. J¨ anecke, T.W. O’Donnell, V.I. Goldanskii, Phys. Rev. C 66, 024327 (2002). 2. J. J¨ anecke, T.W. O’Donnell, V.I. Goldanskii, Nucl. Phys. A 728, 23 (2003). 3. G. Audi, A.H. Wapstra, C. Thibault, Nucl. Phys. A 729, 337 (2003). 4. J. J¨ anecke, T.W. O’Donnell, Phys. Lett. B 605, 87 (2005). 5. P. M¨ oller, J.R. Nix, At. Data Nucl. Data Tables 39, 213 (1988). 6. Y. Aboussir, J.M. Pearson, A.K. Dutta, F. Tondeur, Nucl. Phys. A 549, 155 (1992). 7. P. M¨ oller, J.R. Nix, W.D. Myers, W.J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995). 8. W.D. Myers, W.J. Swiatecki, Nucl. Phys. A 601, 141 (1996). 9. T. Tachibana, M. Uno, M. Yamada, S. Yamada, At. Data Nucl. Data Tables 39, 251 (1988). 10. E. Comay, I. Kelson, A. Zidon, At. Data Nucl. Data Tables 39, 235 (1988). 11. J. J¨ anecke, P.J. Masson, At. Data Nucl. Data Tables 39, 265 (1988). 12. P.J. Masson, J. J¨ anecke, At. Data Nucl. Data Tables 39, 273 (1988). 13. L. Satpathy, R.C. Nayak, At. Data Nucl. Data Tables 39, 241 (1988). 14. E.P. Wigner, Phys. Rev. 51, 106 (1937). 15. D. Lunney, J.M. Pearson, C. Thibault, Rev. Mod. Phys. 75, 1021 (2003). 16. J. J¨ anecke, T.W. O’Donnell, in preparation.

2 Radioactivity 2.1 Neutron-rich nuclei

Eur. Phys. J. A 25, s01, 83–87 (2005) DOI: 10.1140/epjad/i2005-06-120-3

EPJ A direct electronic only

β-decay studies of neutron-rich nuclei P.F. Manticaa NSCL and Department of Chemistry, Michigan State University, East Lansing, MI 48824, USA Received: 15 January 2005 / c Societ` Published online: 27 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Recent results of β-decay studies performed along the expected neutron shell closures at N = 20, 28, 50 and 82 are reviewed and discussed in view of the potentially dynamic nature of neutron single-particle states in nuclei having extreme neutron-to-proton ratios. PACS. 23.40.-s β decay; double β decay; electron and muon capture – 21.10.-k Properties of nuclei; nuclear energy levels

1 Introduction The advancement of β-decay studies into the so-called “terra incognita” region of the chart of the nuclides promises many rewards associated with both nuclear structure and nuclear astrophysics. The nucleon-nucleon effective interactions employed in current nuclear structure models can be more thoroughly tested by examining variations of gross nuclear properties over a wider range of isospin. Characteristics of β decay, as well as the structure of the resulting daughter nuclei populated following the decay, can shed light on new nuclear structure features that are predicted to occur in nuclei with low neutron separation energies. β-decay half-lives, Qβ values, and delayed neutron emission probabilities of neutron-rich nuclei are also important nuclear physics input parameters for network calculations attempting to reproduce rprocess abundances. In fig. 1 is shown a schematic of the β − -decay process. A variety of measurables are available following β decay, and the properties determined will depend on the arrangement of the experimental apparatus. The determination of T1/2 can be achieved by monitoring the decay of the β activity with time. The β-decay Q value can be measured from the β energy spectrum, or by measuring the masses of both the parent and daughter nuclides. Information on the low-energy quantum states in the daughter, as well as branching ratios, can be deduced from delayed γ rays measured in coincidence with β particles. The population of states in the daughter above neutron threshold can be deduced by measuring delayed neutrons in coincidence with β particles. Neutron emission probabilities can also be inferred from γ-ray intensities of A and A−1 species further down the decay chain. Lifetimes of order picoseconds to nanoseconds of excited levels in the daughter nucleus can a

Conference presenter; e-mail: [email protected]

T1/2

A p Xn

b–

Pn n

Qb

b– b–

Sn g

g

g

A -1 p +1

Yn -2

g

A p +1Yn -1

Fig. 1. Schematic of β − decay.

be determined using fast timing coincidence methods. For a collection of parent nuclei that are spin polarized, the β-decay asymmetry can be measured, and used to deduce the static nuclear moments of the β-emitting state. Significant progress in the study of β-decay properties of very neutron-rich nuclides has been made in recent years, and can be attributed in part to the following: increases in primary beam intensities at radioactive beam facilities; advances in the separation of an isotope of interest from other beam contaminants; and the implementation of new and more sensitive detection methods. In this paper, recent results of β-decay measurements on the neutron-rich side of the valley of stability are detailed. Specific focus is placed on the low-energy nuclear structure of nuclides near the N = 20, 28, 50, and 82 neutron closed shells.

2 Island of inversion near N = 20 The weakening of the N = 20 shell gap and intrusion of neutron f p orbitals into the sd shell has been well documented for the neutron-rich 12 Mg and 11 Na isotopes with N ≥ 20 [1, 2, 3, 4, 5]. However, details regarding entry into

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the so called “island of inversion” have been sparse. β decay is one method which researchers have used to populate and study the low-energy excited states of the neutron-rich 13 Al, 12 Mg and 11 Na isotopes. One determination of the entry point into the island of inversion above 32 Mg was attempted by Morton et al. [6], who measured the β-decay half-life of the N = 20 nuclide 33 Al. The desired 33 Al fragments were produced via fast fragmentation of a 40 Ar beam at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University. Implanted species were correlated with subsequent β decays on an event-by-event basis using a 1-mm thick double-sided Si microstrip detector [7]. The half-life for the ground state of 33 Al was deduced to be 41.7 ± 0.2 ms, and agreed with the results of shell model calculations made in the sd shell. Most of the β-decay strength from the 33 Al ground state was determined to directly populate the ground state of the 33 Si daugther, again in agreement with the sd shell model results. Based on the correspondence of the β-decay properties of 33 Al with predictions from the sd shell model, it was concluded that the 33 Al ground state lies mainly outside the island of inversion at N = 20. Morton et al. also measured the β-decay half-life of Mg to be 90.5 ± 1.5 ms. 33 Mg lies inside the island of inversion, and evidence for inversion of the f p and sd singleparticle orbitals was obtained from a study of the β decay of 33 Na at ISOLDE [8]. 33 Na atoms were produced by proton irradiation of a thick UC target, released from the target at high temperature, and ionized using a surface ionization source. The ionized species were then accelerated, mass separated, and implanted into a collection tape. A plastic scintillator was used for β detection, while large volume Ge detectors were used to measure delayed γ rays. Significant β strength to the 33 Mg ground state was deduced. The allowed nature of the ground-state β branch supposes positive parity for the 33 Mg ground state. The odd neutron in 33 Mg would be expected to reside in the neutron f7/2 orbital, which has negative parity. The presence of 1p1h excitations at low-energy, due to a weakened N = 20 shell gap, was used by Nummela et al. to explain the anomalous positive parity ground state of 33 Mg. 33

The weakening of the N = 20 shell gap may also lead to the development of shape coexistence at low energy. One experimental signature of the presence of competing shapes at low energy is the appearance of 0+ states. Nummela et al. [9] searched for excited 0+ states in 34 Si, using β decay as a mechanism to access the low-energy structure of this nucleus. The parent 34 Al was produced and studied in a similar manner to 33 Mg. A γ ray with energy 1193 keV + was suggested as a candidate 2+ 1 → 02 transition, which + would position the 02 state at 2133 keV. An in-beam spectroscopy measurement of 34 Si, produced as a radioactive beam and inelastically scattered in a deuteron target, revealed coincidence between an 1193 keV γ-ray transition + and the 2+ 1 → 01 transition with energy 3326 keV [10]. The presence of intruding states in the even-even Si isotopes still remains an open and important question.

While the discussion above focused on entry into the island of inversion from above 32 Mg, there have been some attempts to systematically describe the entry pathway with increasing neutron number for the 12 Mg and 11 Na isotopes. The ground magnetic dipole moment of 31 Mg has recently been measured, where the β-decay asymmetry from spin-polarized 31 Mg nuclei was monitored as a function of an applied radiofrequency field. With N = 19, 31 Mg borders the island of inversion, and the value of the experimental magnetic moment suggests that the ground state is dominated by 2p2h intruder configurations [11,12]. For the Na isotopes, the systematic behavior of the ground state quadrupole moments, again determined by monitoring the β-decay asymmetry from polarized sources of 26–31 Na, show a regular increase away from Q ∼ 0 mb starting at 28 Na17 [13]. Especially for 30 Na, with N = 19, the theoretical treatment of the experimental quadrupole moment is best achieved when considering admixtures of the pf shell into the ground state [14]. In a recent measurement at the NSCL, the low-energy structure of 27,28,29 Na was studying following the β decay of 27,28,29 Ne, respectively. Detailed level schemes have been proposed for all three nuclides, and compared with results from sd shell model calculations. The low-energy structure of 29 Na is not consistent with sd shell model predictions. It is suggested from this study of the neutron-rich Na isotopes that a reduced N = 20 shell gap is already evident at N = 18 [15].

3 β-decay half-life of

42

Si28

Advancement of knowledge of a potential weakening of the N = 28 shell gap for neutron-rich nuclides has not progressed as rapidly as that around N = 20. Early suggestions of increased collectivity at N = 28 came from the measured short β-decay half-life and small delayed neutron emission probability of 44 S by Sorlin et al. [16]. Subsequent Coulomb excitation experiments on 44 S and neighboring nuclei also provided evidence for a weakened N = 28 shell gap [17,18]. It has taken more than 10 years to get first data for the next even-even nucleus along the N = 28 isotonic chain. The half-life of 42 14 Si28 , along with 11 other neutron-rich nuclides of Mg-Ar, were measured for the first time by Gr´evy et al. [19]. The nuclides were produced using fast fragmentation of a 60 MeV/nucleon 48 Ca beam at GANIL. The half-life of 42 Si was deduced to be T1/2 = 12.5 ± 3.5 ms, and comparison with the results of QRPA calculations suggested strong oblate deformation for the 42 Si28 ground state. Moving back towards 48 Ca, measurement of the gross β-decay properties of the 18 Ar isotopes has now been completed beyond the N = 28 closed shell [20]. The half-lives and delayed neutron emission probabilities of 49,50 Ar were consistent with QRPA calculations assuming small oblate deformation for the parent and daughter ground states. The decay measurements were carried out at ISOLDE, and proved challenging due to the background attributed

P.F. Mantica et al.: β-decay studies of neutron-rich nuclei

to other short-lived radioactive noble gases extracted simultaneously with singly-charged 49,50 Ar from the plasma ion source. By mass selecting doubly-charged 49,50 Ar ion species, the experimenters were able to collect decay time and delayed neutron spectra suitable for analysis.

The high energy of the first excited 2+ state in 52 Ca32 [21], compared to neighboring 50 Ca30 , provided evidence for possible changes in shell structure above 48 Ca. Further investigation of the systematic variation of the 2+ 1 energies of the neutron-rich, even-even Cr isotopes by Prisciandaro et al. [22] demonstrated that the unexpected stability at N = 32 was not limited to the Ca isotopes at the proton closed shell. The appearance of a subshell gap at N = 32 has been attributed to a shift in the neutron f5/2 orbital due to a strong proton-neutron monopole interaction with the proton f7/2 orbital [23]. Indeed, a similar monopole shift between the proton d5/2 and neutron d3/2 orbitals around A = 30 contributes to the erosion of the N = 20 shell closure. A more complete picture of the development of the N = 32 subshell closure with removal of protons from the f7/2 orbital was obtained with the measurement of the energy of the first 2+ state in 54 Ti. γ rays with energies 1002 and 1495 keV were observed following the β decay of 54 Sc and by in-beam γ spectroscopy following deep inelastic collisions of 48 Ca on 208 Pb. [24]. The 1495 keV γ ray + 54 Ti based on was assigned as the 2+ 1 → 01 transition in its intensity in both the delayed and in-beam γ-ray spectra. The low-energy states of the even-even, neutron-rich Ti isotopes were well reproduced by shell model calculations using a new pf shell effective interaction labeled GXPF1 [25, 26]. These same shell model calculations also predicted that the neutron f5/2 orbital should rise significantly above the neutron p1/2 orbital when the proton f7/2 orbital is unoccupied, leading to the development of an N = 34 shell closure for the Ti and Ca isotopes. As evidence for the appearance of an N = 34 shell closure, the first 2+ energy in 56 Ti34 is predicted from the GXPF1 shell model calculations to be similar to that in 54 Ti32 . A subsequent measurement of the first excited 2+ state 56 in Ti via β decay [27] did not lend support to the notion of a shell closure at N = 34 for the Ti isotopes. The measurement was carried out at the NSCL, where the 56 Sc parent nuclides were produced at a rate of ≈ 3 per minute via fast fragmentation of a 86 Kr beam at 140 MeV/nucleon. Several γ rays were observed in the delayed γ-ray spectrum of 56 Sc, and three transitions at 690, 1129, and 1161 keV were assigned as depopulating levels in 56 Ti. The most intense transition at 1129 keV was tentatively as+ + signed as the 2+ 1 → 01 transition, meaning that the 21 56 state in Ti was nearly 400 keV below that predicted by the shell model calculations using the GXPF1 interaction. Detailed analysis of the delayed γ rays following the β decay of 56 Ti [28] provided evidence for the presence of two β-decay states in 56 Sc; a low-spin state with a half-life of

4500 4000 3500 3000 E(2+) [KeV]

4 Shell closure at N = 34?

85

2500

Ca

20

2000 1500 1000

22

Ti

Fe 28Ni

26

500 24

Cr

0 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 Neutron Num ber

Fig. 2. Systematics of the first 2+ energies of the proton f7/2 neutron f p shell nuclei.

35±5 ms, and a high-spin state with half-life 60±7 ms. The existence of high- and low-spin β-decaying states helps explain the complicated allowed decay pattern that was observed for 56 Sc. Direct β feeding was deduced to both the 56 Ti 0+ ground state and to a state at 2980 keV, believe to have spin and parity 6+ based on observations from a complementary in-beam spectroscopy measurement [29]. The existence of isomeric states in the parent nucleus offers unique challenges to β-decay experiments, and is discussed in further detail in the next section. The absence of an N = 34 shell closure for the Ti isotopes has been attributed to a less dramatic monopole shift of the neutron f5/2 orbital with change in occupancy of the proton f7/2 orbital as predicted by the shell model calculations employing GXPF1. A new shell model interaction designated GXPF1a is now under development [30], that may correct some of the observed deficiencies in GXPF1. The current status of the measured 2+ 1 energies for the Ca to Ni isotopes in the f p shell is shown in fig. 2. The systematic increase in 2+ 1 at N = 32 is evident in the 20 Ca, 22 Ti, and 24 Cr isotopes. There is no indication of an increase in the 2+ 1 energy at N = 34 for any of the isotopes shown. In fact, there is a dramatic decrease in the first 2+ energy in the 24 Cr and 26 Fe isotopes beyond N = 34. The 60 Cr36 and 62 Cr38 were determined in β2+ 1 energies in decay experiments by Sorlin et al. [31], where the parent isotopes 60,62 V were produced following fast fragmentation of a 76 Ge beam at 61.8 MeV/nucleon at GANIL. The systematic trend in 2+ 1 energies for Cr and Fe suggests a sudden onset of deformation, which may be traced to the occupancy of the neutron g9/2 orbital. A strong monopole interaction is expected between the proton f7/2 and neutron g9/2 shell model orbitals [32]. Further studies of the low-energy structure of proton f7/2 neutron-rich nuclides

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out to N = 40 are warranted to fully understand the dynamic nature of the neutron single-particle orbitals due to the monopole shift.

5 Towards

78

Ni50

With a full complement of f7/2 protons, the 28 Ni isotopes have been extensively studied by a variety of techniques. For the very neutron-rich 78 Ni50 , a half-life has been determined for the first time [33]. Eleven 78 Ni nuclei were produced following fast fragmentation of a 140 MeV/nucleon 86 Kr beam at the NSCL. The half-life deduced for 78 Ni was considerably shorter than most early predictions from global nuclear structure models, and further details are available in the contribution to these proceeding by Schatz et al. [34]. The systematic variation of the first 2+ energies in the even-even Ni isotopes have now been determined up to 76 Ni. The low-energy levels in 72 Ni and 74 Ni were determined following β decay of 72 Co [35] and 74 Co [36], respectively. In both cases the parent nuclides were made by fast fragmentation of a 86 Kr beam; the 72 Co measurement was completed at GANIL using ancillary γ-ray detectors from EXOGAM, while the 74 Co data were collect at the NSCL using detectors from the SeGA array for 76 Ni was γ-ray detection. The first excited 2+ 1 state in first determined through observation of the decay of the isomeric 8+ seniority state, which is produced directly in projectile fragmentation and has a lifetime of several ten’s of nanoseconds [37]. The same isomer decay sequence was observed in a subsequent experiment at the NSCL [36]. As mentioned in sect. 4, the presence of multiple βdecaying states in a single nucleus can seriously complicate the interpretation of results from a β-decay experiment. Recently, three β-decaying states have been observed in the nucleus 70 Cu [38,39]. Characterization of these three β-decaying states was aided by the selectivity offered by resonance laser ioniziation in an on-line ion source. The 70 Cu species were produced by proton induced fission of a UC target, both at ISOLDE and the LISOL facility at Louvain-la-Neuve. The hyperfine structures of the three states β-decaying states are sufficiently different, due to the difference in the spin value of each state, to permit in-source laser spectroscopy to enhance production of any one of the three states. In addition to determining halflives, β-branching, and competing γ internal transitions, the masses of each β-decaying state were determined using ISOLTRAP [40]. Resonance laser ionization sources provide enhanced efficiencies and reduced backgrounds that will significantly broaden the reach of on-line isotope separators in terms of more available isotopes (including refractory metals) with larger N/Z ratios. The opportunties are well outlined in the next section, as well as elsewhere in these proceedings [41].

6 Shell quenching at N = 82 Dillman et al. have deduced the mass of 130 Cd82 from a β-decay endpoint measurement [42]. Here the 130 Cd nu-

clides were produced at ISOLDE using a two-step fission target [43] and efficiently extracted from the on-line ion source using resonant laser ionization. The experimental Qβ value of 8.34 MeV was higher than the predictions of global mass models that do not include quenching of the N = 82 shell gap. The authors have suggested this is an indication of shell quenching below 132 Sn82 . Another early indication of the potential quenching of the N = 82 shell gap has come from the systematic variation of the first excited 2+ states in the even-even 48 Cd isotopes, where the 126 Cd to 645 keV E(2+ 1 ) value decreases from 652 keV in 128 131 in Cd [44]. Even in Cd83 , the short half-life and low delayed neutron probability for this nuclide did not compare favorably to theoretical predictions [45]. Additional β-decay studies of the very neutron-rich Sn isotopes have also been carried out at the high resolution mass separator at ISOLDE. Delayed γ-ray spectroscopy has been completed out to 135 Sn85 [46]. A significant decrease in the energy difference between the lowest energy 7/2+ and 5/2+ levels has been observed in the Sb51 isotopes at 135 Sb84 . To investigate the origin of this dramatic change in low-energy structure, which might be associated with the large N/Z ratio of ≈ 1.6 in 135 Sb, the lifetime of the first excited 5/2+ state was measured [47] using the βγγ(t) method with fast timing plastic scintillator and BaF2 detectors [48]. The lifetime of the 5/2+ state in 135 Sb was much longer than predicted by shell model calculations using interactions which include the most recent data on nearby 133 Sb and 133 Sn. Further removed from 132 Sn, neutron-rich nuclides in the Tc-Cd isotopes have been produced by fast fragmentation of a 120 MeV/nucleon 136 Xe beam and studied by both delayed γ-ray and delayed neutron spectroscopies. The low-energy structure of 120 Pd has been deduced from the delayed γ rays observed following the β decay of 120 Rh [49]. The most intense γ-ray transition at 438 keV + 120 Pd. The syswas assigned to the 2+ 1 → 01 transition in + tematic variation of the 21 energies in the 46 Pd isotopes show a symmetry about N = 68, where the 2+ 1 energy of 108 Pd is reported as 434 keV. In addition, there is also similarity in the first 2+ energies of the four proton hole 120 128 46 Pd74 and isotonic 54 Xe74 , which has four proton particles outside Z = 50. The conclusion reached is that, from a valence-particle standpoint, both 128 Xe74 and 120 Pd74 appear to see the same N = 82 and Z = 50 shell closures. Both 130 Cd82 and 135 Sb84 exhibit anomalous properties near the ground state that may be attributed to the extreme N/Z ratio of these nuclides. Continued investigations of the β-decay properties and low-energy structure of nuclides along N = 82 may help to confirm or refute the quenching of this shell gap.

7 Summary Allowed β decay is a selective process, and provides a means to access excited states of nuclei far from stability. Measured and deduced properties that can be obtained by studying β decay include: half-lives, decay energies,

P.F. Mantica et al.: β-decay studies of neutron-rich nuclei

absolute branching ratios, delayed neutron probabilities, as well as low-energy structure of daughter nuclide(s). New β-decay data for very neutron-rich nuclides have been obtained at both isotope separation on-line ion source and fragmentation facilities. The use of resonance laser ionization has broadened the reach of on-line ion source experiments, providing access to new elements with a high degree of selectivity. The characterization of fast fragmentation beams on an event-by-event basis and direct implant-β correlation methods have allowed first study of 78 Ni and other far off stability nuclides. Future enhancements in selectivity, detector sensitivity, and rare isotope beam production over the near term will provide new data on the β-decay properties of neutron-rich nuclides to learn more of the dynamic nature of single-particle states in nuclides far from the valley of stability.

This work was supported in part by the National Science Foundation PHY-01-10253.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

T. Motobayashi et al., Phys. Lett. B 346, 9 (1995). B.V. Pritychenko et al., Phys. Lett. B 461, 322 (1999). V. Chiste et al., Phys. Lett. B 514, 233 (2001). Y. Yanagisawa et al., Phys. Lett. B 566, 84 (2003). B.V. Pritychenko et al., Phys. Rev. C 63, 011305R (2000). A.C. Morton et al., Phys. Lett. B 544, 274 (2002). J.I. Prisciandaro et al., Nucl. Instrum. Methods Phys. Res. A 505, 140 (2003). S. Nummela et al., Phys. Rev. C 64, 054313 (2001). S. Nummela et al., Phys. Rev. C 63, 044316 (2001). N. Iwasa et al., Phys. Rev. C 67, 064315 (2003). M. Kowalska et al., these proceedings. G. Neyens et al., Phys. Rev. Lett. 94, 022501 (2005).

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13. M. Keim, ENAM98, Exotic Nuclei and Atomic Masses, edited by B.M. Sherrill, D.J. Morrissey, C.N. Davids (AIP, Woodbury, 1998) p. 50. 14. Y. Otsuno et al., Phys. Rev. C 70, 044307 (2004). 15. V. Tripathi et al., these proceedings. 16. O. Sorlin et al., Phys. Rev. C 47, 2941 (1993). 17. H. Scheit et al., Phys. Rev. Lett. 77, 3967 (1996). 18. T. Glasmacher et al., Phys. Lett. B 395, 163 (1997). 19. S. Gr´evy et al., Phys. Lett. B 594, 252 (2004). 20. L. Weissman et al., Phys. Rev. C 67, 054314 (2003). 21. A. Huck et al., Phys. Rev. C 31, 2226 (1985). 22. J.I. Prisciandaro et al., Phys. Lett. B 510, 17 (2001). 23. T. Otsuka et al., Phys. Rev. Lett. 87, 082502 (2001). 24. R.V.F. Janssens et al., Phys. Lett. B 546, 55 (2002). 25. M. Honma et al., Phys. Rev. C 65, 061301R (2002). 26. M. Honma et al. Phys. Rev. C 69, 034335 (2004). 27. S.N. Liddick et al., Phys. Rev. Lett. 92, 072502 (2004). 28. S.N. Liddick et al., Phys. Rev. C 70, 064303 (2004). 29. B. Fornal et al., Phys. Rev. C 70, 064304 (2004). 30. M. Honma et al., these proceedings. 31. O. Sorlin et al., Eur. Phys. J. A 16, 55 (2003). 32. A.M. Oros-Peusquens, P.F. Mantica, Nucl. Phys. A 669, 81 (2000). 33. P. Hosmer et al., Phys. Rev. Lett. 94, 112501 (2005). 34. H. Schatz et al., these proceedings. 35. M. Sawicka et al., Phys. Rev. C 68, 044304 (2003). 36. C. Mazzocchi et al., these proceedings. 37. M. Sawicka et al., Eur. Phys. J. A 20, 109 (2004). 38. J. VanRoosbroeck et al., Phys. Rev. Lett. 92, 112501 (2004). 39. J. VanRoosbroeck et al., Phys. Rev. C 69, 034313 (2004). 40. F. Herfurth et al., J. Phys. B 36, 931 (2003). 41. P. van Duppen et al., these proceedings. 42. I. Dillman et al., Phys. Rev. Lett. 91, 162503 (2003). 43. J.A. Nolen et al., AIP Conf. Proc. 473, 477 (1999). 44. T. Kautszch et al., Eur. Phys. J. A 9, 201 (2000). 45. M. Hannawald et al., Phys. Rev. C 62, 054301 (2000). 46. J. Shergur et al., Phys. Rev. C 65, 034313 (2002). 47. A. Korgul et al., these proceedings. 48. H. Mach et al., Nucl. Phys. A 523, 197 (1991). 49. W.B. Walters et al., Phys. Rev. C 70, 034314 (2004).

Eur. Phys. J. A 25, s01, 89–92 (2005) DOI: 10.1140/epjad/i2005-06-209-7

EPJ A direct electronic only

The structure of nuclei near

78

Ni from isomer and decay studies

R. Grzywacza University of Tennessee, Knoxville, TN 37996, USA and Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Received: 18 January 2005 / Revised version: 20 February 2005 / c Societ` Published online: 15 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Recent progress in experimental decay studies in the region of the doubly magic nucleus 78 Ni is discussed. In particular new data on low-energy excitations in nickel isotopes has been obtained in experiments employing fragmentation reactions. The experimental data are confronted with different shellmodel calculations. The position of the 2+ energy levels and behavior of 8+ isomers in even-even 70–76 Ni isotopes has been interpreted. PACS. 21.60.Cs Shell model – 25.70.Mn Projectile and target fragmentation – 27.50.+e 59 ≤ A ≤ 89 – 23.40.-s β decay; double β decay; electron and muon capture

1 Introduction Understanding of nuclei with very large neutron excess requires development of increasingly complex many body models. The half-century old nuclear shell model, a very successful tool describing properties of nuclei, is undergoing a period of revival [1], enabled by the availability of computing power. The predictive power of the calculations has to be tested by experiments on nuclei with large proton-neutron asymmetry. Magic nuclei are the best benchmarks. The shell-model structure of neutron-rich Z = 28 nuclei was investigated for the first time by the study of 68 Ni produced in a multi-nucleon transfer reaction [2]. Evidence for shell closure at N = 40 was found. The subject of the N = 40 magicity has been addressed in a number of papers, for example [3, 4,5,6]. Since then, the use of fragmentation reactions made it possible to study more exotic nuclei toward 78 Ni and along N = 40. Several experiments on neutron-rich nuclei Z ≈ 28 and 40 < N < 50 have been performed using fragmentation reactions of 86 Kr beams at intermediate energies at GANIL [7,8,9, 10,11] and NSCL [12,13,14] facilities using high-acceptance fragment separators to select nuclei of interest. Detection systems sensitive to beta and gamma radiation enabled spectroscopy of states populated in de-excitation of short-lived isomers and following beta decay. A variety of other gamma-spectroscopy methods have been applied to study the properties of these nuclei [4, 15, 16]. These sensitive measurements provided, among other results, such as observation of microsecond isomers, see fig. 1, the first observation of the energies a

Conference presenter; e-mail: [email protected]

Fig. 1. Fragment of the chart of nuclei around 68 Ni and 78 Ni with selected known microsecond isomers observed using 86 Kr fragmentation [7, 10, 11, 30].

of the lowest excited states in the even-even magic nickel nuclei from 70 Ni to 76 Ni, see fig. 2. Neutron-rich iron and cobalt nuclei studied, showed indications of the onset of deformation [11]. The shell-model framework applied in the case of 68 Ni [2,17, 18] could not satisfactorily reproduce the measured properties of the more exotic nickel nuclei for example the disappearance of the 8+ isomer in 72,74 Ni [18] and its reappearance in 76 Ni. These new observations resulted in a successful revision of the shell-model approach to the nickel isotopes [18, 19].

2 Experimental technique The experiments using the fragmentation of heavy ions to produce exotic nuclei rely on event-by-event identification of mass, charge and atomic number via measurements of their time of flight, magnetic rigidity, energy loss in detector material and of total kinetic energy [20]. The decay properties of each identified ion can be measured with a

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Energy (2+ → 0+) (keV)

3000

in exotic nuclei. In several experiments the J π = 8+ isomers were sought in the even-even isotopes of nickel for N > 40. It was expected that using the very efficient and selective method of microsecond isomer detection [24] information about low level excited states, in particular first J π = 2+ excitations in 70,72,74,76 Ni isotopes, could be obtained in relatively uncomplicated experiments. The first of the expected isomers was discovered in 70 Ni [7]. The isomers in 72 Ni and 74 Ni could not be detected, even though a sufficient number of ions were measured. The lifetime limits have been deduced [25,8]. The lifetime limits are outside those expected from theory and this presented a challenge for the shell-model calculations.

Z=28

2500 2000 1500 1000 500 0

54 56 58 60 62 64 66 68 70 72 74 76 78

Mass Number +

Fig. 2. Experimental energies of the first-excited 2 levels in magic even-even nickel isotopes (black dots). The most neutron-rich nuclei 70–76 Ni has been measured using isomer and beta-decay spectroscopy methods using fragmentation of the 86 Kr beam [7, 8, 30]. Shown are also theoretical predictions using different shell-model approaches (SM-S3V [18], SMNowacki [4], and SM-Lisetskiy [19]).

radiation detection setup, consisting of beta detectors [8, 9, 12], gamma detectors [7, 15,16] or conversion electron detectors [21]. The data described below has been obtained in experiments performed at GANIL using LISE2000 and at NSCL with the A1900 spectrometer. The beams of 86 Kr accelerated to energies of 58 A MeV (80 pnA) and 140 A MeV (16 pnA) have been used. Thick targets can be used thus maximizing the production rates. A 300 μm thick rotating tantalum target was used in the GANIL experiment and a 2226 μm thick fixed beryllium target at NSCL. The aim of the experiments was to measure gamma radiation emitted in the beta and isomeric decay of the exotic ions. State of the art detectors have been used for the decay radiation measurement. Gamma radiation was measured using an array of germanium detectors consisting of four clover detectors or twelve detectors of the SEGA array [22] array with similar detection efficiencies of about 6% and 4.6% at 1.3 MeV. To achieve high coincidence efficiency between gammas and beta decay electrons, thick (1 mm - GANIL, 1.5 mm - NSCL) double-sided silicon strip detectors (16 × 16 strips, 3 mm wide at GANIL and 40×40 strips, 1 mm wide at NSCL) have been used [8, 23]. The beta detection efficiencies amounted to about 20% (GANIL) and 30% (NSCL). The earlier GANIL (100 h long) experiment aimed at search for 8+ isomers in 72 Ni and 74 Ni and beta-decay studies of 72 Co and its neighbors. The NSCL experiment was aimed to improve on the measurement of the decay of 72 Co (27 h long) and to extend the information on 74 Ni via 74 Co decay (68 h long). Both experiment used the same experimental method [24] to detect microsecond isomers.

3 Low-energy states in neutron-rich nickel isotopes Beta and electromagnetic decay of long-lived nuclear states can provide information on low-energy excitations

These 8+ excitations have very simple nature in these spherical nuclei. In the spherical shell-model picture for the N > 40, Z = 28 nuclei, the valence neutrons are starting to occupy the g9/2 orbital. Two valence neutrons can be coupled to states with maximum available spin J π = 8+ . The positive parity and the high angular orbital momentum l = 4 of the g9/2 orbital prevents this state from being mixed with fp-shell (l = 1, 3, π = −1) states, hence the wave function of this state should in all cases be a rather pure two-neutron (g9/2 )2 excitation. The isomerism is caused predominantly by the yrast nature of this state and the low energy difference between the 8+ and the nearest state available for electromagnetic transition J π = 6+ . For 70 Ni this energy is 182 keV and results in a 230(3) ns lifetime [7,26] of the state decaying via E2 photon emission. The transition strength is about 0.7 W.u. indicating the non-collective nature of the states involved. For the 72 Ni and 74 Ni this transition will be slowed down due to the B(E2) quenching in the mid-shell [18], but the isomerism was robustly predicted by various shellmodel calculations. For the pure configurations the isomeric properties are linked to the values of interaction two-body matrix elements (TBME). The relevant values of these TBME are dominated by the short-range nature of nuclear interactions which leads to near degeneracy of the 6+ and 8+ states [27]. Such behavior is independent of j and the example of such isomers can be found across the nuclear chart. The arguments presented above advocate that the presence of the 8+ isomers reflects a fundamental behavior of residual interactions and the anomalies may possibly uncover new nuclear structure effects. Several hypotheses have been brought about to explain the absence of the isomerism in 72,74 Ni. One suggested very long lifetime of 8+ states, into the milliseconds range, rendering them difficult to detect. Another idea called for the onset of deformation which would effectively introduce strong mixing and would deem the above single-particle picture invalid. The non-observation of the 8+ isomers in 72 Ni and 74 Ni suggested a beta decay of 72 Co and 74 Co as a method to populate and investigate the levels in these nickel isotopes. The Z = 27 cobalt isotopes are rather difficult to describe within the shell model, because of the large model space needed to include the full fpg shell for neutrons and opening of the Z = 28 closed shell. But rather simple arguments are pointing to the fact that the beta decay of odd-odd cobalt isotopes will populate excited states

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78

Ni from isomer and decay studies

91

Fig. 4. The gamma rays observed in correlation with 76 Ni ions. + Four lines belonging to the decay of the T1/2 = 590+180 −110 ns 8 isomer have been identified. Fig. 3. The calculated and experimental level schemes for even-even nickel isotopes [19]. The migration of the seniority ν = 4 J π = 6+ level is shown.

in even-even nickel isotopes. This is because of the coupling between the f7/2 proton hole and g9/2 neutron will generate only negative-parity states thus making the allowed Gamow-Teller transition to the 0+ ground state of even-even nickels impossible if any of the negative-parity and high-spin states becomes a ground state. The lowlying state with paired g9/2 neutrons and vacancy in p1/2 leads to the generation of 3+ and 4+ states at low energies. Again, in this case the ground-state beta decay will not be allowed by selection rules. Thus the decay of cobalt isotopes will be dominated by the Gamow-Teller transitions to either negative-parity states in nickel or to excited positive-parity states. The caveat of choosing beta decay to study excited states in nickel isotopes is that the cobalt isobars are much more difficult to produce and a penalty has to be paid not only in having more complicated experimental system, which have to be sensitive to beta-gamma coincidences, but also because production cross-sections are roughly a hundred times smaller. In addition, the beta-delayed neutron emission [28] competes with beta-delayed gamma decay, as observed experimentally [14]. Despite these difficulties the experiments have been successful. The experiment by Sawicka et al. [8] led among others to the measurement of excited states in 72 Ni. The strongest lines at 1096 keV and 845 keV have been interpreted as the E2 decays of the 2+ and 4+ states. It has been noticed that the adopted 2+ energy at 1096 keV is lower by about 330 keV than the SM calculations with S3V TBME [18], which have been working reasonably well for the N < 40 nickels [17]. The predicted energy was already lower for 70 Ni, but systematic observations proved it is not just a single case anomaly. It led Grawe [18] to link the energies of the 2+ states with disappearance of the 8+ isomers in the mid-shell. The “experimental” TBME elements has been extracted from 70 Ni choosing a very simple model space of two valence neutrons in the g9/2 orbital and an inert 68 Ni core. These calculations for 72,74 Ni led to a new interpretation of the structure of the 8+ states. These calculations in a very restricted model space have been recently replaced by the full fpg model space shell model with a new set of TBME extracted from the experimen-

tal data [19]. The interpretation for the disappearance of the isomerism in refs. [18, 19] is based on the existence of the second low-lying 6+ state which is a result of coupling four neutrons. The calculations for the series of even-even nickel isotopes for 40 < N < 50 is shown in fig. 3. The position of the second 6+ state is sensitive to small changes of the TBME. The new calculations pushed the energy below the energy of the 8+ state opening up a new decay channel with large B(E2). According to the calculations by Lisetskiy the lifetime of the 8+ level in 72 Ni is 6 ns with small strength (B(E2) ∼ 0.1 W.u.) to the seniority ν = 2 6+ state and with much larger strength (B(E2) ∼ 3 W.u.) to the ν = 4 state. Isomers with such short lifetime are usually inaccessible by the standard detection method. The same modification of the TBME which leads to generation of the seniority ν = 4 and spin 6+ state is also responsible for the lowering of the energies of the first 2+ excited states. This is done by introducing additional mixing to the 2+ and 0+ states. Not surprisingly, the new SM predicts robust isomerism for 70 Ni and 76 Ni, where the creation of ν = 4 states would require promoting neutrons from the fp shell, or across N = 50 shell gap. The expected isomer in 76 Ni has indeed been observed for the first time in the GANIL experiment [11] and its full decay cascade and lifetime (fig. 4) have been determined in the NSCL experiment. The overall agreement between shell model and experiment is good. Particularly impressive is the good reproduction of the gap between 8+ and 6+ states (144 keV exp. vs. 135 keV th.), the B(E2) ∼ 0.7 W.u.) values and the position of the 2+ state. In the NSCL experiment the first evidence for the 2+ and 4+ energies in 74 Ni has been obtained completing the lowest-level systematics for the isotopic chain of 40 < N < 50 nickel isotopes. The energies of these states are close to the theoretical ones. The second 6+ states have not been observed in either experiment. thus the interpretation presented above is still not fully confirmed experimentally. Either an experiment with high statistics on 72 Co decay or an experiment sensitive to isomers with few nanosecond lifetimes with 72 Ni has to be performed. However, even assuming that this circumstantial evidence favors Grawe and Lisetskiy’s calculations, we have to answer the question of what is the fundamental reason for such modification of the TBME. The other set of experimental data crucial in constraining the theories should come from odd-even nickel isotopes. Here

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Fig. 5. The calculated and experimental level schemes for oddmass nickel isotopes [19]. The correspondence between experimental and theoretical levels is tentative.

the long-lived 1/2− and short-lived high-spin isomers were expected for the series 71,73,75,77 Ni [25]. The experimental data [29, 30], however, are much more difficult to interpret. Very low statistics precludes reliable correlation between experiment and theory, the attempt is presented in fig. 5. No evidence for the short-lived isomers has been found yet and evidence for long-lived 1/2− isomers is difficult to extract from the data.

4 Other experimental developments In the time between the two ENAM conferences a number of other measurements have been performed which probe in detail the nature of excited states in the region of neutron rich nickel isotopes. These experiments require more statistics than the “discovery” experiments presented above and thus are concentrated around 70 Ni. A pioneering experiment on g-factor measurements of isomeric states was performed studying the structure of the wave function of the isotopes 69,71 Cu and 67 Ni [16] and more recently on 61 Fe [31]. Here the surprising result for the J π = 9/2+ isomer in 67 Ni was obtained, indicating strong mixing of the previously supposed pure g9/2 state. A very important study of level lifetimes below the isomers was performed using the delayed coincidence method with BAF2 [15]. Nano- and subnanosecond lifetimes in 67,69,70 Ni and 72 Cu have been studied, and the B(E2) values have been compared with S3V SM [18]. These experiments can be employed to study more exotic isotopes with only small investments into the experimental setup. The attempts to study the structure of the 2+ states via B(E2) measurements using Coulomb excitation of the relativistic ion beams has been performed on 68 Ni [4].

5 Summary In a series of experiments using fragmentation reactions and efficient beta and gamma ray detection systems, experimental evidence for the lowest excited states of nickel

isotopes has been obtained. The shell-model approach which reproduces well the excitations of even-even isotopes has been developed. The calculation can explain the lower than previously expected positions of the 2+ excited states and link it to the disappearance of the 8+ isomerism. The data on odd-mass isotopes are still tentative and need improved measurements. The evidence for the seniority ν = 4 states at low energies still has to be found. One possible way is to search for the now predicted to be very short-lived isomers in 72,74 Ni. A short-lived 8+ isomer was found in 68 Ni in a challenging experiment using a multi-nucleon transfer reactions [5] with a combination of stable beams and targets. This method can potentially be used with radioactive ion beams with sufficient intensity, to search for the isomers in 72,74 Ni. This work was supported by the U.S. DOE through Contract No. DE-FG02-96ER40983. ORNL is managed by UT-Battelle, LLC, for the U.S. DOE under Contract DE-AC05-00OR22725.

References 1. A. Arima et al., Nucl. Phys. A 704, 1c (2002) and other publications in this volume. 2. R. Broda et al., Phys. Rev. Lett. 74, 868 (1995). 3. W.F. Mueller et al., Phys. Rev. Lett. 83, 3613 (1999). 4. O. Sorlin et al., Phys. Rev. Lett. 88, 092501 (2002). 5. T. Ishii et al., Phys. Rev. Lett. 84, 39 (2000). 6. K. Langanke et al., Phys. Rev. C 67, 044314 (2003). 7. R. Grzywacz et al., Phys. Rev. Lett. 81, 766 (1998). 8. M. Sawicka et al., Phys. Rev. C 68, 044304 (2003). 9. O. Sorlin et al., Nucl. Phys. A 660, 3 (1999); 669, 351 (2000)(E). 10. J.M. Daugas et al., Phys. Lett. B 476, 213 (2000). 11. M. Sawicka et al., Eur. Phys. J. A 16, 51 (2003). 12. J.I. Prisciandaro et al., Phys. Rev. C 60, 054307 (1999). 13. P. Hosmer et al., NSCL workshop 2003. 14. C. Mazzocchi et al., these proceedings. 15. H. Mach et al., Nucl. Phys. A 719, 213c (2003). 16. G. Georgiev et al., J. Phys. G 28, 2993 (2002). 17. T. Pawlat et al., Nucl. Phys. A 574, 623 (1994). 18. H. Grawe et al., Nucl. Phys. A 704, 211c (2002). 19. A. Lisetskiy et al., Phys. Rev. C 70, 044314 (2004). 20. D. Bazin et al., Nucl. Phys. A 515, 349 (1990). 21. F. Becker et al., Eur. Phys. J. A 4, 103 (1999). 22. W.F. Mueller et al., Nucl. Instrum. Methods A 466, 492 (2001). 23. J.I. Prisciandaro et al., Nucl. Instrum. Methods A 505, 90 (2003). 24. R. Grzywacz et al., Phys. Lett. B 355, 439 (1995). 25. R. Grzywacz, Second International Conference on Fission and Neutron-rich Nuclei, St. Andrews, Scotland 1999 (World Scientific, 2000) p. 38. 26. M. Lewitowicz et al., Nucl. Phys. A 682, 175c (2001). 27. N. Anantarman, J.P. Schiffer, Phys. Lett. B 37, 229 (1971). 28. P. M¨ oller et al., At. Data Nucl. Data Tables 66, 131 (1997). 29. M. Sawicka et al., Eur. Phys. J. A 22, 455 (2004). 30. C. Mazzocchi et al., in Conference on Nuclei at the Limits, Argonne, IL, 26–30 July 2004, edited by D. Seweryniak, T.L. Khoo, AIP Conf. Proc. 764, 164 (2005). 31. I. Matea et al., Phys. Rev. Lett. 93, 142503 (2004).

Eur. Phys. J. A 25, s01, 93–94 (2005) DOI: 10.1140/epjad/i2005-06-212-0

EPJ A direct electronic only

Beta-delayed γ and neutron emission near the double shell closure at 78Ni C. Mazzocchi1,a , R. Grzywacz1,2 , J.C. Batchelder3 , C.R. Bingham1,2 , D. Fong4 , J.H. Hamilton4 , J.K. Hwang4 , olas4,5,b , S.N. Liddick7 , A.C. Morton7,c , P.F. Mantica7 , W.F. Mueller7 , K.P. Rykaczewski2 , M. Karny6 , W. Kr´ 7 M. Steiner , A. Stolz7 , and J.A. Winger8 1 2 3 4 5 6 7 8

Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Oak Ridge Associated Universities, Oak Ridge, TN 37831, USA Department of Physics, Vanderbilt University, Nashville, TN 37235, USA Joint Institute for Heavy Ion Research, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Institute of Experimental Physics, Warsaw University, Warsaw, PL-00681, Poland National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Department of Physics, Mississippi State University, Mississippi State, MS 39762, USA Received: 7 December 2004 / Revised version: 28 March 2005 / c Societ` Published online: 10 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. An experiment was performed at the National Superconducting Cyclotron Laboratory at Michigan State University to investigate β decay of very neutron-rich cobalt isotopes. Beta-delayed neutron emission from 71–74 Co has been observed for the first time. Preliminary results are reported. PACS. 23.60.+e α decay – 27.50.+e 59 ≤ A ≤ 89

Nuclear structure in the vicinity of the double shell closure at Z = 28, N = 50 has garnered increasing interest in recent years [1, 2,3, 4, 5,6,7]. The large neutron excess in this region is expected to affect the nucleon-nucleon interaction and lead to new phenomena as changes to the traditional shell gaps and magic numbers [8]. These nuclei are relevant to nuclear astrophysics as they are believed to take part in nucleosynthesis near the origin of the rprocess [9]. Beta-delayed neutron (βn) emission close to 78 Ni is of particular interest as its investigation can reveal information on the Gamow-Teller β-strength distribution and on decay branching ratios. These observables are astrophysically-important, serving as input parameters to r-process network calculations. Several experimental studies have been performed for nuclei approaching 78 Ni [2, 3, 4,5, 6] and a new theoretical description was recently developed [7]. In the present contribution we report on preliminary results from the investigation of the decay of neutron-rich Co isotopes. The experiment was performed at the National Superconducting Cyclotron Laboratory at Michigan State University. The nuclides studied were produced by fragmena

Conference presenter; e-mail: [email protected] Present address: Institute of Nuclear Physics, Krakow, PL31342, Poland. c Present address: TRIUMF, Vancouver B.C., V6T 2A3, Canada. b

tation of a 140 A · MeV 86 Kr beam in a 9 Be target, separated using the A1900 spectrometer [10] and implanted into a 1.5 mm thick double-sided silicon strip detector (DSSD) positioned within a silicon detector telescope [11]. Ion implants and their subsequent β decays were observed in this detector and correlated in software. Time correlations were allowed between the implanted ion and electrons detected in the pixel itself or in any neighboring pixel. The detection correlation efficiency was ∼ 30%. The correlation time was selected to be ∼ 4–5 times the decay half-life. The implantation detector was surrounded by 12 detectors from the MSU Segmented Germanium Array (SeGA) [12] to enable observation of both implantand decay-coincident γ-rays. The total photopeak detection efficiency of the SeGA was 4.6% at 1.3 MeV. Two different ion-optics settings of the A1900 spectrometer, optimized for transmission of 72 Co and 74 Co were used during the measurement in order to maximize the rate at the counting station for the fragments of interest. An analysis of β-delayed γ-rays (βγ) from decay events correlated with 71–74 Co implantation events has confirmed the decay half-lives of 71–74 Co and the known transitions in 71–73 Ni [13] and provided the first spectroscopic information on 74 Ni [14]. The first evidence for β-delayed neutron emission from very neutron-rich cobalt isotopes has also been obtained. The correlated βγ spectra show not only transitions previously assigned to the β-decay daughter, but also transitions within the βn daughter.

94

The European Physical Journal A 775(1) keV

Table 1. Compilation of Q-values for β decay (Qβ ) and βn decay (Qβn ) from systematics [15] and mass predictions [16] for 71–74 Co. Predicted branching ratios for βn emission (bβn ) [16] are also given in comparison with the preliminary lower limits from this measurement. The number of collected ions and measuring time are also reported for each isotope.

71

Co

Counts / 2 keV

1259(1) keV (βn)

239(2) keV (βn)

74

Co

Nucleus Ions (hours) 71

Energy (keV)

Fig. 1. Background-subtracted β-coincident γ-ray spectra of Co decay between 700 and 1300 keV (upper panel) and of 74 Co decay between 100 and 500 keV (lower panel) showing the evidence for βn emission. 71

71

Co

β

12

59

ke

V

n

Sn

4120

70

Ni

Co 46675 (27) 72 Co 11733 (27) 73 Co 3442 (68) 74 Co 482 (68)

Qβ (MeV)

Qβn (MeV)

bβn (%)

11.33(92) 7.21(91) – 10.82 6.89 2.61 14.64(74) 7.83(70) – 13.98 7.04 4.80 12.83(76) 8.83(82) – 12.26 8.29 4.82 16.12(90) 9.54(86) – 15.50 9.01 6.90

Ref. bβn (exp) (%)

[15] [16] [15] [16] [15] [16] [15] [16]

≥ 3(1) ≥ 6(2) ≥ 9(4) ≥ 26(9)

the β- and in the βn-delayed γ-ray peaks, corrected for efficiency and intensity, preliminary lower limits for the βn branching ratios have been determined, see table 1. Evidence for ground-state feeding of the βn daughter was also obtained from the observation of granddaughter activity, the data are currently being evaluated. In summary, we have investigated the β decay of 71–74 Co. Beta-delayed γ-rays were observed and the halflives measured, confirming previously reported results from the decay of 71–73 Co [13] with improved statistics and providing the first spectroscopic information on 74 Co [14]. Moreover, the first evidence for βn from these nuclei was obtained. Further analysis of the data is in progress. This work was supported in part by the NSF Grant PHY-01-10253 (MSU) and by the DOE Grants DE-FG0296ER40983 (UT), DE-ACO5-00OR22725(ORNL) and DEFG05-88ER40407 (Vanderbilt).

71

Ni

Fig. 2. Schematic representation of the decay mechanism studied in this work for the case of 71 Co. Observed decay channels are shown as solid lines, while βn emission to the ground state, unobserved in this measurement, is shown as a dashed line. The neutron separation energy (Sn ) in 71 Ni is also marked as a dashed line and its value ([15]) is expressed in keV.

A 1259 keV line from the (2+ ) → 0+ transition in 70 Ni [2] is clearly identified in the 71 Co decay spectrum, while a 239 keV transition in 73 Ni [13] is observed in the decay spectrum of 74 Co (fig. 1). Similarly, a 566 keV γ line from a low-lying transition in 71 Ni [13] and a 1096 keV line from the (2+ ) → 0+ decay in 72 Ni [3] are identified in the decay spectra of 72 Co and 73 Co, respectively. These γ-rays are hallmarks of the βn decay mechanism, which is shown for the case of 71 Co in fig. 2. Beta-delayed neutron emission is expected on the basis of the large Q-values —several MeV in each case— from mass systematics [15] and theoretical predictions [16]. From the number of counts observed in

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

H. Grawe, Nucl. Phys. A 704, 211c (2002). R. Grzywacz et al., Phys. Rev. Lett. 81, 766 (1998). M. Sawicka et al., Phys. Rev. C 68, 044304 (2003). W.F. Mueller et al., Phys. Rev. C 61, 054308 (2000). S. Franchoo et al., Phys. Rev. Lett. 81, 3100 (1998). J. Van Roosbroeck et al., Phys. Rev. C 69, 034313 (2004). A.F. Lisetskiy et al., Phys. Rev. C 70, 044314 (2004). T. Otsuka et al., Eur. Phys. J. A 13, 69 (2002). K.L. Kratz et al., Hyperfine Interact. 129, 185 (2000). D. Morrissey et al., Nucl. Instrum. Methods Phys. Res. B 204, 90 (2003). J.I. Prisciandaro et al., Nucl. Instrum. Methods Phys. Res. A 505, 90 (2003). W.F. Mueller et al., Nucl. Instrum. Methods Phys. Res. A 466, 492 (2001). M. Sawicka et al., Eur. Phys. J. A 22, 455 (2004). R. Grzywacz, these proceedings. G. Audi et al., Nucl. Phys. A 729, 1 (2003). P. M¨ oller et al., At. Data Nucl. Data Tables 66, 131 (1997).

Eur. Phys. J. A 25, s01, 95–96 (2005) DOI: 10.1140/epjad/i2005-06-158-1

EPJ A direct electronic only

Exotic nuclei near

78

Ni in a shell model approach

A.F. Lisetskiy1,a , B.A. Brown1 , and M. Horoi2 1 2

National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 USA Physics Department, Central Michigan University, Mount Pleasant, MI 48859 USA Received: 11 November 2004 / c Societ` Published online: 14 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The shell model predictions for even 68−76 Ni isotopes and odd-A Cu isotopes with newly derived effective interaction for the f5/2 p3/2 p1/2 g9/2 model space are presented. PACS. 21.30.Fe Forces in hadronic systems and effective interactions – 21.60.Cs Shell model .

The region close to 78 28 Ni50 nucleus is an example of the exotic part of the nuclide chart that attracts growing interest [1, 2,3, 4]. The main issue is the doubly magic nature of the 78 28 Ni50 nucleus and properties of the effective nucleonnucleon interaction at high isospins. Since the most important shell-model orbitals (namely p3/2 , f5/2 , p1/2 and g9/2 ) for valence neutrons in nuclei with Z = 28 and N = 28–50 (56 Ni-78 Ni) are the same as those for valence protons in nuclei with N = 50 and Z = 28–50 (78 Ni-100 Sn), the study and comparison of these two groups of nuclei helps to learn about the properties of the T = 1 part of the effective interaction at extreme values of isospin (T = 11 for 78 Ni, for example). Studies of the evolution of the single-particle orbitals with an increase of isospin contributes to the understanding of the properties of spin-orbital interaction, monopole terms of residual interaction and their interplay. Experimental investigations of neutron-rich nuclei have greatly advanced the last decade providing access to many new regions of the nuclear chart. This indicates the growing need for theoretical interpretations in the framework of shell-model, for example, which, however, is lacking in well determined effective interactions for exotic regions. Recently we have reported on the T = 1 part of the effective interaction for the above mentioned pf5/2 g9/2 model space [5]. It was derived from a fit to experimental data for Ni isotopes from A = 57 to A = 78 and N = 50 isotones from 79 Cu to 100 Sn for neutrons and protons, respectively. The starting point for the fitting procedure was a realistic G-matrix interaction based on the Bonn-C N N potential together with core-polarization corrections based on a 56 Ni core. The properties of neutron-rich nickel isotopes between 68 Ni and 78 Ni are of our particular interest. It is useful to look at the structure of these nuclei and compare them to a

Conference presenter; e-mail: [email protected]

.

. – p.12/16

+ + + Fig. 1. Calcualted B(E2; 2+ 1 → 01 ) and B(E2; 41 → 21 ) values for Z = 28 isotopes with A = 70–76 (upper part) and N = 50 isotones with A = 92–98 (lower part).

A = 90–98 N = 50 isotones taking into account that the shell model calculations are performed in the same configurational space. Our calculations show that the nuclear n structure is dominated by the (pf5/2 )12 0+ (g9/2 )J configurations (n = 2–8 for A running from 70 [92] to 76 [98] for neutrons [protons]) in both cases. However, the effective two-body interaction for the g9/2 orbital in a vicinity of 78 Ni is very different from that in a region close to 100 Sn. The neutron interaction is stronger in J π = 2+ and J π = 4+ channels that drastically changes some of the nuclear structure features for Ni-isotopes as compared to corresponding N = 50 valence mirror symmetry partners. First, the seniority s = 4 J π = 6+ state is pushed below the 8+ state with s = 2 reducing the lifetime of the latter by three orders of magnitude in 72,74 Ni as compared to 94 Ru and 96 Pd, respectively [6]. Second the 4+ s=4 state

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.

(MeV)

Theory Expt.

. – p.9/15

Fig. 2. Calculated and experimental excitation energies of the lowest states with J π = 3/2− , 5/2− for A-odd Cu isotopes. Experimental points are connected by the solid line and theoretical by the dashed one.

appears as the lowest 4+ state in 72,74 Ni that is in contrast to 94 Ru and 96 Pd where the lowest 4+ state has s = 2. This changes the character of the E2 strength systematic + resulting in enhanced B(E2; 4+ 1 → 21 ) values near the 72,74 Ni) while reduction is appromiddle of the g9/2 shell ( priate for the 94 Ru and 96 Pd. This difference is illustrated by fig. 1. This difference indicates a transition from the seniority scheme with strong pairing appropriate for the N = 50 isotones to a vibrational-like collective picture in the single g9/2 orbital for neutron-rich nickel isotopes [7]. Experimental confirmation of such changes is of great interest for the understanding of the doubly-magic nature of the 78 Ni nucleus [8]. Proceeding towards the proton-neutron part of the effective interaction we have analyzed the odd-mass Cu isotopes. Since Cu isotopes have one proton above the assumed 56 Ni core their spectra is influenced only by the neutron-neutron and the proton-neutron parts of the interaction. Furthermore the odd-A Cu isotopes are sensitive only to the monopole part of the proton-neutron interaction. Therefore fitting odd-A Cu isotopes one can determine the proton-neutron monopole part of the effective interaction. To do this we have taken the T = 1 proton-neutron monopole part to be identical to the neutron-neutron one. Than the T = 0 monopole part of the original G-matrix was modified to fit known experimental energies of the odd-A Cu isotopes and to link proton single-particle energies determined in the vicinity of 56 Ni with the ones in 79 Cu predicted with the new effective interaction

for N = 50 isotones. Combining the monopole corrected T = 0 part of G-matrix and the T = 1 part of the newly fitted interaction we have made calculations for the unknown states in neutron-rich Cu isotopes with A = 71–77. Our calculations predict a near degeneracy of the J π = 3/2− and J π = 5/2− states in 73 Cu that is illustrated in fig. 2. The situation is more certain for the A = 75, 77 and 79 where the excited 3/2− state is predicted to be well above the ground 5/2− state. This is supported by recent preliminarily data for the magnetic moment of the ground state of 75 Cu [9] which is in good agreement with the calculated one for the J π = 5/2− state. The NSF support of this research, Grant No. PHY-0244453, is greatly appreciated.

References 1. 2. 3. 4. 5. 6. 7. 8. 9.

R. Grzywacz et al., Phys. Rev. Lett. 81, 766 (1998). O. Sorlin et al., Phys. Rev. Lett. 88, 092501 (2002). M. Sawicka et al., Phys. Rev. C 68, 044304 (2003). J. Van Roosbroeck et al., Phys. Rev. Lett. 92, 112501 (2004). A.F. Lisetskiy, B.A. Brown, M. Horoi, H. Grawe, Phys. Rev. C 70, 044314 (2004). A.F. Lisetskiy, B.A. Brown, M. Horoi, H. Grawe, AIP Conf. Proc. 726, 231 (2004). A. Volya, Phys. Rev. C 65, 044311 (2002). J.J. Ressler et al., Phys. Rev. C 69, 034317 (2004). L. Weissman, U. K¨ oster, private communication.

Eur. Phys. J. A 25, s01, 97–98 (2005) DOI: 10.1140/epjad/i2005-06-049-5

EPJ A direct electronic only

Beta decays of 8He, 9Li, and 9C D.J. Millenera Brookhaven National Laboratory, Upton, NY 11973, USA Received: 23 October 2004 / c Societ` Published online: 3 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The beta decays of 8 He, 9 Li, and 9 C are interpreted in terms of shell-model calculations in a p-shell basis. Particular attention is paid to the observed low-energy decays that exhibit large B(GT) values. PACS. 23.40.-s β decay; double β decay; electron and muon capture – 21.60.Cs Shell model – 27.20.+n 6 ≤ A ≤ 19

1 Introduction Supermultiplet symmetry is essentially conserved by the central part of the p-shell Hamiltonian and is broken mainly by the spin-orbit interaction. Apart from terms involving n and n2 the SU4 invariant terms of a typical interaction look like [1]  Pij + 0.59L2 − 1.08S 2 + 0.59T 2 . H ∼ −3.91 ij

Thus the central interaction favors low T and high S for states with the same spatial symmetry [f ]. This opens up the possibility of low-energy Gamow-Teller (GT) transitions with large Gamow-Teller matrix elements (no change in spatial quantum numbers).

2 8 He decay The situation for 8 He(β − )8 Li is shown in fig. 1. From table 1, the first three states have mainly [31] symmetry — the mixture of 1 P , 3 P , and 3 D varies considerably for different interactions— and owe their GT strength to small admixtures of [22] symmetry. On the other hand, the large B(GT) value, defined by f t . B(GT) = 6144.4 s, for the 1+ 4 state is due to the match of spatial quantum numbers with the 8 He ground state and does not vary much in different calculations. The 1+ 4 state takes a large fraction of eff 2 eff the Ikeda sum rule 12(gA ) ∼ 14, where gA ∼ 1.07 [2]. The ∼ 9.3 MeV state can decay by neutron emission (Sn = 2.03 MeV) and triton emission (St = 5.39 MeV), mainly through the [31] component. The shell-model spectroscopic factors lead to comparable neutron and triton widths and a total width of ∼ 1 MeV. Details are given in table 2. Existing fits [3, 4,5] give Ex ∼ 9.0 → 9.7 MeV a

Conference presenter. e-mail: [email protected]

Fig. 1. Level spectrum showing the four 1+ levels of reached in the β − decay of 8 He. Energies are in MeV.

8

Li

Table 1. Symmetry content and B(GT) values for the 1+ final states of 8 Li (see fig. 1) in the β − decay of 8 He. The 8 He initial state is 74% [22] symmetry with L = 0 and S = 0 (26% [211] symmetry with L = 1 and S = 1). The 84(1)% branch to 1+ 1 combined with t1/2 = 119.0(15) ms gives B(GT) = 0.391(7).

Jnπ

% [31]

% [22]

B(GT)

1+ 1 1+ 2 1+ 3 1+ 4

93.6 91.0 92.2 10.6

2.3 8.3 2.8 71.5

0.32 0.71 0.37 11.7

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The European Physical Journal A

Table 2. Calculated triton and neutron widths for the 1+ 4 state of 8 Li. The S values are the shell-model spectroscopic factors. The widths are estimated by matching R-matrix observed widths to single-particle widths from Woods-Saxon wells [1] and include integration over two-level R-matrix profile functions [6] for the broad 5 He final states.

Decay

S

Γ (keV)

5 − 1+ 4 → He(3/2 ) t 5 − → He(1/2 ) n → 7 Li(3/2− ) n → 7 Li(1/2− )

0.030 0.066 0.041 0.018

254 253 316 129

t

and B(GT) = 5 → 8 for the 1+ 4 level but include only the ground-state triton channel and sometimes omit neutron channels [3]; see also [5]. Triton emission to the 1/2− state of 5 He needs to be included in a new many-level, manychannel R-matrix analysis along the lines of ref. [4] but including averaging over the profiles of the 5 He states.

3 9 Li and 9 C decay A comparison of these mirror decays, based on analyses of experimental data, is shown in table 3. The initial states have mainly [32] symmetry with L = 1 and S = 1/2 (78%). Therefore, large B(GT)’s can occur for final states with [32] symmetry and L = 1 with S = 1/2 or S = 3/2, giving rise to five possible final states in the limit of good supermultiplet symmetry. The properties of the five corresponding shell-model states are given in table 4. It should be noted that all final states except for the 9 Be ground state decay into the α + α + N channel, in many cases by nucleon emission through the broad firstexcited state of 8 Be or via α emission through the unbound states of 5 He or 5 Li (or perhaps by three-body breakup) making for a difficult analysis. The mirror transitions to low-lying states with dominant [41] symmetry have small B(GT) values and are in quite good agreement. However, there is a large asymmetry for decays to 5/2− levels near Ex = 12 MeV. This is unexpected for states with large B(GT) values. The B(GT) value for the decay of 9 C to the 12.19 MeV state of 9 B is consistent with the theoretical prediction in table 4. Suspicion falls on the very large B(GT) value for the 11.81 MeV state of 9 Li because, in the limit of good supermultiplet symmetry, the 5/2− state eff 2 ) ∼ 10.4. takes only 1/3 of the Ikeda sum rule = 9(gA The previously known [32] symmetry states with T = − 1/2 are the 7/2− 2 and 5/24 states, both with dominant L = 2, S = 3/2 components. These states are strongly populated in pickup and knockout reactions on 10 B. The observed energies [7] are 11.81 and 14.48 MeV in 9 Be and 11.65 and 14.7 MeV in 9 B. The energies are well reproduced by the shell-model calculation. Table 4 show the 1/2− , 3/2− , and 5/2− states that are predicted to have large B(GT) values. As already noted, the energy and B(GT) value for the 5/2− 3 state can account for the properies of the 12.19 MeV level observed in 9 C(β + ). However, an explanation of the 9.0(10)% p0 decay branch via

Table 3. Experimental data on the decays of 9 C and 9 Li [7]. The data for 9 C(β + ) are from [8] after normalization to the ground-state branch of 54.1(15)% from [9]; also B(GT) = 1.92(24) for the 12.19 MeV level [9]. For 9 Li(β − ) decay see [2, 10]; also B(GT) = 8.5(1.5) for the 11.81 MeV level [11].

Jπ

9 B Ex

3/2− 1 5/2− 1 1/2− 1

0 2.36 2.75

0.0295(8) 0.053(12) 0.013(2)

5/2− 3

12.19 14.0 14.65

2.16(22) 0.36(5) ∼0

3/2− ; 3/2

9

C(β + ) B(GT)

Li(β − ) B(GT)

9

9

Be Ex

0 2.43 2.78 11.28 11.81

0.0292(9) 0.046(5) 0.011(5) 1.4(5) 8.9(1.9)

14.39

Table 4. Results from a typical shell-model calculation. The first line gives the total [32] symmetry content for each shellmodel eigenstate. The second line gives the dominant component, all with L = 1. The energies are given relative the 7/2− 2 state (83.4% [32] L = 2 S = 3/2) at 11.65 MeV in 9 B (see eff text). The B(GT)’s are given for gA = 1.

%[32] %(S) Ex (9 B) B(GT)

1/2− 2

3/2− 3

5/2− 3

1/2− 3

3/2− 4

89.8 87(3/2) 10.61 0.29

97.2 86(3/2) 10.67 1.45

88.1 84(3/2) 12.10 2.46

89.5 83(1/2) 14.07 1.53

89.2 54(1/2) 14.48 1.22

f -wave emission lies beyond the scope of a p-shell calculation. Beta-decay strength is also predicted to a number of 1/2− and 3/2− states. If these states mainly decay by α emission, as suggested by the calculation, their effect on the measured alpha spectra may be difficult to see. A multi-level, multi-channel R-matrix analysis of the the β-delayed particle decay of 9 C has been attempted [12]. An analysis that makes use of shell-model input, preferably from an extended basis (at least (0+2)ω) shell-model calculation, would seem to be indicated. This work is supported by the US Department of Energy under Contract No. DE-AC02-98CH10886.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

D.J. Millener, Nucl. Phys. A 693, 394 (2001). W.-T. Chou et al., Phys. Rev. C 47, 163 (1993). M.J.G. Borge et al., Nucl. Phys. A 560, 664 (1993). F.C. Barker, E.K. Warburton, Nucl. Phys. A 487, 269 (1988). F.C. Barker, Nucl. Phys. A 609, 38 (1996). C.L. Woods et al., Aust. J. Phys. 41, 525 (1988). D.R. Tilley et al., Nucl. Phys. A 745, 155 (2004). E. Gete et al., Phys. Rev. C 61, 064310 (2000). U.C. Bergmann et al., Nucl. Phys. A 692, 247 (2001). G. Nyman et al., Nucl. Phys. A 510, 189 (1990). Y. Prezado et al., Phys. Lett. B 576, 55 (2003). L. Buchmann et al., Phys. Rev. C 63, 034303 (2001).

Eur. Phys. J. A 25, s01, 99 (2005) DOI: 10.1140/epjad/i2005-06-200-4

EPJ A direct electronic only

Halo neutrons and the β-decay of

11

Li

F. Sarazin1 2 a , J.S. Al-Khalili2 3 , G.C. Ball2 , G. Hackman2 , P.M. Walker2 3 , R.A.E. Austin4 b , B. Eshpeter2 , P. Finlay5 , P.E. Garrett6 c , G.F. Grinyer5 , K.A. Koopmans4 , W.D. Kulp7 , J.R. Leslie8 , D. Melconian9 , C.J. Osborne2 d , M.A. Schumaker5 , H.C. Scraggs2 e , J. Schwarzenberg10 , M.B. Smith2 , C.E. Svensson5 , J.C. Waddington4 , and J.L. Wood7 1 2 3 4 5 6 7 8 9 10

Departement of Physics, Colorado School of Mines, Golden, CO 80401, USA TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, V6T 2A3 Canada Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, L8S 4K1 Canada Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1 Canada Lawrence Livermore National Laboratory, Livermore, CA 94551, USA School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA Department of Physics, Queen’s University, Kingston, Ontario, K7L 3N6 Canada Department of Physics, Simon Fraser University, Burnaby, Bristish Columbia, V5A 1S6 Canada Department of Nuclear Physics, University of Vienna, Waehringerstrasse 17, Vienna, 1090 Austria Received: 12 September 2004 c Societ`  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The β-decay of 11 Li has been studied at ISAC/TRIUMF using the 8pi spectrometer, an array of 20 Compton-suppressed high-purity germanium detectors. Most of the 11 Li β-decay strength is observed to proceed through unbound states in 11 Be, which subsequently decay by one-neutron emission to 10 Be. This results in the observation of a γ-spectrum dominated by the decay of the excited states in 10 Be. These transitions exhibit characteristic Doppler broadened lineshapes, due to the the recoiling effect induced by the neutron emission. A Monte-Carlo simulation was developed to analyze the complex shape of these γ-lines. Both the half-lives of states in 10 Be and the energies of the β-delayed neutrons feeding those states were obtained. It was also possible to determine the excitation energies of the parent states in 11 Be. The present contribution was the subject of a publication in a scientific journal (F. Sarazin et al., Phys. Rev. C 70, 031302(R) (2004)) shortly before the conference. It was judged not appropriate to submit for peerreviewing a contribution with nearly the same content. The reader is therefore invited to read the original publication. PACS. 23.20.-g Electromagnetic transitions – 23.40.-s β decay; double β decay; electron and muon capture – 27.20.+n 6 ≤ A ≤ 19

a

e-mail: [email protected] Present address: Department of Physics and Astronomy, Saint Mary’s University, Halifax NS, B3H 3C3 Canada. c Present address: Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1 Canada. d Present address: Max Planck Institut fur Kernphysik, Heidelberg, 69117 Germany. e Present address: Department of Physics, University of Liverpool, Liverpool, L69 7ZE, UK. b

Eur. Phys. J. A 25, s01, 101–103 (2005) DOI: 10.1140/epjad/i2005-06-124-y

EPJ A direct electronic only

Voyage to the “Island of Inversion”:

29

Na

V. Tripathi1,a , S.L. Tabor1 , P.F. Mantica2,3 , C.R. Hoffman1 , M. Wiedeking1 , A.D. Davies2,4 , S.N. Liddick2,3 , W.F. Mueller2 , A. Stolz2 , B.E. Tomlin2,3 , and A. Volya1 1 2 3 4

Department of Physics, Florida State University, Tallahassee, FL 32306, USA National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Department of Chemistry, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA Received: 4 October 2004 / Revised version: 25 March 2005 / c Societ` Published online: 29 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The low energy level structure of neutron-rich 28,29 Na has been investigated through β-delayed γ spectroscopy. The present work, which presents the first detailed spectroscopy of 29 Na, clearly demonstrates that for Na isotopes between 28 Na (N = 17) and 29 Na (N = 18), intruder configurations start dominating the low lying excited states, suggestive of the small N = 20 shell gap. PACS. 23.40.-s β decay; double β decay; electron and muon capture – 23.20.Lv γ transitions and level energies – 21.60.Cs shell model

1 Introduction Nuclei with N = 20 for Z = 10 − 12 are characterized by anomalously large binding energies [1] and low-lying first excited states with large B(E2) transition probabilities to the ground state, e.g., in 32 Mg [2]. The cause for this behavior, or “inversion” [3], has been attributed to the effects of intruder neutron configurations involving the f p shell in the ground state of these nuclei. Recently, large scale Monte Carlo Shell Model (MCSM) calculations by Otsuka et al., [4] showed that the dominance of intruder configurations is related to the varying gap between the d3/2 and f7/2 orbitals, which can be explained by the shell evolution mechanism of ref. [5] in terms of the spin-isospin property of the effective nucleon-nucleon (N N ) interaction. According to these calculations, the N = 20 shell gap should be narrower in neutron-rich nuclei than that in stable nuclei and will be reflected in the ground state properties as well as those of excited states for nuclei having N near 20. For the Na isotopes, the comparison of the experimental masses to the shell model results within the sd shell [6] suggests that the onset of intruder dominance of the ground state occurs sharply at N = 20, consistent with the “island of inversion” picture. However, the electric and magnetic moments of the N = 19, 20 Na isotopes cannot be reproduced by the USD model at all, whereas for 29 Na (N = 18), a ∼ 42% mixing of intruder configurations in the ground state of 29 Na [7] is a

Conference presenter; e-mail: [email protected]

required to reproduce the experimental value. The spectrum of excited states provides another way to probe the mixing between normal and intruder configurations which is related to the shell gap. In the present work, we performed detailed β-delayed γ-spectroscopy measurements of 28,29 Na (N = 17, 18) to investigate the transition from normal-dominant to intruder-dominant states in the chain of neutron-rich Na isotopes.

2 Experimental details The nuclei, 28,29 Ne, were produced by the fragmentation of a 140 MeV/nucleon 48 Ca20+ beam in a 733 mg/cm2 Be target located at the object position of A1900 at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University. The fragments were implanted in a double-sided Si microstrip detector (DSSD), which is part of the NSCL β counting system (BCS) [8]. Fragments were identified by a combination of multiple energy loss signals and time of flight. Fragment-β correlations were established in software. The β-delayed γ rays were detected using 12 detectors of the SEgmented Germanium Array (SEGA) [9] arranged around the BCS. The Ge detectors were energy and efficiency calibrated using standard calibrated sources. Details of the experiment and analysis are discussed elsewhere [10].

102

The European Physical Journal A

Fig. 1. β-delayed γ-ray spectra for events coming within the first 100 ms after a 29 Ne implant. The insert shows the β-γ-γ coincidence between the 72 keV and 1516 keV transitions.

3 Results and discussion The energy spectrum of β-delayed γ rays emitted within 100 ms (∼ 5 half lives) of a valid 29 Ne implant is shown in fig. 1, where transitions associated with the β-decay of 29 Ne are identified. Decay curves generated in coincidence with these γ lines yielded half lives consistent with each other, justifying their placement in the level scheme of 29 Na, which is shown in fig. 2. The observation of pairs of lines, 1177 keV (5% ± 1%)-1249 keV (12% ± 1%) and 1516 keV (16% ± 2%)-1588 keV (11% ± 2%) differing by 72 keV and the observation of the 72 keV (54%±9%) transition itself, confirmed the first three excited states. Also coincidences were observed between the 72 keV and the 1516 keV transition (insert in fig. 1). The other strong γrays, 2578 keV (5% ± 1%) and 2917 keV (3.5% ± 0.5%) depopulate the 4166 keV level. The β-decay branching and the log f t values for the observed levels are shown in fig. 2. As the Q-value and the half life are known with good accuracy, the error in the branching is the main source of uncertainty in the log f t values. The comparison of the level scheme for 29 Na established in the current study with shell model calculations using the USD interaction [6] clearly shows marked discrepancies (fig. 2). The measured ground state spin of 29 Na is 3/2+ [11] instead of 5/2+ and the large β branch to the 72 keV level makes it a likely candidate for the 5/2+ state. This implies that the order of the predicted ground state doublet is reversed. The predicted β-decay branch (∼ 20%) [12] to the ground state is not observed experimentally. The experimental levels at 1249 keV and 1588 keV have large β-decay branches, implying spin assignments of 1/2+ to 5/2+ (J π of 29 Ne ground state is calculated to be 3/2+ ). However the USD calculation predicts only one state in this spin range below 2.8 MeV with a weak β-decay branch. This is an indication of the failure of the USD shell model to explain the β-decay of 29 Ne. The MCSM calculations using SDPF-M interaction [7], which allow for excitations across the shell gap and mixing between the normal and intruder configurations, predict 3

Fig. 2. Proposed level scheme for 29 Na. The absolute β-decay branching to each level per 100 decay is indicated along with the calculated log f t values. The neutron decay branches as well as the half life were taken from the present study. Also shown are USD shell model calculation and Monte-Carlo Shell Model (MCSM) calculations with SDPF-M interaction.

states within this spin range below 2.5 MeV. The 3/2+ 2, states which have dominant 2p-2h intruder configu5/2+ 2 ration are good candidates for the 1249 keV and 1588 keV experimental levels. The better agreement between the experimental results and the MCSM calculations for 29 Na suggests that 2p-2h excitations play an important role in the low-energy level structure of N = 18 isotope. Contrary to this, the level scheme for 28 Na [10] shows good agreement with USD calculations, suggesting that 28 Na can be described rather well with pure sd shell configurations without invoking interference of intruder configurations. Thus the transition from normal to intruder domination for the Na isotopes happens between N = 17 and N = 18 as reflected in the low-energy excitations. This work was supported by the National Science Foundation Grants PHY-01-39950 (FSU) and PHY-01-10253 (MSU). The authors acknowledge the efforts of the NSCL operations staff in the smooth conduct of the experiment.

References 1. C. Thibault et al., Phys. Rev. C 12, 644 (1975). 2. T. Motobayashi et al., Phys. Lett. B 346, 9 (1995). 3. E.K. Warburton et al., Phys. Rev. C 41, 1147 (1990).

V. Tripathi et al.: Voyage to the “Island of Inversion”: 4. Y. Utsuno et al., Phys. Rev. C 60, 054315 (1999). 5. T. Otsuka et al., Phys. Rev. Lett. 87, 082502 (2001). 6. B.A. Brown, B.H. Wildenthal, Annu. Rev. Nucl. Part. Sci. 38, 29 (1998). 7. Y. Utsuno et al., Phys. Rev. C 70, 044307 (2004). 8. J.I. Prisciandaro et al., Nucl. Instrum. Methods Phys. Res. A 505, 140 (2003).

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Na

103

9. W.F. Mueller et al., Nucl. Instrum. Methods Phys. Res. A 466, 492 (2003). 10. V. Tripathi et al., Phys. Rev. Lett. 94, 162501 (2005). 11. G. Huber et al., Phys. Rev. C 18, 2342 (1978). 12. B.H. Wildenthal et al., Phys. Rev. C 28, 1343 (1983).

Eur. Phys. J. A 25, s01, 105–109 (2005) DOI: 10.1140/epjad/i2005-06-159-0

EPJ A direct electronic only

New structure information on

30

Mg,

31

Mg and

32

Mg

H. Mach1a , L.M. Fraile2,3 , O. Tengblad4 , R. Boutami4 , C. Jollet5 , W.A. Pl´ociennik6† , D.T. Yordanov7 , M. Stanoiu8 , M.J.G. Borge4 , P.A. Butler2,9 , J. Cederk¨all2,10 , Ph. Dessagne5 , B. Fogelberg1 , H. Fynbo11 , P. Hoff12 , A. Jokinen13 , A. Korgul14 , U. K¨oster2 , W. Kurcewicz14 , F. Marechal5 , T. Motobayashi15 , J. Mrazek16 , G. Neyens7 , T. Nilsson2 , S. Pedersen11 , A. Poves17 , B. Rubio18 , E. Ruchowska6 , and the ISOLDE Collaboration 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Department of Radiation Sciences, Uppsala University, S-61182 Nyk¨ oping, Sweden ISOLDE, Division EP, CERN, CH-1211 Geneva, Switzerland Universidad Complutense, E-28040, Madrid, Spain Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain Institut de Recherches Subatomiques, IN2P3-CNRS, F-67037 Strasbourg, Cedex 2, France ´ The Andrzej Soltan Institute for Nuclear Studies, 05-400 Swierk, Poland K.U. Leuven, IKS, Celestijnenlaan 200 D, 3001 Leuven, Belgium IPN, IN2P3-CNRS and Universit´e Paris-Sud, F-91406 Orsay Cedex, France Oliver Lodge Laboratory, University of Liverpool, Liverpool, L69 3BX, United Kingdom Department of Physics, Lund University, S-22100 Lund, Sweden Institut for Fysik og Astronomi, Aarhus Universitet, DK-8000 Aarhus C, Denmark Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway Department of Physics, P.O. Box 35 (yfl), FIN-40014 University of Jyv¨ askyl¨ a, Finland Institute of Experimental Physics, Warsaw University, Ho˙za 69, PL 00-681 Warsaw, Poland RIKEN, Hirosawa 2-1, Wako, Saitama 351-0198, Japan Nuclear Physics Institute, 25068 Rez, Czech Republic Departamento de F´ısica Te´ orica C-XI, Universidad Aut´ onoma de Madrid, E-28049 Madrid, Spain Instituto de F´ısica Corpuscular, CSIC University of Valencia, E-46071 Valencia, Spain Received: 16 January 2005 / Revised version: 28 March 2005 / c Societ` Published online: 19 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005

In the memory of Weronika Plo ´ciennik deceased on December 25, 2004. She was a young and talented researcher in experimental and theoretical physics. Abstract. The fast timing βγγ(t) method was applied to investigate the level lifetimes in 30,31,32 Mg. Levels in Mg have been populated in β and β-delayed neutron emission of Na at the ISOLDE facility. From the γγ coincidences a number of new states have been identified and new level schemes were constructed for 30,31,32 Mg. The following preliminary half lives have been determined: T1/2 = 3.9(4) ns for the 1789 keV state in 30 Mg, T1/2 = 133(8) ps and 10.5(8) ns for the 221 keV and 461 keV states in 31 Mg, respectively, and T1/2 = 16(4) ps for the 885 keV level in 32 Mg. The 1789 keV level was established as a candidate for the intruder 0+ configuration in 30 Mg with a possible strong E0 branch to the ground state. PACS. 21.10.Tg Lifetimes – 23.20.Lv γ transitions and level energies – 27.30.+t 20 ≤ A ≤ 38

1 Introduction A number of recent experiments using a variety of advanced probes has been focused on the structure of exotic Mg nuclei and nuclei in their close vicinity. This region is called “the island of inversion” [1, 2] where the shell model configurations are strongly rearranged. Despite many exa

Conference presenter; e-mail: [email protected] † Deceased.

perimental attempts on these exotic nuclei there remains a number of issues still to be resolved. A very active research program in the heavy Mg region is carried out at the ISOLDE facility at CERN using complementary techniques. At this conference the results on the Coulomb excitation on 30 Mg have been reported by Scheit et al. [3] and the laser spectroscopy and β-NMR results on 31 Mg were presented by Kowalska et al. [4]. Here we discuss preliminary findings from fast timing measurements using the Advanced Time Delayed βγγ(t) Method [5] on 30,31,32 Mg.

The European Physical Journal A

(11/2-)

693 E2

106

T1/2 1154

(11/2-) 1p1h (5/2+) (5/2+)

E (MeV)

1

(3/2+) (7/2-) 1p1h

(7/2-)

Fig. 1. Schematic representation of the level scheme of 31 Mg. The experimental results obtained by Klotz et al. [2] are shown in the middle, their theoretical interpretation [2] is illustrated on the left hand side, with the configuration assignment on the far right. The current status is shown on the right hand side (Exp-cor) and includes the ground state spin assignment of 1/2+ [4, 6] and a new candidate for 11/2− .

(3/2-)

171 E1

Exp-cor

51 M1

Exp-1993 Klotz et al.

221 E1

Theory A.Poves

(3/2-) 1p1h (3/2+) 2p2h 1/2+ 2p2h 240 E2

0

(3/2+) 1/2+

461

10.5(8) ns

221

133(8) ps

51 0

16(3) ns

31 Mg

The isotopes 30,31,32 Mg are the key nuclei located at the border of “the island of inversion”. In particular, the nuclei of 30 Mg and 31 Mg are expected [1,2] to exhibit coexistence of spherical and intruder configurations, yet it is not clear how to classify the excited states observed at low excitation energy into members of these configurations. Our aim was to obtain new information that would better characterize the excited states in 31 Mg and to search for a candidate for the intruder 0+ state in 30 Mg. Another objective was to verify information on the excited states in 32 Mg populated by the β decay of 32 Na and to measure the half-life of the first excited 2+ state in 32 Mg by the time-delayed method. This state is located at only 885 keV indicating that the ground state in 32 Mg is dominated by the intruder configurations. As discussed in [3], there are discrepancies in the B(E2) values reported for 30 Mg and 32 Mg, thus a direct lifetime measurement would yield an independent B(E2) value for 32 Mg.

2 Experimental setup The time-delayed βγγ(t) experiment, IS 414, was performed at the ISOLDE facility at CERN. The setup [5] included a thin plastic scintillator as a β detector, which provided uniform time response to β rays of different energies, two fast response BaF2 detectors for γ-rays, and two large volume Ge detectors, whose high energy resolution allowed to select γ cascades. The fast response detectors were prepared at the OSIRIS mass separator at Studsvik in Sweden. The levels in 30 Mg and 31 Mg were populated in the β and β-delayed neutron emission of 30 Na and 31 Na, and 31 Na and 32 Na, respectively, while the levels in 32 Mg were populated in the β decay of 32 Na. The neutron-rich Na isotopes were produced by 1.4 GeV proton induced reactions in a UCx graphite target. For 32 Na, the beam gate was opened about 8 ms after the proton pulse and closed about 100 ms later. The source strength of 32 Na was about 50–100 dps. No tape system was used since the activities mostly decayed out before the next proton pulse

Fig. 2. A partial level scheme of 31 Mg and preliminary level lifetimes established in this work, except for the 51 keV level, which is taken from [2]. The suggested spin/parity assignments for the excited levels and transition multipolarities are model dependent [2] although supported by the observed transition rates.

arrived after 2.4 s on the average. The Na ions were deposited onto an aluminum foil in front of the β detector. Other detectors were placed in a close geometry. The data were collected mainly as triple coincidences involving βGe-Ge, which allowed to construct the decay scheme, and β-Ge-BaF2 coincidences for lifetime measurements.

3 Results for

31

Mg

Figure 1 on the right hand side (Exp-cor), shows the current status of the interpretation of the levels in 31 Mg. It includes a new possible location of the 1p1h 11/2− state coming from our coincidence data, and the new 1/2+ 2p2h configuration of the ground state established in refs. [4,6]. The aim of the study was to verify the expected long lifetime (of the order of 11 ns) for the 461 keV level, which was suggested [2] to be 7/2− de-excited by a collective E2 transition, and a short one (of the order of 50 ps) for the 221 keV state expected to be 3/2− and depopulated by E1 transitions. The 461 and 1154 keV levels are populated in the β-delayed neutron emission of 32 Mg, while the other states are populated in the β decay of 31 Na. The new results are illustrated in figs. 2-4. If the model interpretation of levels in 31 Mg shown in fig. 1 is correct then, the 461 keV state is the 1p1h intruder and the 240 keV γ-ray is the collective E2 7/2− → 3/2− transition. Indeed, its B(E2) = 67(6) e2 fm4 compares very closely to the value for the 2p2h intruder state in 32 Mg of B(E2; 2+ → 0+ ) = 67(14) e2 fm4 taken from ref. [7] (other B(E2) values measured for 32 Mg are even higher, see [3]). On the other hand, if it is a spherical configuration then it would follow more closely the B(E2) value

30

H. Mach et al.: New structure information on

Mg,

31

Mg and

32

Mg

107

2

10

T1/2 = 133(8) ps

10

10

T1/2 = 3.9(4) ns

Counts

Counts

10

2

1

1

10

0

0

10

-700

0

700

1400

2100

0

2800

5

10

15

20

25

30

35

40

Time (ns)

Time (ps)

Fig. 3. Time-delayed βγ(t) spectrum due to the lifetime of the 221 keV state in 31 Mg measured in the β decay of 31 Na. It was gated in Ge on transitions feeding the 221 keV state from above and by the 221 and 171 keV transitions recorded in the BaF2 detector. The lifetime value was determined from slope fitting. A Gaussian curve at T = 0 shows the prompt time response used in the fitting.

Fig. 5. Time-delayed βγ(t) spectrum due to the lifetime of the 1789 keV state in 30 Mg measured in the β-delayed neutron decay of 31 Mg. It was gated by the 306 keV γ-ray in Ge and by the 1482 keV transition recorded in BaF2 . The lifetime value was measured from slope fitting.

40

2

Counts

10

Counts

T1/2 = 10.5(8) ns

20

1

10

0 1400

1500

1600

1700

1800

1900

Energy (keV) 0

7000

14000

21000

28000

35000

42000

Time (ps)

Fig. 4. Time-delayed βγ(t) spectrum due to the lifetime of the 461 keV state in 31 Mg; measured in the β-delayed neutron decay of 32 Mg. It was gated on the 240, 221 and 171 keV transitions recorded in the BaF2 detector. The lifetime value was determined from slope fitting.

for the “core” nucleus of 30 Mg, for which the B(E2; 2+ → 0+ ) ∼ 40 e2 fm4 was measured by Scheit et al. [3]. According to the interpretation given in ref. [2] (and corrected for the ground state spin/parity of 1/2+ ) the 171 and 221 keV transitions are E1, with the predicted reduced transition rate of B(E1; 3/2− → 3/2+ ) = 8.4 × 10−4 e2 fm2 and B(E1; 3/2− → 1/2+ ) = 3.4 × 10−3 e2 fm2 , respectively. Assuming the E1 multipolarity, the measured values are 4.6(5) × 10−3 e2 fm2 and 9.1(9) × 10−5 e2 fm2 for these transitions. Considering the difficulty in the shell model predictions of the E1 rates, the observed agreement is very good. To summarize, our experimental results closely confirm the model interpretation of the observed states in 31 Mg, albeit do not provide a unique identification. Nevertheless, the measured lifetimes provide strong constraints on any alternative interpretation of these states.

4 Results for

30

Mg

While investigating the states in 31 Mg from the β decay of 31 Na, we have established a long lifetime for the 1789 keV in 30 Mg populated in the β-delayed neutron

Fig. 6. A partial γγ coincidence spectrum gated by the 3178 keV γ-ray, which feeds the 1789 keV level in 30 Mg from above. It shows no trace of the 1789 keV line in channel 1280, which should be about 1/4 of the strong 1482 keV line seen in channel 1060, if the 1789 keV line de-excites the 1789 keV level.

emission of 31 Na, see fig. 5. Although a long lifetime makes the 1789 keV state a natural candidate for the intruder 0+ state, yet such assignment was contradicted by the 1789 keV γ-ray previously reported to de-excite the 1789 keV state to the ground state, e.g.: see [2]. On the other hand the deduced limits on transition rates are not in agreement with the other possible positive parity assignments, while states of negative parity are definitely not expected at such low energy. Our investigation of the decay scheme of 30 Mg from the β decay of 30 Na using γγ coincidences, has established a new placement for the 1789 and 1820 keV transitions. The 3178 γ-ray feeding the 1789 keV level from above shows no coincidences with the 1789 keV line (fig. 6), while the 1789 keV γ-ray is in strong coincidences with the 1482 and 1820 keV lines (fig. 7). This defines the 1789-1820-1482 keV cascade and new levels at 3302 and 5091 keV, although the latter may actually be the same as the already established and close-lying state at 5093 keV [2]. Figure 8 summarizes the current situation in 30 Mg. Below 3.3 MeV there are only 3 known excited states: 2+ 1482, (0+ ) 1789, and (2+ ) 2467 keV. There is now an intensity inbalance for the 1789 keV state: with 15.7(10) units of intensity feeding and 11.4(7) units de-exciting the state [2]. The inbalance of 4.3(12) could be due to a systematical error in intensities or a very strong E0 transition to the ground state. Both cases

The European Physical Journal A 2151

108

Counts

30

T1/2 3036

20

10

1400

1500

1600

1700

1800

1900

Energy (keV)

2+

0+

1820

5091 4967

0

Fig. 9. A partial level scheme of 32 Mg showing the key 2151885 keV two-γ cascade used in the lifetime measurement of the 885 keV level. The 885 keV level lifetime is preliminary. 8

2467

< 5 ps

1789

3.9(4) ns

1482

2.0(5) ps

0

0+

30 Mg

Centroid position (channels)

306 E2

2+

6 5 4 3 2 1 0

800

Fig. 8. A partial level scheme of 30 Mg and preliminary level lifetimes established in this work. The lifetime of the 1482 keV level is deduced from [4].

require further investigation. If the 306 keV line is E2, 4 + 2 then B(E2; 2+ 1 → 02 ) = 10.8(11) e fm is slow as would be expected for a transition between intruder collective and normal spherical states; for a comparison, for the 1482 4 + 2 keV line, the B(E2; 2+ 1 → 01 ) ∼ 40 e fm , see [3]. We also 4 + + 2 note B(E2; 22 → 21 ) ≥ 123 e fm if a pure E2 character is assumed for the 985 keV transition de-exciting the 2467 keV state. Thus most likely the 985 keV transition has a dominant M 1 component. The de-excitation pattern 28 Mg. for this state is somewhat similar to the 2+ 2 state in 32

16(4) ps

7

1482 E2

(0+)

T1/2

3303

985 (M1)

(2+)

5 Results for

885

32 Mg 3178

1789

Fig. 7. A partial γγ coincidence spectrum gated by the 1789 keV γ-ray in 30 Mg. It shows two strong coincidence lines at 1482 and 1820 keV in channels 1060 and 1295, respectively.

885

0

Mg

We report a preliminary lifetime result for the 885 keV in 32 Mg. The starting point in the analysis was verification of the level scheme using the γγ coincidences. This allowed to established a new decay scheme of 32 Na (not presented here). The lifetime measurement of the 885 keV state was done by the centroid shift technique using triple coincidences between β and 885 and 2151 keV γ-rays (see fig. 9) recorded in the β, Ge, and BaF2 detectors, respectively. The centroid of the time-delayed spectrum due to the β-2151 keV γ-ray coincident with the 885 keV transi-

1100

1400 1700 2000 Gamma Energy (keV)

2300

2600

Fig. 10. Centroid shift analysis for 32 Mg: time response of the BaF2 detector for the energy range 898-2754 keV, and the time shift due to a pair of points in 32 Mg, at 2151 keV (reference point normalized to the response curve) and at 885 keV. The shift of the latter point from the response curve is due to the lifetime of the 885 keV level.

tion recorded in the Ge detector gives the reference point. Then the centroid of the β-885 keV spectrum in coincidence with the 2151 keV transition recorded in the Ge detector is shifted from the reference point (corrected for the time response of the BaF2 detector, see fig. 10) due to the lifetime of the 885 keV level. Important was to select β sources providing on-line time response calibrations of the BaF2 detectors for the full energy peaks matching as closely as possible the energies of 2151 and 885 keV, and cascading via levels of precisely known lifetimes. Using the two-point calibrations for the energy pairs 898-1836 keV (88 Rb), 1263-2235 keV (30 Al) and 1369-2754 keV (24 Na), we have established the time response calibration of BaF2 detector for the energy range from 898 to 2754 keV, see fig. 10. The results presented here for 32 Mg are based on 1/3 of data being analysed. The preliminary lifetime of the 885 keV level was found as T1/2 = 16.0(42) ps, yielding B(E2; 0+ → 2+ ) = 327(87) e2 fm4 , which is among the lowest values reported [3] for 32 Mg almost overlapping with the result from [7].

H. Mach et al.: New structure information on

References 1. E. Caurier, F. Nowacki, A. Poves, Nucl. Phys. A 693, 374 (2001). 2. G. Klotz et al., Phys. Rev. C 47, 2502 (1993). 3. H. Scheit et al., these proceedings.

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31

Mg and

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Mg

109

4. M. Kowalska et al., these proceedings, see also [6]. 5. H. Mach et al., Nucl. Phys. A 523, 197 (1991) and references therein. 6. G. Neyens et al., Phys. Rev. Lett. 94, 22501 (2005). 7. B.V. Pritychenko et al., Phys. Lett. B 461, 322 (1999).

Eur. Phys. J. A 25, s01, 111–113 (2005) DOI: 10.1140/epjad/i2005-06-179-8

EPJ A direct electronic only

Observation of the 0+ 2 state in

44

S

S. Gr´evy1,a , F. Negoita2 , I. Stefan3 , N.L. Achouri1 , J.C. Ang´elique1 , B. Bastin1 , R. Borcea2 , A. Buta2 , J.M. Daugas4 , azek6 , F. De Oliveira3 , O. Giarmana4 , C. Jollet5 , B. Laurent1 , M. Lazar2 , E. Li´enard1 , F. Mar´echal5 , J. Mr´ D. Pantelica2 , Y. Penionzhkevich7 , S. Pi´etri8 , O. Sorlin3 , M. Stanoiu9 , C. Stodel3 , and M.G. St-Laurent3 1 2 3 4 5 6 7 8 9

Laboratoire de Physique Corpusculaire, IN2P3-CNRS, ENSICAEN and Universit´e de Caen, F-14050 Caen cedex, France Institute of Atomic Physics, IFIN-HH, Bucharest-Magurele, P.O. Box MG6, Romania Grand Accel´erateur National d’Ions Lourds, CEA/DSM-CNRS/IN2P3, BP 5027, F-14076 Caen cedex, France CEA/DIF/DPTA/PN, BP 12, 91680 Bruy`eres le Chˆ atel, France IReS, IN2P3/ULP, 23 rue du Loess, BP 20, F-67037 Strasbourg, France Nuclear Physics Institute, AS CR, CZ-25068 Rez, Czech Republic FLNR, JINR, 141980 Dubna, Moscow region, Russia CEA Saclay, DAPNIA/SPhN, F-91191 Gif-sur-Yvette, France Institut de Physique Nucl´eaire d’Orsay, IN2P3-CNRS, F-91406 Orsay cedex, France Received: 1 February 2005 / c Societ` Published online: 28 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 44 S. This state, Abstract. We report preliminary results on the observation of the isomeric 0 + 2 state in populated in the fragmentation of a 48 Ca beam, is located at 1365±1 keV and has a half-life of 2.3±0.3 μs. The observation of this isomer is the first experimental evidence of shape coexistence in 44 S which was predicted by various theoretical approaches. In particular, we found a good agreement with shell model calculations.

PACS. 23.20.Lv γ transitions and level energies – 23.20.Nx Internal conversion and extranuclear effects – 27.40.+z 39 ≤ A ≤ 58

1 Introduction The evolution of the shell closures at large N/Z ratios is one of the most fascinating quest in nuclear structure. In particular, the evolution of the N = 28 shell closure below 48 Ca has been the subject of several theoretical publications which predict a progressive onset of deformation with either spherical/prolate [1] or oblate/prolate [2, 3, 4, 5] shape coexistence in 44 S. It is therefore important to characterize this nucleus by searching for a low-lying 0+ 2 state. This would give information about both the importance and the origin of the deformation at Z = 16. Moreover, whether the deformation persists in the 42 Si nucleus is highly debated [6] and critically depends on the structure of 44 S. Recent experimental data for E(2+ ) and B(E2) values [7,8], E(4+ )/E(2+ ) ratios [9], and β-decay studies below 48 Ca [10] point to a likely region of deformation in the S isotopic chain. In addition, low-energy isomers have been observed in the N = 27 45 Ar [11] and 43 S [12] isotones suggesting that excitations across the N = 28 gap a

Corresponding author; e-mail: [email protected]

are important. The evidence of such a cross shell excitation in 44 S would manifest itself through the presence of an 0+ 2 isomer that has not yet been found. A dedicated experiment has been performed to detect the delayed converted electrons arising from the decay of an E0 isomer. We report here the first observation of the 44 S. low-lying isomeric 0+ 2 state in

2 Experimental setup The experiment has been performed at the GANIL facility. The 44 S were produced by fragmentation of a 60 A MeV 48 Ca beam on a 611 μm thick Be target and selected by the LISE3 spectrometer. The nuclei were implanted in a 45 μm kapton foil tilted at 28◦ with respect to the beam direction (effective thickness ∼ 96 μm), see fig. 1. The identification was made event by event utilizing two 300 μm Si detectors that provided A and Z identification by energy loss and time-of-flight information, the second Si detector (position sensitive) being used to obtain information about the profile of the beam on the kapton foil. The third and fourth Si detectors (500 μm each) were mounted on a rotatable

112

The European Physical Journal A

44 Fig. 3. Proposed decay scheme of the 0+ S and the 2 state in corresponding levels calculated by shell model calculations [1].

3 Experimental results

Counts / 0.4 μsec

Fig. 1. Schematic view of the detection setup at the end of the LISE spectrometer.

Counts / 1 keV

Time (μsec)

Electron energy (keV)

Fig. 2. Decay time (top) and energy spectra (bottom) of the conversion electrons corresponding to the E0 transition detected in the Si(Li) detector obtained in coincidence with 44 S ions. The inset shows a zoom on the region of the peak.

arm to adjust the effective matter thickness and implant the ions of interest in the last 30 μm of the catcher foil. The depth of implantation was controlled using the veto Si detector (500 μm) that was also used to reject fragments which passed through the implantation foil. The setup surrounding the collection point consisted of several detectors arranged perpendicularly to the beam axis: a liquid nitrogen cooled Si(Li) on the top for the conversion electrons and two segmented Ge clovers (Exogam) on the sides. The total efficiency of the Si(Li) and Ge detectors was estimated to be ∼ 6% for energies between ∼ 200 keV and 2 MeV and ∼ 3.5% at 1.3 MeV, respectively.

The evidence for the presence of a 0+ 2 isomer was inferred from both the observed E0 and E2 transitions which feed + the 0+ 1 (ground state) and 21 (1329 keV) states, respectively. The electron energy spectra obtained in the Si(Li) detector in delayed coincidence with the implantation of 44 S ions is shown in fig. 2 along with the corresponding decay-time between the implantation and the decay. A peak at 1362.5±1.0 keV is clearly seen in the figure and has been attributed to the E0 transition by internal conversion electrons (IC) from the 0+ 2 state located at 1365 ± 1 keV with a half-life of 2.3 ± 0.3 μs. Since the energy of the 0+ 2 state is greater than 1022 keV, it also decays by internal pair formation (IPF). This is confirmed from the time spectra measured in coincidence with the 511 keV gamma ray in the Ge detectors. Finally, the assumption of a 0+ 2 state is confirmed from the observation in the Ge detectors of the 1329 keV gamma ray which correspond to the de-excitation of the known 2+ state in 44 S with a half-life of 2.3 ± 0.5 μs, the very low energy (36 keV) transition + 0+ 2 → 21 being unobserved. The resulting decay scheme is shown in fig. 3.

4 Discussion As shown in fig. 3, a good agreement is found between calculated and measured energies of the first excited states in 44 S. In this shell model calculation, the two 0+ states are described as a mixture of closed-shell and np-nh excitations. The presence of a low-lying 0+ 2 state is considered as a signature of a spherical-deformed coexistence in the mean field and the present data therefore support the weakening of the N = 28 shell gap. The data analysis is in progress to obtain the B(E0) and B(E2) values for the decay of the 0+ 2 state. This would help in the better understanding of the nature of this isomer, and in particular the difference in shapes between the two 0+ states. We expect a large B(E0) value between spherical and deformed states and a small value for an oblate-to-prolate transition. These experimental results will be compared to the models predicting both energy and transition probabilities to infer the origin of the shell weakening.

S. Gr´evy et al.: Observation of the 0+ 2 state in

References 1. 2. 3. 4. 5.

E. Caurier et al., Nucl. Phys. A 742, 14 (2004). T.R. Werner et al., Nucl. Phys. A 597, 327 (1996). G.A. Lalazissis et al., Phys. Rev. C 60, 014316 (1999). S. Peru et al., Eur. Phys. J. A 9, 35 (2000). R. Rodr´ıguez-Guzm´ an et al., Phys. Rev. C 65, 024304 (2002).

6. 7. 8. 9. 10. 11. 12.

44

S

S. Gr´evy et al., Phys. Lett. B 594, 252 (2004). H. Scheit et al., Phys. Rev. Lett. 77, 3967 (1996). T. Glasmacher et al., Phys. Lett. B 395, 163 (1997). D. Sohler et al., Phys. Rev. C 66, 054302 (2002). O. Sorlin et al., Phys. Rev. C 47, 2941 (1993). Z. Dombradi et al., Nucl. Phys. A 727, 195 (2003). F. Sarazin et al., Phys. Rev. Lett. 84, 5062 (2000).

113

Eur. Phys. J. A 25, s01, 115–116 (2005) DOI: 10.1140/epjad/i2005-06-028-x

EPJ A direct electronic only

A novel way of doing decay spectroscopy at a radioactive ion beam facility C.J. Gross1,a , K.P. Rykaczewski1 , D. Shapira1 , J.A. Winger2 , J.C. Batchelder3 , C.R. Bingham4 , R.K. Grzywacz4 , P.A. Hausladen1 , W. Krolas4,5,6 , C. Mazzocchi4 , A. Piechaczek7 , and E.F. Zganjar7 1 2 3 4 5 6 7

Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Department of Physics and Astronomy, Mississippi State University, Mississippi State, MS 39762, USA UNIRIB, Oak Ridge Associated Universities, Oak Ridge, TN 37831, USA Department of Physics, University of Tennessee, Knoxville, TN 37966, USA Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, USA Joint Institute for Heavy Ion Research, Oak Ridge, TN 37831, USA Department of Physics, Louisiana State University, Baton Rouge, LA 37831, USA Received: 9 December 2004 / c Societ` Published online: 20 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A technique to enhance the purity of accelerated radioactive ion beams for decay studies is presented. The technique requires a 3 MeV/nucleon beam and a transmission ionization chamber. The gas pressure in the multi-anode ionization chamber is adjusted so that high-Z components of the beam are ranged out in the gas transmitting the more exotic, low-Z components to the measuring station. Initial tests with a radioactive 120 Ag and 120 In mixed beam indicate at least a factor of 5 relative enhancement of the 120 Ag decay transitions. PACS. 23.40.-s β decay; double β decay; electron and muon capture – 29.40.Cs Gas-filled counters: ionization chambers, proportional, and avalanche counters – 27.60.+j 90 ≤ A ≤ 149

1 Introduction Beta-decay studies on nuclei far from stability have traditionally been carried out at isotope separator facilities [1] and at the focal plane of recoil and fragment separators [2,3]. The isotope separator facilities extract and accelerate beams to a few tens of kilovolts, mass analyze the beam to one part in 1000, and rely on the purity of the resulting beam to study these nuclei. Recoil and fragment separators rely on the reaction kinematics to convey enough energy to either spatially separate and/or electronically tag the ions prior to implantation and study of the decay properties. Both techniques offer advantages and disadvantages. Isotope separator facilities often use extremely thick targets and large primary beams which can produce copious amounts of isotopes. However, the chemistry of how these ions diffuse in the catcher material and are released from the surfaces inside the ion source can cause long hold-up times making it difficult to study nuclei with short halflives. Recoil and fragment separators usually produce much weaker beams but with fast separation and tracking detectors the study of very short-lived species is possible. In both cases, very weak components of the beams can be swamped by contaminants. In order a

Conference presenter; e-mail: [email protected]

to improve upon the isotope separator technique we propose to accelerate the ion beams to approximately 3 MeV per nucleon and use an ionization chamber to detect and enhance the purification of a beam of neutron-rich nuclei. Beams of neutron-rich nuclei are produced at the Holifield Radioactive Ion Beam Facility (HRIBF) through proton-induced fission of a uranium carbide target. While many different ion sources may be used, the electronbeam-plasma ion source is presently most often used to produce neutron-rich beams. Isotopes diffuse out of the hot target and are extracted and ionized to form a beam of ions. The beam is mass analyzed and passed though a charge-exchange cell where positive ions are converted to negatively charged ions for injection into the 25 MeV tandem accelerator. Prior to injection, the ions are mass analyzed again. At the terminal potential of the accelerator, the ions are passed through a dilute gas or carbon foil and electrons are stripped off the ion. The positively charged ions have a distribution in charge; ions with one charge state are delivered to the experimental end station.

2 Technique The experimental end station consists of a microchannelplate-plus-thin-foil detector for counting the beam, an ionization chamber filled with CF4 gas for identifying the

The European Physical Journal A

Optimum setting Ag (Z=47) Ag In (Z=49) 165 Torr

151 Torr

Ag

197 keV

Counts/channel

Energy loss on last anode (arbitrary units)

116

In

117 Torr

Ag

197 keV

165 Torr

117 Torr

Channel number

157 Torr

Energy in silicon detector (arbitrary units)

Fig. 1. Energy loss on the last anode of the ionization chamber versus implantation energy in the Si detector for A = 120 ions at the indicated CF4 gas pressures. An analysis of γ-rays detected after the ionization chamber indicate that 165 torr is optimum to transmit 120 Ag and suppress 120 In.

various isobars, and whatever equipment is required for decay spectroscopy. In our test runs described here, we used a 25 cm2 square position sensitive Si detector and a single, unshielded Ge detector. For actual experiments we will use a thick double-sided Si detector (DSSD) for halflife measurements or a compact four clover Ge detector array surrounding plastic β-detectors and a tape system for removal of unwanted decay products. The key to our technique is the energy-loss difference between ions of the same energy [4] as they travel through matter; at our energies, high-Z nuclei lose more energy than low-Z nuclei. Thus, it should be possible to stop some ions in the CF4 gas and thin mylar exit window while transmitting lower-Z ions to the measuring station. This ranging-out of ions requires a well-defined beam (good emittance as is typical of tandem beams), careful adjustment of the gas pressure, and some signal such as decay-γ-rays which are not dependent on the low-energy thresholds of the ionization chamber and the Si implantation detector. Spectra showing the influence of gas pressure on a beam of 120 Ag and 120 In ions are shown in fig. 1. Although excellent suppression of the In component of the beam appears possible, these spectra are sensitive to the signal threshold of the ionization chamber electronics and do not indicate that the In ions have been stopped in the chamber or its exit window. In order to better judge the effectiveness of this technique, we look at the characteristic A = 120 γ-rays [5] emitted at the Si detector position. Portions of the spectra taken at 117 and 165 torr are shown in fig. 2. A suppression factor of 5 has been measured for the radioactivity of 120 In relative to 120m Ag. While not as dramatic as the electrical suppression had indicated, we will continue to explore this technique’s potential. In these tests, the Si detector was approximately 15 cm from the 1.6 cm diameter exit window of the ionization chamber. The ions traversed approximately 7.8 cm of gas in the ionization chamber. The single-crystal Ge detector was unshielded, located at a small angle directly be-

Ag

In

Ag

In

203 keV

203 keV

Fig. 2. Ungated γ-ray spectra for A = 120 ions at 117 torr and 165 torr gas pressure in the ionization chamber. Note the enhancement of the 203 keV, T 1 = 0.3 s isomeric transition

in

120

2

Ag. A factor of 5 enhancement is observed.

hind the flange holding the Si detector. The implantation width of the ions is estimated to be 3 cm full-width halfmaximum; these widths are well-suited to 25 cm2 square DSSDs and our 35 mm wide tape. We are considering using a smaller tape located at the exit to the ionization chamber and moving it at 0.25 s intervals. Other improvements include lead shielding, thinner dead layers on the Si detectors, and possibly gas catching and transport of the ions to the tape.

3 Conclusion We have established a ranging-out technique to study the radioactive decay of neutron-rich beam components. By using an ionization chamber and adjusting its gas pressure, we have reduced the contaminants of the transmitted beam by a factor of 5 for isobars with ΔZ = 2 for Z ≈ 50. This reduction of contaminants should offset the loss in statistics due to the typical 10% overall beam transmission through the tandem accelerator. Our first experiments will explore Cu, Ga, and Ge isotopes near doubly magic 78 Ni and the r-process path. This work was supported by the U. S. Department of Energy under contracts DE-AC05-00OR22725 (ORNL), DEFG02-96ER41006 (MSU), DE-AC05-76OR00033 (ORAU), DE-FG02-96ER40983 (UT), DE-FG05-88ER40407 (VU), DEFG05-87ER40361 (JIHIR), and DE-FG02-96ER40978 (LSU). Oak Ridge National Laboratory is managed by UT-Battelle, LLC.

References 1. E. Roeckl, Nucl. Instrum. Methods B 204, 53 (2003). 2. C.J. Gross et al., Nucl. Instrum. Methods Phys. Res. A 450, 12 (2000). 3. D. Morrissey et al., Nucl. Instrum. Methods B 204, 90 (2003). 4. U. Littmark, J.F. Ziegler, Handbook of Range Distributions for Energetic Ions in All Elements (Pergamon Press, New York, 1980). 5. K. Kitao, Y. Tendow, A. Hashizume, Nucl. Data Sheets 96, 241 (2002).

Eur. Phys. J. A 25, s01, 117–118 (2005) DOI: 10.1140/epjad/i2005-06-197-6

EPJ A direct electronic only

Structure of neutron-rich even-even

124,126

Cd

T. Kautzsch1 , A. W¨ ohr2,3,4,a , W.B. Walters3 , K.-L. Kratz1,5 , B. Pfeiffer1,5 , M. Hannawald1 , J. Shergur3,b , O. Arndt1 , 1 S. Hennrich , S. Falahat1,5 , T. Griesel1,5 , O. Keller1 , A. Aprahamian2,4 , B.A. Brown6 , P.F. Mantica6 , M.A. Stoyer3,7 , H.L. Ravn8 , and the ISOLDE IS333 and Rochester CHICO/Gammasphere Collaborations 1 2 3 4 5 6 7 8

Institut f¨ ur Kernchemie, Universit¨ at Mainz, D-55128 Mainz, Germany Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA Department of Chemistry, University of Maryland, College Park, MD 20742, USA JINA, http://www.jina-web.org, USA VISTARS, http://www.vistars.de, Germany Department of Physics and Astronomy and NSCL, Michigan State University, East Lansing, MI 48824-1321, USA Lawrence Livermore National Laboratory, Livermore, CA 94550, USA ISOLDE, PH Department, CERN, 1211 Gen`eve 23, Switzerland Received: 4 November 2004 / Revised version: 3 March 2005 / c Societ` Published online: 15 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. New levels are reported for 124,126 Cd populated in the decay of 124,126 Ag isomers, respectively. In addition, new data from direct population of levels in 124 Cd from alpha-induced fission of 238 U are reported, along with new shell-model calculations for 126 Cd. PACS. 23.40.-s β decay; double β decay; electron and muon capture – 21.10.-k Properties of nuclei; nuclear energy levels – 21.60.-n Nuclear structure models and methods

Owing to the importance of the structure and decay of Cd for r-process nucleosynthesis calculations, we have pursued the study of the structure of lighter even-even Cd nuclides [1]. In particular, we reported new 2+ and 4+ energies for 124,126,128 Cd that included the unexpected downturn for these energies in 128 Cd relative to 126 Cd [2]. In this paper, additional data for the structure of 124 Cd and 126 Cd are reported, both from study of Ag decay [3] and from direct population of 124 Cd levels in alphainduced fission of 238 U [4]. The decay studies were performed at ISOLDE where neutron-rich Ag isotopes were ionized using the Resonance Ionization Laser Ion Source (RILIS) and isolated with the on-line mass separator. There is a strong synergy between experimental data from radioactive decay and experimental data from studies of high-spin states in nuclear reactions performed with large γ-ray arrays. In radioactive decay, identification of the origin of γ-rays is determined by the mass separator following chemically selective ionization. Moreover, as the laser can be turned off, mistaken identity can be avoided. In contrast, data taken with large γ-ray detector arrays, such as Gammasphere, are taken non-selectively with respect to the nucleus of origin. However, the use of triple-coincidence data analysis methods prove to be quite selective if two or more members of 130

a b

Conference presenter; e-mail: [email protected] e-mail: [email protected]

the yrast cascade in any product nuclide can be identified. The alpha-induced fission data used in this study were taken with Gammasphere and sorted into triplecoincidence cubes with broad mass gates. For these data, the mass gate was set for 110 ≤ A ≤ 130. A new partial level scheme for 124 Cd is shown in fig. 1. The intensity values shown are from the decay of the particular mixture of isomers obtained in these experiments at ISOLDE. As can be seen, the 613 keV level is populated far more strongly than any of the other levels, indicating population in the decay of a low-spin 124 Ag isomer, with J probably ≥ 2. Two yrast cascades were identified in the double gates set in the α-induced fission data that are indicated by circles in fig. 1, one from the 2936 keV level tentatively identified as the 10+ yrast level, and another from the 7− level at 2384 keV. As these data suggest that the 10+ level is populated indirectly, in the decay of the higher-spin 124 Ag isomer, it is likely that the spin of the high spin isomer is 7 or greater. A new partial level scheme for 126 Cd is shown in fig. 2. The yields for 126 Ag that can be obtained at ISOLDE drop by about a factor of 10 for each additional neutron in the parent nuclide, hence far fewer data are available for analysis than were available for 124 Ag decay. In particular, no second 2+ level has been identified that decays to both the ground and first-excited state in a manner similar to the 1428 keV level in 124 Cd. As the first 2+ level at

The European Physical Journal A

(3+,4+) 52+ 4+

497(1.4) 1312(3.0)

534(5)

3138 3122 3060 2752 2698 2580 2495 2464 2443 2423 2420 2105 1902 1880

1466

4+ 2+

1594

652

2+

740

263(0.4)

8+ 10+ 8+ 55+ 76-+ 4 6+ 0+ 2+ 0+ 5-+ 3

2936

2683 2673 2561 2384 2139 1978 1924 1915 1847

252(6) 170(12) 6-,72120 6-,71950 82(23) 5402(49) 1868 4+

1428

613

1410

814(56)

1385 613(100)

2+

488(1.6) 530(0.5) 1303(1.7)

(2+) (4+,3+)

772(57) 814(12) 1428(2.3) 461(39)

6+

593(0.3) 1366(0.9) 1978(0.5)

7-

754(16)

8+ 5-

244(7) 538(19)

4-,5-

175(15) 715(0.4) 1175(0.3)

(10+)

836(7) 1296(1)

118

2+ 652 (100)

0+

0

124 Cd 76 48

Fig. 1. Level scheme for 124 Cd. The round filled dots indicate the observation of the coincidence in both 124 Ag decay and in fission, the filled squares indicate coincidences observed only in the decay data, and the open circle, a coincidence observed only in the fission data.

613 keV is populated much more strongly than other levels, it must be assumed that there are also two isomers in 126 Ag undergoing β − decay. Another interesting feature of the level scheme is the near equality for the intensities of the 814 keV 4+ to 2+ transition and the 402 keV 5− to 4+ transition. This near equality suggests that there is little population of higher-spin positive-parity 6+ , 8+ , and 10+ levels that cascade directly to the 1466 keV 4+ level as was observed for the decay of the high-spin isomer in 124 Ag. In a recent study of radioactive decay and isomeric decay performed at the NSCL using the β-counting system and the SEGA array, decay of an isomeric state was identified in 126 Cd [5]. The cascade from the 5− level at 1868 keV was quite strongly populated along with a number of additional γ-rays not observed in 126 Ag decay. Owing to a low-energy γ-ray background in the NSCL data, γ-rays below 200 keV were not observed, hence, it was not possible to determine whether the 82 and 170 keV γ-rays were a part of the isomeric decay observed in that experiment. As had been done for 124 Cd, a double gate was set on the 652 and 814 keV γ-rays in the fission data set. No additional γ-rays were observed, indicating that most of the population of 126 Cd in fission is to the isomeric level or levels. The structure of 126 Cd that is calculated using the shell-model code OXBASH is shown in fig. 2. These calculations used the same parameter set as used for the 130 Cd calculations reported by Dillmann et al. [1], except that it was necessary to truncate the calculation by including the

0+ 126 48

0

Cd 78

0+ 0 126 48 Cd 78 OXBASH 2003

Fig. 2. Observed and calculated levels for

126

Cd.

deep f5/2 proton hole as a part of the core. Both full and truncated calculations were performed for 128 Cd. For the full calculation, the energies of most of the positive-parity levels (including the 10+ level) were from 100 to 200 keV higher than for the truncated calculation. In contrast, the second 2+ and the negative-parity 5− and 7− levels were at about the same positions in both calculations. Thus, it might be expected that a full calculation for 126 Cd would place most of the positive-parity levels slightly above the positions found in the truncated calculation and shown in fig. 2. Recently, Scherillo et al., reported an experimental and theoretical study of structures of neutron-rich In and Cd nuclides [6]. These authors, who did not observe an isomerism in 126 Cd, presented a calculated level structure for 126 Cd that was further truncated by neglecting contributions from the neutrons. Hence, their calculated 2+ and 4+ energies of 950 and 1784 keV, respectively, are far above the calculated levels we show in fig. 2.

References 1. I. Dillmann et al., Phys. Rev. Lett. 91, 162503 (2003). 2. T. Kautzsch et al., Eur. Phys. J. A 9, 201 (2000). 3. T. Kautzsch, PhD Thesis, University of Mainz, 2004, unpublished. 4. M.A. Stoyer et al., to be published. 5. W.B. Walters et al., Phys. Rev. C. 70, 034314 (2004). 6. A. Scherillo et al., Phys. Rev. C. 70, 054318 (2004).

Eur. Phys. J. A 25, s01, 119–120 (2005) DOI: 10.1140/epjad/i2005-06-064-6

EPJ A direct electronic only

Structure of doubly-even cadmium nuclei studied by β − decay S. Rinta-Antila1,a , Y. Wang1 , P. Dendooven1 , J. Huikari1 , A. Jokinen1,2 , A. Kankainen1 , V.S. Kolhinen1 , ¨ o1,2 , and aj¨ arvi1 , J. Szerypo1 , J.C. Wang1 , J. Ayst¨ G. Lhersonneau1 , A. Nieminen1 , S. Nummela1 , H. Penttil¨a1 , K. Per¨ the ISOLDE Collaboration 1 2

University of Jyv¨ askyl¨ a, Department of Physics, P.O. Box 35 (YFL), FIN-40014 Jyv¨ askyl¨ a, Finland Helsinki Institute of Physics, P.O. Box 64, FIN-00014 University of Helsinki, Helsinki, Finland Received: 13 January 2005 / c Societ` Published online: 10 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We have studied the structure of even-even cadmium isotopes via beta decay of ground and excited isomeric states of parent silver isotopes. Measurements of mass A = 116, 118 and 120 cadmium nuclides were carried out at an ion guide isotope separation on-line facility at the University of Jyv¨ askyl¨ a. Decay schemes of 116m Ag, 118m Ag, 120g Ag and 120m Ag are considerably extended. Obtained data have enabled extension of available systematics of the three-phonon states to more neutron-rich cadmium nuclei. As a continuation we have conducted an experiment at ISOLDE, CERN to study heavier A = 122, 124, and 126 cadmium nuclides, the analysis of the collected data is underway. PACS. 27.60.+j 90 ≤ A ≤ 149 – 23.20.Lv γ transitions and level energies – 21.10.Re Collective levels

1 Introduction Main features of the cadmium nuclei, which span over a full neutron shell from N = 50 to N = 82, can be described in the framework of an anharmonic vibrator when the neutron number is few particles or holes away from the closed shells. In addition, around the mid neutron shell so called intruder states can be detected with low excitation energies. These two phenomena can be combined in IBA-1 calculation by performing separate calculation for both normal configuration and intruder configuration with two extra bosons from 2p-2h excitation across the proton shell gap and then finally coupling them by introducing a mixing Hamiltonian [1]. This approach has been used successfully for cadmium nuclei [2]. Microscopic approaches have also been used to describe cadmium nuclei. Because a full shell model calculation is not feasible to derive properties of the whole cadmium chain one must use some kind of truncation of the shell model. One such truncation is developed lately to describe low-lying two-phonon states and electromagnetic transitions from them [3]. This model has been used to derive properties of low-energy vibrational states in even 110–120 Cd nuclei [4] and the work will be continued for the heavier cadmium isotopes. Same group has also calculated, within this same theoretical framework, betafeeding properties to the low-energy excited states of the a

Conference presenter; e-mail: [email protected]

116–130

Cd [5]. However, omission of the intruder states is the drawback of this microscopic description. Experimental data is used to test the above mentioned theoretical predictions. So far the experimental knowledge of the heaviest cadmium nuclei above A = 124 is limited to the half-life information and neutron emission probabilities which were obtained from the beta-delayed neutron emission experiments done at ISOLDE, CERN [6]. In addition the lowest yrast states are proposed up to 130 Cd based on γ singles data collected at ISOLDE [7]. Some of these first yrast states are also detected in a microsecond isomer decay experiment at LOHENGRIN, Grenoble [8]. As a complementary method to the decay studies, an experiment using Coulomb excitation has recently been done at REX-ISOLDE facility at CERN to obtain B(E2) values for ground state to the first 2+ -state transition of 122,124 Cd [9].

2 Experimental techniques and results Few years back we have launched a program to study the structure of neutron-rich cadmium isotopes via β decay of silver isotopes. The aim of this experimental program is to complete the cadmium level schemes up to medium spins that are reachable by this method, main emphasis being on studying the evolution of vibrator and intruder states as the neutron number increases. Experiments were carried out using on-line isotope separator technique to produce beta decaying silver source.

120

The European Physical Journal A

Fig. 1. Beta gated gamma spectrum taken with multichannel analyser from mass A = 124. Peaks from transitions following the decay of 124 Ag, 124 In and 124m In are marked with A, B and C, respectively.

Silver itself was produced in induced fission of uranium target nuclei. Lighter mass neutron-rich cadmium isotopes A = 116, 118 and 120 were studied at the ion guide isotope separator on-line (IGISOL) facility of the University of Jyv¨ askyl¨a [10, 11]. At IGISOL the symmetric fission of a natural uranium target was induced by 25 MeV protons with an intensity of 5 to 10 μA. Fission fragments were then thermalised as 1+ ions in helium gas and transported with gas flow out of the stopping chamber after which ions were guided through a differential pumping region by electric fields and finally accelerated to 40 keV energy. After mass separation the beam was implanted in to a movable collection tape inside a thin cylindrical plastic scintillator. Implantation point was viewed by four germanium detectors placed in close geometry. Data were collected in β-γ and γ-γ triggered event mode. Every event was also time stamped with a 1 ms resolution relative to the tape movement cycle. Based on the collected data a considerable number of newly found states and transitions were assigned to decay schemes of 116m Ag, 118m Ag, 120g Ag and 120m Ag. For more details see refs. [12, 13]. For the IGISOL facility 122 Ag is at the limit of feasible yield. Therefore, it was necessary to continue towards the heavier isotopes at ISOLDE, CERN, where thick target together with resonant ionisation laser ion source provide much higher silver yields. Detection set-up consisting of thin plastic scintillator and five large germanium detectors was used to get γ-γ coincidence data of the decays of 116,118,120 Ag. As the analysis of the collected data is not yet started we can show only a beta gated multichannel analyser spectrum of one of the germanium detectors from mass A = 124 as an example of the data (see fig. 1). Collection time of this spectrum was one fifth of the total time spent on mass A = 124.

Fig. 2. Partial level schemes showing the vibrational states up to the three-phonon quintuplet in 116,118,120 Cd nuclei [13].

phonon quintuplet in both of these nuclei. For more details about new levels and reassignments see refs. [12,13]. Also in 120 Cd candidates for three-phonon states are suggested, see fig. 2. Study of the β decay properties has also shown that the decays of 116m Ag and 118m Ag are similar but the decay of 120m Ag is different as the decay strength is spread over more levels in 120 Cd, which might indicate the onset of occupation of h11/2 neutron orbital. In order to test the predictions of different theoretical models, in addition of extending the level schemes, further measurements of B(E2) values and angular correlations are needed. Therefore, for instance a level life-time measurement of these heavier cadmium isotopes with advanced time-delayed technique by Mach et al. [14] would have an interest from the theory point of view. This research was supported by the Academy of Finland under the Finnish Centre of Excellence Programme 2000-2005 (Project No. 44875, Nuclear and Condensed Matter Physics Programme at JYFL).

References 1. 2. 3. 4. 5. 6. 7. 8. 9.

3 Discussion and outlook

10.

Experiments done at IGISOL on the β decay of silver isotopes have led to an observation of a large number of new levels in 116,118,120 Cd. Especially, newly found 1869.7 keV 4+ level in 116 Cd and 2023.0 keV 2+ level in 118 Cd enables suggestion of a complete set of quadrupole three-

11. 12. 13. 14.

P.D. Duval, B.R. Barrett, Nucl. Phys. A 376, 213 (1982). K. Heyde et al., Nucl. Phys. A 586, 1 (1995). D.S. Delion, J. Suhonen, Phys. Rev. C 67, 034301 (2003). J. Kotila, J. Suhonen, D.S. Delion, Phys. Rev. C 68, 014307 (2003). J. Kotila, J. Suhonen, private communication. K.-L. Kratz et al., Hyperfine Interact. 129, 185 (2000). T. Kautzsch et al., Eur. Phys. J. A 9, 201 (2003). A. Scherillo et al., Phys. Rev. C 70, 054318 (2004). T. Behrens et al., ISOLDE Workshop, December 2004, http://isolde.web.cern.ch/ISOLDE/. P. Dendooven, Nucl. Instrum. Meth. Phys. Res. B 126, 182 (1997). ¨ o, Nucl. Phys. A 693, 477 (2001). J. Ayst¨ Y. Wang et al., Phys. Rev. C 64, 054315 (2001). Y. Wang et al., Phys. Rev. C 67, 064303 (2003). H. Mach et al., Nucl. Phys. A 523, 197 (1991).

Eur. Phys. J. A 25, s01, 121–122 (2005) DOI: 10.1140/epjad/i2005-06-071-7

EPJ A direct electronic only

New level information on Z = 51 isotopes, 134,135 Sb83,84

111

Sb60 and

J. Shergur1,2,a , N. Hoteling1,b , A. W¨ ohr1,2,3 , W.B. Walters1 , O. Arndt4 , B.A. Brown5 , C.N. Davids2 , D.J. Dean6 , 4 4 K.-L. Kratz , B. Pfeiffer , D. Seweryniak2 , and the ISOLDE Collaboration7 1 2 3 4 5

6 7

Department of Chemistry, University of Maryland, College Park, MD 20742, USA Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA Institut f¨ ur Kernchemie, Universit¨ at Mainz, D-55128 Mainz, Germany Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824-1321, USA Physics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831, USA ISOLDE, PH Department, CERN, 1211 Gen`eve 23, Switzerland Received: 4 November 2004 / Revised version: 3 March 2005 / c Societ` Published online: 9 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. New data for low-spin low-energy levels in 111,134,135 Sb are presented. The observed structures are compared to shell-model calculations. The monopole shifts for the d5/2 and g7/2 single-proton levels and the spin-orbit splitting for the d5/2 and d3/2 orbitals as N/Z moves from ∼1 up to 1.6 are discussed. PACS. 23.40.-s β decay; double β decay; electron and muon capture – 21.10.-k Properties of nuclei; nuclear energy levels – 21.60.-n Nuclear structure models and methods

1 Introduction The systematic changes in structures of the low-spin states below 2.0 MeV of odd-A Sb nuclides from 101 Sb to 135 Sb provide important information regarding the monopole shift of the g7/2 single-proton state between the N = 50 and N = 82 closed neutron shells and beyond. Levels below 2.0 MeV arise from coupling the 2+ phonon of the Sn core to single-particle g7/2 and d5/2 states, and the presence or absence of degeneracy with the position of the 2+ core level is one indication of the extent of configuration mixing. For odd-A Sb nuclei with 115 ≤ A ≤ 133, the structures of states below 2.0 MeV have been established by a number of different experiments. Whereas, only a recent study of the structure of 109 Sb by Ressler et al. [1], has provided new data for low-spin levels below 113 Sb. In this paper new data for levels in 111 Sb populated in the decay of 111 Te are presented. Above the N = 82 shell closure, single-particle states have been identified in 133 Sb [2], and the d5/2 singleparticle state has been identified in 135 Sb [3]. The positions of these single-particle levels are important for understanding the evolution of nuclear structure as N/Z exa b

e-mail: [email protected] Conference presenter; e-mail: [email protected]

ceeds 1.5 and the neutron dripline is approached. Also presented in this paper are new data for the low-spin states of both 134 Sb and 135 Sb.

2 Experimental Low-spin states in 111,113,115 Sb were populated via β + /EC decay of 111,113,115 Te nuclei that were produced at Argonne National Laboratory using the 58 Ni(56 Fe,2pn)111 Te, 60 Ni(56 Fe,2pn)113 Te, and 62 Ni(56 Fe,2pn)115 Te fusionevaporation reactions. Reaction products were separated in the Fragment Mass Analyzer on the basis of their mass to charge (A/Q) ratio, and following mass separation, the recoils were implanted in the tape of a moving tape collector (MTC). As the half-life of 111 Te (T1/2 = 26.2(6) s) is shorter than nuclei produced from other reaction channels, the tape was moved periodically to a Pb-shielded counting station to maximize coincidence events; and to reduce contribution to the γ spectra from both the decays of daughter and granddaughter nuclides, and the decays of nuclides that are collected on the tape owing to similar A/Q values. Levels in 134,135 Sb were populated by βdn and β − decay of 135 Sn, respectively. Neutron-rich Sn nuclei were produced at ISOLDE, CERN by using a 1.4 GeV proton beam pulse to induce fission of a UC2 target. Sn isotopes were then selectively ionized using the Resonance Ionization Laser Ion Source which consists of three copper vapor

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The European Physical Journal A

pumped dye lasers tuned to two resonant atomic excitations and a third to an energy which allowed for ioniztion of the electron into the continuum. Following mass separation, 135 Sn was implanted into the tape of a moving tape collector, data were collected, and the tape was moved to remove daughter, granddaughter, and isobaric nuclides prior to the next proton pulse. Data were collected with the “laser-on” and with the “laser-off” to distinguish which peaks in the γ spectra could be assigned to the decay of Sn, and which were a result of the decay of surface ionized 135 Cs. In both experiments, γ singles, γ-time, and γ-γ coincidences were collected.

7/2135

Sn

50

0

85

β−

On the neutron-rich side, new level structures have been identified in 135 Sb and 134 Sb where the levels were populated following direct β − and β-delayed neutron decays of 135 Sn, respectively. The observed levels in 135 Sb below 1.0 MeV are shown in fig. 1, along with the results of a shell model calculation using the CD Bonn interaction, where the single-proton d5/2 and d3/2 levels have been lowered by 300 keV as described previously, thereby holding the spin-orbit splitting the same as for 133 Sb [3]. As can be seen, the positions for the calculated levels are in good agreement with the positions of the observed levels. The new levels populated in β-delayed neutron decay in odd-odd 134 Sb below 1.5 MeV are also shown in fig. 1, along with the levels calculated in an OXBASH calculation using the KH5082 interaction. Levels in 134 Sb at 13, 330, and 383 keV were previously reported by Korgul et al. [7]. Again, an excellent fit is found, in spite of the fact that the KH5082 interaction for this mass region has been imported from the 208 Pb region and scaled by A−1/3 .

(5-)

1385

5-

1328

6-

617

6-

645

4-

555

4-

565

5-

442 32279

422

383 330

5237-

13 0

01-

8 0

n

CD Bonn d3/2&d5/2 shifted - 300 keV 9/2+ 855

3 Levels in proton-rich Sb nuclides

4 Levels in neutron-rich Sb nuclides

5-

Sn = ~3.6(1) MeV

11/2+ 664

On the proton-rich side, eleven new states were identified in 111 Sb, including tentative assignments of the yrast 1/2+ and 3/2+ levels at 487 and 881 keV, respectively [4]. These data were combined with similar levels in 109 Sb [1] to improve the estimate for the positions of the s1/2 and d3/2 single-proton basis states in 101 Sb that underlie nuclear structure calculations in this mass region. With the position of the d3/2 level at 2.9 MeV, the spin-orbit splitting in 101 Sb can be seen to be about twice the 1477 keV separation known for the d5/2 to d3/2 separation in 133 Sb, in agreement with the conjecture made by Schiffer et al. [5]. There are, of course, numerous other approaches to a full description of the spin-orbit splitting, however, we note that a further reduction of the d5/2 to d3/2 separation is found going from 133 Sb82 to 207 Tl126 where that separation is reduced to > 1332 keV [6]. We include the “greater than” symbol to recognize that, although the 3/2+ level at 351 keV has a large spectroscopic factor, the 5/2+ level at 1653 keV does not contain all of the d5/2 strength. Hence, the centroid of the spin-orbit splitting is surely larger than 1332 keV, perhaps even approaching the 1477 keV splitting observed in 133 Sb.

KH5082 1516

525 ms

9/2+

798

11/2+

707

(1/2 +) (556) 7-

1/2+ 502 3/2+ 365 5/2+ 306

7/2+

0

OXBASH

3/2+

440

5/2+

282

7/2+

0

1-

0-

134

Sb 83 51

358 351 305

OXBASH

135

Sb 84

51

Fig. 1. The β − and βdn decays of 135 Sn. The structures of 134 Sb and 135 Sb are compared with shell model calculations with the parameters described in the text.

5 Conclusions These new data have provided improved values for the monopole shifts of single-proton states from 109 Sb58 through 135 Sb85 . For both light and heavy Sb nuclides, shell model calculations provide a good description of the observed structures. It should be noted that other approaches to monopole shifts in neutron-rich nuclides have recently been published by both Otsuka et al. [8], and by Hamamoto [9]. This work was supported by the U.S. Department of Energy, Office of Nuclear Physics, under Contract W-31-109-ENG-38.

References 1. 2. 3. 4. 5. 6.

J.J. Ressler et al., Phys. Rev. C 66, 024308 (2002). B. Fogelberg et al., Phys. Rev. Lett. 82, 1823 (1999). J. Shergur et al., Phys. Rev. C 65, 034313 (2002). J. Shergur et al., to be published in Phys. Rev. C (2005). J.P. Schiffer et al., Phys. Rev. Lett. 92, 162501 (2004). W.B. Walters, Second International Workshop on Fission and Properties of Fission-Product Nuclides, Seyssins, Grenoble, France, AIP Conf. Proc. 447, 196 (1998). 7. A. Korgul et al., Eur. Phys. J. A 15, 181 (2002). 8. T. Otsuka et al., Phys. Rev. Lett. 87, 082502 (2001). 9. I. Hamamoto, Nucl. Phys. A 731, 211 (2004).

Eur. Phys. J. A 25, s01, 123–124 (2005) DOI: 10.1140/epjad/i2005-06-040-2

EPJ A direct electronic only

On the structure of the anomalously low-lying 5/2+ state of 135 Sb A. Korgul1,a , H. Mach2 , B.A. Brown3 , A. Covello4 , A. Gargano4 , B. Fogelberg2 , R. Schuber2,5 , W. Kurcewicz1 , E. Werner-Malento1 , R. Orlandi6,7 , and M. Sawicka1 1 2 3 4 5 6 7

Institute of Experimental Physics, Warsaw University, Warsaw, Poland Department of Radiation Sciences, Uppsala University, Uppsala, Sweden Department of Physics and Astronomy and NSCL, Michigan State University, East Lansing, MI, USA Dipartimento di Scienze Fisiche, Universit` a di Napoli Federico II and Istituto Nazionale di Fisica Nucleare, Napoli, Italy Department of Physics, University of Konstanz, Konstanz, Germany Institut Lave-Langevin, Grenoble, France Schulster Laboratory, University of Manchester, Manchester, UK Received: 20 December 2004 / Revised version: 18 February 2005 / c Societ` Published online: 3 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Recently the first-excited state in 135 Sb has been observed at the excitation energy of only 282 keV and, due to its properties, interpreted as representing mainly a configuration of a d 5/2 proton coupled to the 134 Sn core. It was suggested that its low-excitation is due to a relative shift of the proton d5/2 and g7/2 orbits due to the neutron excess. With the aim to provide more spectroscopic information on this anomalously low-lying 5/2+ state, we have measured its lifetime by the Advanced Time-Delayed βγγ(t) method at the OSIRIS fission product mass separator at Studsvik. The preliminarily measured + −4 2 half-life, T1/2 = 6.0(7) ns, yields an exceptionally low B(M 1; 5/2+ μN . The 1 → 7/21 ) value of ≤ 2.9 × 10 result is discussed in the framework of shell model calculations. PACS. 21.10.-k Properties of nuclei; nuclear energy levels – 21.10.Tg Lifetimes – 23.40.-s β decay; double β decay; electron and muon capture

Theoretical studies predict that very neutron-rich medium-heavy nuclei are governed by a shell structure that differs from that established along the line of stability [1]. Although the “neutron skin effects” are expected to occur at a very high neutron excess, thus closer to the neutron drip line, yet some limited effects related to specific orbits, could perhaps be observed much earlier. This study is focused on 135 Sb as new experimental results on this nucleus have been puzzling. Recently, its first-excited state was identified at the OSIRIS facility to lie at only 282 keV [2]. A subsequent study at ISOLDE concluded [3] that the energy of this state seems anomalous —likely due to a high neutron excess that decreases the relative separation energy between the d5/2 and g7/2 orbitals. This idea can be examined via combined experimental and theoretical studies. A strong β-feeding to the 282 keV state in 135 Sb [3] from the ground state of 135 Sn points towards a strong d5/2 single-particle component in this state. The M 1 transition is forbidden between the d5/2 and g7/2 singleparticle states and E2 collectivity is small in these nuclei. Consequently, one would expect for the 282 keV transition a

Conference presenter; e-mail: [email protected]

in 135 Sb a very slow B(M 1) rate if there is shift of the orbits, and a faster one if the lowering of the state is due to collective effects. Thus, a new insight can be provided by the B(M 1) rate for the 282 keV γ-ray. The measurement has been performed at the OSIRIS fission-product mass separator at Studsvik, operated by the Uppsala University. The levels in 135 Sb were populated in the β decay of 135 Sn produced in the thermal neutron induced fission of 235 U. The mass-separated beam of A = 135 isobars was implanted into an aluminized mylar tape at the experimental station, where two Ge detectors and fast timing β and BaF2 γ detectors were positioned in a close geometry (for more details on the βγγ(t) method see [4]). A partial level scheme of 135 Sb is presented in fig. 1. By selecting in the Ge spectrum the 732 and 923 keV γ-rays feeding the 282 keV state from above [2] and in the coincident BaF2 spectrum the very strong and clean 282 keV peak (fig. 2) one obtains the time-delayed βγ(t) spectrum due to the lifetime of the 282 keV state in 135 Sb (fig. 3). The feeding γ transitions do not carry any time-delayed components, which could affect fitting of the slope (they are semi-prompt with T1/2 ≤ 0.3 ns).

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β

135

Sn

Table 1. Comparison of the experimental B(M 1) values and shell model predictions of by Brown (B) and Covello and Gargano (CG).

−

1205.1

1014.1 923.4 [32(6)]

732.4

B(M 1)exp

B(M 1)B free

B(M 1)B eff

B(M 1)CG

(μ2N )

(μ2N )

(μ2N )

(μ2N )

< 0.29 · 10−3

4.8 · 10−3

2.2 · 10−3

44 · 10−3

[41(5)]

+

(5/2 )

281.7 281.7 [100(4)]

+

(7/2 )

0.0 135

Sb

Fig. 1. Partial level scheme of

135

Sb [2].

281.7 keV

BaF2 detector

Fig. 2. The BaF2 spectrum measured in coincidences with the 732 and 923 keV transitions observed in the Ge detectors. 135Sb:

281.7 keV level

T1/2=6.0(7) ns

Fig. 3. The time-delayed βγ(t) spectrum due to the 282 keV level in 135 Sb; see text for discussion.

The (preliminary) half-life of the level is measured as T1/2 = 6.0(7) ns. Since the M 1/E2 mixing ratio for the transition is not known, we deduce the upper limits for the B(M 1) and B(E2) rates, assuming either a 100% pure M 1 or 100% pure E2 transition, respectively. We have performed shell model calculations in order to understand the low excitation energy of the 5/2+ state and its very low B(M 1) value. Table 1 presents a comparison of the experimental B(M 1) values to the shell model predictions by Covello and Gargano (CG) and Brown (B). The calculations by Covello and Gargano use two-body effective interactions derived from CD-Bonn nucleon-nucleon potential with standard parameters for 132 Sn region (not adjusted for 135 Sb) and single-particle energies taken from the experimental spectrum od 133 Sb and 133 Sn. Transitions rates were calculated using the free g-factors and

ep (eff) = 1.55, en (eff) = 0.7. The calculations predict a fast B(M 1) for the 282 keV transition. Morevover, a relatively pure 7/2+ ground state is predicted as predominantly representing g7/2 proton coupled to the 134 Sn core with 78% πg7/2 (νf7/2 )2 , while the 5/2+ state calculated at 560 keV, has significant admixtures with the leading terms of 44% πd5/2 (νf7/2 )2 + 27% πg7/2 (νf7/2 )2 . (Lowering the separation energy between the proton d5/2 and g7/2 states by 400 keV would indeed decrease the excitation energy of the 5/2 state to the experimental value of 282 keV, and would also lower the B(M 1) rate by about a factor of 5, bringing it thus somewhat closer to the experimental limit. In addition, the composition of the state would become more pure: 65% πd5/2 (νf7/2 )2 + 6% πg7/2 (νf7/2 )2 .) The calculation performed by Brown makes use of the wave functions obtained in ref. [3]. These were calculated with the CD-Bonn G-matrix evaluated in an osˆ cillator potential with a renormalization based on the Qbox method that includes nonfolded diagrams to third order and folded diagrams to infinite order. The singleparticle energies are taken from the experimental level scheme of 133 Sb and 133 Sn, except for the proton d5/2 energy, which is shifted down by 300 keV [3]. As discussed in [3] part of this shift may be attributed to the difference between the G-matrix monopole interactions for the g7/2 -d5/2 splitting and that obtained in a HartreeFock (finite-well) potential. With free-nucleon g-factor B(M 1) = (0.172 − 0.102)2 = 4.8 · 10−3 μ2N ; the terms inside the brackets are from the orbital and spin contributions, respectively. With the effective M 1 operator, one obtains B(M 1) = (0.160−0.045−0.163)2 = 2.2·10−3 μ2N , where the terms inside the bracket are from effective orbital, spin and tensor operators, respectively. The low excitation energy of the 5/2+ state in 135 Sb + and an exceptionally low B(M 1; 5/2+ 1 → 7/21 ) value of −4 2 ≤ 2.9 · 10 μN tend to support the concept of a diffused core. However, caution must be taken in the comparison to the theory since due to a delicate balance between terms of the M 1 operator of opposite signs, a better determination of these terms in this region is required before more firm conclusions can be drawn. Our effort is now focused on the lifetime and angular correlation measurements in 135 Te, 135 I and 137 I.

References 1. 2. 3. 4.

K. Amos et al., Phys. Rev. C 70, 024607 (2004). A. Korgul et al., Phys. Rev. C 64, 021302(R) (2001). J. Shergur et al., Phys. Rev. C 65, 034313 (2002). H. Mach et al., Nucl. Phys. A 523, 197 (1991) and references therein.

Eur. Phys. J. A 25, s01, 125–126 (2005) DOI: 10.1140/epjad/i2005-06-169-x

EPJ A direct electronic only

Discovery of a new 2.3 s isomer in neutron-rich

174

Tm

R.S. Chakrawarthy1,a , P.M. Walker2 , M.B. Smith1 , A.N. Andreyev1 , S.F. Ashley2 , G.C. Ball1 , J.A. Becker3 , J.J. Daoud1,2 , P.E. Garrett3,4 , G. Hackman1 , G.A. Jones2 , Y. Litvinov5 , A.C. Morton1 , C.J. Pearson1 , C.E. Svensson4 , S.J. Williams2 , and E.F. Zganjar6 1 2 3 4 5 6

TRIUMF, 4004 Wesbrook Mall, Vancouver V6T 2A3, Canada Department of Physics, University of Surrey, Guildford, GU2 7XH, UK Lawrence Livermore National Laboratory, Livermore, CA 94550-9234, USA Department of Physics, University of Guelph, Ontario NIG 2W1, Canada GSI, Planckstrasse 1, 642901 Darmstadt, Germany Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA Received: 23 November 2004 / c Societ` Published online: 7 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A new program of K-isomer research has been initiated with the 8π spectrometer sited at the ISAC facility of TRIUMF. We discuss in this paper the identification of a new 2.3 s isomer in 174 Tm and its implications. PACS. 21.10.Tg Lifetimes – 23.20.Lv γ transitions and level energies – 27.70.+q 150 ≤ A ≤ 189

174

1 Experiment and results The detection and study of high-K isomers is an active area of current nuclear structure research. In particular, one of the goals of a future study involving neutron-rich nuclei in the Dy-Hf region is to search for the possible existence of an “island” of β-decaying high-K isomers [1]. The close proximity of high-K states to the Fermi surface in neutron-rich A = 170–190 nuclei makes this region very attractive to search for high-K isomers [1, 2]. In the present work, nuclei far from stability are produced at the ISAC facility sited at TRIUMF, using 500 MeV proton-induced reactions on Ta targets, extracted using a surface ionization source, and accelerated to an energy of 30 keV. A high-resolution mass analyzer separates species with different mass number, which are then transported to the experimental stations such as the 8π spectrometer. This spectrometer is an array of 20 Compton-suppressed highpurity germanium detectors [3] which is used to detect γ-rays from the implanted nuclei. The detection system has been augmented with a moving tape transport facility, to reduce the contaminating activity present in an isobaric beam. In two sets of experiments several of the known high-K isomers in the Dy-Hf region, with half-lives ranging from a few ms to several minutes could be accessed [4]. We report here the discovery of a new isomer in the neutronrich nucleus 174 Tm. The A = 174 isobaric beam was implanted onto a moveable tape transport facility, with a

Conference presenter; e-mail: [email protected]

Tm 2.29(1) s Isomer

A

152.1 B C

100.3 (4 − )

Fig. 1. Partial level scheme of 174 Tm. Dotted transitions have not been observed in the present experiment.

beam-on/beam-off cycling times of 2s/2s, 3s/3s (“short”), 10s/10s and 100s/50s. The accumulated γ-ray data were dominated by the ground-state β-decay of 174 Tm (with a half-life of 5.4 min). In addition, two known coincident γ-rays with energies of 100.3 and 152.1 keV were observed (fig. 1). These two γ-ray transitions are known to be present in the ground-state β-decay of 174 Er, which has a half life of 3.3 min [5]. In the present experiment we found no evidence for the production of 174 Er. This important argument is based on the non-observation of other strong γ-ray transitions from the β-decay of 174 Er [5]. In the present experiment, a half life of 2.29(1) s was deduced from γ-time matrices gated by the 100 and

126

The European Physical Journal A 40000

2000

Counts

Counts

beam-on

beam-off

20000

1000

end of cycle

152.1

Tm K X-ray

30000

1500

100.3

Tm K X-ray

2500

10000

500 *

beam-off

0

0

0

1

2

3

4

5

6

7

8

9

50

100

150

200

250

Energy (keV)

10

Time (sec)

Fig. 2. Time spectrum gated by the 100.3 keV γ-ray transition. The beam-off/beam-on/beam-off tape-cycling times correspond to 2s-3s-3s.

152 keV γ-ray transitions (fig. 2). A “short” time-gated singles spectrum, obtained by subtracting out the longlived β-decays, shows prominently only the Tm K X-rays and the 100 and 152 keV γ-ray transitions (fig. 3). Based on the singles and the coincidence data, a new isomer in 174 Tm with a half life of 2.29(1)s is established unambiguously. From the coincidence data the K-conversion coefficients for the 100 and 152 keV γ-ray transitions were deduced to be 3.1(1) and 1.13(6) respectively, suggesting mainly M 1 multipolarity with a E2 admixture. The new data are in close agreement with the theoretically expected values of 2.69 and 0.82 for M 1 multipolarity, respectively, but differ from the values 1.7(3) and 0.54(6), respectively, reported in [5]. A careful analysis of the “singles” spectrum (fig. 3) did not yield any new γ-ray transitions that could be candidate γ-ray transitions between the isomer and the known excited states (labeled in fig. 1 as “A”, “B”, “C”), as well as between the excited states and the ground state. These data suggest the possibility of the existence of very lowenergy and highly-converted transitions in the decay of the isomer and the excited states. It is to be noted that we prefer to identify the isomeric level as a new excited state in 174 Tm as opposed to the excited state “A” itself being isomeric. This is based on, a) a large intensity difference between the two observed γ-ray transitions (γ 100 ∼ four times γ 152), indicating direct feeding of the excited state “B” by a cascade of low energy γ-ray transitions and/or highly converted transitions, and b), anomalously large hindrance factors if the level “A” itself were to be the isomeric state. Furthermore, if the origin of isomerism is presumed to be partly due to K-hindrance (in line with several known examples in this mass region) then this level could possibly have a high K value. Based on systematics and Nilsson model calculations of the single-particle levels in 174 Tm [5], the isomer is tentatively assigned to have a K π = (8− )π7/2− [523]⊗ν9/2+ [624] Nilsson configuration, while the other excited states (“B” and/or “C”) may be based on K π = ((4/5)+ )π1/2+ [411] ⊗ ν9/2+ [624] configu-

Fig. 3. Singles spectrum in the “short”-cycling time of 2s-3s-3s corresponding to the beam-off/beam-on/beam-off periods. The dominant component due to the longer-lived 174 Tm β-decay (T1/2 = 5.4 min) has been subtracted. The peak marked by the asterisk is a remnant of the subtraction procedure.

rations. Thus the levels involved in the isomer decay may have spins greater than the low values suggested from the previous works [5]. The present interpretation would be consistent with the earlier data only if the decay through the 100 and 152 keV transitions originates from a highspin β-decaying isomer in 174 Er instead of the groundstate β-decay of 174 Er. In addition, the absence of 174 Yb X-rays/γ-ray transitions in the ‘short’ time-gated singles spectrum (fig. 3) rules out significant β-decay of the 2.3 s isomer in 174 Tm.

2 Summary A new isomeric state with a half-life of 2.29(1) s has been identified in the neutron-rich odd-odd nucleus 174 Tm. If the isomer exists because of K-hindrance, then the levels populated in the decay have spins higher than the ones deduced by the earlier 174 Er β-decay studies, and could possibly imply the existence of a high-spin β-decaying isomer in 174 Er. Research supported by NSERC, Canada, DOE and DARPA Microsystems Technology Office through US AFOSR Contract F49620-03-C-0024 with Brookhaven Technology Group, Inc. USA.

References 1. P.M. Walker, G.D. Dracoulis, Hyperfine Interact. 135, 83 (2001). 2. K. Jain et al., Nucl. Phys. A 591, 61 (1995). 3. C.E. Svensson et al., Nucl. Instrum. Mehods B 204, 660 (2003). 4. M.B. Smith et al., Nucl. Phys. A 746, 617 (2004). 5. K. Becker et al., Nucl. Phys. A 522, 557 (1991); R.M. Chasteler et al., Z. Phys. A 332, 239 (1989).

2 Radioactivity 2.2 Proton-rich nuclei

Eur. Phys. J. A 25, s01, 129–130 (2005) DOI: 10.1140/epjad/i2005-06-036-x

EPJ A direct electronic only

Beta-delayed gamma and proton spectroscopy near the Z = N line A. Kankainen1,a , S.A. Eliseev2,3 , T. Eronen1 , S.P. Fox4 , U. Hager1 , J. Hakala1 , W. Huang1 , J. Huikari1 , D. Jenkins4 , A. Jokinen1 , S. Kopecky1 , I. Moore1 , A. Nieminen1 , Yu.N. Novikov2,5 , H. Penttil¨a1 , A.V. Popov2 , S. Rinta-Antila1 , ¨ o1 , and the IS403 Collaboration7 H. Schatz6 , D.M. Seliverstov2 , G.K. Vorobjev2,5 , Y. Wang1 , J. Ayst¨ 1 2 3 4 5 6 7

Department of Physics, P.O. Box 35, FIN-40014 University of Jyv¨ askyl¨ a, Jyv¨ askyl¨ a, Finland Petersburg Nuclear Physics Institute, 188300 Gatchina, St. Petersburg, Russia GSI, Postfach 110552, D-64291 Darmstadt, Germany Department of Physics, University of York, Heslington, York YO105DD, UK St. Petersburg State University, St. Petersburg 198904, Russia Michigan State University, East Lansing, MI 48824, USA CERN, CH-1211 Geneva, Switzerland Received: 13 January 2005 / c Societ` Published online: 20 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A series of beta decay experiments on nuclei near the Z = N line has been performed using the ISOL technique at the IGISOL facility in Jyv¨ askyl¨ a and at ISOLDE, CERN. The decay properties of these neutron-deficient nuclei are important in astrophysics as well as in the studies of isospin symmetry. PACS. 23.20.Nx Internal conversion and extranuclear effects – 23.40.-s β decay; double β decay; electron and muon capture – 27.40.+z 39 ≤ A ≤ 58 – 27.50.+e 59 ≤ A ≤ 89

1 Introduction Nuclei close to the Z = N line provide an opportunity to study symmetry properties of nuclei. For example, the isospin symmetry of transitions can be probed by comparing the Gamow-Teller (GT) strengths of analogous transitions. From an astrophysical point of view, these nuclei are deeply involved in the rapid proton capture (rp) process. A series of beta decay experiments on nuclei near the Z = N line has recently been performed at the IGISOL facility in Jyv¨askyl¨a and at ISOLDE, CERN. Since the IGISOL method is fast and not limited by chemical or physical properties of elements, a large variety of nuclei close to the Z = N line can be studied. In the following sections the beta decay studies of 31 Cl, 58 Zn and selected nuclei close to A = 80 are presented.

2 Beta decay of

31

Cl

In massive ONe novae, where nucleosynthesis of elements heavier than phosphorous is concerned, two paths for the synthesis of 32 S both proceeding via 30 P(p, γ) have been suggested [1]. The reaction rate of 30 P(p, γ)31 S, which is a

Conference presenter; e-mail: [email protected]

needed to determine the end-point of that nucleosynthesis cycle, can be inversely studied via beta-delayed proton and gamma decay of 31 Cl. This has recently been done at IGISOL where 31 Cl ions were produced by a 40 MeV proton beam on a ZnS target. Accelerated and mass-separated 25 keV Cl ions were implanted into a thin carbon foil. The set-up consisted of three double-sided silicon strip detectors backed with thick silicon detectors, the ISOLDE Silicon Ball [2] and a 70% HPGe detector. Beta decay of 31 Cl has been previously studied using the He-jet method. Altogether eight proton peaks were reported in ref. [3] but all peaks except those of 986 keV and 1520 keV were later claimed to have come from 25 Si [4]. Due to mass separation at IGISOL, most of the controversial proton peaks can now be confirmed to arise from the decay of 31 Cl (see fig. 1).

3 Beta decay of

58

Zn

The beta decay of 58 Zn can be used to probe the isospin symmetry of transitions. The GT strength of the transitions from 58 Zn (TZ = −1) to the states in 58 Cu (TZ = 0) can be compared to the GT strength of analogous transitions from 58 Ni (TZ = +1) to 58 Cu studied via (3 He, t) charge-exchange reactions at RCNP in Osaka [5].

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The European Physical Journal A 85

Fig. 1. Beta-delayed protons from mass-separated 31 Cl [6]. The inset is an enlargement of the spectrum above 1.1 MeV. Table 1. The GT strengths B(GT) to the states of

Ex (58 Cu)

0 keV 1051 keV

58

Ni(3 He, t) [5]

0.155(1) 0.265(13)

58

Zn(β + ) [7]

< 0.31 0.54(26)

58

58

Cu.

Zn(β + ) [6]

< 0.5 0.37(10)

Zr, 86 Mo and 86 Nb have been investigated at IGISOL. A beam of 32 S on 54 Fe and nat Ni targets was used to produce the isotopes of interest which were accelerated to 40 kV, mass-separated and implanted into a tape at the first detector station which had two HPGe detectors and a plastic scintillator for betas. After some time of accumulation, the implanted ions were delivered to the second station consisting of a low energy Ge detector (LeGe) and the ELLI electron spectrometer which transported electrons to a cooled Si(Au) surface barrier detector. As a by-product at mass A = 81, internal conversion coefficients for a 190.5 keV transition of 81m Kr (13.1 s) were determined, αK = 0.50 ± 0.07 and αK /αL+M = 4.7 ± 0.1, favouring E3 multipolarity. These data were used to calculate the EC branching ratio from 81m Kr to 81 Brg.s. (QEC = 471.1 keV) which is needed for the estimation of the neutrino capture rate on 81 Br. Our log ft value of 5.13±0.09 for 81 Br(ν, e− )81m Kr supports the conclusion that 81 Br can be used as a solar neutrino detector. At mass A = 85 a transition with an energy of 69 keV was observed in 85 Nb. The measured half-life of the transition was 3.3 ± 0.8 s. Since the multipolarity of the transition is most likely E2 or M 2, the half-life cannot be fully explained by this kind of transition. The main interest at mass A = 86 lies in the half-life of 86 Mo, which is a waiting-point nucleus in the rp-process. The weighted average half-life of 19.1 ± 0.3 s confirmed the earlier result [9]. However, the isomeric state with a half-life of 56 s in 86 Nb claimed in [9] was not observed.

5 Future prospects 58

Fig. 2. Beta decay of Zn. The half-life of 83(10) ms [6] agrees with the earlier results, 86(18) ms [7] and 83(10) ms [8].

The Zn isotopes were produced via spallation reactions induced by a 1.4 GeV proton beam on a Nb foil target at ISOLDE, CERN. A chemically selective laser ion source was used to purify the 58 Zn beam, which was accelerated, mass-separated and implanted into a movable tape. With a set-up consisting of a 4πβ-detector and two Miniball detectors we could confirm the earlier results concerning the gamma rays and the half-life (see table 1 and fig. 2) but no beta-delayed protons were observed with the ISOLDE Silicon Ball set-up. The proton spectroscopy part was repeated with the ISOLDE Silicon Ball using 58 Ni(3 He, 3n)58 Zn fusion-evaporation reactions to produce 58 Zn at IGISOL. The analysis is in progress.

4 Isomers of astrophysical interest at masses A = 81, 85 and 86 The flow of the rp-process beyond the Zr-Nb cycle depends on the spectroscopic properties of the nuclei close to A = 80. The beta decays of 81 Y, 81 Sr, 81m Kr, 85 Nb,

In the future, a chemically selective laser ion source at IGISOL will substantially reduce background contaminants particularly in the region near A = 80. In addition, the binding energies and Q-values important both in astrophysical modeling and studies of GT strength can be measured for nuclei in this region at the JYFLTRAP. This work was supported by the Academy of Finland under the Finnish Center of Excellence Program 2000-2005 (Project No. 44875, Nuclear and Condensed Matter Physics Program at JYFL). The Russian participants are grateful for the help within the framework of agreement between the Finnish and Russian Academies (Project No. 8).

References 1. J. Jos´e et al., Astrophys. J. 560, 897 (2001). ¨ o, Nucl. Instrum. Methods A 513, 287 2. L.M. Fraile, J. Ayst¨ (2003). ¨ o et al., Phys. Rev. C 32, 1700 (1985). 3. J. Ayst¨ 4. T.J. Ognibene et al., Phys. Rev. C 54, 1098 (1996). 5. Y. Fujita et al., Eur. Phys. J. A 13, 411 (2002). 6. A. Kankainen et al., to be published. 7. A. Jokinen et al., Eur. Phys. J. A 3, 271 (1998). 8. M.J. L´ opez Jim´enez et al., Phys. Rev. C 66, 025803 (2002). 9. T. Shizuma et al., Z. Phys. A 348, 25 (1994).

Eur. Phys. J. A 25, s01, 131–133 (2005) DOI: 10.1140/epjad/i2005-06-051-y

EPJ A direct electronic only

Study of the (21+) isomer in

94

Ag

I. Mukha1,2,a , E. Roeckl2,b , H. Grawe2 , J. D¨ oring2 , L. Batist3 , A. Blazhev2,4 , C.R. Hoffman5 , Z. Janas6 , R. Kirchner2 , M. La Commara7 , S. Dean1 , C. Mazzocchi2,c , C. Plettner2,d , S.L. Tabor5 , and M. Wiedeking5 1 2 3 4 5 6 7

Instituut voor Kern- en Stralingsfysica, K. U. Leuven, B-3001 Leuven, Belgium Gesellschaft f¨ ur Schwerionenforschung, D-64291 Darmstadt, Germany St. Petersburg Nuclear Physics Institute, RU-188350 Gatchina, Russia University of Sofia, BG-1164 Sofia, Bulgaria Florida State University, Tallahassee, FL, USA Warsaw University, PL-00681 Warsaw, Poland Universit` a “Federico II” and INFN Napoli, I-80126 Napoli, Italy Received: 24 February 2005 / c Societ` Published online: 20 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The experimental decay properties of the (21+ ) isomer in

94

Ag are briefly discussed.

PACS. 21.10.-k Properties of nuclei; nuclear energy levels – 23.40.-s β decay; double β decay; electron and muon capture – 27.60.+j 90 ≤ A ≤ 149

Spin-gap isomers near doubly closed shell nuclei offer the chance to measure properties of single-particle states and to thus test predictions of the nuclear shell model [1]. An example is the (7+ ,9+ ) isomer in 94 Ag, which was found [2] in a β-delayed proton study to have a long halflife of 0.42(5) s, the spin/parity assignment being based on a comparison with shell model predictions. This as well as follow-up experiments [3,4,5,6], which narrowed the assignment down to (7+ ) and gave evidence for the existence of a second long-lived isomer in 94 Ag with a (21+ ) assignment, were performed at the on-line mass separator [7] of GSI Darmstadt. The status of the research on the (21+ ) isomer will be reviewed in this paper. The 94 Ag nuclei were produced by 58 Ni(40 Ca, p3n) fusion-evaporation reactions, stopped in a catcher inside the ion source of the on-line mass separator and released as singly charged ions. In the experiments considered here [3, 4,5,6] a FEBIAD-E or FEBIAD-B2C ion source, respectively, was used [8,9]. The latter one was equipped with cold pockets which enabled one to reach a beam intensity of 2 atoms/s for the long-lived 94 Ag isomers while suppressing the 94 Pd contamination. The mass-separated A = 94 beam was implanted into a tape which was poa

On leave from RRC “Kurchatov Institute”, RU-123481 Moscow, Russia; e-mail: [email protected] b e-mail: [email protected] c Present address: University of Tennessee, Knoxville, TN 37996, USA. d Present address: Yale University, New Haven, CT 06520, USA.

sitioned in the center of an array of charged-particle and γ-ray detectors and was regularly removed from the measuring position in order to avoid build-up of long-lived daughter activities. Originally we used a plastic scintillator for recording positrons and 12 germanium crystals for performing γ-ray spectroscopy in high resolution [3]. In the more recent measurements [4, 5,6], three silicon-strip detectors were used for the former and 17 germanium crystals for the latter purpose. Moreover, the properties of the 94 Ag isomers were studied [6] by mean of a total absorption spectrometer [10]. The following decay properties have been ascribed to the (21+ ) isomer in 94 Ag: – By observing feeding of known [11] high-spin states in 94 Pd in β-γ-γ measurements [3], the existence of the higher-lying isomer was shown and a lower limit of 17 was deduced for its spin. – Improved β-γ-γ data [4], obtained by using the silicon detectors for recording positrons, allowed us to extend the 94 Pd level scheme up to the (20+ ) level at 7700 keV. The experimental 94 Pd level energies are in very good agreement with predictions of an empirical shell model. However, a large-scale shell model calculation is required to lower the 21+ yrast state in 94 Ag below the 19+ one, thus making the former an E4 spingap isomer. Based on this calculation, a tentative spinparity assignment of (21+ ) for the higher-lying of the two isomers in 94 Ag and a value of 6300 keV for its excitation energy were deduced. An upper limit of 10% was found for the branching ratio of the internal deexcitation of the (21+ ) isomer.

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The European Physical Journal A

– By gating on high-energy events recorded in the silicon detectors, the β-delayed proton decay of the (21+ ) isomer was investigated [5]. States in 93 Rh were found to be populated up to a (33/2+ ) level at 4708 keV and a (39/2− -47/2− ) level at 6858 keV, whose properties are partially known from in-beam work [12]. These results confirm the existence of the (21+ ) isomer. The halflives of the (7+ ) and (21+ ) isomers were re-determined with improved accuracy to be 0.61(2) and 0.39(4) s, respectively. The total-absorption data confirmed the existence of two long-lived activities of 94 Ag, characterized by distinctly different β-endpoint energies, and showed that the (21+ ) isomer is populated with a fraction of about 10 % of their total reaction yield. – Beta-delayed two-proton decay of the 94 Ag isomers was searched for by gating on low-lying γ transitions in 92 Ru. In a preliminarily data analysis, a few events of this type have been registered [6] in proton-γ-γ coincidences for the 865 and 990 keV γ-transitions in 92 Ru [13], corresponding to a branching ratio of 0.2(2)% for β-delayed two-proton emission. – Evidence for direct proton decay of the (21+ ) isomer was obtained by demanding coincidences between single-hit events recorded in the silicon and γ-γ coincidence events observed in the germanium detectors [6]. The latter trigger was based on the known 93 Pd scheme [14]. The decay proton spectrum has a fine structure indicating two proton peaks 0.79(3) and 1.01(3) MeV. From these data, the excitation energy of the (21+ ) isomer was found to be 6.6(3) MeV, assuming a proton separation energy of 0.89(5) MeV for 94 Ag [15]. – Finally, a fourfold coincidence condition was used between double-hit events in the silicon and γ-γ correlations in the germanium detectors, the latter ones being based on the known 92 Rh scheme [16]. In this way, preliminarily evidence for direct two-proton radioactivity of the (21+ ) isomer was deduced, the two-proton sum energy amounting to 1.7(1) MeV [6]. These results are characterized by several exceptionally interesting features: – An important prerequisite for the success of this work was the excellent release properties of the FEBIAD sources with sinter-graphite catchers for short-lived silver isotopes, which has also lead to the identification of (23/2+ ) and (37/2+ ) isomers in 95 Ag, their upper half-life limits being 16 and 40 ms, respectively [17]. – The fusion-evaporation reactions used in our work appear to exclusively populate high-spin levels but not the ground state of 94 Ag. The latter one has most probably a 0+ assignment as can be deduced from the short half-life of 28(+29 −10 ) ms [18] which was obtained by using fragmentation reactions and indicates superallowed Fermi decay. – For the case of the β-delayed and direct two-proton radioactivity of the (21+ ) isomer in 94 Ag, the detection sensitivity corresponds to partial fusion-evaporation cross sections of about 140 and 350 pb, respectively. This sensitivity level is considerably below that reached in searching for decay properties of 100 Sn [19].

– The potential of decay spectroscopy of the (21+ ) isomer can be seen from the fact that the high-spin schemes of 94 Pd, 93 Pd and 93 Rh have been improved compared to those obtained previously by in-beam spectroscopy. – To our knowledge this work represents the first successful attempt to use multiple γ-γ coincidences to “tag” direct proton and two-proton emission. This technique is routinely used in studies of β- or γ-delayed chargedparticle emission (see [20] for a recent work on the latter disintegration mode). However, it has not been applied to study direct proton or two-proton radioactivity, except for the search for charged particle-γ anticoincidence events in the latter case [21]. All in all, we have identified a (21+ ) isomer in 94 Ag, the heaviest odd-odd N = Z nucleus with known decay properties. This isomer represents an unprecedented nuclear state in the entire Segr´e chart. It features a high excitation energy of 6.6(3) MeV, a short half-life of 0.39(4) s and no less than five decay modes, i.e. β-delayed γ-ray, proton and two-proton emission as well as direct proton and twoproton radioactivity. In particular, the direct emission of protons and two-protons from the same long-lived nuclear state is a unique phenomenon. Thus we have very good reasons to call 94m Ag (21+ ) a truly exotic nuclear state. It is a challenge to future experiments to, firstly, confirm the existence of the two-proton radioactivity of 94m Ag (21+ ) by accumulating better counting statistics for proton-proton-γ-γ events and, secondly, measure the angular correlations between the two protons and to thus clarify the emission process. Compared to such measurements of other cases of two-proton decay (see [21] for a recent review), 94m Ag (21+ ) samples prepared by means of an on-line mass separator offer a triple advantage: They are of high purity and comparatively large source strength and allow one to distinguish proton and two-proton radioactivity by means of γ-γ coincidence tagging.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

H. Grawe et al., these proceedings. K. Schmidt et al., Z. Phys. 350, 88 (1994). M. La Commara et al., Nucl. Phys. A 708, 167 (2002). C. Plettner et al., Nucl. Phys. A 733, 20 (2004). I. Mukha et al., Phys. Rev. C 70, 044311 (2004). I. Mukha et al., submitted to Phys. Rev. Lett. E. Roeckl et al., Nucl. Instrum. Methods Phys. Res. B 204, 53 (2003). R. Kirchner, Nucl. Instrum. Methods Phys. Res. B 26, 204 (1987); 204, 179 (2003). R. Kirchner, Nucl. Instrum. Methods Phys. Res. B 70, 186 (1992). M. Karny et al., Nucl. Instrum. Methods Phys. Res. B 126, 411 (1997). M. G´ orska et al., Z. Phys. 353, 233 (1995). H. A. Roth et al., J. Phys. G 21, L1 (1995). C. M. Baglin, Nucl. Data Sheets 81, 423 (2000). C. Rusu et al., Phys. Rev. C 69, 024307 (2004). G. Audi et al., Nucl. Phys. A 729, 337 (2003).

I. Mukha et al.: Study of the (21+ ) isomer in 16. D. Kast et al., Z. Phys. 356, 363 (1997). 17. J. D¨ oring et al., Phys. Rev. C 68, 034306 (2003). 18. A. Stolz et al., in Proceedings of the International Workshop on Selected Topics on N=Z Nuclei (PINGST 2000), Lund, Sweden 2000, edited by D. Rudolph, M. Hellstr¨ om

94

Ag

133

(Lund University, Lund Institute of Technology, Lund, Sweden, 2000), LUIP 003, p. 113. 19. M. Karny et al., these proceedings. 20. D. Rudolph et al., Phys. Rev. Lett. 350, (1994) 88. 21. M. Pf¨ utzner et al., these proceedings.

Eur. Phys. J. A 25, s01, 135–138 (2005) DOI: 10.1140/epjad/i2005-06-037-9

EPJ A direct electronic only

Beta-decay studies near

100

Sn

M. Karny1,a , L. Batist2 , A. Banu3 , F. Becker3 , A. Blazhev3,4 , K. Burkard3 , W. Br¨ uchle3 , J. D¨ oring3 , T. Faestermann5 , 3 3 1 6 3,7 3,7 M. G´orska , H. Grawe , Z. Janas , A. Jungclaus , M. Kavatsyuk , O. Kavatsyuk , R. Kirchner3 , M. La Commara8 , S. Mandal3 , C. Mazzocchi3 , K. Miernik1 , I. Mukha3 , S. Muralithar3,9 , C. Plettner3 , A. Plochocki1 , E. Roeckl3 , 1 ˙ adel3 , K. Schmidt11 , R. Schwengner12 , and J. Zylicz M. Romoli8 , K. Rykaczewski10 , M. Sch¨ 1 2 3 4 5 6 7 8 9 10 11 12

Institute of Experimental Physics, University of Warsaw, Warsaw, Poland St. Petersburg Nuclear Physics Institute, St. Petersburg, Russia Gesellschaft f¨ ur Schwerionenforschung, Darmstadt, Germany University of Sofia, Sofia, Bulgaria Technische Universit¨ at M¨ unchen, M¨ unchen, Germany Departamento de Fisica Te´ orica, Universidad Autonoma de Madrid, Madrid, Spain Taras Shevchenko Kiev National University, Kiev, Ukraine Dipartimento Scienze Fisiche, Universit` a “Federico II” and INFN Napoli, Napoli, Italy Nuclear Science Center, New Delhi, India Oak Ridge National Laboratory, Oak Ridge, TN, USA Continental Teves AG & Co., Frankfurt am Main, Germany Forschungszentrum Rossendorf, Dresden, Germany Received: 20 December 2004 / Revised version: 14 February 2005 / c Societ` Published online: 2 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The β-decay of 102 Sn was studied by using high-resolution germanium detectors as well as a Total Absorption Spectrometer (TAS). A decay scheme has been constructed based on the γ-γ coincidence exp data. The total experimental Gamow-Teller strength BGT of 102 Sn was deduced from the TAS data to 100 be 4.2(9). A search for β-delayed γ-rays of Sn decay remained unsuccessful. However, a Gamow-Teller hindrance factor h = 2.2(3), and a cross-section of about 3 nb for the production of 100 Sn in fusionevaporation reaction between 58 Ni beam and 50 Cr target have been estimated from the data on heavier tin isotopes. The estimated hindrance factor is similar to the values derived for lower shell nuclei. PACS. 21.10.-k Properties of nuclei; nuclear energy levels – 23.40.-s β decay; double β decay; electron and muon capture – 27.60.+j 90 ≤ A ≤ 149

1 Introduction For several years β-decay studies have tried to answer the question: why two different values for the axial-vector (gA ) coupling constant are needed, one for the description of the free neutron decay and another one for β-decay of atomic nuclei? In the latter case a renormalization of gA is required in order to get agreement between experimental data and theoretical predictions. Although a final explanation of the problem is the subject of the theoretical work, experiment should yield relevant data for a meaningful comparison. The experimentally derived quantity which can be directly compared to the theoretical predictions is the strength function. In some regions of the chart of nuclei due to the non-occurrence of Fermi-type transitions this can be limited to the Gamow-Teller (GT) strength function. In this case the theoretically derived a

Conference presenter; e-mail: [email protected]

GT strength is just the squared matrix element of the free στ operator acting between the initial (Ψi ) and final (Ψf ) wave functions: Bfth = Ψf |στ |Ψi 2 .

(1)

Bfth should be compared to the experimental value derived as 6147 s Iβ , (2) · Bfexp = 2 (gA /gV ) f (QEC − E ∗ ) · T1/2

where gA and gV are the axial-vector and vector coupling constants, respectively, Iβ the β-decay intensity to the final level f , QEC the total decay energy available, f (QEC − E ∗ ) the statistical rate function for the transition to the level at the excitation energy E ∗ , and T1/2 the half-life of the decaying nucleus (in seconds).

136

The European Physical Journal A Table 1. Hindrance factors derived for light nuclei.

Shell

hhigh

Reference

p sd pf

1.49(3) 1.67(4) 1.81(4)

[1] [2] [3]

Fig. 1. Section of the chart of nuclides near 100 Sn, with full squares representing isotopes studied at the GSI on-line mass separator with focus on the total GT strength determination. Numbers [4, 5, 6, 7, 8, 9, 10, 11, 12, 13] refer to the papers reporting results of the corresponding studies.

The ratio between the summed GT strength from theory and experiment defines a hindrance factor h  th th BGT f Bf  (3) h= exp . exp = BGT f Bf

The hindrance factor defined above can be split into two components h = hlow ·hhigh , with hlow being due to the limitation of the shell model calculation used, while hhigh being associated with higher-order effects. The hlow value is assumed to be 1 for a large-space shell model calculations (0¯ hω), while hhigh is directly linked to the quenching factor q used to renormalize the axial-vector coupling constant (hhigh = 1/q 2 ). The hindrance factors derived for lighter nuclei [1, 2,3] show a weak mass dependence as presented in table 1. Beta-decay studies near 100 Sn provide more information on the mass dependence of the hindrance factor. For exotic nuclei around 100 Sn most of the GT strength is expected to be located within the QEC window enabling observation via β-decay techniques. Moreover, β-decay in this region is governed by the pure GT transition of g9/2 protons to g7/2 neutrons. Figure 1 summarizes the β-decay studies in the 100 Sn region performed by using the GSI on-line mass separator for determining the total GT strength [4, 5, 6, 7,8, 9, 10, 11, 12, 13]. In this contribution we present preliminary results of the study of 102 Sn β-decay performed on the GSI on-line mass separator as well as results of a search for 100 Sn β-delayed γ-rays.

2 Experimental techniques The tin isotopes were produced in fusion-evaporation reactions between 58 Ni beam and 50 Cr target. On the basis of HIVAP calculations the beam energies on target were set to maximize the cross-section, i.e. 4.6 MeV/u and 5.8 MeV/u for 102 Sn and 100 Sn, respectively. Targets of around 3 mg/cm2 were placed inside a FEBIAD-B2C ion source, which was operated with the addition of CS2 and thus very selectively produced tin nuclei as SnS+ molecular ions [14]. Two complementary experimental set-ups were used for decay spectroscopy of mass-separated samples. Set-up (i) was a high-resolution array consisting of one Cluster, two Clover and 2 smaller volume coaxial detectors for γ-ray detection (γ = 7.9% for 1.3 MeV 60 Co line) surrounding the Si detectors for β-particle detection (β = 40%). Mass-separated ions were implanted into a mylar tape which was positioned in the center of the setup (i) and was used to remove the implanted activity after measuring times of 4 s. Set-up (ii) consisted of the Total Absorption Spectrometer (TAS) [15]. In this case massseparated ions were implanted into the mylar tape and periodically moved into the center of TAS for 4 s of measurement. Set-up (i) allowed us to establish the decay scheme based on γ-intensity and γ-γ coincidence data, while the TAS yielded information on the β-feeding to excited states in 102 In, and thus on the GT strength.

3 Beta-decay of

102

Sn

Figure 2 shows the 102 Sn decay scheme including two levels (dashed lines) which were added to the decay scheme in order to reproduce the TAS spectrum. The accuracy of the energy of the latter two levels is approximately 30 keV. The level scheme shown in fig. 2 resembles the main structure of that proposed earlier by Stolz et al. [16,17] without knowledge of γ-γ coincidences. The main difference is the non-observation of a 53 keV line in our experiment and thus a change in the tentative 102 In groundstate spin assignment from (7+ ) to (6+ ). This assignment is consistent with the one adopted in in-beam studies [18]. The TAS-based β-feedings (Iβ ) and comparative half-lives (log(f t)) are also shown in fig. 2, yielding the exp value of 4.2(9) for the decay of 102 Sn. This total BGT value, compared to a theoretical calculation performed in a π(p1/2 , g9/2 )11 , ν(g7/2 , d5/2 , d3/2 , s1/2 , h11/2 )3 model space [19], yields a hindrance factor of 3.7(7). This result agrees qualitatively with the hindrance factors obtained for other nuclei around 100 Sn, i.e. 97 Ag: 4.3(6) [11], 98 Ag: 4.6(6) [12], 98 Cd: 3.8(7) [19], 100 In 4.1(9) [5]. Unfortunately, large-space shell model calculation cannot be performed for 102 Sn decay and therefore it is not possible to deduce the hhigh part of the hindrance factor for this exp values nucleus. Nevertheless the systematics of the BGT and the resulting hindrance factor in the vicinity of 100 Sn will be discussed in sect. 5.

M. Karny et al.: Beta-decay studies near

100

Sn

137

Fig. 4. Production cross-section for light tin isotopes, deduced on the basis of the data collected at the GSI on-line mass separator. In the top left corner the cross-section for the production of 100 Ag is shown [21]. The experimental results were obtained at different 58 Ni beam on target energies which range from 3.8 MeV/u for 105 Sn to 5.8 MeV/u for 100 Sn.

Fig. 2. 102 Sn β-decay scheme. Transitions and levels established in the high-resolution experiment are presented by solid lines. Dashed lines represent levels and γ-transitions added to the level scheme in order to reproduce the TAS spectrum.

Fig. 3. β-gated γ spectrum for A = 100 + 32. Lines marked with diamonds belong to the decay of 100 Ag. Some of the strong transitions are marked by their energies in keV.

4 Search for β-delayed γ-rays of

100

Sn

In the last experiment at the GSI on-line mass separator, which has been decommissioned meanwhile, we spent 69 hours in a search for β-delayed γ rays of 100 Sn. Figure 3 presents a β-gated γ spectrum summed over all detectors. All identified lines (also in γ-γ coincidences) belong to the decay of 100 Ag with a transition intensity above 1% [20]. The sensitivity limit for the search for β-delayed γ-rays of 100 Sn was estimated on the basis of the non-observation of a γ line between 1 and 2 MeV, that could be assigned to the 100 Sn decay in the β-gated γ spectrum. It was assumed that such a line to be significant should have an

area of around 3σ of the average background in this region and a width of 3 keV, which corresponds to ≈ 27 counts. The following input data were used: 5.7% [14, 22] for separation efficiency for SnS+ ions of T1/2 = 0.94 s [23], 45 particle nA for average 58 Ni beam intensity, 3 mg/cm2 for 50 Cr target thickness, 7.5% and 40% for gamma and β detection efficiency, respectively, 100% for intensity of the γ transition searched for, 4.2 s for the length of the tape cycle (measurement plus transport) and 69 hours for the total measuring time. The resulting estimate of the sensitivity limit is on the level of 10 nb. The decay data obtained in this work for 101 Sn [24] to 105 Sn yield information on cross-sections for the production of these isotopes in the fusion-evaporation reaction between 58 Ni beam and 50 Cr target. The results are presented in fig. 4. The extrapolated cross-section for the 100 Sn production is about 3 nb. This result is considerably below the previously reported value of 40 nb given in [25] as well as below the achieved sensitivity limit, and explains the non-observation of 100 Sn β-delayed γ-rays in this experiment.

5 Total Gamow-Teller strength exp Figure 5 presents experimental BGT results for nuclei exp 100 Sn. As can be seen from the data the BGT around values for neutron-deficient tin and indium isotopes show a linear dependence as a function of the mass number. This feature can be qualitatively interpreted as reflecting the influence of the number of πg9/2 particles and νg7/2 holes in the parent and daughter nucleus. By extrapolatexp slope for tin isotopes to A = 100, the ing the linear BGT 100 BGT value of Sn is found to be ≈ 4.7. This result can be compared to the value of 6.5(1), calculated by using a shell model Monte Carlo method [26]. In this calculation

138

The European Physical Journal A exp from 100 Sn have not been observed, the BGT systematic allowed us to estimate the expected hindrance factor for 100 Sn decay to be h = 2.2, in agreement, within the respective uncertainties, with the hindrance factor observed for the lower f p shell.

The authors would like to thank W. H¨ uller for his contributions to the development and operation of the GSI on-line mass separator. This work was supported in part by the Polish Committee for Scientific Research funds of 2004, under Contract No. 2P03B 035 23, and the European Community RDT Project TARGISOL under Contract No. HPRI-CT-2001-50033.

exp Fig. 5. Experimental total BGT values of isotopes studied at the GSI on-line mass separator. Dashed lines mark the fitted linear dependency for tin and indium isotopes. The large black dot represents the extrapolated BGT value for 100 Sn.

the στ + operator was renormalized by 1/1.26 [26]. Thereth = 6.5(1)·1.262 = 10.3(2) fore, in the final comparison BGT should be taken yielding a hindrance factor h = 2.2. Since the calculations were performed in the complete 0¯hω shell the hlow is 1, yielding hhigh = 2.2. Although this value is somewhat larger than the hindrance factor for f p shell nuclei (see table 1), uncertainty of about 15% makes the two values comparable. Similar hindrance factors for f p shell nuclei and 100 Sn suggest a flat dependence of the quenching factor for masses of A = 100 and higher. The extrapolated BGT value can also serve as a basis for the estimate of the position of the only 1+ state expected to be fed in the β-decay of 100 Sn. With a QEC value of 7.39(66) [27] and a half-life T1/2 = 0.94+0.54 −0.27 s [23] the BGT value of 4.7 corresponds to a 100% β-feeding to a 100 In state at an excitation energy of ≈ 2.3 MeV.

6 Summary With the use of molecular SnS+ beams at the GSI on-line mass separator the β-decay of 102–105 Sn has been studied. In this contribution we presented in particular β-decay studies of 102 Sn. They include high-resolution γ-γ coincidence data, allowing us to build the decay scheme of 102 Sn as well as information on the GT strength distribution from a TAS measurement. Although β-delayed γ-rays

References 1. W.T. Chou, E.K. Warburton, B.A. Brown, Phys. Rev. C 47, 163 (1993). 2. B.H. Wildenthal, M.S. Curtin, B.A. Brown, Phys. Rev. C 28, 1343 (1983). 3. G. Martinez-Pinedo, A. Poves, E. Caurier, A.P. Zuker, Phys. Rev. C 53, R2602 (1996). 4. M. Kavatsyuk et al., these proceedings. 5. C. Plettner et al., Phys. Rev. C 66, 044319 (2002). 6. M. Gierlik et al., Nucl. Phys. A 724, 313 (2003). 7. M. Karny et al., Nucl. Phys. A 640, 3 (1998). 8. M. Karny et al., Nucl. Phys. A 690, 367 (2001). 9. M. La Commara et al., Nucl. Phys. A 708, 161 (2002). 10. L. Batist et al., Nucl. Phys. A 720, 245 (2003). 11. Z. Hu et al., Phys. Rev. C 60, 024315 (1999). 12. Z. Hu et al., Phys. Rev. C 62, 064315 (2000). 13. L. Batist et al., Z. Phys. A 351, 149 (1995). 14. R. Kirchner, Nucl. Instrum. Methods Phys. Res. B 204, 179 (2003). 15. M. Karny et al., Nucl. Instrum. Methods Phys. Res. B 126, 411 (1997). 16. A. Stolz, PhD Thesis, Universit¨ at M¨ unchen, 2001. 17. A. Stolz et al., AIP Conf. Proc. 638, 259 (2002). 18. D. Sohler et al., Nucl. Phys. A 708, 181 (2002). 19. B.A. Brown, K. Rykaczewski, Phys. Rev. C 50, R2270 (1994). 20. B. Singh, Nucl. Data Sheets 81, 1 (1997). 21. R. Schubart et al., Z. Phys. A 352, 373 (1995). 22. R. Kirchner, private communication. 23. R. Schneider, PhD Thesis, Universit¨ at M¨ unchen, 1996. 24. O. Kavatsyuk et al., submitted to Eur. Phys. J. A. 25. M. Chartier et al., Phys. Rev. Lett. 77, 2400 (1996). 26. D.J. Dean et al., Phys. Lett. B 367, 17 (1996). 27. G. Audi, A.H. Wapstra, C. Thibault, Nucl. Phys. A 729, 337 (2003).

Eur. Phys. J. A 25, s01, 139–141 (2005) DOI: 10.1140/epjad/i2005-06-038-8

EPJ A direct electronic only

Beta-decay spectroscopy of

103,105

Sn

M. Kavatsyuk1,2,a , O. Kavatsyuk1,2 , L. Batist3,4 , A. Banu1 , F. Becker1 , A. Blazhev1,5 , W. Br¨ uchle1 , K. Burkard1 , 1 6 1 1 7 8 7 orska , H. Grawe , Z. Janas , A. Jungclaus , M. Karny , R. Kirchner1 , J. D¨ oring , T. Faestermann , M. G´ 4 1 M. La Commara , S. Mandal , C. Mazzocchi1 , I. Mukha1 , S. Muralithar1,9 , C. Plettner1 , A. Plochocki7 , E. Roeckl1 , 7 ˙ adel1 , R. Schwengner10 , and J. Zylicz M. Romoli4 , M. Sch¨ 1 2 3 4 5 6 7 8 9 10

GSI, Darmstadt, Germany National Taras Shevchenko University of Kyiv, Kyiv, Ukraine St. Petersburg Nuclear Physics Institute, St. Petersburg, Russia Universit` a “Federico II” and INFN, Napoli, Italy University of Sofia, Sofia, Bulgaria Technische Universit¨ at M¨ unchen, M¨ unchen, Germany University of Warsaw, Warsaw, Poland Instituto Estructura de la Materia, CSIC and Departamento de Fisica Te´ orica, UAM Madrid, Madrid, Spain Nuclear Science Center, New Delhi, India Forschungszentrum Rossendorf, Dresden, Germany Received: 9 December 2004 / Revised version: 12 January 2005 / c Societ` Published online: 29 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Experimental and theoretical β-decay properties of

103,105

Sn are discussed.

PACS. 23.40.-s β decay; double β decay; electron and muon capture – 27.60.+j 90 ≤ A ≤ 149 – 21.10.Tg Lifetimes – 21.10.-k Properties of nuclei; nuclear energy levels

Experimental data on the structure of nuclei in the Sn region allow one to test predictions of the nuclear shell model. Two complementary setups were used to investigate the decay of 103,105 Sn (for the results on even-even tin isotopes see [1]), namely an array of highresolution silicon and germanium detectors as well as a total-absorption spectrometer (TAS) [2]. The experiment was performed at the GSI on-line mass separator. 103,105 Sn were produced in fusion-evaporation reactions, namely 50 Cr(58 Ni, αn)103 Sn and 50 Cr(58 Ni, 2p1n)105 Sn. A 5 MeV/u 58 Ni beam of about 40 particle-nA from the linear accelerator UNILAC impinged on an enriched 50 Cr target (3–4 mg/cm2 , enrichment 97%). A FEBIAD-B3C ion source with carbon, niobium and ZrO2 catchers, respectively, was used. High chemical selectivity for tin was achieved by adding CS2 vapour to the ion source [3,4]. Using this technique about 60% of the tin ion-output is shifted to the SnS+ molecular side-band, thus suppressing strongly the In, Cd, Ag, and Pd isobaric contaminants. After ionization, acceleration to 55 keV, and mass separation in a magnetic sector field, the A = 103 + 32 (A = 105 + 32) ions were directed to the high-resolution setup or to the TAS. The production yields of 103,105 Sn are given in ref. [1]. 100

a

Conference presenter; e-mail: [email protected]

The β-delayed γ-rays of 103 Sn were measured for the first time with a high-resolution gamma array. An array consisting of three silicon detectors and 17 germanium crystals (FZR-Cluster and two GSI VEGA SuperClover detectors) allowed for the detection of β-γ and β-γ-γ coincidences. In addition to the transitions from the 1078 keV (11/2+ ) and 1273 keV (13/2+ ) states known from in-beam spectroscopy [5], 20 new γ transitions in 103 In were identified. The half-life of 103 Sn was determined to be 7.0(3) s in agreement with a previous measurement [6]. The level scheme of the daughter nucleus 103 In, shown in fig. 1, was constructed by using the β-γ-γ coincidence data (for more details, see in [7]). It was impossible to make reliable spinparity assignment from the experimental data. The tentative spin and parity assignment for low-lying 103 In levels stem from a comparison of experimental excitation energies with shell model predictions. However, this method does not yield unambiguous results for high-lying 103 In states. Moreover, the apparent feeding of 103 In levels by β-decay of the (5/2+ ) ground state of 103 Sn cannot be used for spin and parity assignment either. This is due to the fact that the TAS data show that almost all levels are not directly fed in β-decay but by γ transitions from high-lying states. The β-decay in the 100 Sn region is dominated by the allowed Gamow-Teller (GT) πg9/2 → νg7/2 transition, with

140

The European Physical Journal A 2106 1611 1841



2 Table 1. Experimental and calculated BGT [gA /4π] for 103,105 Sn. The respective occupancies of neutron νg7/2 orbital (N7/2 ) and hindrance factors (h) are also given.

3462

2813 636

3281 3197



2813 103

965 2209 853 821 752 627 356 1909 831 1669 314 1429 351 1397 1356 1273 1078

2321 2209 2177 2149 2025 1908 1670 1429 1397 1356 1273 1078

(13/2+) (11/2+)

(9/2+)

0 103

In

GT strength measured by the TAS

Shell Model 0.04

0 0

1

2

3

4 E [MeV]

103

Sn

QEC = 7.66(10) MeV

2

BGT/0.02 MeV [gA /4π]

Fig. 1. Partial level scheme of 103 In obtained from β-decay high-resolution measurements.

0.08

105

5

6

7

Fig. 2. GT strength distribution for 103 Sn obtained from the TAS measurement (solid line) and resulting from the shell model calculations (dashed line). The theoretical distribution was normalized to the summed experimental BGT .

almost all GT strength (BGT ) lying within the respective QEC windows. The GT strength distributions of 103,105 Sn were measured using the TAS, being most appropriate to determine β feeding of weakly populated high-lying states in the daughter nucleus. As the total absorption efficiency of the TAS-differs from 1, the response function of the TAS for de-exciting γ cascades differs from a δ-function and is obtained through a Monte Carlo simulation. The latter requires as input information the level scheme of the daughter nucleus, in this case 103 In or 105 In. For the case of 103 Sn the scheme shown in fig. 1 was used for the analysis of the TAS data. For 105 Sn, the decay scheme was taken from [8]. Figure 2 shows a comparison of experimental and theoretical GT strength distributions for 103 Sn. The shape of the experimental distribution is dominated by a resonance structure extending between 3.5 and 5 MeV excitation energy in 103 In. This decay characteristics are interpreted as the GT decay of the eveneven core to the three-quasiparticle configurations. The

Sn Sn

exp BGT

3.5(5) 2.9(4)

N7/2

1.26 1.95



SM BGT

15.0 13.4

h

4.3(6) 4.6(6)

theoretical BGT distribution, shown in fig. 2, is resulting from a shell model calculation performed in the π(1g9/2 , 2p1/2 )12 -ν(1g7/2 , 2d5/2 , 2d3/2 , 3s1/2 , 1h11/2 )3 model space [9,10] and normalized to the summed experexp ). The theoretical distribuimental GT strength ( BGT tion qualitatively agrees with general shape of the measured GT strength but it is shifted by 400 keV towards higher excitation energies.  exp BGT values, given in Table 1 shows the resulting 2 units of gA /4π. This evaluation for 103 Sn and 105 Sn was based on QEC values of 7.66(10) and 6.23(8) MeV [7] and half-lives of 7.0(3) s and previously  exp measured 34(1) s [8], respectively. In table 1 the BGT results are compared with the estimate of the modified independent-particle  SM N N9/2 0 (1 − 7/2 shell model BGT = 10 8 )BGT . Here N9/2 denotes the number of protons filling the πg9/2 orbital, N7/2 the corresponding value for the νg7/2 orbital, and 0 BGT = 4(2j> +1)/(2+1) = 160/9 for the πg9/2 → νg7/2 GT transition. The occupancies N7/2 were deduced from wave functions of the 5/2+ ground states obtained from the shell model calculations mentioned above. The resulting N7/2 values for 103 Sn and 105 Sn are 1.26 and 1.95, respectively. Because of the model space restriction, the N9/2 value is 10 for both nuclei. To check the accuracy of  SM such an estimate the BGT value for 103 Sn was compared with that obtained by the shell model calculation mentioned above, yielding good agreement. However, the calculated total strength is significantly larger than the  GT exp measured B  SM  GTexpvalues. The hindrance factors h, defined / BGT ratio, amounts to 4.3(6) and 4.6(6) for as BGT 103 Sn and 105 Sn, respectively. In summary, measurements performed with the use of the TAS provided qualitatively new data on the GT strength distribution for 103,105 Sn. The results obtained constitute a solid ground for the test of theoretical calculations and call for more advanced shell model calculations. This work was partially supported by the European Community RTD Project TARGISOL under Contract No. HPRI-CT2001-50033. Authors from Warsaw acknowledge support from the Polish Committee of Scientific Research under KBN grant 2 P03B 035 23.

References 1. M. Karny et al., these proceedings. 2. M. Karny et al., Nucl. Instrum. Methods B 126, 411 (1997).

M. Kavatsyuk et al.: Beta-decay spectroscopy of 3. R. Kirchner et al., Nucl. Instrum. Methods B 204, 179 (2003). 4. D. Stracener et al., Nucl. Instrum. Methods B 204, 42 (2003). 5. J. Kownacki et al., Nucl. Phys. A 627, 239 (1997). 6. P. Tidemand-Petersson et al., Z. Phys. A 302, 343 (1981).

103,105

Sn

141

7. O. Kavatsyuk et al., Beta decay of 103 Sn, to be published in Eur. Phys. J. A. 8. M. Pf¨ utzner et al., Nucl. Phys. A 581, 205 (1995). 9. M. Hjorth-Jensen, T.T.S. Kuo, E. Osnes, Phys. Rep. 261, 125 (1995). 10. H. Grawe, M. Lewitowicz, Nucl. Phys. A 693, 116 (2001).

2 Radioactivity 2.3 Proton emitters

Eur. Phys. J. A 25, s01, 145–147 (2005) DOI: 10.1140/epjad/i2005-06-210-2

EPJ A direct electronic only

Discovery of the new proton emitter

144

Tm

R. Grzywacz1,2,a , M. Karny3,4 , K.P. Rykaczewski2 , J.C. Batchelder5 , C.R. Bingham1 , D. Fong6 , C.J. Gross2 , W. Krolas4,6 , C. Mazzocchi1 , A. Piechaczek7 , M.N. Tantawy1 , J.A. Winger8 , and E.F. Zganjar7 1 2 3 4 5 6 7 8

University of Tennessee, Knoxville, TN 37996, USA Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Institute of Experimental Physics, Warsaw University, PL-00681 Warsaw, Poland Joint Institute for Heavy Ion Research, Oak Ridge, TN 37831, USA UNIRIB, Oak Ridge Associated Universities, Oak Ridge, TN 37831, USA Vanderbilt University, Nashville, TN 37235, USA Louisiana State University, Baton Rouge, LA 70803, USA Department of Physics and Astronomy, Mississippi State University, MS 39762, USA Received: 21 December 2004 / Revised version: 20 January 2005 / c Societ` Published online: 15 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Evidence for the proton decay of 144 Tm was found in an experiment at the Recoil Mass Spectrometer at Oak Ridge National Laboratory. The 144 Tm events were found in the weak p5n channel of the fusion reaction using a 58 Ni beam at 340 MeV on a 92 Mo target. The observed proton decay energies are 1.70 MeV and 1.43 MeV and the half-life ∼ 1.9 μs. The decay properties suggest proton emission from the dominant πh11/2 part of the wave function and from the small πf7/2 admixture coupled to a quadrupole vibration. PACS. 23.50.+z Decay by proton emission – 27.60.+j 90 ≤ A ≤ 149

Fine structure in proton emission can be observed only if appropriate final states are available at low excitation energies. Four out of about thirty known proton precursors are known to exhibit fine structure; these are 131 Eu [1], 141 Ho [2], 146 Tm [3] and 145 Tm [4]. The first two involve proton decay of deformed nuclei to the low lying excited 2+ state, a member of the rotational ground-state band of the deformed daughter. The 145 Tm is an example of the decay to the 0+ ground state and the 2+ vibrational state of the 144 Er core. The theoretical models were developed recently [5, 6] to describe such odd-Z, even-N proton emitters. However, prior to this work, only a single odd-odd nuclide 146 Tm, was known to exhibit fine structure in its proton emission spectra [3]. The 146 Tm decay scheme is complex, since the proton-emitting states involve a coupling of proton and neutron orbitals to the even-even 144 Er core states [7, 8]. This paper reports the discovery of a new proton emitting odd-odd isotope 144 Tm, and evidence for fine structure in its decay pattern. The search for the proton decay of 144 Tm was performed in an experiment at the Recoil Mass Spectrometer (RMS) [9] at Oak Ridge. The 144 Tm events were found in the weak (σ ≈ 10 nb) p5n channel of the fusion reaction a

Conference presenter; e-mail: [email protected]

of a 58 Ni beam at 340 MeV on a 92 Mo target. Recoiling A = 144 ions in the charge states q = 27+ and q = 28+ were selected by adjustable slits. A Micro-Channel Plate detector system [10] was used to detect heavy ions before the implantation into a 65 μm thick Double-sided Silicon Strip Detector (DSSD). Four silicon detectors surrounding the front of the DSSD, along with thick Si(Li), mounted behind it, were used for background suppression of the proton/alpha escape signals and beta-decay radiation. All detectors were read by a fast digital-signalprocessing-based acquisition system [11]. Part of the system connected to the DSSD was used in the so called “proton-catcher” mode [4, 11] with an extended sensitivity range of 32 μs. We have developed a new method of pulse shape analysis, which takes into account the properties of each DSSD-strip electronic chain. The pile-up pulses for the microsecond proton emitter 113 Cs have been analyzed and the energy resolution was improved significantly from 75 keV FWHM reported for ∼ 1.7 MeV protons [4] to 35 keV FWHM at 0.96 MeV in this work. Additional data analysis conditions have been imposed: a) pixel correlation between front and back strips of the DSSD, b) anticoincidence condition of the proton signal with the MCP detected recoil, and c) anti-coincidence with the Si(Li) and silicon box detectors.

The European Physical Journal A

E=1.70 MeV 2

COUNTS/ch

COUNTS/ch

146 3 144

Tm→143Er

T1/2 = 1.9+1.2 -0.5 μs 2

E=1.43 MeV 1

1

0

1

1.2

1.4

1.6 1.8 2 ENERGY(MeV)

0

-4

-2

0

2 4 log(TIME(μs))

Fig. 1. Energy (left panel) and time (right panel) distribution of 144 Tm events. The log(t) representation is chosen for the time distribution plot [12] and the shape of the exponential decay curve with the 1.9 μs half-life is drawn.

The reliability of the electronic system and data analysis method has been verified using the known proton emitter 145 Tm (T1/2 = 3.1 ± 0.3 μs), which has been produced in the (58 Ni, p4n) reaction at 315 MeV 58 Ni beam energy. Twelve events have been detected during this measurement; eleven events were concentrated in the 1.73 MeV peak and one event was found at 1.4 MeV. The 1.4 MeV proton transition in the 145 Tm decay populates the 2+ state in 144 Er with a branching ratio Ip (2+ ) ≈ 9.6% [4]. The half-life of the 145 Tm events was determined to be 3.1+1.2 −0.7 μs using the maximum likelihood method and the analysis of uncertainties from [12]. The energies, lifetimes and branching ratios measured for 145 Tm decay are in very good agreement with the values obtained in the previous measurements [4]. The same electronic system and analysis was used for the 144 Tm measurement. The effective data taking time for the A = 144 experiment amounted to about 80 hours at a beam intensity of 10–20 pnA. Seven events out of all detected in the experiment fulfilled the analysis requirements, see fig. 1. Five events are concentrated in the peak at 1700(16) keV and two correspond to an energy of 1430(25) keV. The halflife has been determined to be 1.9+1.2 −0.5 μs using the previously applied method [12]. Both distributions are compatible with this half-life [13]. Despite the low statistics, by comparing these data to the known 145 Tm test data, we interpret these events as belonging to the decay of a single state in 144 Tm to two levels in 143 Er. Thus, the new isotope 144 Tm becomes the fifth proton emitter with fine structure that has been discovered. In the discussion of the result we will be guided by the assumed similarity of the two odd-odd thulium isotopes 144 Tm and 146 Tm and by the modified particle-vibrator model [5] which now includes the coupling of protons and neutrons to the vibrational core states. The observed proton emission from 146 Tm [3, 7, 8] is thought [5] to originate from two levels, the 5− ground state and the 10+ isomer. The main (∼ 50%) components of their wave-functions are proton-neutron configurations (πh11/2 ⊗ νh11/2 )J π =10+ and (πh11/2 ⊗ νs1/2 )J π =5− coupled to the 0+ ground state of the 144 Er core. The respective final states in 145 Er are the (νh11/2 )J π =11/2− isomer and the (νs1/2 )J π =1/2+

ground state, where the l = 5 proton emission dominates the decay width. Similar to 145 Tm [4] the fine structure in 146 Tm decay is caused by an admixture of the f7/2 protons coupled to the 2+ core vibration. The ∼ 3% configurations (πf7/2 ⊗ νh11/2 ⊗ 2+ )J π =10+ and (πf7/2 ⊗ νs1/2 ⊗ 2+ )J π =5− will mix with the main configuration and lead to l = 3 proton emission to the (νh11/2 ⊗ 2+ )J π =13/2− and (νs1/2 ⊗ 2+ )J π =3/2+ excited states in 145 Er. According to Hagino’s model calculations [5], large components (∼ 40%) of the wave function for both 10+ and 5− states involve core vibrations: (πh11/2 ⊗ νh11/2 ⊗ 2+ )J π =10+ and (πh11/2 ⊗ νs1/2 ⊗ 2+ )J π =5− . These parts of the wave function would be responsible for l = 5 proton emission to the final 13/2− and 3/2+ states (neutron coupled to core vibration), but this decay width is smaller than that for an l = 3 transition of the same energy, and does not contribute appreciably to the total decay width. On the contrary, the large contribution of such configurations reduces the total proton emission probability. The above description developed for 146 Tm should, in general, be valid for 144 Tm. Indeed, the calculation, using the same model, shows that l = 5 proton emission is expected from the 10+ and 5− states, to respective states in the daughter nucleus. However, in the experiment, there is evidence for two proton transitions originating from one level. In both scenarios, the 10+ and 5− lifetimes are predicted to be similar (assuming the 1.70 and 1.43 MeV energies of the protons), so it is difficult to decide which state is actually observed. Again, guided by the 146 Tm data we assume that we most likely observed the decay of the 10+ state. The low-spin 5− state is expected to have much lower population in the fusion reaction. Alternatively, the 10+ state could be very short lived and decay in flight during the ∼ 3 μs magnetic separation process, and not be observed. In conclusion, the new proton-emitting isotope 144 Tm, the fifth case of fine structure in the proton decay, has been observed. The observed decay energy of about 1.7 MeV and the half-life of ∼ 1.9 μs suggest proton emission from the dominant πh11/2 ⊗0+ and small πf7/2 ⊗2+ wave function components. Combined with 145 Tm and 146 Tm, a consistent picture of component wave function systematics is established in the ground states and long-lived isomers in the exotic Tm isotopes. This work was supported by the U.S. DOE through Contracts No. DE-FG02-96ER40983, DE-FG02-96ER41006, DE-FG0588ER40407, DE-FG02-96ER40978, and DE-AC05-76OR00033. ORNL is managed by UT-Battelle, LLC, for the U.S. DOE under Contract DE-AC05-00OR22725.

References 1. A. Sonzogni et al., Phys. Rev. Lett. 83, 1116 (1999). 2. K.P. Rykaczewski et al., in Mapping The Triangle: International Conference on Nuclear Structure, Grand Teton National Park, Wyoming, 22–25 May 2002, edited by A. Aprahamian, J.A. Cizewski, S. Pittel, N.V. Zamfir, AIP Conf. Proc. 638, 149 (2002).

R. Grzywacz et al.: Discovery of the new proton emitter 3. 4. 5. 6. 7.

T.N. Ginter et al., Phys. Rev. C 68, 034330 (2003). M. Karny et al., Phys. Rev. Lett. 90, 012502 (2003). K. Hagino et al., Phys. Rev. C 64, R041304 (2001). C. Davids, H. Esbensen, Phys. Rev. C 64, 034317 (2001). K. Rykaczewski et al., in Conference on Nuclei at the Limits, Argonne, IL, 26–30 July 2004, edited by D. Seweryniak, T.L. Khoo, AIP Conf. Proc. 764, 223 (2005). 8. J.C. Batchelder et al., these proceedings.

144

Tm

147

9. C.J. Gross et al., Nucl. Instrum. Methods A 450, 12 (2000). 10. D. Shapira et al., Nucl. Instrum. Methods A 454, 409 (2000). 11. R. Grzywacz, Nucl. Instrum. Methods B 204, 649 (2003). 12. K.H. Schmidt, Z. Phys. A 316, 19 (1984). 13. K.H. Schmidt, Eur. Phys. J. A 8, 141 (2000).

Eur. Phys. J. A 25, s01, 149–150 (2005) DOI: 10.1140/epjad/i2005-06-010-8

EPJ A direct electronic only

Study of fine structure in the proton radioactivity of

146

Tm

J.C. Batchelder1,a , M. Tantawy2 , C.R. Bingham2,3 , M. Danchev2 , D.J. Fong4 , T.N. Ginter5 , C.J. Gross3 , R. Grzywacz2,3 , K. Hagino6 , J.H. Hamilton3,4 , M. Karny7 , W. Krolas4,8 , C. Mazzocchi2 , A. Piechaczek9 , A.V. Ramayya4 , K.P. Rykaczewski3 , A. Stolz5 , J.A. Winger10 , C.-H. Yu3 , and E.F. Zganjar9 1 2 3 4 5 6 7 8 9 10

UNIRIB, Oak Ridge Associated Universities, Oak Ridge, TN 37831, USA University of Tennessee, Knoxville, TN 37996, USA Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Vanderbilt University, Nashville, TN 37235, USA NSCL/Michigan State University, E. Lansing, MI 48824, USA Department of Physics, Tohoku University, Sendai 980-8578, Japan Institute of Experimental Physics, Warsaw University, Pl-00681 Warsaw, Poland Joint Institute for Heavy Ion Research, Oak Ridge, TN 37831, USA Louisiana State University, Baton Rouge, LA 70803, USA Mississippi State University, Mississippi State, MS, USA Received: 4 November 2004 / c Societ` Published online: 14 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Measurement of fine structure in proton emission allows one to deduce the composition of the parent and daughter state’s wavefunction populated by proton emission. This paper presents new experimental data on the fine-structure decay of 146 Tm, and a new interpretation of its decay properties. PACS. 23.50.+z Decay by proton emission – 27.60.+j 90 ≤ A ≤ 149 – 21.10.Pc Single-particle levels and strength functions

Proton emission from a spherical (odd-Z, even N ) nucleus typically occurs to the 0+ ground state of the eveneven daughter. The situation with the decay of an oddodd nucleus to an (even-Z, odd-N ) isotope is quite a bit more complicated. The proton-emitting state consists of coupled proton and neutron states, with the final state being a low-energy neutron state in the daughter nucleus. The study of fine structure in the decay of these odd-odd nuclei can be used to identify and determine the relative energies of these low-energy neutron levels. In a previous experiment by this research group [1], fine structure in the proton radioactivity of 146 Tm was observed, which populated excited neutron states in 145 Er. Three fine-structure transitions of energies 0.89(1), 0.94(1) and 1.014(15) MeV were observed. Due to the low statistics of the data, only the 0.89 and 0.94 MeV transitions could be assigned based on their measured half-lives. Because of this, we re-investigated the decay of 146 Tm. Thulium-146 was produced via the 92 Mo(58 Ni, p3n) reaction with a beam energy of 297 MeV (292 MeV at the target mid-point), at the Oak Ridge Holifield Radioactive Ion Beam Facility (HRIBF), using the 25 MV Tandem Accelerator. Recoil nuclei of interest were separated a

Conference presenter; e-mail: [email protected]

by the HRIBF Recoil Mass Spectrometer (RMS) [2]. A microchannel plate detector (MCP) [3] at the focal plane was used to identify the A/Q of the recoils. Following the MCP, the ions were implanted into a ≈ 65 μm thick double-sided silicon strip detector (DSSD) [4] with 40 horizontal and 40 vertical strips. Signals from the DSSD are read by the preamps and then fed directly into a digital spectroscopy system using 25 DGF-4C modules (produced by X-ray Instrumentation Associates) [5,6]. It uses 40 MHz flash ADCs and on-board digital signal processors. In this experiment, a “Si-box” consisting of four 700 μm thick Si detectors was added to the system to veto escaping alphas and protons. With these detectors, we were able to significantly clean up the proton spectra. The existence of these three fine-structure peaks were confirmed, as is shown in fig. 1. The measured energies and half-lives are detailed in table 1. Based on the halflives, we assign the 0.89 MeV transition to the 198 ms highspin state (along with the 1.12 MeV line). The 0.94 and 1.01 MeV transitions are assigned to the 75 ms low-spin state (along with the 1.19 MeV line). From a simple shell model picture, one expects that 146 Tm would have 5 proton particles above the Z = 64 proton subshell, and 5 neutron holes below the N = 82 closed shell. The available single particle orbitals for both protons and neutrons are therefore h11/2 , d3/2 and s1/2 .

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Fig. 1. Spectrum of proton events obtained in this study. Table 1. Preliminary values for the proton energies, half-lives, and counts from 146 Tm. Intensities for the isomer and ground state are calculated relative to the 1.12 MeV and 1.19 MeV transitions, respectively.

Energy (keV)

T1/2 (ms)

Counts

Rel. Intensity

888(10) 1119(5)

190(80) 198(5)

170(30) 9450(250)

1.8(3) 100

938(10) 1016(10) 1189(5)

60(20) 70(15) 75(5)

290(30) 370(40) 1350(80)

22(2) 28(3) 100

From the experimental level systematics of heavier oddodd Tm isotopes and N = 77 isotones, one would expect an isomer with a spin of 8+ to 11+ (πh11/2 ⊗ νh11/2 ), and a ground state of 5− or 6− (πh11/2 ⊗ νs1/2 ). These states can have a complex structure with admixtures of πs1/2 ⊗ νh11/2 , πd3/2 ⊗ νh11/2 , and πh11/2 ⊗ νd3/2 contributing to their wave functions. The possible wave function compositions of both the isomer and ground state of 146 Tm were analyzed in the particle-core vibration coupling model [7,8] and compared with the experimental data (see table 2). In the case of the high-spin isomer, the calculations show that if the level was 8+ as previously assigned [1], both the branching ratio for the fine-structure decay and the half-life would be much smaller than the experimental data. The wave function composition that gives values most consistent with the experimental values is fine-structure decay from a 10+ state in the parent to the 13/2− state in the daughter. The relatively long proton half-life (compared to the measured half-life) indicates that the decay of this state proceeds mostly (≈ 75 percent) via beta decay. For the low-spin ground state, the two possibilities that agree with experiment for the 1.02 MeV transition are 5− → 3/2+ and 6− → 5/2+ . From the systematics of the N = 77 isotopes, one would expect the 5/2+ (νs1/2 ⊗ 2+ ) state to be greater than 200 keV, and the 3/2+ (νs1/2 ⊗ 2+ ) state to lie somewhere between 160 and 180 keV. We therefore assign the 1016 keV transition to the 3/2+ state. The  = 0 0.94 MeV transition is ascribed to a small (≈ 2%) admixture of πs1/2 νh11/2 in the ground state as in ref. [1]. The proposed decay scheme with the composition of the various levels is shown in fig. 2.

Fig. 2. Partial decay scheme of in MeV.

146

Tm. All energies are listed

Table 2. Possible initial- and final-state configurations for 146 Tm analyzed in the particle-core vibration coupling model [7, 8]. The experimental half-life values are the total halflife for the state. The proton partial T1/2 is adjusted for the experimental branching ratio (≈ 15%) of the 0.94 MeV transition.

i. s.

final states

f. s. BR

p T1/2 (ms)

8+ 8+ 9+ 9+ 10+ 10+ 10+ 11+ 11+

0.18 MeV Isomer 11/2− , 7/2− ; ν(11/2 ) ⊗ 2+ 11/2− , 9/2− ; ν(11/2 ) ⊗ 2+ 11/2− , 7/2− ; ν(11/2 ) ⊗ 2+ 11/2− , 9/2− ; ν(11/2 ) ⊗ 2+ 11/2− , 9/2− ; ν(11/2 ) ⊗ 2+ 11/2− , 13/2− ; ν(11/2 ) ⊗ 2+ 11/2− , 15/2− ; ν(11/2 ) ⊗ 2+ 11/2− , 13/2− ; ν(11/2 ) ⊗ 2+ 11/2− , 15/2− ; ν(11/2 ) ⊗ 2+ Experimental values:

0.004% 0.011% 0.002% 0.002% 0.04% 1.24% 1.07% 0.048% 2.33% 1.7(3)%

68 51 28 44 758 746 740 807 683 198(5)

5− 5− 6− 6−

Ground State 1/2+ , 3/2+ ; ν(s1/2 ) ⊗ 2+ 1/2+ , 5/2+ ; ν(s1/2 ) ⊗ 2+ 1/2+ , 3/2+ ; ν(s1/2 ) ⊗ 2+ 1/2+ , 5/2+ ; ν(s1/2 ) ⊗ 2+ Experimental values:

15.3% 3.0% 0.38% 15.6% 19(2)%

79 87 96 74 75(3)

References 1. T.N. Ginter et al., Phys. Rev. C 68, 034330 (2003). 2. C.J. Gross et al., Nucl. Instrum. Methods Phys. Res. A 450, 12 (2000). 3. D. Shapira et al., Nucl. Instrum. Methods Phys. Res. A 454, 409 (2000). 4. P.J. Sellin et al., Nucl. Instrum. Methods Phys. Res. A 311, 217 (1992). 5. B. Hubbard-Nelson et al., Nucl. Instrum. Methods Phys. Res. A 422, 411 (1999). 6. R. Grzywacz, Nucl. Instrum. Methods Phys. Res. B 204, 649 (2003). 7. K. Hagino, Phys. Rev. C 64, 041304R (2001). 8. M. Karny et al., Phys. Rev. Lett. 90, 012502 (2003).

Eur. Phys. J. A 25, s01, 151–153 (2005) DOI: 10.1140/epjad/i2005-06-194-9

EPJ A direct electronic only

Study of the N = 77 odd-Z isotones near the proton-drip line M.N. Tantawy1,a , C.R. Bingham1,2 , C. Mazzocchi1 , R. Grzywacz1,2 , W. Kr´olas3,4,5 , K.P. Rykaczewski2 , J.C. Batchelder6 , C.J. Gross2 , D. Fong4 , J.H. Hamilton4 , D.J. Hartley1 , J.K. Hwang4 , Y. Larochelle1 , A. Piechaczek7 , A.V. Ramayya4 , D. Shapira2 , J.A. Winger8 , C.-H. Yu2 , and E.F. Zganjar7 1 2 3 4 5 6 7 8

Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Joint Institute for Heavy Ion Research, Oak Ridge, TN 37831, USA Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, USA H. Niewodnicza´ nski Institute of Nuclear Physics, PL-31342, Krak´ ow, Poland Oak Ridge Associated Universities, Oak Ridge, TN 37831, USA Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA Department of Physics and Astronomy, Mississippi State University, Mississippi State, MS 39762, USA Received: 14 January 2005 / Revised version: 27 April 2005 / c Societ` Published online: 11 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The evolution of the πh11/2 νh11/2 and πh11/2 νs1/2 isomeric configurations was studied for the N = 77 isotones near the proton drip line. The decays of metastable levels in 140 Eu, 142 Tb , and 144 Ho were measured by means of X-, gamma- and conversion electron spectroscopy at the Recoil Mass Spectrometer at Oak Ridge. The sequence of isomeric levels in 140 Eu was experimentally determined. The half-life of the πh11/2 νh11/2 state in 142 Tb was remeasured to be 25(1) μs. The spins and parities of 5− and 8+ for the πh11/2 νs1/2 and πh11/2 νh11/2 142 Tb isomers, respectively, were established from measured multipolarities. No evidence for the expected 1+ ground state was found in the 144 Ho decay data. PACS. 21.10.Hw Spin, parity, and isobaric spin – 21.10.Tg Lifetimes – 23.20.Lv γ transitions and level energies – 27.60.+j 90 ≤ A ≤ 149

The interpretation of the structure of proton-emitting nuclei often suffers from the lack of data on nuclei next to the proton drip line. For an odd-odd N = 77 isotone 146 Tm, two proton-radioactive states are known and both exhibit fine structure in the proton emission spectra [1, 2, 3]. However, there was an ambiguity in the spin and configuration assignment and even a possibility of a third proton emitting state was considered [1]. In order to understand the evolution of the proton-neutron states beyond the proton drip line, we have studied the N = 77 even-mass isotones next to 146 Tm, namely 144 Ho,142 Tb, and 140 Eu. These nuclei were produced at the HRIBF in fusion-evaporation reactions between 54 Fe projectiles, at 225 MeV, 250 MeV and 315 MeV, respectively, and a 98.7% enriched, 1 mg/cm2 , 92 Mo target. Recoiling ions were separated according to their mass to charge (A/Q) ratio by means of the RMS [4]. After passing the position sensitive MCP detector [5], the recoils with desired A/Q were implanted into a collection foil or a tape [6] in front of the X-ray, gamma and conversion electron detectors assembled in a CARDS array [7]. For the 142 Tb studies involving conversion electron counting with a high a

Conference presenter; e-mail: [email protected]

resolution BESCA [6] spectrometer, a degrader foil (2.3 mg/cm2 Cu) was placed in front of the implantation point. This foil slowed the 70 MeV 142 Tb ions to about 10 MeV, resulting in an implantation depth of ∼ 3.3 μm. Electrons with energies below 20 keV emitted at this depth were stopped in the tape, and measured energies of 85 keV electrons were shifted down by about 3 keV. The signals from all RMS detectors were processed using 40 MHz Digital Gamma Finder XIA modules [8,9]. 140 Eu: a metastable state 140m1 Eu, T1/2 = 125 ms, was previously reported [10]. We identified a second isomeric level, 140m2 Eu [11], with T1/2 = 302(4) ns. The results were in agreement with two independent studies [12, 13]. Figure 1 displays the 175 keV and 185 keV transitions, known from the 140m1 Eu decay, in the γ-energy spectrum following the 302 ns activity within 200 ms. It shows experimentally the sequence of levels, with the 302 ns 140m2 Eu being above the 125 ms 140m1 Eu as was suggested in [12,13]. 142

Tb: there were two isomeric levels reported for Tb, the 15(4) μs 142m2 Tb at 620 keV [14] and the 303 ms 142m1 Tb at 280 keV [10]. We had more statistics than [14], thus we obtained a half-life of 142m2 Tb of 142

152

The European Physical Journal A 

3M 8 RAYS

OU TS E6



KE6

KE6



KE6

KE6

KE6



 

KE6



# 



 









 



%NER G Y K E6

   K

E6 %G 

E6

   K

E6

% +

   K

%+ E6

E6

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    K   K

   K

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E6

   K

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   K

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   K    K

  K

Fig. 1. Gamma rays following the decay of the 302 ns isomer (140m2 Eu) within 200 ms less those following by 200–400 ms. The presence of the 175 and 185 keV lines indicates that the 302 ns 140m2 Eu activity feeds the 125 ms 140m1 Eu. All labeled peaks are believed to be random statistical correlations except for the 175 and 185 keV peaks.  % + E6

  







%NERGY KE6



Fig. 2. 142m2 Tb conversion electron data measured with the BESCA detector within 90 μs after ion implantation. Table 1. K/L ratios and deduced transition multipolarities for some of the isomeric decays in 142 Tb.

Eγ (keV)

K/L (exp)

137 165 303 182 212

4.9(7) 4.5(6) 4.1(3) 5.4(3) 2.56(7)

K/L (calc) M1 E2

Multipolarity

6.89 6.91 7.02 6.92 6.93

E2, M 1 E2, M 1 E2 E2, M 1 E2

1.74 2.24 4.04 2.53 2.96

 % -

N

25(1) μs based on the decay pattern of 37, 137, 165, 219 and 303 keV lines with a total number of counts of about 1.25 × 106 in the first 210 μs. The observed K-to-L ratio of intensities for respective electron lines, see fig. 2, allowed determination of the multipolarities of 137, 165, and 303 keV transitions, see table 1. From the gamma intensities balance, the multipolarities of E1, M 1, M 2 and E3 were deduced for the 37, 84, 68 and 98 keV lines, respectively. The multipolarities of the transitions indicate a spin and parity of 5− for the πh11/2 νs1/2 142m1 Tb (see fig. 3). The sequence of derived multipolarities, the E2 and E1 for the 303 keV and 37 keV, respectively, allows assignment of 8+ to the πh11/2 νh11/2 142m2 Tb. The mixed multipolarities of M 1/E2 observed for the 137 keV and 165 keV lines agree with the level scheme and properties displayed in fig. 3.



%





KE6

K

SHƒQH 

4 PS

  % -

 %



 % -

4  MS -

 % -

  %



%



 % -

 4 B

Fig. 3.

142

 

Tb decay scheme.

144 Ho: we measured the half-life of 144m Ho to be 455(77) ns, in agreement with 500(50) ns [15]. In addition to the known transitions, we observed a 40 keV transition with a sub-microsecond half-life, but we were unable to assign it to the 144 Ho level scheme due to the lack of γ-γ coincidence statistics. Shorter or longer recoil-gamma correlation times did not reveal new activities. Since there are only up to three gamma lines following the decay of the high-spin (7+ ,8+ ) πh11/2 νh11/2 144m Ho [15], there is no clear evidence for feeding of a possible 1+ ground state. A 1+ ground state of 144 Ho can be expected from the simple extrapolation of the level systematics of the neighboring lower-mass N = 77 isotones, 140 Eu and 142 Tb. Our observation might indicate that the 1+ configuration does not minimize the energy of N = 77 even-mass isotones at the proton drip line, and the moderate spin πh11/2 νs1/2 level becomes the ground state [1,2, 3]. In summary, the systematic study of the p-n configurations in odd-odd N = 77 isotones was started. The spins and parities 8+ and 5− of πh11/2 νh11/2 and πh11/2 νs1/2 states in 142 Tb were established, and the level schemes of 140 Eu and 144 Ho were verified. The level scheme of 144 Ho to resembles the properties of 146 Tm, with an apparent absence of the 1+ ground state known for lower-mass N = 77 isotones. Further work is needed to explain the evolution and relative energies of the 1+ state versus the higher spin isomeric configurations.

This work was supported by the U.S. DOE through contract No. DE-FG02-96ER40983, DE-FG02-9ER41006, DE-FG0588ER40407, DE-FG02-96ER40978, and DE-AC05-76OR00033. ORNL is managed by UT-Battelle, LLC, for the U.S. DOE under contract DE-AC05-00OR22725.

References 1. 2. 3. 4.

T.N. Ginter et al., Phys. Rev. C 68, 034330 (2003). K.P. Rykaczewski et al., AIP Conf. Proc. 764, 223 (2005). J.C. Batchelder et al., these proceedings. C.J. Gross et al., Nucl. Instrum. Methods A 450, 12 (2000). 5. D. Shapira et al., Nucl. Instrum. Methods A 454, 409 (2000).

M.N. Tantawy et al.: Study of the N = 77 odd-Z isotones near the proton-drip line 6. J.C. Batchelder et al., Nucl. Instrum. Methods B 204, 625 (2003). 7. W. Kr´ olas et al., Phys. Rev. C 65, 031303R (2002). 8. http://www.xia.com. 9. R. Grzywacz, Nucl. Instrum. Methods B 204, 649 (2003). 10. R.B. Firestone et al., Phys. Rev. C 43, 1066 (1991). 11. K.P. Rykaczewski et al., Proceedings of the Third International Conference on Exotic Nuclei and Atomic Masses

12. 13. 14. 15.

153

ENAM2001, H¨ ameenlinna, Finland, 2–7 July 2001, edited ¨ o, P. Dendooven, A. Jokinen, M. Leino by J. Ayst¨ (Springer-Verlag, Berlin, Heidelberg, New York, 2003). D.M. Cullen et al., Phys. Rev. C 66, 034308 (2002). A. Hecht et al., Phys. Rev. C 68, 054310 (2003). I. Zychor et al., GSI report No.89-1(1989). C. Scholey et al., Phys. Rev. C 63, 034321 (2001).

Eur. Phys. J. A 25, s01, 155–157 (2005) DOI: 10.1140/epjad/i2005-06-143-8

EPJ A direct electronic only

Recoil decay tagging study of

146

Tm

A.P. Robinson1,a , C.N. Davids2 , D. Seweryniak2 , P.J. Woods1 , B. Blank2,3 , M.P. Carpenter1 , T. Davinson2 , S.J. Freeman2,4 , N. Hammond1 , N. Hoteling5 , R.V.F. Janssens1 , T.L. Khoo1 , Z. Liu2 , G. Mukherjee1 , C. Scholey6 , J. Shergur5 , S. Sinha1 , A.A. Sonzogni7 , W.B. Walters5 , and A. Woehr2,5 1 2 3 4 5 6 7

University of Edinburgh, Edinburgh, UK Argonne National Laboratory, Argonne, IL 60439, USA CEN Bordeaux-Gradignan, IN2P3-CNRS, France University of Manchester, Manchester, UK University of Maryland, College Park, MD 20742, USA University of Jyv¨ askyl¨ a, Jyv¨ askyl¨ a, Finland NNDC Brookhaven National Laboratory, Upton, NY 11937, USA Received: 20 January 2005 / c Societ` Published online: 10 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Gamma-rays from the odd-odd transitional proton-emitting nucleus 146 Tm have been observed using the recoil-decay tagging technique. A rotational band similar to the h11/2 decoupled band in 147 Tm has been observed. The particle decay of 146 Tm has been measured with improved statistics. A new decay scheme for 146 Tm is discussed with reference to prompt and delayed γ-rays detected in coincidence with particle decays. PACS. 23.20.Lv γ transitions and level energies – 23.50.+z Decay by proton emission – 27.60.+j 90 ≤ A ≤ 149

1 Introduction The phenomenon of one proton radioactivity occurs from odd-Z nuclei which are situated beyond the proton dripline, that is they are unbound to the emission of a proton from their ground state. Proton emission offers a unique laboratory in which to gain information on the structure of nuclei beyond the proton dripline. The combination of highly segmented double-sided silicon strip detectors (DSSD) with large high-efficiency Ge arrays allows detailed information on the excited states of proton-rich nuclei to be established. The thulium proton-emitting isotopes 145,146,147 Tm lie in a region of predicted shape change [1], moving from a prolate shape for 145 Tm to an oblate shape for 147 Tm. Fine structure has been observed in the decay of 145 Tm [2], with a branch to the first 2+ excited state of the daughter nucleus (Ep = 1728(10) keV and t1/2 = 3.1(3) μs, Ep = 1393(10) keV and t1/2 = 3.1(3) μs, respectively). A total of 5 separate proton transitions were observed in 146 Tm [3, 4]. Excited states in 147 Tm have been observed using the recoil decay tagging (RDT) technique with a modest array of Ge detectors [5]. a

Conference presenter; e-mail: [email protected]

Fig. 1. Decays in DSSD within 500 ms of A = 146 implant.

2 Experimental results In a recent RDT study a 92 Mo beam from the ATLAS accelerator was used with a 58 Ni target to produce 145,146,147 Tm via the 1p4n, 1p3n and 1p2n fusion-evaporation channels, respectively. The GAMMASPHERE Ge array was used in conjunction with the standard FMA and DSSD setup at Argonne National

156

Fig. 2. Proposed level scheme for spin and parity assignments.

The European Physical Journal A

146

Tm showing tentative

Laboratory [6]. A parallel semi-Gaussian shaping amplifier and fast delay-line amplifier system was used to instrument the DSSD allowing recoil-decay correlations to be observed for times down to 1 μs [7]. Fig. 3. Recoil-decay tagged γ-rays for (a) 890 keV proton transition and (b) 1122 keV proton transition.

3 Results and discussion The five previously observed proton transitions in 146 Tm were remeasured with improved statistics, fig. 1. The energies of the transitions were found to be in good agreement with previous measurements. New, more precise values were measured for the half-lives of the five transitions. A proposed rotational band feeding the high-spin isomer emitting 1122 keV protons is shown in fig. 2. The spin and parity assignments are based on the systematics of similar rotational bands observed in the N = 77 isotones [8]. The energies of the transitions are very similar to those of the ground state band in 147 Tm [5] which is based on the h11/2 proton state. 146 Tm is an odd-odd proton emitter which lies in the transitional region between predicted deformed and near-spherical shapes. It is potentially a rich source of information regarding the role of the odd neutron in proton decay. The improved statistics in this experiment allow some of the long-standing difficulties with the level scheme of 146 Tm to be addressed. The most intense ∼ 200 ms 1122 keV transition is assigned as an l = 5 transition from a (10+ , 9+ , 8+ ) state based on the πh11/2 νh11/2 configuration, which agrees with previous work. High spin isomer states are strongly populated in fusion-evaporation reactions in this region. From the half-life measurements it appears that the 937 keV, 1010 keV and 1192 keV transitions occur from the same state with a weighted half-life of 82(4) ms. As in previous work the 1192 keV transition is assigned as an l = 5 transition from a (6− , 5− ) state based on the

πh11/2 νs1/2 configuration to the ground state of 145 Er. The neighboring N = 77 isotones have a number of lowlying 3/2+ and 5/2+ states below the 11/2− state. On the basis of this, and the delayed γ-rays seen in coincidence with the 937 keV and 1010 keV transitions, the 937 keV and 1010 keV transitions are assigned as decays from the (6− , 5− ) state in 146 Tm to low-lying states in 145 Er. This is the first example of decay to 3 states in the daughter nucleus from a proton emitter. The placement of the 890 keV transition is more problematic. It has previously been assigned as a decay from the (10+ ) isomeric state in 146 Tm to a 9/2− state in 145 Er [4], however this assignment would require a significant admixture of the πf7/2 orbital to the emitter wave function. An alternative assignment could be the l = 0 decay of a low-lying (1+ ) state in 146 Tm to the ground state of 145 Er. A similar state is seen in neighboring odd-odd isotopes. The half-life measured here suggests that the 890 keV transition occurs from a third state with a half-life of 155(20) ms. This would seem to favor decay from a low-lying 1+ state in 146 Tm to the ground state of 145 Er. The recoil-decay tagged γ-ray spectra for the 890 keV transition and the 1122 keV transition are shown in fig. 3. Despite the low statistics in the 890 keV spectrum it is clear that the most intense 476 keV transition from the 1122 keV gated spectrum is not present, again suggesting that the decays occur from two separate states in 146 Tm.

A.P. Robinson et al.: Recoil decay tagging study of

146

Tm

157

A comparison of experimental partial proton decay halflives with detailed theoretical calculations is needed to fully determine the structure of 146 Tm.

4 Summary The combination of the FMA-DSSD system with GAMMASPHERE provides a powerful tool for studying excited states in proton-rich nuclei. The excited states of 146 Tm have been observed for the first time. Improved particle decay statistics have allowed all the observed proton transitions from this nucleus to be placed in a decay scheme for the first time. This work was supported by the U.S., D.O.E., under Contract No. W-31-109-ENG-38. A.P.R would like to acknowledge funding from EPSRC. P.J.W would like to acknowledge receipt of an EPSRC research grant.

References Fig. 4. Proposed

146

Tm decay scheme.

The absence of delayed γ-rays in coincidence with the 890 keV transitions suggests that the decay is to the ground state. As such the transition is assigned as decay from a low-lying 1+ state to the ground state of 145 Er. The proposed decay scheme for 146 Tm is shown in fig. 4.

1. 2. 3. 4. 5. 6. 7. 8.

P. M¨ oller et al., At. Data Nucl. Data Tables 66, 131 (1997). M. Karny et al., Phys. Rev. Lett. 90, 012502 (2003). K. Livingston et al., Phys. Lett. B 312, 46 (1993). T.N. Ginter et al., Phys. Rev. C 68, 034330 (2003). D. Seweryniak et al., Phys. Rev. C 55, R1237 (1997). C.N. Davids et al., Phys. Rev. C 55, 2255 (1997). A.P. Robinson et al., Phys. Rev. C 68, 054301 (2003). C. Scholey et al., Phys. Rev. C 63, 034321 (2001).

Eur. Phys. J. A 25, s01, 159–160 (2005) DOI: 10.1140/epjad/i2005-06-166-1

EPJ A direct electronic only

Particle-core coupling in the transitional proton emitters 145,146,147 Tm D. Seweryniak1,a , C.N. Davids1 , A. Robinson2 , P.J. Woods2 , B. Blank3 , M.P. Carpenter1 , T. Davinson2 , S.J. Freeman4 , N. Hammond1 , N. Hoteling5 , R.V.F. Janssens1 , T.L. Khoo1 , Z. Liu2 , G. Mukherjee1 , J. Shergur5 , S. Sinha1 , A.A. Sonzogni6 , W.B. Walters5 , and A. Woehr5,2 1 2 3 4 5 6

Argonne National Laboratory, Argonne, IL 60439, USA University of Edinburgh, Edinburgh, UK CEN Bordeaux-Gradignan, IN2P3-CNRS, Gradignan Cedex, France University of Manchester, Manchester, UK University of Maryland, College Park, MD 20742, USA NNDC Brookhaven National Laboratory, Upton, NY 11937, USA Received: 20 December 2004 / Revised version: 3 February 2005 / c Societ` Published online: 7 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Excited states in 3 transitional proton emitters 145,146,147 Tm were studied using the Gammasphere Ge array coupled with the Argonne Fragment Mass Analyzer. The 147 Tm level scheme was extended and the unfavored signature partner of the decoupled proton h11/2 band was found. A rotational band feeding the high-spin isomer in 146 Tm was observed with properties similar to the 147 Tm ground-state band. A regular sequence of γ rays correlated with the ground-state 145 Tm proton decay has properties of the h11/2 band as well. In addition, coincidences between the fine structure proton line and the 2 + → 0+ γ-ray transition in the daughter nucleus were detected. Comparison between level energies measured and calculated using the Particle Rotor model indicates that 145 Tm might be γ-soft. PACS. 23.20.Lv γ transitions and level energies – 23.50.+z Decay by proton emission – 27.60.+j 90 ≤ A ≤ 149

1 Introduction In recent years, proton emitters have become a testing ground for nuclear structure far from the line of stability. The discovery of the deformed proton emitters 131 Eu and 141 Ho [1] and the proton-decay fine structure in 131 Eu [2] initiated detailed studies of the role of deformation in proton decay. The observation of excited states in 141 Ho elucidated the role of the Coriolis interaction in proton decay [3].

2 Experimental results In this work, excited states in the moderately deformed proton emitters 145,146,147 Tm were studied using the Recoil-Decay Tagging method. A 92 Mo beam at 417, 460 and 512 MeV impinged on a 0.6 mg/cm2 58 Ni target to produce 147 Tm, 146 Tm, and 145 Tm, respectively. Prompt γ rays were detected in the Gammasphere Ge array. The γ rays were tagged by proton decays observed in a DoubleSided Si Strip Detector placed at the focal plane of the Argonne Fragment Mass Analyzer (FMA). Excited states a

Conference presenter; e-mail: [email protected]

Fig. 1. Gamma rays correlated with protons emitted from 145 Tm.

in 147 Tm have been studied previously using a modest Ge array [4]. Due to a much larger γ detection efficiency the 147 Tm ground-state band was significantly extended and evidence was found for the unfavored signature partner band. The 146 Tm proton emitter exhibits a complex protondecay level scheme. At least 5 proton lines have been associated with this nucleus [5]. In this work prompt γ-ray spectra correlated with the individual 146 Tm proton lines

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Eg(keV)

Fig. 2. The level schemes proposed for

145,147

Tm isotopes.

500

400

300

Fig. 4. Calculated and measured (crosses) level energies in 145 Tm for different values of β2 (b) and γ (g) (see the legends). The moment of inertia was adjusted to fit the 2+ excitation energy of the core.

200

100

0 0

500

1000

1500

2000

2500 Ep(keV)

Fig. 3. 145 Tm proton-gamma coincidences detected at the focal plane of the FMA.

were obtained. A rotational band feeding the high-spin isomer, which decays via 1122 keV proton emission, was established in 146 Tm. The energies of the transitions in the band are very similar to those of the ground-state band in 147 Tm. This suggests that both bands are based on the h11/2 proton state and that both nuclei have similar deformation. The 145 Tm ground state decays primarily to the 0+ ground state in the daughter 144 Er nucleus. A branch to the 2+ state has been observed recently [6]. The crosssection for producing 145 Tm is about 200 nb. The 145 Tm half-life is only 3 μs. To avoid pileup of protons with implants, fast delay-line amplifiers were developed. They allowed the observation of protons with decay times as short as 1 μs. The γ-ray spectrum tagged by the 145 Tm protons is shown in fig. 1. A regular sequence of mutually coincident γ rays have properties of a decoupled proton h11/2 band. The 145 Tm and 147 Tm level schemes are shown in fig. 2. In addition, coincidences between the proton fine structure line and the 2+ → 0+ transition in 144 Er were detected at the focal plane of the FMA (see fig. 3). This is the first time that coincidences between ground-state proton decays and γ rays have been seen. A precise energy of 329(1) keV was measured for the 2+ state in 144 Er.

3 Discussion The calculated deformation changes rapidly from oblate in Tm (β2 = −0.18) to prolate in 145 Tm (β2 = 0.25) [7].

147

The dominant γ-ray sequences feeding the ground states in 147 Tm and 145 Tm have properties of decoupled πh11/2 bands. The Eγ (15/2− → 11/2− ) energies, which are close to E(2+ ) in the even-even core, indicate deformation lower than calculated for both 145 Tm and 147 Tm. The E(19/2− ) to E(15/2− ) ratio, equivalent to E(4+ )/E(2+ ) ratio, is about 2.5, which is characteristic of a γ-soft rotor, and is greater than 2.2 for a typical harmonic vibrator, but below the rotor value of 3.33. This suggests an alternative way of viewing the proton decay in 145,147 Tm as emission of the h11/2 proton aligned with the angular momentum of the γ-soft deformed core. Results of Particle-Rotor model calculations for the level energies in the 145 Tm ground-state band are shown in fig. 4. The best agreement between the experimental and calculated values both for 145 Tm and 147 Tm was found for an asymmetry parameter of γ ≈ 30◦ . This work was supported by the U.S. Department of Energy, Office of Nuclear Physics, under contract No. W-31-109-ENG38.

References 1. 2. 3. 4. 5. 6. 7.

C.N. Davids et al., Phys. Rev. Lett. 80, 1849 (1998). A.A. Sonzogni et al., Phys. Rev. Lett. 83, 1116 (1999). D. Seweryniak et al., Phys. Rev. Lett. 86, 1458 (2000). D. Seweryniak et al., Phys. Rev. C 55, R2137 (1997). T.N. Ginter et al., Phys. Rev. C 68, 034330 (2003). M. Karny et al., Phys. Rev. Lett. 90, 012502 (2003). P. Moeller et al., At. Data Nucl. Data Tables 59, 185 (1995).

Eur. Phys. J. A 25, s01, 161–163 (2005) DOI: 10.1140/epjad/i2005-06-090-4

EPJ A direct electronic only

Nuclear pairing and Coriolis effects in proton emitters A. Volya1,a and C. Davids2 1 2

Department of Physics, Florida State University, Tallahassee, FL 32306-4350, USA Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA Received: 12 October 2004 / c Societ` Published online: 23 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We introduce a Hartree-Fock-Bogoliubov mean-field approach to treat the problem of proton emission from a deformed nucleus. By substituting a rigid rotor in a particle-rotor model with a mean field, we obtain a better description of experimental data in 141 Ho. The approach also elucidates the softening of kinematic coupling between particle and collective rotation, the Coriolis attenuation problem. PACS. 23.50.+z Decay by proton emission – 21.60.-n Nuclear structure models and methods

Proton emission is a weak single-particle (s.p.) process with widths about 20 orders of magnitude smaller than the usual MeV scale of other nuclear interactions. This makes observation of proton radioactivity an ideal and powerful tool for non-invasive probing of the single-proton inmedium dynamics. Recent studies have already explored numerous nuclear mean-field properties of proton emitters including deformations, vibrations [1] rotations [2], pairing and other many-body correlations [3, 4]. In this work, using proton emission from deformed nuclei, we concentrate on an old problem known as Coriolis attenuation problem [5] in the particle-rotor model (PRM). Recent studies of proton decay [2,4] highlight the same lack of kinematic coupling between the particle and the deformed rotor as was inferred decades ago from observations of the energy spectra of odd-A nuclei [5,6]. The second purpose of this work is to gain an understanding of and to develop a better theoretical technique to describe particle motion in the deformed mean-field. Here the notion of a core as a rigid rotor is inadequate and, as emphasized in numerous works [5, 7,8], the residual twobody interaction and collective modes are important parts of the dynamics. We consider an axially-symmetric deformed proton emitter and assume that the total Hamiltonian is composed of a collective Hcoll = R2⊥ /2L and intrinsic parts Hintr =

 Ω

Ω a†Ω aΩ −

1 GΩΩ  a†Ω˜ a†Ω aΩ  aΩ˜ . 4 

(1)

ΩΩ

Here R denotes the rotor angular momentum, involving only the part perpendicular (⊥) to the symmetry axis, and a†Ω and aΩ stand for s.p. creation and annihilation a

Conference presenter; e-mail: [email protected]

operators of state |Ω) in the deformed body-fixed meanfield potential. Nuclear pairing involves body-fixed time˜ and describes the residual reversal s.p. states |Ω) and |Ω) two-body interaction. In contrast to the usual PRM this model assumes some odd number of valence particles. In the limit where the valence space covers the entire nucleus the collective rotor variables become redundant. Kinematic coupling between the intrinsic system and collective rotor occurs due to conservation of total angular momentum I = R + j, where j is the angular momentum of the valence particles. Components of this operator can be expressed in the a intrinsic body-fixed basis as   jΩΩ  a†Ω aΩ  , (2) j3 = ΩΩ a†Ω aΩ , j+ = Ω

ΩΩ 

† . The coefficients jΩΩ  = (Ω|j+ |Ω  ) similarly for j− = j+ are obtained using expansion of states |Ω) in spherical basis. Excluding a trivial rotational part from the total Hamiltonian H = I2 /(2L) + H  , we obtain

H =

1 1 2 (j+ I− + j− I+ ) + Hintr , (j − 2j32 ) − 2L 2L

(3)

which is to be solved via many-body techniques using basis I states formed as products of Wigner DM K (ω)-functions of collective angles ω, and any complete set of many-body intrinsic states such as Slater determinants. Here we implement a Hartree-Fock-Bogoliubov (HFB) approach that allows one to determine a s.p. mean-field, which is a combination of the rotor degrees of freedom and even-particle valence system, and absorbs in the best way kinematic couplings and residual nucleon-nucleon correlations. By making a Bogoliubov transformation to quasi  i † aΩ and with the requireparticles αi = Ω uiΩ aΩ + vΩ

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Table 1. Comparison of different theoretical results and experimental data for the case of 141 Ho proton emission.

Γ0 (×10−20 MeV)

PRM

Adiabatic Coriolis Coriolis + pairing Experiment

Fig. 1. The average Coriolis suppression factor as a function of the pairing gap in 141 Ho.

ment that the elementary quasiparticle excitations are stationary we obtain the usual HFB equations  i ∗ uiΩ ei + ΔΩ vΩ = εΩΩ  uiΩ  , Ω ∗

i ei + ΔΩ uiΩ = − vΩ



i εΩΩ  vΩ  .

(4)

Ω

Here in full analogy to PRM the diagonal part of the s.p. potential is given by the usual s.p. energy corrected with the recoil term and decoupling factor ΔE [5] εΩΩ = Ω +

 1  (Ω|j2 |Ω) − 2Ω + δΩ,1/2 ΔE . 2L

(5)

The off-diagonal term in eq. (4) violates deformation alignment, the K-symmetry, which manifests itself through non-vanishing average mean-field expectations j+  =

j−  = j while j3  = 0. This average mean-field value enters the off-diagonal s.p. potential  1  (I − Ω)(I + Ω + 1) − j jΩ+1 Ω , εΩ+1,Ω = − 2L (6) and is to be determined in a self-consistent solution  i i jΩ+1,Ω vΩ+1 vΩ . (7)

j = 2 i, Ω>0

This is analogous to non-conservation of particle number N , a common situation in the HFB approach. Particle number is restored on average via the introduction of a chemical potential H  → H  − μN, so that the pairing gap and chemical potential in eq. (4) are self-consistently determined    ∗ 1  i i i GΩΩ  uiΩ  vΩ vΩ vΩ . ΔΩ = − , N = 2 2  i i Ω

RHBF

15.0 15.0 5.9 1.4 7.0 1.7 10.9 ± 1.0

Γ2 /Γ0 (%) PRM RHFB

0.73 1.8 1.7

0.73 1.2 0.3

0.71 ± 0.15

besides acting on an odd particle, also perturbs an evenparticle mean-field, thus producing a suppression of the Coriolis mixing. The Coriolis interaction takes the form −(I − j)⊥ j/L similar to the Routhian in the Cranking Model [5], and is suppressed. This is in contrast with the PRM, where by definition the rotor is rigid and  j = 0.   2 The quantity ξ = 1 − j/ I(I + 1) − Ω  is the av-

erage suppression factor; for the case of 141 Ho (see below), it is shown as a function of pairing gap in fig. 1. The idea to phenomenologically substitute the spin of the rotor R = (I−j)⊥ for the operator I in order to explain Coriolis attenuation was suggested in [9], and contributions from the j2 operator in the mean-field approach are discussed in [10]. Other contributions coming from non-rigidity of the core are also considered [5,8]. We apply this approach to the proton emitter 141 Ho where partial decay widths Γ0 for decay to the 0+ ground state and Γ2 to the 2+ first excited state in 140 Dy are known from experiment. The spectrum of 140 Dy is used to determine deformation and moment of inertia. The valence space is limited to a negative parity subspace coming from spherical h11/2 orbital, but particle depletion due to pair excitation onto positive parity states is included. The decay amplitudes computed using appropriate deformed Woods-Saxon potential and expressed via normalization of the wave function [2]   Ω Ω , where Glj is the irreguAlj (k) = φlj (r)/Glj (kr) r=∞

lar Coulomb function. The decay width is given by [4]  2  IK i Ω C u A Γ = μk 2(2R+1)  jK,R0 Ω lj  , where C is a Ω>0 2I+1 Clebsch-Gordan coefficient and the uΩ factors come from the solution of eq. (4). The results of this calculation, labeled as RHFB, are compared with PRM and experiment in table 1. The Coriolis attenuation problem is transparent; e.g., for Γ0 (first column), the unjustified theoretically adiabatic limit (L → ∞) overestimates experiment. When improving this by introduction of Coriolis mixing which is softened by pairing correlations the result extremely overreduces Γ0 . The HFB calculation shown in table 1 is limited to a very small valence space, but gives a reasonable description, and most importantly, as a better founded approach clarifies the reason for weakened Coriolis coupling.

Ω>0

(8) The term j in eq. (6) is due to HFB linearization of the recoil operator j2 ∼ j(j+ + j− )/2 + Ω 2 which,

This work was supported by the U.S. Department of Energy, Office of Nuclear Physics, under contracts DE-FG0292ER40750 and W-31-109-ENG-38.

A. Volya and C. Davids: Nuclear pairing and Coriolis effects in proton emitters

References 1. C. Davids, H. Esbensen, Phys. Rev. C 61, 054302 (2000); 64, 034317 (2001); 69, 034314 (2004). 2. H. Esbensen, C. Davids, Phys. Rev. C 63, 014315 (2001). 3. S. ˚ Aberg, P. Semmes, W. Nazarewics, Phys. Rev. C 56, 1762 (1997). 4. G. Fiorin, E. Maglione, L. Ferreira, Phys. Rev. C 67, 054302 (2003).

163

5. P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, Berlin, Heidelberg, 2000). 6. E. Muller, U. Mosel, J. Phys. G 10, 1523 (1984). 7. K. Hara, S. Kusuno, Nucl. Phys. A 245, 147 (1975). 8. P. Protopapas, A. Klein, Phys. Rev. C 55, 1810 (1997). 9. A. Kreiner, Phys. Rev. Lett. 42, 829 (1979). 10. P. Ring, in Proceedings of the International Workshop on Gross Properties of Nuclei and Excitations V, Hirschegg, Austria, 1977, edited by F. Beck (Technische Hochschule, Darmstadt, West Germany, 1977).

Eur. Phys. J. A 25, s01, 165–168 (2005) DOI: 10.1140/epjad/i2005-06-061-9

EPJ A direct electronic only

Two-proton emission M. Pf¨ utznera Institute of Experimental Physics, Warsaw University, Ho˙za 69, 00-681 Warszawa, Poland Received: 7 December 2004 / c Societ` Published online: 12 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A review of experimental and theoretical achievements obtained in the field of the direct twoproton emission in the the last three years is given. The topics discussed include emission from excited states of 17 Ne and 18 Ne as well as from the ground state of 45 Fe. A search for other candidates of twoproton radioactivity is mentioned. A design of a new type of time projection chamber with optical readout, suitable for studies of proton-proton correlations in the decay of 45 Fe, is presented. PACS. 23.50.+z Decay by proton emission – 27.20.+n Properties of specific nuclei listed by mass ranges: 6 ≤ A ≤ 19 – 27.40.+z Properties of specific nuclei listed by mass ranges: 39 ≤ A ≤ 58 – 29.40.Cs Gas-filled counters: ionization chambers, proportional, and avalanche counters

1 Introduction Two-proton (2p) emission from nuclear states is a process known since 1983 when it was observed to proceed from excited states populated in the β decay of 22 Al and 26 P [1, 2]. Later, several other excited states were found to emit two protons, following both the β decay and nuclear reactions [3,4]. Decays in all these cases, however, were found to be consistent with a sequence of two one-proton emissions proceeding through states in the intermediate nucleus. Similarly, the ground state of 12 O, being a broad resonance, was found to emit two protons sequentially via very broad intermediate states [5, 6]. There is an intriguing possibility, predicted by Goldansky already in 1960 [7], that the diproton (2 He) correlation may play an important role in the mechanism of the 2p emission. This possibility continues to inspire and motivate studies in this field. Recently, a few experimental achievements renewed this interest and brought hopes for substantial progress. The purpose of the present paper is to review experimental as well as theoretical results obtained in the field of 2p emission studies since 2001. Firstly, the emission from excited states will be discussed. Secondly, the discovery of the ground-state 2p radioactivity of 45 Fe will be recapitulated and searches for other cases exhibiting such a decay mode will be mentioned. Finally, an approach to study the proton-proton (pp) correlations in the decay of 45 Fe will be presented. An important element of the latter project is the development of a new type of time projection chamber with optical readout.

a

e-mail: [email protected]

Table 1. Partial width (in eV) for the 2p emission from the 1− resonance at 6.15 MeV in 18 Ne. Experimental results, as well as predictions of two models, are given for two scenarios of the decay mechanism.

Exp. [8] R-matrix [9] SMEC [10]

Diproton

Alternative

21 ± 3 3–10 0.8–2

57 ± 6 (a) 9–19 (b) 15–24 (b)

(a ) Simultaneous, independent emission. (b ) Sequential transition through the ghost of the 1/2+

state in

17

F.

2 Two-proton emission from excited states In an experiment performed at the HRIBF facility (ORNL) the reaction of a radioactive beam of 17 F on hydrogen was used to populate excited states of 18 Ne [8]. The observation of 2p emission from the 1− resonance at 6.15 MeV yielded hopes that the evidence for the direct 3-body 2p decay was obtained. This suggestion was based on the fact that no states in the intermediate nucleus (17 F) are known through which sequential emission could proceed. The measured distribution of the opening angle between two protons was compared with the theoretical predictions for two extreme assumptions: the independent, uncorrelated emission of both protons, and the emission of a diproton particle. The experimental points, with large uncertainties due to limited statistics, were found to be located just between the two theoretical curves. Thus, no firm conclusion on the decay mechanism could be drawn. Since the coverage of the solid angle was limited in the experiment, the partial width determined for the 2p branch

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depends on the decay mechanism. The values deduced for the two assumed scenarios are given in table 1. Recently, new theoretical models of the 2p emission were developed, one based on the improved R-matrix approach [9], and another one formulated within the Shell Model Embedded in Continuum (SMEC) [10]. They consider, apart from the diproton mechanism, yet a different possibility for the decay in the 18 Ne∗ case: the sequential transition via a ghost (resonant halo) of the 1/2+ state in 17 F. The latter mechanism is in fact, according to both models, the dominant decay mode, see table 1. The predicted widths, however, fall short of the experimental result by a factor of 3–4. On the other hand, Grigorenko et al. [11] pointed out that other processes, like independent simultaneous emission from the 2− state at 6.35 MeV in 18 Ne, and/or direct breakup of 17 F projectile on target protons, can possibly contribute to the observed 2p width. Thus, the experimental data for 18 Ne∗ and their interpretation are far from being unambiguous, and further studies are evidently needed in this case. An even more interesting situation is found in the neighbouring, more neutron-deficient isotope: 17 Ne. The first excited state of this nucleus (3/2− at 1.288 MeV) is bound by about 200 keV with respect to the emission of one proton but unbound relative to the direct 2p emission to the 15 O ground state. Decays of 17 Ne∗ states were studied first by Chromik et al. [12] who used Coulomb excitation of the 59 A · MeV 17 Ne beam on a gold target, followed by the kinematically complete detection of reaction products at the NSCL/MSU facility. Unfortunately, no evidence for the simultaneous 2p emission from the first excited state was obtained which apparently decays by an electromagnetic transition to the ground state instead. In turn, the second excited state (5/2− at 1.764 MeV) was found to decay by the sequential emission of two protons to 15 O, in agreement with expectations. In another experiment performed at GANIL, Zerguerras et al. [13] populated 17 Ne∗ states by the one-neutron stripping from the 36 A · MeV 18 Ne beam in a beryllium target. Decay products were detected by the MUST array (light particles) and the SPEG spectrometer (heavy fragment) allowing the full kinematical reconstruction of the process. Indeed, 2p emission from 17 Ne∗ states was observed and the proton-proton angular correlations established. For the first two proton-emitting states (5/2− and 1/2+ ) the isotropic distribution was found, consistent with the result of Chromik et al. However, the angular distribution of protons from higher lying states (E ∗ > 2 MeV) showed a correlation pattern characterized by a clear maximum for emission angles around 50◦ . Such a pattern is expected in case of the diproton emission. A quantitative analysis suggested that up to 70% of decays may proceed through this channel. Such a scenario, however, is not supported by the distribution of energy difference between protons. Instead of equal energy sharing, as expected for diproton emission, the energy difference of about 2 MeV and more was found for most of events. Thus, the question whether the diproton correlation indeed contributes to the 2p emission in this case remains open. It is possible that other mech-

anism, like final-state interactions, are responsible for the peculiar angular distribution observed. Clearly, more detailed measurements are needed, as well as an application of a rigorous 3-body model to the analysis of protonproton correlations in this case. It is interesting to note that the next lighter neon isotope, 16 Ne, most probably belongs to the class of “democratic” 2p emitters [14], like 6 Be and 12 O. In the latter two cases the width of the decaying state is comparable with the energy taken by the first proton [15]. Experimentally, only the width of the ground state of 16 Ne was estimated to be Γ = 110(40) keV [16] so far. Detection of protons emitted by 16 Ne and the measurement of their correlations remains to be an important goal for future studies.

3 Ground-state 2p radioactivity The phenomenon of the 2p radioactivity, as noticed by Goldansky [7], is expected to occur in medium mass, extremely neutron-deficient even-Z nuclei in which the emission of a single proton is energetically forbidden and where due to Coulomb barrier the relevant states are narrow. Over years of theoretical efforts to calculate masses of very proton-rich nuclei as precise as possible, a choice of best candidates was narrowed down to three cases: 45 Fe, 48 Ni, and 54 Zn [17,18, 19, 20]. Experimental attempts progressing in parallel [21, 22,23, 24] were crowned in 2002 by finding the first evidence for the 2p radioactivity of 45 Fe [25,26]. This breakthrough profited mainly from the development of extremely sensitive experimental methods utilizing projectile fragmentation of heavy ions, in-flight separation of reaction products, and identification of single ions. Indeed, the decay of 45 Fe was detected in two experiments employing the fragmentation technique: one performed at the FRS separator at GSI [25], the other at the LISE facility at GANIL [26]. In both of them, ions of interest were produced by the fragmentation of 58 Ni beam. At GSI the primary beam at 650 A · MeV and having an average intensity of ≈ 5 · 108 ions/s impinged on a 4 g/cm2 thick beryllium target, while at GANIL the beam energy was 75 A · MeV, its average intensity was ≈ 9 · 1011 ions/s, and a natural nickel target of 213 mg/cm2 thickness was used. In both experiments the selected ions were implanted into a silicon detector telescope mounted at the final focus of the separator. Finally, 22 ions of 45 Fe were detected at the LISE, while 6 ions were identified at the FRS. The smaller statistics recorded at GSI was partly compensated by using a dead-time free data acquisition system, based on the digital electronics modules [27]. This system allowed, in contrast to the standard system used at GANIL, to record all signals from each detector in the period of 10 ms after implantation of the 45 Fe ion. Thus, the implantationdecay correlations and discrimination against background could be established with a high degree of statistical significance. Moreover, the telescope mounted at the final FRS focus was surrounded by a set of large volume NaI detectors providing a large efficiency (93%) for detection of γ-rays following β-delayed proton emission (βp), and

thus allowing a sensitive discrimination against β decay events. For similar reason, the set-up mounted at GANIL included a thick Si(Li) detector to register positrons emitted by β + -decaying nuclei stopped in the telescope. The careful analysis of data collected in both experiments yielded results consistent within experimental uncertainties. Taken together they led to the conclusion that the half-life of 45 Fe is 3.8+2.0 −0.8 ms and that it decays predominantly by emission of particle(s) with the total energy of 1.14 ± 0.05 MeV with no γ-rays or β-particles in coincidence. Such pattern is characteristic for the 2p radioactivity and such an interpretation is the only one fitting the data. The measured decay energy is in excellent agreement with predictions for the 2p decay of 45 Fe which are (1.154 ± 0.094) MeV [17], (1.279 ± 0.181) MeV [18], and (1.218 ± 0.049) MeV [19]. Additionally, the measured half-life is consistent with predictions of a rigorous threebody model developed by Grigorenko et al. [11,14], as well as with the model of Brown and Barker based on the R-matrix approach [9]. However, one decay event observed at GSI is consistent with the β decay (release of 10 MeV energy plus occurrence of a γ-ray in coincidence) suggesting that this decay mode may occur for 45 Fe with the branching ratio of roughly 20%. It is evident that more accurate measurements on decay properties of 45 Fe, with much larger statistics, are needed to make the comparison with different versions of theoretical models conclusive. Independently, the search for the 2p ground-state decay in other nuclei is of great importance, as it may offer new insights into the structure of nuclei at and beyond the proton-drip line. Very recently, the evidence for the 2p emission from 54 Zn was reported from GANIL [28]. In the same experiment, the first decay data for 48 Ni were obtained but no firm conclusion could be drawn. Additionally, other candidates are being proposed by theoretical predictions and considered by experimentalists. The implantation technique may possibly be applied to study decays of 67 Kr and 71 Sr [9]. An interesting case is 19 Mg which is predicted to decay in a picosecond time range [29,30]. In an experiment, currently under preparation at GSI, ions of 19 Mg will be produced by one-neutron knock-out from a 20 Mg beam in a thin secondary target located in the middle focal plane of the FRS [31]. The decay will occur in-flight within centimeters after leaving the target. Thus tracking of the products (17 Ne + p + p) will allow the full kinematical reconstruction of the process. It is expected that such an in-flight decay method may also be applicable to other proposed short-lived candidates, like 30 Ar, 34 Ca, 62 Se, and 66 Kr [32].

4 Approach to pp correlations in

45

Fe

A serious disadvantage of the implantation technique is that only the total decay energy is registered and no information on pp correlations can be deduced. Thus, the detection of the two emitted protons separately and the measurement of their momenta represent the crucial next step in the study of the 2p radioactivity of 45 Fe. It will

167

μ

M. Pf¨ utzner: Two-proton emission

Fig. 1. The electron drift velocity as a function of the reduced electric field measured for selected gas mixtures.

constitute a direct experimental proof for the 2p emission and hence may shed light on the decay mechanism, in particular on questions concerning the role of the diproton correlations. To achieve this ambitious goal, special time projection chambers are currently being developed at CEN Bordeaux [33] and independently at Warsaw University. In the following, the latter project will be briefly presented. The apparatus, called Optical Time Projection Chamber (OTPC), will consist of several parallel wire-mesh electrodes inside a gaseous medium which form the conversion region and the multi-stage charge amplification structure. A selected gas mixture of argon and helium with a small addition of nitrogen or triethylamine (TEA) will provide strong emission of UV photons during the avalanche process. These photons will be converted into visible light by means of a wavelength shifter foil. A CCD camera located outside the detection volume will record a 2-D image of the decay process. The drift time of primary ionization charge towards the amplification stage will provide the third coordinate. Correlation of the 2-D image with the drift-time structure will allow 3-D reconstruction of the decay topology. The underlying idea of optical detection of particle tracks has been demonstrated by Charpak et al. for gas mixtures containing TEA vapour [34]. A similar technique using pure TEA vapour at low pressure has been used by Titt et al. [35]. In the course of design studies the electron drift velocity has been measured for various gas mixtures containing TEA vapour. All measurements were performed under atmospheric pressure and at room temperature (24 ◦ C). Pure noble gases (or their mixtures) were bubbled through liquid TEA at 0 ◦ C. The results for selected mixtures are shown in fig. 1. The mixtures containing equal amounts of argon and helium with the small addition of TEA and/or nitrogen are expected to represent a good compromise between providing enough stopping power for heavy ions like 45 Fe and yielding long enough tracks for low-energy protons. Assuming a drift velocity of 1.5 cm/μs and 100 MHz sampling rate, the position measurement in such mixtures will be possible with an accuracy of 150 μm.

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of 45 Fe. Other cases of 2p radioactivity are sought for. The most promising candidates considered are 54 Zn, 48 Ni, and 19 Mg. The author is grateful to Prof. E. Roeckl for careful reading of the manuscript. The construction and testing of the OTPC ´ detector is performed mainly by W. Dominik, M. Cwiok, K. Miernik, A. Wasilewski, H. Czyrkowski from IEP Warsaw University. This work was partially supported by the EC under contract HPRI-CT-1999-50017.

References Fig. 2. Image of a few α-particle tracks recorded with a lownoise CCD device. The exposure time is 0.1 s.

First tests of imaging capabilities were performed with a small prototype chamber having 20 cm × 20 cm active area and 20 mm thick drift volume followed by a double amplification structure. The detector was filled with 49.5% Ar + 49.5% He + 1% N2 gas mixture under atmospheric pressure. A low-intensity 241 Am source was mounted inside the active volume in such a way that α-particles, having 4.5 MeV effective energy due to internal absorption, were emitted perpendicularly to the drift direction. Images were taken with help of a low-noise, Peltier cooled, 15-bit CCD camera. A few α tracks are visible on an example shown in fig. 2. It should be stressed that no image intensifier was used, yet single tracks can be clearly distinguished from the background. More details on the construction of the OTPC detector and on results of the test studies are given in ref. [36].

5 Summary In this review the main achievements obtained in the 2p emission studies since 2001 are summarized. The correlations between protons emitted from excited states in 18 Ne and in 17 Ne were accomplished. Although the data obtained for the 1− resonance at 6.15 MeV in 18 Ne are not yet conclusive, mainly because of low statistics, the theoretical predictions, based on the modern version of the R-matrix approach as well as on the newly developed Shell Model Embedded in Continuum, suggest that sequential transitions through ghost states in the intermediate 17 F nucleus dominate in this case. The results for the states in 17 Ne, especially those with excitation energies above 2 MeV, seem to provide evidence for the strong correlation between protons, consistent with a substantial contribution from the diproton mechanism. Also in this case, the further measurements are necessary. In the decay of 45 Fe the first case of 2p ground-state radioactivity was established. Since only the total decay energy and the lifetime were determined, no information on the emission mechanism could be deduced. To settle this problem, special TPC detectors are being developed at Bordeaux and Warsaw with the aim to study the pp correlations in case

1. 2. 3. 4. 5. 6. 7. 8. 9.

10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36.

M.D. Cable et al., Phys. Rev. Lett. 50, 404 (1983). J. Honkanen et al., Phys. Lett. B 133, 146 (1983). C.R. Bain et al., Phys. Lett. B 373, 35 (1996). H.O.U. Fynbo et al., Nucl. Phys. A 677, 38 (2000). R.A. Kryger et al., Phys. Rev. Lett. 74, 860 (1995). A. Azhari, R.A. Kryger, M. Thoennessen, Phys. Rev. C 58, 2568 (1998). V.I. Goldansky, Nucl. Phys. 19, 482 (1960). J. Gomez del Campo et al., Phys. Rev. Lett. 86, 43 (2001). B.A. Brown, F.C. Barker, in Proceedings of the 2nd International Symposium PROCON 2003, Legnaro, Italy, 12-15 February 2003, AIP Conf. Proc. 681, 118 (2003). J. Rotureau, J. Okolowicz, M. Ploszajczak, Acta Phys. Pol. B 35, 1283 (2004); J. Rotureau et al., these proceedings. L. Grigorenko et al., Phys. Rev. C 65, 044612 (2002). M.J. Chromik et al., Phys. Rev. C 66, 024313 (2002). T. Zerguerras et al., Eur. Phys. J. A 20, 389 (2004). L.V. Grigorenko et al., Phys. Rev. Lett. 88, 042502 (2002); L.V. Grigorenko et al., Eur. Phys. J. A 15, 125 (2002). O.V. Bochkarev et al., Sov. J. Nucl. Phys. 55, 955 (1992). C.J. Woodward, R.E. Tribble, D.M. Tanner, Phys. Rev. C 27, 27 (1983). B.A. Brown, Phys. Rev. C 43, R1513 (1991). E. Ormand, Phys. Rev. C 53, 214 (1996). B.J. Cole, Phys. Rev. C 54, 1240 (1996). W. Nazarewicz et al., Phys. Rev. C 53, 740 (1996). B. Blank et al., Phys. Rev. C 50, 2398 (1994). B. Blank et al., Phys. Rev. Lett. 77, 2893 (1996). B. Blank et al., Phys. Rev. Lett. 84, 1116 (2000). J. Giovinazzo et al., Eur. Phys. J. A 10, 73 (2001). M. Pf¨ utzner et al., Eur. Phys. J. A 14, 279 (2002). J. Giovinazzo et al., Phys. Rev. Lett. 89, 102501 (2002). M. Pf¨ utzner et al., Nucl. Instrum. Methods Phys. Res. A 493, 155 (2002). B. Blank, these proceedings. L.V. Grigorenko, I.G. Mukha, M.V. Zhukov, Nucl. Phys. A 714, 425 (2003). I. Mukha, G. Schrieder, Nucl. Phys. A 690, 280c (2001). I. Mukha et al., Proposal for an experiment at GSI, 2002. L.V. Grigorenko, M.V. Zhukov, Phys. Rev. C 68, 054005 (2003). J. Giovinazzo, B. Blank, private communication. G. Charpak et al., Nucl. Instrum. Methods Phys. Res. A 269, 142 (1988). U. Titt et al., Nucl. Instrum. Methods Phys. Res. A 416, 85 (1998). ´ M. Cwiok et al., to be published in 2004 IEEE Nuclear Science Symposium Conference Record, 16-22 October, 2004, Rome, Italy, and to be published in IEEE Trans. Nucl. Sci.

Eur. Phys. J. A 25, s01, 169–172 (2005) DOI: 10.1140/epjad/i2005-06-012-6

EPJ A direct electronic only

First observation of

54

Zn and its decay by two-proton emission

B. Blank1,a , N. Adimi2 , A. Bey1 , G. Canchel1 , C. Dossat1 , A. Fleury1 , J. Giovinazzo1 , I. Matea1,3 , F. De Oliveira3 , I. Stefan3 , G. Geogiev3 , S. Gr´evy3 , J.C. Thomas3 , C. Borcea4 , D. Cortina5 , M. Caamano5 , M. Stanoiu6 , and F. Aksouh7 1 2 3 4 5 6 7

CENBG, Le Haut Vigneau, F-33175 Gradignan Cedex, France Facult´e de Physique, USTHB, BP32, El Alia, 16111 Bab Ezzouar, Alger, Algeria Grand Acc´el´erateur National d’Ions Lourds, B.P. 5027, F-14076 Caen Cedex, France Institute of Atomic Physics, P.O. Box MG6, Bucharest-Margurele, Romania Departamento de Fisica de Particulas, Universidad de Santiago de Compostela, E-15782 Santiago de Compostela, Spain Institut de physique nucl´eaire d’Orsay, 15 rue Georges Clemenceau, F-91406 Orsay Cedex, France Instituut voor Kern- en Stralingsfysica, Celestijnenlaan 200D, B-3001 Leuven, Belgium Received: 3 December 2004 / Revised version: 25 January 2005 / c Societ` Published online: 15 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. In an experiment performed at the LISE3 facility of GANIL, the isotope 54 Zn and its decay via two-proton emission were observed for the first time. In addition, preliminary results indicate that three implantation events of 48 Ni were observed. One of the associated decay events is compatible with a two-proton emission. New data on the decay of 45 Fe and its two-proton branch were recorded at the same time. The results for 54 Zn are compared to theory. PACS. 23.50.+z Decay by proton emission – 23.90.+w Other topics in radioactive decay and in-beam spectroscopy – 27.40.+z 39 ≤ A ≤ 58

1 Introduction Nuclear structure experiments near the proton drip line represent an important tool to investigate the properties of the atomic nucleus. The mapping of the proton drip line provides a first stringent test for mass models. The information is refined by the observation of the radioactive decay of isotopes at the proton drip line via e.g. β-delayed protons and by half-life measurements. One of the most exciting phenomena at the proton drip line is probably the occurrence of the ground-state two-proton (2p) decay which has been predicted about 40 years ago [1]. Although considerable efforts have been made in order to observe this radioactivity, it was observed only recently in the decay of 45 Fe [2, 3]. Other possible candidates according to theoretical predictions [4, 5,6] are 48 Ni, 54 Zn, and 59 Ge with predicted half lives in the 1 μs–10 ms range. The study of 2p radioactivity may be a tool to test mass predictions very far away from stability, may allow to determine single-particle level sequences, and in particular to study pairing in nuclei. However, up to now, only very rough information can be obtained about this decay process. Therefore, research in this domain goes mainly in two directions: i) obtaining more refined information about 2p a

Conference presenter; e-mail: [email protected]

radioactivity such as the energy sharing between the two protons and their angular correlation and ii) searching for new 2p emitters. The paper presents very recently obtained results for the observation and the decay of 54 Zn as well as for the decay of 48 Ni. In addition, new results on the decay of 45 Fe are discussed, which nicely agree with the published data and allow therefore to decrease the overall errors on its half-life, its 2p decay energy and on the branching ratios.

2 Experimental details In two experiments performed in April/May 2004 at the SISSI-LISE3 facility of GANIL, we used the projectile fragmentation of a 58 Ni primary beam at 75 MeV/nucleon to produce proton-rich nuclei in the range Z = 20–30. After production in a nat Ni target in the SISSI device, the fragments of interest were selected by the Alpha/LISE3 [7] separator equipped with an intermediate beryllium degrader. At the focus of the LISE3 separator, a set-up was mounted to identify and stop the fragments of interest as well as to study their radioactive decays. This set-up consisted in two channel-plate detection systems for timing

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Fig. 1. Isotope identification spectra with the energy loss in the first silicon detector as a function of the ToF of the isotopes. (a) Setting optimized for 54 Zn which allows to observe 7 events for this isotope. In this plot, the statistics comes only from runs where we detected a 54 Zn isotope. Therefore, the relative intensities are biased. (b) Setting optimized on 48 Ni with 3 events observed for this nucleus.

purposes mounted at the first LISE focal point and a silicon detector stack with a silicon-strip detector being the implantation device. Two silicon detectors adjacent to the strip detector served also to observe β-particles emitted in radioactive decays. For more details about the detection setup, see ref. [2]. We obtained an average production rate of about two 54 Zn per day for a setting optimized on this nucleus and rates of one 48 Ni per day in a setting optimized for 48 Ni.

3 Experimental results The fragment identification was performed by means of the standard ΔE–time-of-flight (ToF) technique using the first silicon detector and one of the channel-plate detectors. Additional energy-loss information from the other detectors and the other ToF information was used to clean the spectra. Figure 1 shows the preliminary identification spectra for the two settings. Seven 54 Zn events are observed for the first time (fig. 1a). 54 Zn is therefore the most neutron-deficient zinc isotope. Basically all modern

Fig. 2. Energy (a) and time (b) spectra for decay events correlated with the implantation of 54 Zn. A peak at 1.47(5) MeV is observed yielding a half-life of 3.6+2.5 −1.0 ms.

mass predictions agree on its particle instability, however, with much varying decay energies. This spread in decay energy is so large that some predictions see it rather β-decay, whereas from others one can deduce a half-life which would make it unobservable in the present type of experiments. In the experiment optimized for the identification and spectroscopy of 48 Ni, three 48 Ni nuclei have been identified together with 14 events for 45 Fe (fig. 1b). The observation of the three 48 Ni events confirms for the first time our 1999 results where this doubly-magic nucleus was identified for the first time [8]. The decay of these three nuclei (45 Fe, 48 Ni, 54 Zn) was then studied by correlating these implantations in time with subsequent decays in the same pixel of the silicon strip detector. In this way, basically pure decay spectra, “contaminated” only by the daughter decays, can be generated. The resulting decay spectra for 54 Zn, still preliminary at this stage, are presented in fig. 2. A peak of six events at an energy of 1.36(5) MeV is observed (fig. 2a). Corrected for the β pile-up for the nuclei used to calibrate the spectrum, the 2p energy is 1.47(5) MeV. The other events come from daughter decays as well as from the β-decay of one 54 Zn. Two events in the vicinity of the

B. Blank et al.: First observation of

45

6

54

Zn and its decay by two-proton emission

171

Fe

Counts

5 4

(a)

3 2 1 0

0

1

2

3

4

5

6

7

8

Energy (MeV) 6

Counts

5 4

Fig. 4. Comparison of our preliminary experimental results for 54 Zn with the di-proton model and the three-body model of Grigorenko et al. [12, 13]. Best agreement is obtained with the three-body model assuming a pure p-wave emission of the two protons.

(b)

3 2 1 0

0

10

20

30

40

50

Time (ms)

Fig. 3. Energy (a) and time (b) spectra for decay events correlated with the implantation of 45 Fe. A peak at 1.14(4) MeV is observed yielding a half-life of 1.6+0.9 −0.4 ms.

1.36 MeV peak are due to the decay of 52 Ni, the 2p daughter of 54 Zn, which decays with a branching ratio of about 15% by emission of protons with energies of 1.06 MeV and 1.34 MeV [9]. These decays follow a first decay event attributed to 54 Zn and occur 25 ms and 35 ms, respectively, after the implantation of 54 Zn, in nice agreement with the half-life of 52 Ni (T1/2 = 40.1(7) ms). One of them is in coincidence with a β-particle in the adjacent detector. The decay-time distribution of all these events is also shown (fig. 2b) and yields a preliminary half-life of 3.6+2.5 −1.0 ms for 54 Zn. The data shown in fig. 3 confirm the results already published for 45 Fe [2, 3]. Preliminary values are E2p = 45 Fe 1.14(4) MeV and T1/2 = 1.6+0.9 −0.4 ms. In both cases, 54 and Zn, the half-life of the daughter activity is in agreement with previously measured values [9]. In addition, for none of the events in either of the two peaks, a β-particle could be observed in coincidence in the adjacent silicon detectors. Although the β efficiency of our set-up is not yet determined, the absence of any β-particle strongly supports the identified peaks to be of 2p origin. In the case of 48 Ni, the conclusions are more elusive. Two of the three implantation events seem to be followed by decays the characteristics of which are in contradiction with a 2p emission pattern: Either we missed the first ra-

dioactive decay after implantation due to dead time which we think is unlikely (we still have to determine the exact dead time) or the disintegration proceeds via β-decay. This is still under study. The third event, however, has all characteristics of a 2p emission: No coincident β-decay, a decay energy of about 1.4 MeV roughly 1.7 ms after the implantation. This event could be a first indication of a 2p decay of 48 Ni. However, higher-statistics data are needed to confirm this hypothesis.

4 Comparison to theory The two-proton decay Q value of Q2p = 1.47(5) MeV for 54 Zn can be compared to different model predictions for this Q value. Brown et al. [10] predicts a value of 1.33(14) MeV in agreement with our result. Ormand [11] calculated a value of 1.87(24) MeV. Finally, Cole [6] proposes a Q value of 1.79(12) MeV. The latter two values are slightly higher than our experimental value. In fig. 4, we compare our results on the 2p decay of 54 Zn to two different theoretical approaches: i) the diproton model and ii) the three-body model of Grigorenko et al. [12, 13]. In the di-proton model, the two protons are considered to be a structureless 2 He particle which is preformed in the nucleus and to be emitted together, i.e. no internal degrees of freedom for 2 He are considered and the total angular momentum of 2 He is zero. The emission then depends only on the channel radius in the R-matrix sense. The three-body model treats the core-proton as well as the proton-proton interaction realistically and adds thus dynamics to the decay. The best agreement is indeed obtained with the more realistic three-body model assuming

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a pure p-wave emission (see fig. 4) which is in agreement with the protons being in the p3/2 orbital as predicted by the shell model. However, a much more refined analysis is still required. For example, it is not yet clear how non-zero spectroscopic factor for other orbitals modify the picture. In a similar way, our data should be compared to the Brown-Barker model [14] which is based on the R-matrix model.

5 Conclusion and outlook With the observation of 2p radioactivity for 54 Zn, a second 2p emitter could be clearly identified. Combined with additional data for 45 Fe, different theories of 2p radioactivity can now be confronted to our data. Future studies will concentrate on higher statistics for already observed 2p emitters, which will allow for a detailed comparison to theory in particular concerning the 2p branching ratios, the half-lives and the decay energies, as well as on more refined data such as the energy of the individual protons and their angular correlation. For this last topic, we have developed a time-projection chamber which will allow for

the visualisation in 3D of the trajectories of the decay protons.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

14.

V.I. Goldansky, Nucl. Phys. 19, 482 (1960). J. Giovinazzo et al., Phys. Rev. Lett. 89, 102501 (2002). M. Pf¨ utzner et al., Eur. Phys. J. A 14, 279 (2002). B.A. Brown, Phys. Rev. C 43, R1513 (1991). W.E. Ormand, Phys. Rev. C 53, 214 (1996). B.J. Cole, Phys. Rev. C 54, 1240 (1996). A.C. Mueller, R. Anne, Nucl. Instrum. Methods B 56, 559 (1991). B. Blank et al., Phys. Rev. Lett. 84, 1116 (2000). C. Dossat, PhD Thesis, University Bordeaux I (2004). B.A. Brown, F. Barker, D. Millener, Phys. Rev. C 65, 051309 (2002). W.E. Ormand, Phys. Rev. C 55, 2407 (1997). L. Grigorenko et al., Phys. Rev. C 64, 054001 (2001). L. Grigorenko, I. Mukha, M. Zhukov, in PROCON-2003 International Symposium on Proton-Emitting Nuclei, AIP Conf. Proc. 681, 126 (2003). B.A. Brown, F. Barker, Phys. Rev. C 67, 041304 (2003).

Eur. Phys. J. A 25, s01, 173–175 (2005) DOI: 10.1140/epjad/i2005-06-121-2

EPJ A direct electronic only

Microscopic theory of the two-proton radioactivity J. Rotureau1,a , R. Chatterjee1 , J. Okolowicz1,2 , and M. Ploszajczak1 1 2

Grand Acc´el´erateur National d’Ions Lourds (GANIL), CEA/DSM-CNRS/IN2P3, BP 55027, F-14076 Caen Cedex 05, France Institute of Nuclear Physics, Radzikowskiego 152, PL-31342 Krak´ ow, Poland Received: 4 November 2004 / c Societ` Published online: 9 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We formulate the microscopic theory of the two-proton radioactivity based on the real-energy continuum shell model. This microscopic approach is applied to describe the two-proton decay from the 18 1− Ne. 2 excited state in PACS. 21.60.-n Nuclear structure models and methods – 27.20.+n Properties of specific nuclei listed by mass ranges: 6 ≤ A ≤ 19

1 Introduction Nuclear decays with three fragments in the final state are very exotic processes. The two-proton (2p) radioactivity is an example of such a process which can occur for even-Z nuclei beyond the proton drip line: if the sequential decay is energetically forbidden by pairing correlations, a simultaneous 2p decay becomes the only possible decay branch. In spite of long lasting efforts, no fully convincing experimental finding of this decay mode has been reported (see however data on 2p radioactivity of the ground state of 45 18 Fe [1, 2,3] and of the second excited 1− Ne [4]). 2 state of Recently, we have developed a theory of 2p radioactivity which is based on the extension of Shell Model Embedded in the Continuum (SMEC) [5, 6] for the two-particle continuum. In this approach, the configuration mixing in the valence space is calculated microscopically and the asymptotic states are obtained in the S-matrix formalism [6]. This is in contrast to R-matrix based Shell Model (SM) formalism [7] or cluster model which does not account for the microscopic structure of the residual core nucleus [8].

2 Two-particle continuum in the shell-model embedded in the continuum The Hilbert space is divided in three subspaces: Q, P and T . In Q subspace, A nucleons are distributed over (quasi-) bound single-particle (qbsp) orbits. In P , one nucleon is in the non-resonant continuum and A − 1 nucleons occupy qbsp orbits. In T , two nucleons are in the non-resonant continuum and (A − 2) are in qbsp orbits. The coupling between Q, P and T subspaces changes the “unperturbed” a

Conference presenter; e-mail: [email protected]

SM Hamiltonian (HQQ ) in Q into the effective Hamiltonian: (eff)

HQQ = HQQ + HQT G+ T (E)HT Q  (+)  ˜ + HQP + HQT G+ T (E)HT P GP (E)   (+) × HP Q + HP T GT (E)HT Q ,

(1)

˜ (E) = [E + − HP P − HP T G (E)HT P ]−1 is where: G P T the Green’s function in P modified by the coupling to T , (+) and GT (E) = [E + − HT T ]−1 is the Green’s function in T . In the above equations, HP P , HT T are the unperturbed Hamiltonians in P , T subspaces, respectively, and HQP , HP Q , HP T , HT P are the corresponding coupling terms between Q, P , and T subspaces. The second term on the r.h.s. of eq. (1) describes a di-proton emission, and the third term describes the modification due to the mixing of sequential 2p, di-proton and 1p decay modes. In solving (eff) SMEC problem with HQQ , the radial single-particle wave functions in Q and the scattering wave functions in P and T are generated by a self-consistent procedure starting with the average potential of Woods-Saxon type with the spin-orbit and Coulomb parts included, and taking into account the residual coupling between Q, P and Q, T subspaces [5, 6, 9]. For the SM effective interaction in HQQ we take either WBT or (psdfp) interaction [9]. (+)

(+)

2.1 Two-proton decay with three-body asymptotics We consider the 2p decay mode from the 1− 2 state in 18 Ne at the excitation energy of 6.15 MeV. In the limit of no coupling between P and T subspaces, the effective

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The European Physical Journal A p

Table 1. Widths (Γ (seq) ) and branching ratios (B (seq) ) for the sequential decay and widths (Γ (2p) ) for di-proton cluster decay with different SM effective interactions.

x y

p

A−2

Fig. 1. The three-body Jacobi coordinate system. The hyper radius is ρ = x2 + y 2 .

(seq)

Interaction

Γ (seq) (eV)

B[17 F∗ (1/2+ )]

Γ (2p) (eV)

psdfp WBT

88.80 13.60

92.80% 80.20%

1.89 1.01

Hamiltonian (eq. (1)) reduces to [9] (eff)

+ HQQ = HQQ + HQP G+ P (E)HP Q + HQT GT (E)HT Q .

First, we calculate the contribution due to coupling with one proton in the continuum of 17 F + −

1− i |HQQ + HQP GP (E)HP Q |1j ,

1− 2

mix

18

which yields a “mixed” state (φ ) of Ne. From this state we go on to calculate the widths due to coupling with mix . This can the 2p continuum: φmix |HQT G+ T (E)HT Q |φ be written formally as w|ω, where w| = φmix |HQT is identified as the source term and ω, which is an extension of the discrete state wave function in the continuum and mix . It is expanded in is given by: |ω = G+ T (E)HT Q |φ hyperspherical harmonics (HH) 3-body Jacobi coordinate system (see fig. 1):  lx ,ly ωc (ρ)YK,L,S (Ω5 ). ω(x, y) = ρ−5/2 c≡(t,K,L,S,lx ,ly )

In the above equation, a channel (c) is specified by t —a bound state of the (A − 2) residual nucleus, lx —the relative angular momentum between the two protons, ly —the relative angular momentum between the two protons and the (A − 2) nucleus, S-the total spin of the two protons, L = lx ⊗ly , and K-the hyper angular momentum. lx ,ly (Ω5 ) is the HH function and ωc (ρ) is the solution of YK,L,S inhomogeneous integro-differential coupled channel equations with the SM source wc (ρ): 

 2 (K + 3/2)(K + 5/2) d h2 ¯ − E ωc (ρ) (2) − − ρ2 2m dρ2   dρ Vccn- loc (ρ )ωc (ρ ) = wc (ρ). + Vccloc  (ρ)ωc (ρ)+ c

c

In the above equation, the local potential Vccloc  (ρ) contains the interactions between the two protons in continuum states. The non-local potential Vccn- loc (ρ ) in eq. (2) is a direct consequence of accounting for the 2-body residual interaction between the emitted protons and all the valence particles in the (A − 2) residual nucleus. The Coulomb problem is treated approximately by the use of Coulomb functions of half-integer order with Sommerfeld parameter corresponding to an “effective charge” in each hyperspherical channel found by neglecting the off-diagonal Coulomb matrix elements (which are much smaller than the diagonal ones) in the previous equation. In future studies, this

will allow us to investigate the influence of the effective SM interaction on the correlations between emitted protons and from that data extract information about the pairing field in the parent nucleus.

2.2 Sequential and cluster emissions as limits of the effective Hamiltonian (1) In the limit of HQT (HT Q ) being zero in eq. (1), we can calculate the contribution of the sequential 2p emission mix ) of 18 Ne as from the “mixed” 1− 2 state (φ ! ˜ (+) (E)HP T G(+) (E)HT P G(+) (E)HP Q |φmix . φmix |HQP G P T P In another limit of eq. (1), we can also consider a cluster emission of two protons with HP T (HT P ) being zero and protons in the cluster being coupled to total spin S = 0 and with relative orbital angular momentum between them (lx ) to be zero. In this limit, s-wave final state interaction in p + p intermediate system can be included phenomenologically [10]. In both these limits the microscopic structure of the residual nucleus is still accounted for, although the asymptotics become 2-body. The widths (seq) Γ (seq) , and the branching ratios B[17 F∗ (1/2+ )] to the 1/2+ 1 1

continuum states of 17 F for the sequential decay, and the widths for the di-proton cluster decay, for different SM effective interactions are shown in table 1, obtained with a spin-exchange contact force residual interaction [9]. These results indicate that the 2p decay in 18 Ne is essentially a sequential process. Strong dependence of Γ (seq) on the SM effective interaction is found. The dominant contribution to Γ (seq) comes from the resonant continuum of the 17 F. weakly bound 1/2+ 1 state of

3 Conclusions We have extended the SMEC to describe the 2p radioactivity. This fully microscopic approach with 3-body asymptotics and with realistic finite range interactions will allow us to study the relation between an effective NN interaction and radial features of the pairing field, on one side, and also the proton-proton correlations in the asymptotic state. The calculations for heavy 2p emitters are now being pursued.

J. Rotureau et al.: Microscopic theory of the two-proton radioactivity

References 1. M. Pf¨ utzner et al., Eur. Phys. J. A 14, 279 (2002). 2. M. Pf¨ utzner et al., Nucl. Instrum. Methods A 493, 155 (2002). 3. J. Giovinazzo et al., Phys. Rev. Lett. 89, 102501 (2002). 4. J. Gomez del Campo et al., Phys. Rev. Lett. 86, 43 (2001). 5. K. Bennaceur et al., Nucl. Phys. A 651, 289 (1999).

175

6. J. Okolowicz, M. Ploszajczak, I. Rotter, Phys. Rep. 374, 271 (2003). 7. F.C. Barker, Phys. Rev. C 68, 054602 (2003). 8. L.V. Grigorenko, M.V. Zhukov, Phys. Rev. C 68, 054005 (2003). 9. J. Rotureau, J. Okolowicz, M. Ploszajczak, Acta Phys. Pol. B 35, 1283 (2004). 10. F.C. Barker, Phys. Rev. C 63, 047303 (2001).

2 Radioactivity 2.4 Alpha decay

Eur. Phys. J. A 25, s01, 179–180 (2005) DOI: 10.1140/epjad/i2005-06-089-9

EPJ A direct electronic only

Alpha-decay studies using the JYFL gas-filled recoil separator RITU J. Uusitalo1,a , S. Eeckhaudt1 , T. Enqvist1 , K. Eskola2 , T. Grahn1 , P.T. Greenlees1 , P. Jones1 , R. Julin1 , S. Juutinen1 , anen1 , P. Nieminen1 , M. Nyman1 , J. Pakarinen1 , P. Rahkila1 , H. Kettunen1 , P. Kuusiniemi1 , M. Leino1 , A.-P. Lepp¨ 1 and C. Scholey 1 2

Department of Physic, University of Jyv¨ askyl¨ a, P.O. Box 35, FI-40014, Jyv¨ askyl¨ a, Finland Department of Physics, University of Helsinki, FI-00014, Helsinki, Finland Received: 14 January 2005 / c Societ` Published online: 29 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Neutron-deficient α-decaying nuclei have been produced using fusion-evaporation reactions. A gas-filled recoil separator was used to separate the fusion products from the scattered beam. The activities were implanted in a position sensitive silicon detector. The isotopes were identified using spatial and time correlations between implants and decays. During ten years of operation time about twenty new α-decaying isotopes have been identified in the translead region. In addition numerous α-decay studies have been performed on already known isotopes yielding much improved precision for the measured decay properties. An overview of the α-decay studies performed for the translead nuclei employing the gas-filled recoil separator will be given. PACS. 23.60.+e α decay – 27.80.+w 190 ≤ A ≤ 219

The gas-filled recoil separator RITU [1] at Jyv¨ askyl¨a Accelerator Laboratory (JYFL) has been used intensively for α-decay studies of heavy neutron-deficient nuclei for about ten years. Most of these studies have been performed in the translead region at the extreme limit of nuclear existence. The low production yields due to the strong fission competition have demanded high performance from the separator system and from the focal plane detector system used in these studies. In the present work α-decay hindrance factors HF and reduced widths δ 2 , determined according to Rasmussen [2], have been used to obtain structure information of the decaying states. The hindrance factor is defined as the ratio of the reduced width of the ground state to ground state transition in the closest even-even neighbor to the reduced width of the transition in question. In odd-mass nuclei a hindrance factor of less than 4 implies an unhindered decay between states of equal spin, parity, and configuration [3]. For even-even nuclei the systematic study of reduced widths δ 2 is used to obtain important structure information on the decaying states. In the lead region the multiproton-multihole intruder states and the occurrence of shape coexistence have been investigated using α-decay as a spectroscopic tool [4,5]. In addition the vicinity of the proton drip line has offered the possibility a

Conference presenter; e-mail: [email protected]

to study proton-unbound systems and even to search for direct proton emission [6, 7,8]. While in the lead region the proton drip line crosses the magic proton number 82 at the neutron mid-shell, in the uranium region the drip line crosses the magic neutron number 126. One of the recently investigated isotopes has been the semi magic nucleus 218 U for which two α-decaying isomeric states were observed [9]. In addition to the structural information the present α-decay studies have given a lot of valuable information for the mass evaluations [10]. When the reduced widths for the ground state to ground state transitions are reviewed it can be noticed that they remain constant for even-mass Po isotopes lighter than 196 Po and even decrease significantly for 188 Po. This behaviour is illustrated in fig. 1a. The reason for this is that the α-decays from the Po 0+ ground states to the proton (2p-2h) 0+ intruder states in Pb nuclei are getting increasingly favorable. The interpretation has been that the ground states of neutron-deficient Po isotopes are mixtures of different configurations, spherical π(2p-0h), oblate π(4p-2h) (and prolate π(6p-4h)). Recently α-decay properties of very neutron-deficient Rn nuclei were studied in Jyv¨ askyl¨a [11]. Intriguingly it was noticed that the α-decays of 198 Rn and 196 Rn were clearly faster than the smooth behaviour of heavier even-mass Rn isotopes predicts (fig. 1a.). The conclusion from this study was that especially in the case of 196 Rn the α-decay is taking place between deformed (and strongly mixed) 0+ ground states.

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Fig. 1. Reduced α-decay width values of neutron-deficient Fr, Rn, At and Po isotopes. (a) Radons and poloniums are compared, (b) poloniums and astatines are compared and (c) radons and franciums are compared.

+ The α-decaying proton intruder state ((πs−1 1/2 )1/2 ) has been shown to exist in many odd-mass Bi isotopes [12] and in At isotopes (investigated recently in Jyv¨ askyl¨a) [6,7]. A falling trend of excitation energy of + the (πs−1 1/2 )1/2 state as a function of decreasing neutron + number has been observed. Actually the (πs−1 1/2 )1/2 pro195 ton intruder state becomes the ground state in At [6] + )1/2 proton intruder and in 185 Bi [13, 14]. The (πs−1 1/2 state remains as a ground state in 193 At and in 191 At [7]. In fig. 1b the reduced widths determined for the odd-mass At isotopes are shown together with the reduced widths determined for the even-mass Po isotopes. The reducedwidth values obtained for the α-decays from the high-spin isomers ((πh9/2 )9/2− ) in At follow nicely the reducedwidth values obtained for the ground state to ground state decays in Po. However, the reduced-width values obtained for the α-decays from the low-spin isomeric + intruder states ((πs−1 1/2 )1/2 ) in At are slightly higher. When more neutron-deficient nuclei are considered these reduced-width values start to follow the reduced-width values obtained for the α-decays from the Po 0+ ground states to the proton (2p-2h) 0+ intruder states in Pb. The

work has been extended and recently the neutron-deficient Fr isotopes were examined using RITU [8]. For the first + time, a (πs−1 1/2 )1/2 proton intruder state was also identified in a Fr isotope, namely in 201 Fr. This is illustrated in fig. 1c from where it can be noticed that again the α-decay from the low-spin isomeric intruder state is relatively faster than the α-decay from the high-spin ground state. The work [8] and the work [6] suggest the existence of a low-lying 1/2+ proton intruder isomeric (ground) state in 199 Fr. Since the (πh9/2 )9/2− state is associated with + the spherical shape and the (πs−1 1/2 )1/2 proton intruder state is associated with an oblate character an onset of substantial deformation is expected to occur at neutron number N = 112 in odd-mass Fr isotopes. In conclusion, the reduced widths deduced from the measured decay properties for the neutron-deficient oddmass Fr isotopes and even-mass Rn isotopes suggest an onset of substantial deformation at neutron number N = 112 and at N = 110, respectively. This can be compared to the prediction of M¨ oller et al. [15] where the predicted onset of deformation for Fr nuclei occurs at neutron number N = 116 and for Rn nuclei occurs at neutron number N = 114. This work was supported by the Academy of Finland under the Finnish Centre of Excellence Programme 2002-2005 (Project No. 44875, Nuclear and Condensed Matter Physics Programme at JYFL).

References 1. M. Leino et al., Nucl. Instrum. Methods Phys. Res. B 99, 653 (1995). 2. J.O. Rasmussen, Phys. Rev. 113, 1593 (1959). 3. Nucl. Data Sheets 15, No. 2, VI (1975). 4. A.N. Andreyev et al., Phys. Rev. Lett. 82, 1819 (1999). 5. A.N. Andreyev et al., Nature (London) 405, 430 (2000). 6. H. Kettunen et al., Eur. Phys. J. A 16, 457 (2003). 7. H. Kettunen et al., Eur. Phys. J. A 17, 537 (2003). 8. J. Uusitalo et al., to be published in Phys. Rev. C. 9. A. -P. Lepp¨ anen et al., to be submitted to Phys. Rev. C. 10. Yu.N. Novikov et al., Nucl. Phys. A 697, 92 (2002). 11. H. Kettunen et al., Phys. Rev. C 63, 044315 (2001). 12. E. Coenen, K. Deneffe, M. Huyse, P. Van Duppen, J.L. Wood, Phys. Rev. Lett. 54, 1783 (1985). 13. C.N. Davids et al., Phys. Rev. Lett. 76, 592 (1996). 14. G.L. Poli et al., Phys. Rev. C. 63, 044304 (2001). 15. P. M¨ oller, J.R. Nix, W.D. Myers, W.J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995).

Eur. Phys. J. A 25, s01, 181–182 (2005) DOI: 10.1140/epjad/i2005-06-114-1

EPJ A direct electronic only

Decay studies of neutron-deficient odd-mass At and Bi isotopes H. Kettunen1,a , T. Enqvist1 , K. Eskola2 , T. Grahn1 , P.T. Greenlees1 , K. Helariutta1,b , P. Jones1 , R. Julin1 , a¨ a1 , A. Keenan1 , H. Koivisto1 , P. Kuusiniemi1,c , M. Leino1 , A.-P. Lepp¨ anen1 , S. Juutinen1 , H. Kankaanp¨ M. Miukku1,d , P. Nieminen1,e , J. Pakarinen1 , P. Rahkila1 , and J. Uusitalo1 1 2

Department of Physics, University of Jyv¨ askyl¨ a, P.O. Box 35, FIN-40014 Jyv¨ askyl¨ a, Finland Department of Physics, University of Helsinki, FIN-00014 Helsinki, Finland Received: 12 September 2004 / c Societ` Published online: 24 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Alpha-decay properties of the isotope 191 At were investigated for the first time and the decay properties of 193 At and 195 At were studied with improved accuracy. The nuclei were produced in fusionevaporation reactions of 54 Fe and 56 Fe ions with 141 Pr and 142 Nd targets. The fusion products were separated in-flight using the gas-filled recoil separator RITU and implanted into a position-sensitive silicon detector. The isotopes were identified using position, time and energy correlations between the implants and subsequent alpha decays. New information concerning the low-lying states in the corresponding alphadecay daughter nuclei 187 Bi, 189 Bi and 191 Bi was also gained using alpha-gamma coincidences. PACS. 23.60.+e α decay – 27.80.+w 190 ≤ A ≤ 219 – 23.20.Lv γ transitions and level energies – 21.10.Dr Binding energies and masses

1 Introduction The region of neutron-deficient nuclei far from stability around the closed Z = 82 proton shell and the N = 104 neutron mid-shell offers an interesting challenge for various theoretical models as well as experimental instruments. A variety of nuclear phenomena, like shape coexistence and development of intruder states, can be observed in this limited region of the nuclear chart and understood by the coupling of the particles and particle holes to the proton-magic Pb core. In addition, the vicinity of the proton drip line in odd-Z nuclei offers an opportunity to observe proton emission in this region. More detailed discussions about the analysis and the results of the present article are published in references [1,2]. A summary of fusion-evaporation reactions used in the present work along with the measured production cross-sections of the primary products is presented in table 1. a

Conference presenter; e-mail: [email protected] b Present address: Laboratory of Radiochemistry, P.O. Box 55, FIN-00014 Helsinki, Finland. c Present address: Gesellschaft f¨ ur Scwerionenforschung, D-64200 Darmstadt, Germany. d Present address: Radiation and Nuclear Safety Authority, P.O. Box 14, FIN-00881 Helsinki, Finland. e Present address: Department of Nuclear Physics, Australian National University, Canberra, ACT 0200, Australia.

Table 1. Measured production cross-sections of the reactions used in the present work. Beam energies in the middle of the target are given. The 195 At experiment was dedicated to the production of a new radon isotope 195 Rn [3] and the astatine isotope was obtained as a side-product. A transmission of 40% for the evaporation residues in the RITU separator was assumed.

Reaction

Cross-section

Ebeam

Nd(56 Fe, p2n)195 At 141 Pr(56 Fe, 4n)193 At 141 Pr(54 Fe, 4n)191 At

200 nb 40 nb 300 pb

262 MeV 266 MeV 260 MeV

142

2 Results Three alpha-decaying states were identified for 193 At, and two for both 191 At and 195 At nuclei. For each of these isotopes the 1/2+ intruder state was observed to be the ground state. The alpha decays of the 7/2− states in 195 At and 193 At were observed to feed the excited 7/2− states at 148.7(5) keV and 99.6(5) keV in the corresponding daughter nuclei 191 Bi and 189 Bi, respectively. The spin, parity and excitation energy of these final states, observed for the first time, were determined using the properties of gammaray transitions observed in coincidence with the alpha decay of the 195 At and 193 At isotopes. The identification of the 13/2+ state in 193 At was also based on alpha-gamma coincidences. In 187 Bi the existence of the excited 7/2−

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Fig. 1. Level systematics of odd-mass Bi and At isotopes. Level energies are normalised to the 9/2− ground state in bismuth isotopes using the proton binding energies [2].

state at 63(10) keV was deduced based on the shape of the alpha-decay energy spectrum of 191 At. The spin and parity assignments of the initial states in the astatine isotopes were based on the unhindered alpha decays. The level systematics of the odd-mass bismuth and astatine isotopes are shown in fig. 1. For astatine isotopes the systematics are obtained by using proton binding energies and normalising them to the ground state of the bismuth isotopes. The mass values needed for the proton binding energies were taken from the recent atomic mass measurements [4, 5,6], updated with the new results for 191 At, 193 At, 195 At and 187 Bi [1,2]. The level schemes suggested for 191 At, 193 At and 195 At were observed to differ from those observed in heavier odd-mass astatine isotopes. The intruder 1/2+ state, having a π(4p − 1h) configuration becomes the ground state in 195 At. In the heavier odd-mass astatine isotopes, the ground state is the 9/2− state. In addition, a 7/2− state rather than a 9/2− state is suggested to represent the first excited state in these light astatine isotopes. The emergence of the 7/2− state over the 9/2− state can be understood by assuming a change in deformation between the 197 At and 195 At isotopes. According to the Nilsson diagram a 7/2− state, associated with an oblate 7/2− [514] Nilsson state, becomes available for the 85th proton in odd-mass astatine isotopes if sufficient oblate deformation is assumed. Based on the results of the present work it is proposed that in light A < 197 odd-mass astatine isotopes the deformed three-particle configuration, driving the last proton to the 7/2− [514] Nilsson state, is energetically more favoured than the nearly spherical (πh9/2 )3 configuration. Correspondingly, the existence of a lowlying 7/2− state in bismuth isotopes can be understood

by a 7/2− [514] Nilsson proton state associated with oblate deformed structures. The recent potential energy calculations [7,8] support the 7/2− assignment of this low-lying state observed in 189,191 Bi and deduced to exist in 187 Bi. Based on these calculations this state in 189,191 Bi was associated with the oblate 7/2− [514] configuration as deduced also in the present work. At the mid-shell nucleus 187 Bi104 the excitation energy of the 7/2− state was still observed to come down (see systematics in fig. 1). However, according to the calculations [8] the excitation energy of the oblate structure should already increase in 187 Bi. The downward behaviour was explained by a prolate 7/2− state, originating from the 1/2− [530] orbital, which crosses the oblate configuration between 189 Bi and 187 Bi. In addition, similar crossing of the oblate and prolate structures is most likely occurring in the 1/2+ and 13/2+ states [8]. Proton separation energies of −240(130) keV, −560(140) keV and −1020(140) keV were determined for 195 At, 193 At and 191 At, respectively. This indicates that 195 At is the first proton unbound astatine isotope. Using the WKB barrier transmission approximation [9] and assuming a spectroscopic factor of one, the proton separation energy obtained for 191 At would correspond to a partial half-life of approximately 57 s for an unhindered proton emission from the πs1/2 orbital. This rough estimation suggests that the branching ratio of the proton emission compared to the alpha-decay would be too small to be detected. The proton separation energy of the next odd-mass astatine isotope 189 At can be estimated to be approximately −1500 keV by extrapolating the systematics of the heavier At isotopes. Based on the WKB calculation this value would correspond to a half-life of approximately 50 μs for a proton emission from the πs1/2 orbital assuming a spectroscopic factor of one. An energy of 7900 keV can be extrapolated for the alpha decay of 1/2+ state in 189 At to the 1/2+ state in 185 Bi corresponding to a partial half-life of 400 μs for an unhindered alpha decay. Thus, the 189 At nucleus is a good candidate for the observation of proton emission. For more details see references [1,2]. This work was supported by the Academy of Finland under the Finnish Centre of Excellence Programme 2002-2005 (Project No. 44875, Nuclear and Condensed Matter Physics Programme at JYFL).

References 1. 2. 3. 4. 5. 6. 7. 8. 9.

H. Kettunen et al., Eur. Phys. J. A 16, 457 (2003). H. Kettunen et al., Eur. Phys. J. A 17, 537 (2003). H. Kettunen et al., Phys. Rev. C 63, 044315 (2001). Yu.N. Novikov et al., Nucl. Phys. A 697, 92 (2002). T. Radon et al., Nucl. Phys. A 677, 75 (2000). G. Audi et al., Nucl. Phys. A 624, 1 (1997). P. Nieminen et al., Phys. Rev. C 69, 064326 (2004). A.N. Andreyev et al., Phys. Rev. C 69, 054308 (2004). F.D. Becchetti, G.W. Greenlees, Phys. Rev. 182, 1190 (1969).

Eur. Phys. J. A 25, s01, 183–184 (2005) DOI: 10.1140/epjad/i2005-06-116-y

EPJ A direct electronic only

Alpha-decay study of Z = 92

218

U; a search for the sub-shell closure at

A.-P. Lepp¨ anen1,a , J. Uusitalo1 , S. Eeckhaudt1 , T. Enqvist1 , K. Eskola2 , T. Grahn1 , F.P. Heßberger3 , P.T. Greenlees1 , P. Jones1 , R. Julin1 , S. Juutinen1 , H. Kettunen1 , P. Kuusiniemi1 , M. Leino1 , P. Nieminen1 , J. Pakarinen1 , J. Perkowski1 , P. Rahkila1 , C. Scholey1 , and G. Sletten4 1 2 3 4

Department of Physics, University of Jyv¨ askyl¨ a, P.O. Box 35, FIN-40351, Jyv¨ askyl¨ a, Finland Department of Physics, University of Helsinki, FIN-00014 Helsinki, Finland GSI, Planckstr. 1, D-64291 Darmstadt, Germany Department of Physics, University of Copenhagen, Copenhagen, Denmark Received: 4 November 2004 / c Societ` Published online: 22 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Neutron-deficient uranium isotopes were studied via α spectroscopic methods. A low-lying α-decaying isomeric state was found in 218 U. The new isomeric state was assigned spin and parity I π = 8+ . The isomer decays by α emission with an energy E = 10 678(17) keV and with a half-life 218 T1/2 = (0.56+0.26 U was measured −0.14 ) ms. The known alpha-decay properties of the ground state of with improved statistics. The ground-state α-decay has an energy E = 8612(9) keV and a half-life T1/2 = (0.51+0.17 −0.10 ) ms. PACS. 23.60.+e α decay – 25.70.Gh Compound nucleus – 27.80.+w 190 ≤ A ≤ 219

The neutron-deficient nucleus 218 U is possibly a doubly magic nucleus with Z = 92 and N = 126, assuming a subshell gap at Z = 92 between the h9/2 and the f7/2 proton orbitals. However, recent theoretical calculations by Caurier et al. [1] do not support the shell gap theory. While several other N = 126 isotones have been studied extensively, for 218 U only the α-decay properties of the ground state was known. The occurrence of a low-lying isomeric state in 216 Th speaks against the existence of a shell gap. In 216 Th [2] an 8+ state, with a πh9/2 f7/2 configuration, has been found to come low in energy close to the 6+ state, forming an isomer with a 3% α-decay branch. The discovery of a low-lying isomeric state in 218 U [3] would disprove the existence of a shell gap at Z = 92. The experiments were carried out at JYFL cyclotron laboratory. A beam of 40 Ar at an energy of Elab = 186 MeV was used to bombard a 182 W target of 600 μg/cm2 thickness. The fusion products were separated from the beam particles with the RITU gas-filled separator and implanted into the DSSD of the GREAT spectrometer [4] at the RITU focal plane. The data from two separate experiments, performed one year apart, were analyzed. The experimental data was analyzed with the GRAIN package [5]. Recoils were correlated with an α-decay in a given position and time window. Correlated mother and a

e-mail: [email protected]

Table 1. Calculated hindrance factors.

Δl

0 4 6 8 9 10 11 12 13

216m

Th

14000 2900 520 20 13 3 0.5 0.1

218m

U

69000 15000 2700 280 73 17 3.4 0.6 0.1

219

U

130 24 4.6

daughter alpha-decays were used to form a complete decay chain. In these two experiments a total of 20 of 218g U, 12 of 218m U, 5 of 219 U and 1 of 217 U were identified. The measured production cross-section for 218 U was 1.2 nb. The correlated α-α pairs are presented in fig. 1, the uranium isotopes have been indicated. The possible spin and parity assignment for the new isomeric state in 218 U is either 8+ or 11− based on refs. [1, 2]. These two assignments are the only ones which are consistent with the experimental α-decay data since the electromagnetic transitions from other levels are too fast for α-decay to compete with. In order to determine the spin and parity of the new isomeric state the method of Rasmussen [6] was applied. Tentatively, the α-decay

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Fig. 1. Correlated α-decay events, plotted as a function of the energies of mother and daughter α-decays. Search time for a mother α was 80 ms and the search time for daughter α was 20 s.

Table 2. Summary of the results obtained in this work.

Nucleus E (keV)

Half-life (ms)

217

8024(14)

0.19+1.13 −0.10 0.05

8612(9)

0.51+0.17 −0.10 0.56+0.26 −0.14 0.08+0.10 −0.03

U

218g

U

218m 219

U

U

10 678(17) 9774(18)

Cross-section No. of State (nb) events

1

−

( 12 ) +

0.9

20

0

0.3

12

8+

0.2

5

9+ 2

was determined for the isomer in 218 U. Similarly the Rasmussen method was applied to assign the spin and parity of 9/2+ to the ground state of 219 U. Interestingly, the halflife of the isomer in 218 U agrees with that of its ground state. This is due to the high spin of the decaying isomeric state. All the half-lives and decay energies are presented in table 2.

References branch from this level must be very close to 100%. The hinderance factor of the α-decay from the new isomeric state was compared with that found for the 8+ state in 216 Th [2]. The relevant hindrance factors are listed in table 1. The isomeric states in 216 Th and in 218 U show similar structural behavior. On the basis of this analysis the spin and parity of 11− were ruled out and an 8+ assignment

1. 2. 3. 4.

E. Caurier et al., Phys. Rev. C 67, 054310 (2003). K. Hauschild et al., Phys. Rev. Lett. 87, 072501 (2001). A. Lepp¨ anen et al., to be published in Phys. Rev. C (2005). R.D. Page, Nucl. Instrum. Methods Phys. Res. B 204, 634 (2003). 5. P. Rahkila, to be published in Nucl. Instrum. Methods Phys. Res. A (2005). 6. J.O. Rasmussen, Phys. Rev. 113, 1593 (1959).

3 Moments and radii 3.1 Electromagnetic moments

Eur. Phys. J. A 25, s01, 187–191 (2005) DOI: 10.1140/epjad/i2005-06-099-7

EPJ A direct electronic only

Developments in laser spectroscopy at the Jyv¨ askyl¨ a IGISOL J. Billowesa Schuster Laboratory, University of Manchester, Manchester M13 9PL, UK Received: 7 February 2005 / Revised version: 13 March 2005 / c Societ` Published online: 2 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. This paper describes the programme of work on laser spectroscopy of radioactive atoms being carried out at the IGISOL facility by a Birmingham-Jyv¨ askyl¨ a-Manchester collaboration. The advantageous features of the ion guide ion source, combined with an ion beam cooler-buncher allows a broad range of studies to be pursued. Highlighted in this presentation are collinear beams laser spectroscopic measurements on Zr and Y isotopes, and charge radii determinations for two 8− isomers in 130 Ba and 176 Yb. A laser ion source capability called FURIOS is being developed for the IGISOL which will not only provide isobarically pure beams for experiments, but also allow in-source laser spectroscopy of short-lived isomers of heavy elements. PACS. 21.10.Ft Charge distribution – 21.10.Ky Electromagnetic moments – 32.10.Fn Fine and hyperfine structure

1 Introduction The finite spread of the nuclear charge distribution, and the static nuclear magnetic and electric moments affect the energy levels of the valence electrons at the part per million level. A range of methods of laser spectroscopy can measure the atomic perturbations with such precision that high quality information may be deduced about nuclear properties [1, 2,3]. The hyperfine structure of an optical transition provides the nuclear spin, magnetic dipole and electric quadrupole moments. The change in the mean square charge radius of two isotopes may be deduced from the frequency shift of the transition (the isotope shift) between the two isotopes. Although it is sometimes difficult to get an exact calibration of the size of the radial change, the comparisons of charge radii changes from isotope to isotope are very sensitive to even small structural changes. For example, the change in the proton distribution due to the removal of a single neutron is clearly evident, and a shape change between to isotopes is very obvious. The high sensitivity of the laser techniques allows these studies to be extended to radioactive ions lying an appreciable distance from the region of nuclear stability and to short-lived nuclear state and isomers with half-lives in the millisecond, and even microsecond region. The present status of optical measurements is shown in fig. 1. The standard technique, that has been adapted for use at the IGISOL (Ion Guide Isotope Separator, On-Line) facility, is the collinear beams method which makes efficient use of a

e-mail: [email protected]

the radioactive sample and compresses the Doppler broadening of the optical transitions to a point where it is comparable to the natural linewidth which sets the ultimate limit on the precision of the measurement. A Birmingham-Manchester group have been collaborating with the IGISOL group at the Cyclotron Laboratory, University of Jyv¨askyl¨a (JYFL) for a decade. The facility provides low-energy radioactive ion beams from an ion guide ion source [4] for mass determinations, and nuclear and laser spectroscopy measurements. The ion source consists of a chamber through which helium gas flows. Nuclear reaction products recoil and stop in the flowing gas which carries them out through a 1 mm diameter nozzle. Those products which have not neutralized are drawn through an aperture in a gas “skimmer” plate and enter a conventional mass separator which delivers them to experiments at a beam energy of typically 40 keV. The ion guide has two particularly beneficial features for nuclear research: i) the extraction from the ion source is relatively fast (1 millisecond) compared with conventional thermalrelease ion sources, and ii) ions of any element can be extracted with comparable efficiency, almost independent of their chemistry [4]. Of course, for some experiments this can also be a drawback since the extracted beam will be a cocktail of isobars of different elements. Other drawbacks of the ion guide method are the poor overall efficiency of the source, and the energy spread of the extracted ion beam, which simultaneously increases the Doppler width and reduces the sensitivity of the collinear beams laser spectroscopy method. The solution at JYFL was to insert an “ion beam cooler” in the mass separated beam line [5].

188

The European Physical Journal A

 

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Fig. 1. Present status of optical measurements. The black squares indicate stable isotopes. The dark shade indicates measured isotopes. The figure is taken from ref. [3] and revised by one of the authors (WN).

This also had the ability to accumulate and bunch the ion beam —a feature that led to a new and general technique for background reduction in the subsequent laser measurements.

2 Laser spectroscopy with the ion beam cooler-buncher The cooler-buncher is gas-filled linear Paul trap held on a high-voltage platform a hundred volts or so below the ion source voltage. The IGISOL ion beam is thus decelerated as it enters the gas-filled RFQ structure. The ions are thermalised by viscous collisions with the helium before being carefully extracted and reaccelerated at the far end for delivery to the experiment. The energy-spread of the beam is reduced to less than 1 eV. A small electric potential gradient of about 5 V over the length of the trap draws the ions through the cooler, resulting in a transit time of the order of 1 ms. Alternatively, the exit can be closed by applying a positive voltage to the end plate, creating a potential well just inside the cooler where the ions may be allowed to accumulate for up to a second. Lowering the plate voltage releases these ions in a bunch with a time-spread of 15–20 μs with little effect on the energy spread of the ions. In the laser measurements a CW laser beam overlaps the ion beam collinearly and resonantly scattered photons are observed when the laser frequency is brought to resonance with the atomic or ionic transition. There is a continuous background in the photon signal from scattered laser light and photon detector dark counts. This background is at least two orders of magnitude higher than the

signal from a radioactive isotope beam. If the ion beam is bunched and the photon signal is gated for just the 20 μs period when the ions are present in the laser beam, then the background can be suppressed by more than four orders of magnitude, resulting in a very sensitive method of spectroscopy that can be generally applied to any isotope or element provided the life-time is longer than about 50 ms.

3 Charge radii of Zr and Y isotopes The bunched-beam method of laser spectroscopy has been applied to the neutron-rich [6] Zr isotopes from protoninduced fission of uranium, and the neutron-deficient [7] isotopes produced in 89 Y(p, xn) reactions. The charge radii systematics of this chain [8] are very similar to zirconium’s nearest even-Z neighbour, strontium [9]. The smallest r.m.s. radius occurs in stable 90 Zr at the N = 50 shell closure, and the radii increase steadily with neutron number for both the lighter and heavier isotopes, as seen in fig. 2. A marked increase in deformation is seen at N = 60 which is consistent with nuclear spectroscopic studies in the region [10]. The mean square charge radius dependence on nuclear deformation may be expressed by

5 2 (β2 + β32 + . . .) .

r2 deformed = r2 spherical 1 + 4π

The dashed lines in fig. 2 show the changes in mean square charge radii with neutron number as predicted by the droplet model [11] corrected for quadrupole deformation

J. Billowes: Developments in laser spectroscopy at the Jyv¨ askyl¨ a IGISOL 20.8

22

<β2>=0.4 21 20.4

Zr

20 19

189

the ground state and an (sp) admixture in the 1 P1 state. New laser optics and a Brewster-cut intra-cavity doubling crystal have been installed and on-line measurements have begun on the neutron-deficient isotopes. Measurements on the neutron-rich produced as fission fragments will begin next year.

<β2>=0.3 18

80

100

4 Isomer shifts of multi-quasiparticle isomers

120

<β2>=0.2

2

(fm )

20.0

2

19.6

<β2>=0.1 <β2>=0.0 19.2

18.8

18.4

84

86

88

90

92 A

94 Zr

96

98 100 102 104

Fig. 2. Changes in mean square charge radii for the zirconium isotopes. Filled circles are stable isotopes; open circles are radioactive isotopes. The isodeformation lines are predictions of the droplet model [11].

according to the above formula. The charge radii data thus suggest that there is a slow but steady increase in deformation from the spherical nucleus 90 Zr at N = 50 up to N = 59. This is contrary to nuclear spectroscopic infor+ mation where the the low B(E2; 2+ 1 → 0g.s. ) values [12] suggest the ground state stays spherical for all the stable even isotopes. Unfortunately there is no quadrupole moment information for 93,95 Zr which might shed some light on this contradictory situation. The available B(E3) data suggest it is unlikely that octupole vibrations are responsible for the increase in charge radii [6,13]. The B(E2) strength to all higher 2+ states should be included to get the correct β22 estimate for the droplet model correction. Including the missing strength may resolve the apparent inconsistency between the B(E2) and charge radii data. In order to pursue the problem, a programme of measurements on the yttrium isotope chain has started. This is the odd-Z neighbour between Sr and Zr. The yttrium isotopes are rich in low-lying isomers which will be accessible to laser measurement and a comprehensive study of quadrupole shape evolutions should be possible in this neutron number region. Off-line testing on a number of transitions from the Y+ ionic ground state (224 nm, 311 nm, 363 nm) have been carried out. The strongest transition is the 363 nm (s2 ) 1 S0 → (dp) 1 P1 due to (p2 ) and (d2 ) admixtures in

There are two instances in the literature where an excited nuclear state has a smaller r.m.s. charge radius that the nuclear ground state despite being no less deformed. The most well-known is the 178m2 Hf(16+ ) 4 quasiparticle 31year isomer [14]. The second example is a 3 quasiparticle isomer in the isotone 177 Lu [15]. A possible explanation is that the blocking of orbitals near the Fermi surface by the quasiparticles leads to a reduction of the paring which then reduces the diffuseness of the nuclear surface and thus reduces the mean square charge radius. At JYFL it has been possible to measure two 8− isomers in 176 Yb and 130 Ba which are related to the 2neutron and 2-proton configurations of the 16+ state in 178 Hf. There are a number of experimental problems in these isomer shift measurements. Both K = 8 isomers are two-neutron configurations with small magnetic moments. Consequently, the hyperfine structure is bunched up around the much more intense nuclear ground state resonance peak. Furthermore, the quadrupole interaction can change the order of the hyperfine levels and assignments of the peaks are difficult when some components may be hidden under the ground state peak. Nevertheless, an unambiguous analysis for 130 Ba(8− ) was possible [16] and, like the 178 Hf isomer, the state was found to have a smaller r.m.s. charge radius despite a similar deformation to the ground state. The 176 Yb(8− ) isomer was populated in the 176 Yb(d, pn) reaction at 13 MeV with a deuteron beam current of 5.5 μA. The isomer flux of the A = 176 beam was determined by gamma-ray spectroscopy to be 200 isomers/sec out of a total flux of 8,400 ions/s. The analysis has now been completed [17]. The results are compared with the measured N = 106 isomers in the neighbouring chains of Lu and Hf in fig. 3. For display purposes the data have been normalised to the ground states at N = 99 and 106 (although this is not quite consistent with the atomic factor evaluations used for the extraction of the change in mean square charge radii). It is evident from the figure that all isomers are smaller than their nuclear ground state. A comparison of the β2 deformation parameters derived for the ground states and isomers indicate that none of the isomer shifts can be attributed to a reduction in deformation of the isomer. The reduction in r.m.s. charge radius is greatest for the 4 quasi-particle 16+ state. The 176 Yb(8− ) and 177 Lu(23/2− ) states are both 2 quasi-particle effects compared to their respective ground states, and are about twice the size of the normal oddeven staggering of isotope shifts which might be thought of as a 1 quasi-particle effect. As yet there is no published quantitative theoretical explanation.

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The European Physical Journal A

Yb Lu Hf

1

δ < r 2 > 99,N δ < r 2 > 99,106

0.5

1 0.95 0.9

0

0.85 0.8 -0.5

-1

98

100

102

0.75 105.5

106

104

106

106.5

108

N Fig. 3. Relative changes in mean square charge radii for the N = 106 isomers of Yb [17], Lu [15] and Hf [14]. The isomers are shown in the panel as open symbols. 178 Hf(16+ ): diamond; 177 Lu(23/2− ): square; 176 Yb(8− ): circle.

5 Development of the FURIOS laser ion source facility at JYFL The insensitivity of the ion guide to an element’s chemistry has been essential to many of the laser spectroscopic studies made at JYFL. However, this property can become a disadvantage when working on isotopes very far from the stability line, because the mass-separated beam may contain isobars of other elements produced with much higher fluxes. Considerable work on improving the selectivity of gas-catcher ion sources has been done by the Leuven group [18] who developed the laser resonance ionization ion guide, IGLIS. In order to improve and extend the studies on exotic isotopes at the IGISOL facility a laser ion source project has started at JYFL which will provide improved isobaric purity and higher efficiency without compromising the universality and fast release of the IGISOL system. Several techniques will be developed. One will be similar to the IGLIS concept where pulsed lasers produce ions within the gas cell volume. A second method will use lasers to ionize atoms after they have flowed out of the gas volume. The element selectivity is provided by the laser resonance ionization process whereby a neutral atom is stepwise excited by two or three pulsed laser beams separately tuned to each step of the ionization scheme. Only pulsed lasers can produce the high power densities required to

saturate the transitions in the scheme. To avoid duty cycle losses in some of the laser techniques proposed for the facility, the laser repetition rate rate must be of the order of 10 kHz. In order to cover as broad a range of elements as possible two sets of pulsed lasers will be available, one using well-known dye laser technology, the other using solid state pump and titanium sapphire lasers. The laser facility has been named FURIOS (Fast Universal Resonance laser Ion Source). A schematic layout of FURIOS is shown in fig. 4. All of the lasers have been bought and are being installed and commissioned. A pulsed dye laser and dye amplifier will be pumped by an Oxford Lasers 45 W copper vapour laser with a 1–15 kHz repetition rate. The dye amplifier will be seeded by a CW Spectra Physics 380 ring dye laser. This will provide a Fourier-limited linewidth for the amplified light of less than 100 MHz. The three Ti:Sapphire Z-cavity lasers have been designed and built by Dr K. Wendt’s group at Mainz University. These are pumped at 532 nm by a 100 W Nd:YAG laser with a repetition rate of 1–50 kHz supplied by Lee Lasers. Figure 4 also shows one of the techniques to be developed at JYFL. Atoms flowing out of the helium chamber nozzle will be laser-ionized inside an RF trap. Ionic species from the gas chamber can be completely suppressed and the ion beam extracted from the RF trap will have exceptionally high purity.

J. Billowes: Developments in laser spectroscopy at the Jyv¨ askyl¨ a IGISOL

191

Fig. 4. The planned FURIOS laser ion source facility at JYFL.

An application using the narrow-bandwidth pulsed dye laser light is in-source resonance ionization spectroscopy on sub-millisecond isomers. The laser beams can be introduced through a window at the back of the chamber for illumination of the larger volume. Full operation of this facility is keenly awaited. The on-going work described in this paper is being carried out by a collaboration involving the Universities of Birmingham (G. Tungate, D.H. Forest, B. Cheal, M.D. Gardener, M. Bis¨ o, H. Penttil¨ sel), Jyv¨ askyl¨ a (J. Ayst¨ a, A. Jokinen, I.D. Moore, J. Huikari, S. Rinta-Antila) and Manchester (J. Billowes, P. Campbell, A. Nieminen, K. Flanagan, A. Ezwam, M. Avgoulea, B.A. Marsh and B.W. Tordoff). The 130m Ba measurement was done in collaboration with Dr A. Bruce (University of Brighton), and the 176m Yb work was in collaboration with Professor G. Dracoulis (Australian National University). The FURIOS Collaboration also involves the University of Mainz (K.D.A. Wendt, Ch. Geppert and T. Kessler). The chart in fig. 1 has been kindly supplied by Wilfried N¨ auser. ortersh¨

References 1. E.W. Otten, Treatise on Heavy-Ion Science, Vol. 8 (Plenum, New York, 1989) p. 515. 2. J. Billowes, P. Campbell, J. Phys. G 21, 707 (1995). 3. H-J. Kluge, W. N¨ ortersh¨ auser, Spectrochim. Acta, Part B 58, 1031 (2003). ¨ o, Nucl. Phys. A 693, 477 (2001). 4. J. Ayst¨ 5. A. Nieminen et al., Phys. Rev. Lett. 88, 094801 (2002). 6. P. Campbell et al., Phys. Rev. Lett. 89, 082501 (2002). 7. D.H Forest et al., J. Phys. G 28, L63 (2002). 8. H.L. Thayer et al., J. Phys. G 29, 2247 (2003). 9. R.F. Silverans et al., Phys. Rev. Lett. 60, 2607 (1988). 10. W. Urban et al., Nucl. Phys. A 689, 605 (2001). 11. W.D. Myers, K.H. Schmidt, Nucl. Phys. A 410, 61 (1983). 12. S. Raman et al., At. Data Nucl. Data Tables 36, 1 (1987). 13. H. Mach et al., Nucl. Phys. A 523, 197 (1991). 14. N. Boos et al., Phys. Rev. Lett. 72, 2689 (1994). 15. U. Georg et al., Eur. Phys. J. A 3, 225 (1998). 16. R. Moore et al., Phys. Lett. B 547, 200 (2002). 17. K.T. Flanagan, PhD Thesis, University of Manchester (2004). 18. P. Van Duppen et al., Hypf. Interact. 127, 401 (2000).

Eur. Phys. J. A 25, s01, 193–197 (2005) DOI: 10.1140/epjad/i2005-06-041-1

EPJ A direct electronic only

Laser and β-NMR spectroscopy on neutron-rich magnesium isotopes M. Kowalska1,a , D. Yordanov2 , K. Blaum1 , D. Borremans2 , P. Himpe2 , P. Lievens3 , S. Mallion2 , R. Neugart1 , G. Neyens2 , and N. Vermeulen2 1 2 3

Institut f¨ ur Physik, Universit¨ at Mainz, D-55099 Mainz, Germany Instituut voor Kern- en Stralingsfysica, K.U. Leuven, B-3001 Leuven, Belgium Laboratorium voor Vaste-Stoffysica en Magnetisme, K.U. Leuven, B-3001 Leuven, Belgium Received: 15 January 2005 / Revised version: 24 February 2005 / c Societ` Published online: 3 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Ground-state properties of neutron-rich 29,31 Mg have been recently measured at ISOLDE/CERN in the context of shell structure far from stability. By combining the results of β-NMR and hyperfinestructure measurements unambiguous values of the nuclear spin and magnetic moment of 31 Mg are obtained. I π = 1/2+ and μ = −0.88355(15) μN can be explained only by an intruder ground state with at least 2p-2h excitations, revealing the weakening of the N = 20 shell gap in this nucleus. This result plays an important role in the understanding of the mechanism and boundaries of the so called “island of inversion”. PACS. 21.10.Hw Spin, parity, and isobaric spin – 21.10.Ky Electromagnetic moments – 27.30.+t 20 ≤ A ≤ 38 – 32.10.Fn Fine and hyperfine structure

1 Introduction With the advent of radioactive beam facilities the number of nuclei available for study became much larger than about 300 stable nuclei investigated before. Among the ways of gaining insight into this vast variety of nuclear systems, one is to study their ground-state properties. One of the regions of special interest is the “island of inversion”, comprising highly deformed neutron-rich nuclei with 10 to 12 protons and about 20 neutrons. The large deformation in this region was first suggested after mass measurement of 31 Na [1] and has been since then observed also by other methods in some neighbouring nuclei, such as 30 Ne [2], 30 Na [3] or 32 Mg [2, 4]. The shell model interprets this behaviour as a sign of weakening, or even disappearance of the N = 20 shell gap between the sd and f p shells. Due to this, particle-hole excitations come very low in energy and even become the ground state, giving rise to the inversion of classical shell model levels, thus the name of the region. The exact borders of this “island” are not known. Odd-A neutron-rich radioactive Mg isotopes lie on its onset, or probably even inside it. Their nuclear moments are not known and only the spin of 29 Mg has been firmly assigned [4], and the spins of 31,33 Mg have been assigned tentatively [5, 6] (table 1). It is therefore important to study these systems. a

Conference presenter; e-mail: [email protected]

Table 1. Ground-state properties of measurements).

29,31,33

Mg (before our

Isotope

Half-life

Nuclear spin-parity

29

1.3 s 230 ms 90 ms

3/2+ (3/2)+ (3/2)+

Mg Mg 33 Mg

31

2 Experimental procedure and tests The beams of interest are produced at the ISOLDE mass separator at CERN via nuclear fragmentation reactions in the UC2 target by a 1.4 GeV pulsed proton beam (about 3 × 1013 /s protons per pulse, every 2.4 seconds). They are next ionised by stepwise excitation in the resonance ionisation laser ion source [7], accelerated to 60 kV and guided to the collinear laser spectroscopy setup [8], where laser and β-NMR spectroscopy are performed (fig. 1). The typical ion intensities available are 6.5 × 106 , 1.5 × 105 , and 8.9 × 103 ions/s of 29 Mg+ , 31 Mg+ , and 33 Mg+ , respectively. In the experimental setup the ions are polarised, implanted into a crystal lattice and the angular asymmetry of their β-decay is detected [9]. The polarisation is obtained via optical pumping (see [3]). For this purpose the ions are overlapped with circularly polarised cw laser light and their total spins

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Fig. 1. Experimental setup for laser and β-NMR spectroscopy on Mg ions. For the measurements, either the optical detection or the β-NMR is used.

Fig. 2. Optical pumping of 31 Mg with an assumed spin I = 1/2 and a negative magnetic moment. The process is shown for F = 1 → F  = 2 transitions with positive and negative laser light polarisation, which populate different mF sublevels.

(electron and nuclear) get polarised due to the interaction with the light in presence of a weak longitudinal magnetic field. When positive laser polarisation is chosen (σ + ), after several excitation-decay cycles the ground-state sublevel with highest mF (projection of the total atomic spin F in the direction of the guiding magnetic field) is mostly populated. For σ − the population is highest for the lowest mF = −F (fig. 2). The electric and nuclear spins are next rotated in a gradually increasing guiding field and adiabatically decoupled (fig. 3) before the ions enter the region of a high transversal magnetic field (0.3 T), where they are implanted into a suitable host crystal. With polarised spins the β-decay is anisotropic and the angular asymmetry of the emitted β-particles can be measured in two detectors, placed at 0 and 180 degrees with respect to the magnetic field. The hyperfine structure of the ions can be observed in the change of this asymmetry as a function of the Doppler-tuned optical excitation frequency. For the purpose of β-NMR measurements [9,10], the frequency is tuned to the strongest hyperfine component and the polarisation is destroyed by transitions between different nuclear Zeeman levels caused by irradiation with a tunable radio frequency. In a cubic host crystal the nuclear magnetic resonance takes place when the radio frequency corresponds to the Larmor frequency (νL ) of the implanted nucleus. This frequency allows the deter-

Fig. 3. Behaviour of the ground-state hyperfine structure of 31 Mg for weak and strong magnetic field (I = 1/2 and negative μ assumed).

Fig. 4. β-decay asymmetry as a function of the laser power.

mination of the nuclear g-factor, since νL = gμN B/h (with B as the external magnetic field). A precise g-factor measurement requires high asymmetries and narrow resonances. Both the linewidth and amplitude of the observed resonance can depend strongly on the used implantation

M. Kowalska et al.: Laser and β-NMR spectroscopy on

29,31

Mg

195

Fig. 5. Measured hyperfine structure of 31 Mg D1 and D2 lines for σ + and σ − polarised light. The experimental count rate asymmetry is shown as a function of the Doppler tuning voltage.

crystal. Three cubic crystals were tested. At room temperature MgO turned out to be superior to metal hosts (it gave up to 6.7% asymmetry, compared to 3.1% for Pt and 1.8% for Au, all values taken for 31 Mg, with the linewidths comparable for all three crystals) and was therefore used for further measurements. Fig. 6. Predicted hyperfine structure of 31 Mg D1 and D2 lines for I = 1/2 and a negative magnetic moment.

3 Hyperfine structure and g-factor of

31

Mg

The transitions suitable for optical pumping of Mg ions are the excitations from the ground state to the two lowestlying excited states, 3s 2 S1/2 → 3p 2 P1/2 and 3p 2 P3/2 (D1 and D2 lines). The wavelength (280 nm) is in the ultraviolet range. For better efficiency (about 5%) an external cavity was used to frequency double the 560 nm output of a ring dye laser (Pyrromethene 556 as active medium), which was in turn pumped by a multiline Ar+ laser. The UV powers obtained in this way (about 15 mW) suffice to saturate the transitions (fig. 4). With this setup the hyperfine structure of 31 Mg for both lines was recorded for σ + and σ − polarised light (fig. 5). The structures reveal 1/2 as the most probable nuclear spin, since this is the only case which can reproduce the observed three hyperfine components for both D1 and D2 lines, as shown in fig. 6. For all other spins (e.g., 3/2, 7/2) there should be

4 components in the D1 line (fully resolved) and 6 in the D2 line (at least partly resolved). The positive and negative resonances in fig. 5 reflect the sign of polarisation achieved by optical pumping on the different hyperfine-structure components for which only one example is shown in fig. 2. For a quantitative explanation one has to take into account also the decay from the excited state to the other ground-state level (with F = 0 in the case of fig. 2). The distribution of population over the different |F, mF  levels can be calculated [3] by solving rate equations including the relative transition probabilities for the excitations |F, mF  → |F  , mF   and subsequent decays |F  , mF   → |F, mF . Figure 3 shows the rearrangement of electronic and nuclear spins by the adiabatic decoupling which occurs while the ions enter the strong-magnetic-field region. Apparently, the effect of σ + and σ − optical pumping is asymmetric in the final

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population of |mJ , mI  levels reached in the Paschen-Back regime. Only the distribution over the nuclear Zeeman levels mI is responsible for the β-asymmetry signals observed in the spectra. These are different in amplitude and only partly in sign under reversal of the polarization from σ + to σ − light. After hyperfine structure scans, the acceleration voltage is fixed to the hyperfine component giving largest asymmetry (6.7% for D2 line with σ + ) and β-NMR measurements follow. Several resonances in a cubic MgO lattice give the Larmor frequency νL (31 Mg) = 3859.72(13) kHz. For the calibration of the magnetic field (within 48 hours of taking the data for 31 Mg) a search for Larmor resonances in the same crystal was performed on optically polarised 8 Li with the g-factor g(8 Li) = 0.826780(9) [11]. This nucleus is available from the same ISOLDE target and requires changes in the optical pumping laser system (excitation wavelength around 670 nm), as well as minor modifications to the setup. The reference Larmor frequency is νL (8 Li) = 1807.03(2) kHz. From the above, the deduced absolute value of the g-factor of 31 Mg is |g(31 Mg)| = 1.7671(2) (corrected for diamagnetism) [12]. The final error includes a systematic uncertainty accounting for the inhomogeneities of the magnetic field and its drift between the measurements on 31 Mg and 8 Li.

4 Nuclear magnetic moment and spin of

31

Mg

The hyperfine splitting depends both on the nuclear spin and the g-factor, e.g. the splitting between the groundstate hyperfine components of 31 Mg (the electronic spin J = 1/2) equals Δν = A(I + 1/2), with the hyperfine constant A = gHe /J. Based on the measured gfactor and the hyperfine splitting one can thus determine the spin and the absolute value of the magnetic moment (μ = gIμN ) of 31 Mg. A reference measurement on a different Mg isotope with a known g-factor is also required, in order to calibrate for the magnetic field created by electrons at the site of the nucleus (He ). Δν can be then expressed as Δν = Aref /gref · g(I + 1/2). For this purpose stable 25 Mg was chosen and was studied by means of classical collinear laser spectroscopy with the optical detection method (fig. 1). To verify if our measurements are performed in the correct way, we scanned the hyperfine structure of this isotope in the D1 line (fig. 7). The measured hyperfine-structure constant for the ground state Ags (25 Mg) = −596.4(3) MHz is in excellent agreement with the accurate value quoted in the literature −596.254376(54) MHz [13]. This value, together with the known magnetic moment μ = −0.34218(3) μN and spin I = 5/2 [11] of 25 Mg, as well as the measured value of the ground state splitting of 31 Mg Δν = 3070(50) MHz, reveals the spin I = 1/2 for 31 Mg. This was expected from the number of hyperfine-structure components. From the positions of the resonances also the sign of the magnetic moment can be deduced (μ < 0). The negative value of the magnetic moment implies furthermore a positive parity of this state. It follows both from the earlier β-decay

Fig. 7. Hyperfine structure of 25 Mg+ recorded by detecting the photons emitted during the relaxation of the ions in the optical detection part of the setup.

studies [5], as well as from the large-scale shell model calculations presented in Neyens et al. [12]. Calculations with different interactions, both in the sd and in the extended sd-pf model spaces, predict a positive magnetic moment for the lowest 1/2− state. Thus, our observed negative sign excludes the negative-parity option, in agreement with the assignment based on the β-decay. Therefore we conclude that μ(31 Mg) = −0.88355(10) μN and I π (31 Mg) = 1/2+ . Shell model calculations in the sd model space using the USD interaction [14] predict the lowest I = 1/2+ level only at 2.5 MeV excitation energy. More advanced large-scale shell model calculations, including excitations of neutrons into the pf -shell, and using the interactions as described in [15] and in [16], both predict the 1/2+ level below 500 keV and with a magnetic moment close to our observed value [12]. The wave function of this 1/2+ state consists mainly of intruder configurations, which places this nucleus inside the “island of inversion”. This unambiguous spin-parity measurement allowed us also to make tentative assignments to the lowest-lying excited states in 31 Mg [12]. Similar measurements have also been performed for 29 Mg. They include the nuclear g-factor and the groundstate spin I = 3/2, which is well described in the sd shell model. This measurement places the ground state of 29 Mg outside the “island of inversion”. Study of shorter-lived 33 Mg is planned for the future. This work has been supported by the German Ministry for Education and Research (BMBF) under contract No. 06MZ175, by the IUAP project No. p5-07 of OSCT Belgium and by the FWO-Vlaanderen, by Grant-in-Aid for Specially Promoted Research (13002001).

References 1. C. Thibault et al., Phys. Rev. C 12, 644 (1975). 2. C. Detraz et al., Phys. Rev. C 19, 164 (1979). 3. M. Keim et al., Eur. Phys. J. A 8, 31 (2000).

M. Kowalska et al.: Laser and β-NMR spectroscopy on 4. D. Guillemaud-Mueller et al., Nucl. Phys. A 426, 37 (1984). 5. G. Klotz et al., Phys. Rev. C 47, 2502 (1993). 6. S. Nummela et al., Phys. Rev. C 64, 054313 (2001). 7. U. K¨ oster et al., Nucl. Instrum. Methods B 204, 347 (2003). 8. R. Neugart et al., Nucl. Instrum. Methods 186, 165 (1981). 9. W. Geithner et al., Phys. Rev. Lett. 83, 3792 (1999).

10. 11. 12. 13. 14. 15. 16.

29,31

Mg

197

E. Arnold et al., Phys. Lett. B 197, 311 (1987). P. Raghavan, At. Data Nucl. Data Tables 42, 189 (1989). G. Neyens et al., Phys. Rev. Lett. 94, 22501 (2005). W.M. Itano, D.J. Wineland, Phys. Rev. A 24, 1364 (1981). B.H. Wildenthal et al., Phys. Rev. C 28, 1343 (1983). S. Nummela et al., Phys. Rev. C 63, 44316 (2001). Y. Utsuno et al., Phys. Rev. C 64, 11301 (2001).

Eur. Phys. J. A 25, s01, 199–200 (2005) DOI: 10.1140/epjad/i2005-06-053-9

EPJ A direct electronic only

Measurement of the nuclear charge radii of

8,9

The last step towards the determination of the charge radius of

11

Li

Li

W. N¨ortersh¨ auser1,2,a , B.A. Bushaw3 , A. Dax1,b , G.W.F. Drake4 , G. Ewald1 , S. G¨otte1 , R. Kirchner1 , H.-J. Kluge1 , Th. K¨ uhl1 , R. Sanchez1 , A. Wojtaszek1 , Z.-C. Yan5 , and C. Zimmermann2 1 2 3 4 5

Gesellschaft f¨ ur Schwerionenforschung, D-64291 Darmstadt, Germany Eberhard Karls Universit¨ at T¨ ubingen, Physikalisches Institut, D-72076 T¨ ubingen, Germany Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352, USA Department of Physics, University of Windsor, Windsor, Ontario, N9B 3P4 Canada Department of Physics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3 Canada Received: 8 December 2004 / c Societ` Published online: 12 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Nuclear charge radii of 6,7,8,9 Li have recently been measured at the GSI on-line mass separator using high-resolution resonance ionization mass spectroscopy. We give a brief description of the experimental method. The results for the charge radii are compared with different theoretical predictions. PACS. 21.10.Ft Charge distribution – 21.60.-n Nuclear structure models and methods – 32.10.-f Properties of atoms

Model-independent nuclear charge radii can be determined from isotope shift (IS) measurements on electronic transitions. This approach resulted in an impressive number of data on charge radii during the past decades [1,2]. The IS has two origins: the mass shift (MS), due to the change in nuclear mass between the isotopes, and the field shift (FS), which arises from the difference in the charge distribution inside the nuclei. The FS contains the information required to determine the change in the rootmean-square (r.m.s.) charge radius. Unfortunately, the MS is dominant for light isotopes and obscures the small FS, making it virtually impossible to apply this method for very light elements. Progress in atomic theory during the last decade opened the opportunity to apply this method to the lightest elements (Z ≤ 3). High-precision calculation of the MS in helium- and lithium-like systems are now available and can be used to isolate the FS contribution, provided that the IS can be measured to a relative accuracy of better than 10−6 . This approach was used to determine the change in charge radii between the stable isotope pairs 3,4 He [3] and 6,7 Li [4,5, 6]. Recently, first applications to short-lived nuclei were reported: The charge radii of 8,9 Li were determined at GSI [7], followed by an experiment on 6 He in a magneto-optical trap at Argonne National Laboratory [8]. The experiment at GSI was a precursor for a charge radius determination of the prominent halo nucleus 11 Li, which will resolve the long-standing a b

Conference presenter; e-mail: [email protected] Current address: CERN, CH-1211 Geneva 23, Switzerland.

puzzle whether the additional, loosely bound neutrons affect the distribution of the protons inside the 9 Li-like core. The short-lived isotopes 8,9 Li were produced at GSI in reactions of an 11.4 MeV/u 12 C ion beam impinging on a carbon or a tungsten target. Yields of 200,000 (8 Li) and 150,000 (9 Li) ions per second were obtained out of the surface ion source, mass separated in a 60◦ sector magnet and delivered for laser spectroscopy. The ions were stopped and neutralized inside a thin (80 μg/cm2 ), hot graphite foil. Atoms, diffusing out of the foil, drift into the ionization region of a quadrupole mass spectrometer (QMS). Here they are resonantly laser-ionized using the following excitation and ionization scheme λ λ

τ

2s 2 S1/2 →1 →1 3s 2 S1/2 → 2p 2 P1/2,3/2 , λ

λ1,2

2p 2 P3/2 →2 3d 2 D3/2,5/2 → Li+ . The spontaneous decay from the 3s to the 2p level with a lifetime of τ ≈ 30 ns decouples the precise 2s → 3s two-photon spectroscopy from the efficient ionization via the 3d level. A titanium-sapphire laser (Ti:Sa) provides λ1 = 735 nm for the two-photon transition and a dye laser produces λ2 = 610 nm for the resonance ionization. Both laser beams are resonantly enhanced in an optical cavity around the interaction region and intensities inside the resonator are monitored with photodiodes placed behind the high-reflector of the cavity. Created ions are mass separated inside the QMS and finally detected with a channeltron-type detector. Details of the experimental setup and the laser system were described previously [7].

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experimental interaction cross-sections using Glaubertype calculations [18]. These results show a similar trend of decreasing charge radii, but to a slightly smaller extent. This work is supported from BMBF contract No. 06TU203. Support from the US DOE under contract No. DE-AC0676RLO 1830 (B.A.B.), NSERC and SHARCnet. (G.W.F.D. and Z.-C.Y.) is acknowledged. AW was supported by a MarieCurie Fellowship of the European Community Programme IHP under contract number HPMT-CT-2000-00197.

Fig. 1. The r.m.s. charge radii for 6,7,8,9 Li: (-) this measurement with rc (7 Li) from electron scattering as reference; (•) obtained from interaction cross-section measurements using Glauber theory [18]; (⊕) LBSM [11]; (Θ) NCSM [12]; (∇) SVMC [13]; (Φ) DCM [14]; GFMC calculations using AV8 (×), AV18/UIX (+), AV18/IL2 (◦), AV18/IL3 (), and AV18/IL4 ( ) [15, 16, 17].

To observe the resonance signals, the Ti:Sa frequency is scanned across the two-photon resonances of the different isotopes. The beat signal between the Ti:Sa and a reference diode laser that is locked to an iodine line is used to obtain an accurate frequency axis. For isotope shift determination, the observed resonance profiles are fitted with an appropriate line profile for a two-photon transition and then corrected for residual AC Stark shift. The results were compared with the mass shift calculations of Yan and Drake [9] to extract the change in the r.m.s. charge radii between the isotopes. In order to calculate absolute charge radii, we took the 7 Li charge radius of 2.39(3) fm measured by electron scattering [10] as a reference. The results of 2.30(4) fm (8 Li) and 2.24(4) fm (9 Li) are shown in fig. 1 and compared with predictions from different theories. The point-proton radii rp , given in most theoretical work, have been converted to charge radii rc by folding in the proton and neutron r.m.s. charge radii. Five different approaches are shown in the figure: largebasis shell-model (LBSM) [11], ab-initio no-core shell model (NCSM) [12], stochastic variational multi-cluster (SVMC) [13], dynamic correlation model (DCM) [14] and Greens function Monte Carlo (GFMC) [15,16, 17] calculations. The SVMC approach shows excellent agreement with our experimental results. GFMC calculations were carried out using a variety of effective low-energy model potentials for the two-nucleon interaction (AV8 , AV18) and for the three-nucleon interactions (UIX, IL2, IL3, IL4). Here, the combination of AV18 with the IL2 three-body potential results in the best agreement of the calculated radii with those observed in the experiment. On the other hand, the DCM, LBSM and the NSCM calculations do not agree with our results. For comparison, the figure includes model-dependent rc values derived from

References 1. E.W. Otten, in Treatise on Heavy-Ion Science, edited by D.A. Bromley, Vol. 8 (Plenum Press, New York, 1989) p. 517. 2. H.-J. Kluge, W. N¨ ortersh¨ auser, Spectrochim. Acta, Part B 58, 1031 (2003). 3. D. Shiner, R. Dixson, V. Vedantham, Phys. Rev. Lett. 74, 3553 (1995). 4. E. Riis, A.G. Sinclair, O. Poulsen, G.W.F. Drake, W.R.C. Rowley, A.P. Levick, Phys. Rev. A 49, 207 (1994). 5. J. Walls, R. Ashby, J.J. Clarke, B. Lu, W.A. van Wijngaarden, Eur. Phys. J. D, 22, 159 (2003). 6. B.A. Bushaw, W. N¨ ortersh¨ auser, G. Ewald, A. Dax, G.W.F. Drake, Phys. Rev. Lett. 91, 043004 (2003). 7. G. Ewald, W. N¨ ortersh¨ auser, A. Dax, S. G¨ otte, R. Kirchner, H.-J. Kluge, T. K¨ uhl, R. Sanchez, A. Wojtaszek, B.A. Bushaw, G.W.F. Drake, Z.-C. Yan, C. Zimmermann, Phys. Rev. Lett. 93, 113002 (2004). 8. L.-B. Wang, P. Mueller, K. Bailey, G.W.F. Drake, J.P. Greene, D. Henderson, R.J. Holt, R.V.F. Janssens, C.L. Jiang, Z.-T. Lu, T.P. O’Connor, R.C. Pardo, K.E. Rehm, J.P. Schiffer, X.D. Tang, Phys. Rev. Lett. 93, 142501 (2004). 9. Z.-C. Yan, G.W.F. Drake, Phys. Rev. A 61, 022504 (2000); 66, 042504 (2002); Phys. Rev. Lett. 91, 113004 (2003). 10. C.W. de Jager, H. deVries, C. deVries, At. Data Nucl. Data Tables 14, 479 (1974). 11. P. Navr´ atil, B.R. Barrett, Phys. Rev. C 57, 3119 (1998). 12. P. Navr´ atil, W.E. Ormand, Phys. Rev. C, 68, 034305 (2003). 13. Y. Suzuki, R.G. Lovas, K. Varga, Prog. Theor. Phys. Suppl. 146, 413 (2002). 14. M. Tomaselli, T. K¨ uhl, W. N¨ ortersh¨ auser, G. Ewald, R. Sanchez, S. Fritzsche, S.G. Karshenboim, Can. J. Phys. 80, 1347 (2002). 15. S.C. Pieper, R.B. Wiringa, Annu. Rev. Nucl. Part. Sci. 51, 53 (2001). 16. S.C. Pieper, V.R. Pandharipande, R.B. Wiringa, J. Carlson, Phys. Rev. C 64, 014001 (2001). 17. S.C. Pieper, K. Varga, R.B. Wiringa, Phys. Rev. C 66, 044310 (2002). 18. I. Tanihata, H. Hamagaki, O. Hashimoto, Y. Shida, N. Yoshikawa, K. Sugimoto, O. Yamakawa, T. Kobayashi, N. Takahashi, Phys. Rev. Lett. 55, 2676 (1985).

Eur. Phys. J. A 25, s01, 201–202 (2005) DOI: 10.1140/epjad/i2005-06-195-8

EPJ A direct electronic only

Effects of the pairing energy on nuclear charge radii C. Weber1,2,a , G. Audi3 , D. Beck1 , K. Blaum1,2 , G. Bollen4 , F. Herfurth1 , A. Kellerbauer5 , H.-J. Kluge1 , D. Lunney3 , and S. Schwarz4 1 2 3 4 5

GSI, Planckstr. 1, D-64291 Darmstadt, Germany Institute of Physics, Johannes Gutenberg-University, D-55099 Mainz, Germany CSNSM-IN2P3/CNRS, Universit´e de Paris-Sud, F-91405 Orsay, France NSCL, Michigan State University, East Lansing, MI 48824-1321, USA CERN, CH-1211 Gen`eve 23, Switzerland Received: 14 January 2005 / c Societ` Published online: 19 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Atomic masses of various radionuclides around the Z = 82 shell closure were determined with the ISOLTRAP mass spectrometer. This particular mass region is characterized by strong nuclear structure effects, like, e.g., shape coexistence. In this contribution results derived from mass spectrometry and laser spectroscopy are examined for a possible correlation between mass values and nuclear charge radii. PACS. 07.75.+h Mass spectrometers – 21.10.Dr Binding energies and masses – 27.80.+w 190 ≤ A ≤ 219

1 Experimental mass determination The triple trap mass spectrometer ISOLTRAP [1,2,3] allows for the precise mass determination of exotic nuclides far from stability with uncertainties δm/m of about 10−8 [4]. The mass of an ion stored in a strong magnetic field of a Penning trap is determined via a measurement of its cyclotron frequency νc = qB/(2πm), where B denotes the magnetic field strength. In order to calibrate the magnetic field during a measurement, the cyclotron frequency of a reference nuclide with precisely known mass value is determined in regular time intervals. From the obtained frequency ratio r = νc,ref /νc the mass of the nuclide to be studied is deduced. The region around the Z = 82 shell closure is of huge interest for the study of nuclear structure effects. Those reveal themselves for example at the neutron-deficient side as an odd-even staggering effect in nuclear charge radii [5] and in the observation of triple shape coexistence in the case of 186 Pb [6]. Recent mass measurements on neutron-deficient as well as on some neutron-rich isotopes of thallium, lead, bismuth, francium, and radium were carried out with the ISOLTRAP mass spectrometer [7]. In this region one of the main experimental challenges is the existence of two or even three isomeric states with low excitation energies. Since these are less than 100 keV for particular candidates, a high resolving power R = νc /Δνc,FWHM = m/Δm of up to 107 is required during a measurement. It is determined by the observation time and therefore finally limited by the half-life of the a

Conference presenter; e-mail: [email protected]

Table 1. Radionuclides studied with the ISOLTRAP mass spectrometer in July 2002. x: a possible contamination was not resolved.

Element

Mass number A

Tl Pb Bi

181, 183, 186m, 187x, 196m 187, 187m, 197m 190x, 191, 192m, 193, 194m, 195, 196m, 197x, 215, 216 203, 205, 229 214, 229, 230

Fr Ra

nuclide. Table 1 shows a list of nuclides studied with the ISOLTRAP mass spectrometer in July 2002. For most of these nuclides the deduced mass values could be assigned to a particular isomeric state. Such nuclides, where the resolving power was not sufficiently high to resolve an eventually present contamination of isomeric states are denoted by an “x”. Due to the extensive studies of the ISOLTRAP mass spectrometer using carbon clusters, errors like, e.g., the mass-dependent systematic frequency shift and the residual systematic uncertainty could be quantified [4]. With a new upper limit (δr/r)res ≤ 8 × 10−9 , the average uncertainty in the determination of frequency ratios obtained in these data is (δr/r)avg = 7.5 × 10−8 . This leads to an average error of δmavg = 13 keV in this mass determination in the range of A = 181–230. Figure 1 shows a comparison of some of the ISOLTRAP deduced mass values to a compilation of the AME in 2002 [8]. A detailed description of the data analysis and the isomeric assignment will be published elsewhere.

The European Physical Journal A



Δ

3$,5,1**$3





Δ



δU !





*5281'67$7( ,620(5,&67$7( 67$%/(,62723(6

400

 



0

 

 



-200 186Tl

196Tl

190Bi

192Bi

194Bi

196Bi





216Bi

NUCLIDES OF EVEN MASS NUMBER

 

Fig. 1. Comparison of ISOLTRAP mass data for some oddodd nuclei to a compilation of the AME in 2002 [8]. The zero line represents the AME ground-state mass values. Excited isomers are depicted as open triangles, whereas E m and E n are the energies of the first and second excited isomers, respectively.

















1(87521180%(5 0(5&85<  3$,5,1**$3





Δ  Δ





δU !

*5281'67$7( ,620(5,&67$7( 67$%/(,62723(6

2 Comparison to nuclear charge radii

(−1)N [B(N − 1) + B(N + 1) − 2B(N )] , (1) 2  1 3 Δ (N ) + Δ3 (N − 1) (2) Δ4 (N ) = 2 to the behavior of the nuclear mean square charge radii δ r2  (data from [5,11]) is used to search for a possible correlation. Figure 2 shows the examples of mercury- and thallium-isotopes. In Δ3 (N ) and Δ4 (N ), which are deduced as the second derivative of the nuclear binding energy along an isotopic chain, the shell closure at N = 126 is visible as a maximum. This difference in binding energy of the last neutron represents the size of the n-n interaction strength. In addition, a decrease of the interaction strength is observed around the mid neutron shell N = 104. Its position coincides with those isotopes that show the characteristic staggering effects. This strengthens the idea that the size of the n-n pairing is responsible for the stabilization of a weakly deformed shape. At midshell, the pairing energy is diminished in comparison to the

3$,5,1**$30H9



This work was already initiated by mass spectroscopic results on neutron-deficient mercury isotopes [9]. The appearance of shape coexistence as observed in the large odd-even staggering of the mercury nuclear charge radii near the N = 104 mid-shell region was explained by the size of the neutron pairing energy. As this quantity has an absolute value of only about 1 MeV, mass data available at that time were of insufficient precision for any analysis. First, the high resolving power m/Δm of up to 107 of the ISOLTRAP Penning trap mass spectrometer can resolve isomeric states. Secondly, the recently demonstrated mass uncertainty of δm/m < 10−7 helps to analyze the nuclear fine structure in the neutron-deficient thallium, lead, and bismuth isotopes. New results of laser spectroscopic studies are available for neutron-deficient lead isotopes [10] which will be compared with the lead masses, in an upcoming work. The systematic comparison of the neutron pairing gap energies



 

  



 

 



200

δU !

3$,5,1**$30H9

ISOLTRAP - AME 2002 / keV

7+$//,80 

ISOLTRAP AME 2002 AME + Em AME + En

600

δU !

202

 



  















1(87521180%(5

Fig. 2. Comparison of neutron pairing gap energies Δ(3) , Δ(4) to nuclear mean square charge radii δ r 2 . Note that in thallium the radii of the isomer exhibit the staggering behavior. δ r2  error bars for mercury are drawn within the symbol.

general trend, and a more deformed shape appears. The systematic study of these fine correlations has become possible due to the high precision of the new ISOLTRAP data.

Δ3 (N ) =

References 1. G. Bollen et al., Nucl. Instrum. Methods A 368, 675 (1996). 2. F. Herfurth et al., Nucl. Instrum. Methods A 469, 254 (2001). 3. K. Blaum et al., Nucl. Instrum. Methods B 204, 478 (2003). 4. A. Kellerbauer et al., Eur. Phys. J. D 22, 53 (2003). 5. J. Kluge, W. N¨ ortersh¨ auser, Spectrochim. Acta B 58, 1031 (2003) and references therein. 6. A.N. Andreyev et al., Nature 405, 430 (2000). 7. C. Weber, PhD Thesis, University of Heidelberg, 2003. 8. G. Audi, private communication. 9. S. Schwarz et al., Nucl. Phys. A 693, 533 (2001). 10. H. De Witte, PhD Thesis, University of Leuven, 2004; H. De Witte et al., these proceedings. 11. G. Audi, A.H. Wapstra, C. Thibault, Nucl. Phys. A 729, 337 (2003).

Eur. Phys. J. A 25, s01, 203–304 (2005) DOI: 10.1140/epjad/i2005-06-098-8

EPJ A direct electronic only

First g-factor measurement using a radioactive

76

Kr beam

N. Benczer-Koller1,a , G. Kumbartzki1 , J.R. Cooper2 , T.J. Mertzimekis3 , M.J. Taylor4 , L. Bernstein2 , K. Hiles1 , P. Maier-Komor5 , M.A. McMahan6 , L. Phair6 , J. Powell6 , K.-H. Speidel7 , and D. Wutte6 1 2 3 4 5 6 7

Department of Physics and Astronomy, Rutgers University, New Brunswick, NJ 08903, USA Lawrence Livermore National Laboratory, Livermore, CA 94550, USA NSCL, Michigan State University, East Lansing, MI 48824, USA School of Engineering, University of Brighton, Brighton BN2 4GJ, UK Technische Universit¨ at M¨ unchen, D-85748 Garching, Germany Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Helmholtz-Institut f¨ ur Strahlen- und Kernphysik, Universit¨ at Bonn, D-53115 Bonn, Germany Received: 3 December 2004/ Revised version: 17 February 2005 / c Societ` Published online: 29 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 76 Kr (T1/2 = 14.8 h) has been measured using Abstract. The g factor of the first 2+ 1 state of radioactive projectile Coulomb excitation in inverse kinematics combined with the transient magnetic-field technique. The 76 Kr beam was produced and accelerated in batch mode (re-cyclotron method) at the Lawrence Berkeley National Laboratory 88-Inch Cyclotron. The g factor g(76 Kr; 2+ 1 ) = +0.37(11) was obtained.

PACS. 21.10.Ky Electromagnetic moments – 25.70.De Coulomb excitation

1 Introduction The variation of magnetic moments of excited nuclear states as a function of spin and energy, or across a range of N or Z can provide significant information on the microscopic structure of nuclei. Recently, new methods have been developed which use the transient field technique and Coulomb excitation of a beam by a light target in inverse kinematics. These methods are particularly suited to measurements of nuclei that can only be produced in the form of radioactive beams. This paper describes the production of a beam of 76 Kr (T1/2 = 14.8 h and the procedure used to measure, for the first time, the g factor of the 2+ 1 state. The details have been reported in refs. [1, 2,3] and references therein.

165 mg/cm2 thick metallic 74 Se target. After irradiation the selenium was melted to release the krypton, which was transferred via a He gas flow to a cryogenic trap. After release from the trap into the Advanced Electron Cyclotron Resonance-U ion source(AECR-U) the 88-Inch Cyclotron accelerated 76 Kr+15 ions to 230 MeV producing currents as high as 3 × 108 particles per second and yielding an average current of 4 × 107 particles per second for two hours on target. Three batches were produced. For comparison with radioactive beam facilities providing a continuous beam, a total intensity of 8 × 1011 of 76 Kr was obtained, equivalent to a constant beam of 1.6 × 106 particles per second for five days.

2.2 g-factor measurement

2 Experimental technique 2.1 Production of

76

Kr

The 76 Kr radioactive ions were produced and accelerated using a batch mode method involving only one accelerator and therefore was named the “re-cyclotron method” [2]. Approximately 1014 76 Kr nuclei were produced in the reaction 74 Se(α, 2n)76 Kr during a 17-hour production period using a 38 MeV, 6 particle-μA 4 He, beam on a a

e-mail: [email protected]

The transient field technique in inverse kinematics was used. The target was a layered structure of 26 Mg, gadolinium and copper. Four Clover detectors were used to detect the γ rays, and a solar cell detector was used to detect the Mg ions. The radioactive beam exiting from the target was stopped in a moving tape mounted behind the target. Figure 1 shows the γ-ray spectra obtained from the activity accumulated in the copper layer of the target and the coincidence particle-γ-ray spectra from which all contaminant radiations were removed.

204

The European Physical Journal A 0.25 315.7

50000

B(E2; 2+ −−> 0+)

270.3

Activity 40000

experiment 28
0.20

B(E2;2+−>0+)

511.0

10000

559.1 581.5

406.5 355.3

251.9

20000

452.0

30000

424.0

0

Total coinc.

0.15

0.10

0.05

g(2+)

611.0

511.0

452.0

406.5

0.00

346.0 355.3

100

315.7

200

252.00 270.s0

Counts

300

0.75

Random subtr.

+

200

g (2+)

424.0

0

+

2 --> 0

+

100

0.50

Z/A 0.25

+

0 --> 2

+

+

611.0

346.0

4 --> 2

0.00

0 100

200

300

400

500

600

Energy [keV]

Fig. 1. Top: a background spectrum taken after the end of a 76 Kr beam batch cycle. Middle: a γ-ray spectrum taken in coincidence with particles. Bottom: the same Clover spectrum as shown in the middle panel with random coincidences subtracted. Only the 76 Kr γ-ray lines remain.

The extraction of a g factor requires a knowledge of the particle–γ-ray angular correlation. However, since the angular correlation should be very similar to that obtained under the same kinematic conditions with a stable beam of a neighbouring isotope, and in view of the similarity between the energy level structure of 76 Kr and 78 Kr, angular correlation and precession measurements were carried out with a 78 Kr beam. In six hours, 800 events/Clover in the photopeak of the + 76 Kr, 2+ 1 → 01 transition, were recorded for each field direction. In 2.5 h, 7 × 104 counts/Clover and field direction + were recorded for the 78 Kr, 2+ 1 → 01 transition. + The g factor of the 21 state in 76 Kr can be directly written in terms of the known g factor of the 2+ 1 state (76 Kr) + 78 = +0.37(11), in 78 Kr, g(76 Kr; 2+ ) = g( Kr; 2 ) × 1 1 (78 Kr) where  is related to the change in counting rate observed when the external magnetizing field is changed from the up to the down direction with respect to the γ-ray detection plane.

72

74

76

78

80

82

84

86

88

36

38

40

42

44

46

48

50

52

A N

Fig. 2. B(E2) values in e2 b2 and g factors for even Kr isotopes. The curves are IBA-II calculations as described in ref. [1] and the g factor for 76 Kr is from this work. + Semi-magic 86 50 Kr has a large positive g(21 ) factor of +1.12(14) (off scale in fig. 2) a clear indication of proton excitations. The two g9/2 neutron holes in 84 Kr are responsible for the smaller g factor for the 2+ 1 state. However, as more neutrons are removed, the g factors of the 2+ 1 states increase progressively toward the collective value of Z/A. + At the same time, the g factors of the 4+ 1 and 22 states also tend to be equal to the nominal Z/A value [1]. Calculations based on the interacting boson model IBA-II, a “pairing-corrected” collective model and the shell model are described in refs. [1, 4]. In summary, this experiment provided the first measurement of a g factor carried out by the Coulomb excitation/transient field technique on a radioactive beam and supports the applicability of the method to the measurements of magnetic moments on radioactive beams. The result confirms the collective nature of the structure of 76 Kr. the 2+ 1 state of

The work was performed under the auspices of the U.S. Department of Energy and the U.S. National Science Foundation.

References 3 Discussion The g factors of the 2+ 1 states in the Kr isotopes have been measured across the region from the semi-magic 86 Kr to the lightest, radioactive 76 Kr and are summarized in fig. 2.

1. T.J. Mertzimekis et al., Phys. Rev. C 64, 024314 (2001). 2. J.R. Cooper et al., Nucl. Instrum. Methods Phys. Res. A 253, 287 (2004). 3. G. Kumbartzki et al., Phys. Lett. B 591, 213 (2004). 4. T.J. Mertzimekis, A.E. Stuchbery, N. Benczer-Koller, M.J. Taylor, Phys. Rev. C 68, 054304 (2003).

Eur. Phys. J. A 25, s01, 205–208 (2005) DOI: 10.1140/epjad/i2005-06-123-0

EPJ A direct electronic only

First nuclear moment measurement with radioactive beams by 132 Te recoil-in-vacuum method: g-factor of the 2+ 1 state in N.J. Stone1,2,a , A.E. Stuchbery3 , M. Danchev2 , J. Pavan4 , C.L. Timlin1 , C. Baktash4 , C. Barton5,6 , J.R. Beene4 , N. Benczer-Koller7 , C.R. Bingham2,4 , J. Dupak8 , A. Galindo-Uribarri4 , C.J. Gross4 , G. Kumbartzki7 , D.C. Radford4 , J.R. Stone1,9 , and N.V. Zamfir5 1 2 3 4 5 6 7 8 9

Department of Physics, University of Oxford, Oxford, OX1 3PU, UK Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA Department of Nuclear Physics, ANU, Canberra, ACT 0200, Australia Physics Division, ORNL, Oak Ridge, TN 37831, USA Wright Nuclear Structure Laboratory, Yale University, New Haven, CT 06520-8124, USA Department of Physics, York University, York, YO12 5DD, UK Department of Physics and Astronomy, Rutgers University, New Brunswick, NJ 08903, USA Institute of Scientific Instruments, 624 64 Brno, Czech Republic Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742, USA Received: 14 January 2005 / c Societ` Published online: 9 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Following Coulomb excitation of the radioactive ion beam (RIB) 132 Te at HRIBF, we report the first use of the recoil-in-vacuum (RIV) method to determine the g-factor of the 2+ 1 state to be (+)0.35(5). The advantages offered by the RIV method in the context of RIBs and modern detector arrays are discussed. PACS. 21.10.Ky Electromagnetic moments – 25.70.De Coulomb excitation – 27.60.+j 90 ≤ A ≤ 149 – 23.20.En Angular distribution and correlation measurements

1 Introduction The advent of radioactive ion beams (RIBs) constitutes a major new initiative in nuclear structure investigations, opening up many new opportunities. However, the new beams, being not only orders of magnitude weaker than stable ones, but also producing background radioactivity levels which can mask useful reaction yields, present fresh challenges to experimenters to design methods appropriate for their best exploitation. The g-factors of nuclear excited states yield valuable information as to the make-up of their wave functions. This paper presents the first result of applying the littleused technique of recoil in vacuum (RIV) to exploit its considerable advantages for g-factor measurements in the new RIB regime using modern detector arrays. When an energetic ion beam emerges from a solid into vacuum the ions have a range of charge states and many differing electronic configurations, each with its own total angular momentum J which is assumed to be randomly oriented in space. The hyperfine interaction couples the nuclear spin I and J and causes them to precess about their resultant F. Whenever the nuclear spin is initially a

Conference presenter; e-mail: [email protected]

oriented by a nuclear reaction, such precession forms a de-orientation mechanism. Particularly in highly ionized states, the de-orientation is dominated by the large magnetic interactions with angular frequency proportional to the nuclear g-factor. This is the basis of the so-called recoil in vacuum (RIV) method of measurement of the nuclear g-factor, which was first studied in the 1970s [1]. In recent years the method most widely used for gfactor studies of states of half-life ∼ ns has been the transient field (TF) method. After excitation into an oriented excited state (usually by Coulomb excitation), the nuclei traverse a magnetized ferromagnetic layer of the target in which their spins precess due to the action of the transient field. The precession is measured by the change in angular distribution of the gamma decay of the excited state when the magnetization is reversed and can be analysed to give the magnitude and sign of the g-factor. Giving the sign of the g-factor is an advantage of the TF method as compared to the RIV method. Problems which arise for the TF method with RIBs, several orders of magnitude weaker than stable beams, are that good statistics are required to give an accurate g-factor and that the beam is usually stopped in the target producing high radioactive background. Even if the

The European Physical Journal A

beam, and excited nuclei, are allowed to recoil out of the target (when the longer lived beam activity will leave the target area and the excited nuclei decay nearby), the possibility of contaminant activity can cause large undesirable background. The RIV method by contrast has attractive features when used with RIBs. There is no need for a thick target, so the beam escapes, and the unperturbed angular distributions can be very anisotropic so that attenuations can be measured with relatively poor statistics yet yield a useful g-factor. This paper describes the first application of the RIV method to obtain the g-factor of the first 2+ state of an RIB isotope: 132 Te.

2 Experimental details and data analysis The experiments were carried out at the HRIBF Facility at Oak Ridge National Laboratory using the devices CLARION for γ detection and Hyball, an array of CsI particle detectors [2]. In the RIB measurement a beam of 3 × 107 132 Te ions/s at 396 MeV was incident on a 0.83 mg/cm2 self-supporting C target for 3 days. 29000 de-excitation γ-rays were recorded from the 973.9 keV, 2+ 1 , state, in coincidence with C recoils [3]. Data were taken in event-by-event mode, registering the energies and identifications of the particles detected in the Hyball segments, and the energies deposited in all CLARION detector segments. Data were analyzed by setting particle identification gates on carbon recoils, applying Doppler correction to the γ energy, and correcting for random coincidences. Similar experiments were carried out with stable beams of 122,126,130 Te. The beam energies were respectively 366, 378 and 390 MeV, chosen to ensure that the velocities, and hence the hyperfine interactions, of the Te ions emerging from the back of the C target would be very similar for all isotopes. For each stable isotope, data were taken with two different targets. The first was a 0.956 mg/cm2 self-supporting C foil, from which both Te ions and C recoils escaped into vacuum, and the second consisted of a 0.630 mg/cm2 layer of C, backed with 14.3 mg/cm2 Cu. The Cu backing stopped the Te recoils but allowed the C recoils to emerge and reach the Hyball array without appreciable angular straggling. Results from the un-backed C target show attenuation of the unperturbed distribution, observed from the Cu-backed target. Analysis of the C-γ coincident data was made taking full advantage of the segmented nature of the CLARION and Hyball devices to give a detailed angular distribution. CLARION consists of eleven detectors in the backward hemisphere with respect to the target, five in a ring at θγ = 90◦ , four at θγ = 132◦ and two at θγ = 155◦ to the beam (z-axis). The Hyball particle detection array is in the forward hemisphere. In this work three rings of detectors were used, set in circles about the beam axis. The first ring is segmented into six detectors and receives particles scattered at angles between 7◦ < θp < 14◦ , the second ring has ten detectors with 14◦ < θp < 28◦ and the third ring has 12 detectors with 28◦ < θp < 44◦ . Requiring the carbon recoil to be in a specific segment of a Hyball ring

Ring 3

W(θγ,φ)/W(θγ)

206

2 1.5 1 0.5 0 2 1.5 1 0.5 0 2 1.5 1 0.5 0

θγ=90

o

o

θγ=90

θγ=132

o

θγ=155

θγ=155

90 180 270 360 0

Ring 1

θγ=90

o

θγ=132

0

Ring 2

o

o

θγ=132

o

θγ=155

90 180 270 360 0 φ [degrees]

o

o

90 180 270 360

Fig. 1. Experimental and calculated unattenuated angular distributions for 130 Te corresponding to CLARION detectors at θγ = 90◦ , 132◦ and 155◦ and Hyball rings 1, 2, and 3.

defines, along with the beam axis, the azimuthal angle φp of the reaction plane for each event. Combining this information with φγ of each CLARION detector the angular distribution of the γ rays as a function of both θγ and φ = φp − φγ was obtained. The stable-beam 122,126,130 Te experiments with the Cu-backed target aimed to establish not only that the unperturbed γ anisotropy was independent of the isotope, but also to demonstrate that it could be calculated from first principles. The calculation was carried out using standard formalism for perturbed particle-γ correlation from nuclei oriented in Coulomb excitation √ k∗ 2k + 1ρkq Gk Ak Qk Dq0 (φ, θγ , 0), (1) W (θγ , φ) = k,q

where Gk are the vacuum deorientation coefficients, dependent on the nuclear g-factor. ρkq are statistical tensors, evaluated using Coulomb excitation scattering amplitudes [4] obtained from the Winther-de Boer computer code [5]. All the other symbols have their standard meaning, explained, for example, in ref. [6]. Figure 1 shows comparison of the calculated correlation with data taken with 130 Te. The data have been obtained by normalizing the counts in each CLARION detector coincident with a specific element of a Hyball ring to the sum of counts in the complete Hyball ring. The theory 2π was normalized to the calculated value of W (θγ ) = 0 W (θγ , φ)dφ. The data have not been fitted to the theory in any way. The agreement is extremely good for all nine combinations of Hyball rings and CLARION angles. This is an important result as it gives encouragement that such calculations may be used in the future to give the unattenuated distribution in cases where it is not possible to measure it directly. Performing similar analysis of the data from the unbacked C targets, RIV attenuated distributions were

N.J. Stone et al.: First nuclear moment measurement with radioactive beams by recoil-in-vacuum technique 126

130

W(θγ,φ)/W(θγ)

Te

2 1.5 1 0.5 0 2 1.5 1 0.5 0 2 1.5 1 0.5 0

o

o

θγ=90

θγ=90

θγ=132

132

Te

o

θγ=132

Te

θγ=90

o

o

o

θγ=132

207

undergo Larmor precession about an axis in space determined by their individual F quantization axis F = I + J, which is related to their randomly oriented J angular momentum. For each pair of quantum numbers I and J, integration over time, weighting by the nuclear decay e−t/τ , yields [9]  (2F + 1)2 "F F k #2 + Gk = I I J 2J + 1 F  (2F + 1)(2F  + 1) "F F  k #2 1 . (2) 2 2+1 I I J ω τ 2J + 1 FF  F =F

θγ=155

0

o

90 180 270 360 0

θγ=155

o

90 180 270 360 0 φ [degrees]

o

θγ=155

90 180 270 360

Fig. 2. Experimental and fitted attenuated angular distributions for 126,130,132 Te measured using CLARION detectors at θγ = 90◦ , 132◦ and 155◦ and Hyball ring 3.

found for all three stable Te isotopes and for 132 Te. For each isotope, the full data set, comprising a total of 308 individual W (θγ , φ) points, were fitted simultaneously to yield the best values of the attenuation parameters as described below. The interaction strength will depend upon recoil velocity; the small variation of this recoil velocity between the three Hyball rings has been neglected. Figure 2 shows the ring 3 attenuated angular distributions and best fits for 126,130,132 Te. 126 Te (longer lifetime) shows stronger attenuation than the other two isotopes, while 132 Te is somewhat less attenuated than 130 Te.

3 Results and discussion Detailed theoretical description of the RIV attenuation process is complex. It would require full knowledge of the range and weighting of ionic charge states, electron angular momentum states, their hyperfine interaction strengths and lifetimes. To date two extreme models of the process have been considered. In the first, the “rapid fluctuation” model, the electronic state is assumed to change frequently during the nuclear lifetime, giving abrupt changes in both magnitude and direction of the hyperfine interaction. This chaotic process leads eventually to complete attenuation of the γ anisotropy and can be described, within fairly broad limits, by a single relaxation time τ2 [7, 8]. For purely magnetic hyperfine interactions, the parameters G2 and G4 in eq. (1) are given as functions of τ2 and the nuclear mean life τ by G2 = τ2 /(τ2 + τ ) and G4 = 0.3τ2 /(0.3τ2 + τ ). In this model τ2 = C/g 2 , where C is a constant for isotopes having the same ionic state distribution and there is a relationship G4 = 0.3G2 /(1 − 0.7G2 ). The second extreme, a “static” model, considers the case that the electronic state lifetime is long compared to the nuclear state mean life. For this limit the nuclei

The full expression for Gk averaged over charge state and electronic excitation is a weighted sum of Gk s of the form of eq. (2), each having two terms, a “hard core” maximum attenuation plus a term involving g 2 τ 2 (since ω ∼ g). There is no simple algebraic form for the result of such a summation. Simulations of this model for a wide range of values of J and different hyperfine interaction strengths have been made [10]. The dependence of Gk upon gτ is sensitive to these electronic state parameters, as is the ratio G2 /G4 to lesser degree. Thus in this model the relationship between G2 and G4 is not predictable without detailed knowledge of the distribution of the states of the ions and their hyperfine interactions. The Te isotope 2+ 1 state mean lifetimes, energies and weighted mean gfactors, are given in table 1, which also includes the best fit values of G2 and G4 taken as independent parameters. A simple check shows that these best fit Gk values are in clear disagreement with the relationship required by the random fluctuation model so this model was discarded as a possible route to the g-factor. The experimental values of G2 and G4 for the three “calibration” isotopes 122,126,130 Te, taken as a function of gτ , were then fitted using the static model by adjusting the distribution of J states and the magnitude of the hyperfine interaction. This was an essentially empirical exercise to find dependencies consistent with the calibrations which could be extrapolated to obtain gτ for 132 Te. Two sets of the model parameters were found which gave extremum fits constituting upper and lower limits of the variation of G2 and G4 with gτ . The experimental values of G2 and G4 for 132 Te then each yielded a range for gτ for the first 2+ state. The results, gτ (from G2 ) = 0.92(14) ps and gτ (from G4 ) = 0.90(10) ps agree very well with each other. Thus, taking the lifetime of 132 Te given in table 1, we obtain, using the more precise gτ , the result g = 0.346(38)(35) where the first error arises from the variation between the two sets of model parameters and the second stems from the uncertainty in the lifetime. The final result (with sign from systematics) is   132 Te = (+)0.35(5). (3) g 2+ 1 Theoretical interest in the g-factor of this state is due to the proximity of 132 Te to doubly magic 132 Sn. As the number of valence neutron holes in the double magic configuration decreases, the g-factor is expected to rise since proton contributions to the 2+ excitation will become

208

The European Physical Journal A Table 1. Te 2+ 1 excited state data and fits to attenuated distributions (see text for details).

Isotope

E2+ (keV)

τ2+ (ps) [11]

g-factor [12]

gτ (ps)

G2

G4

564.1 663.3 839.5 973.9

10.8(1) 6.5(2) 3.3(1) 2.6(2) [13]

0.340(10) 0.275(30) 0.295(35)

3.67(12) 1.79(20) 0.97(12) 0.90(10)

0.355(18) 0.505(19) 0.629(19) 0.715(26)

0.214(11) 0.366(12) 0.503(12) 0.522(17)

1

122

Te Te 130 Te 132 Te 126

1

Table 2. Calculated and experimental g-factors for 2+ 1 states in Te isotopes close to N = 82.

Nuclear model

130

132

Te

Te

134

Te

136

Te

Shell model QRPA

+0.347 +0.314

+0.488 +0.491

+0.862 +0.695

+0.360 −0.174

Experiment

+0.295(35)

(+)0.35(5)

−

−

more important. Table 2 displays recent calculated values for the g-factors of heavy Te isotopes close to the closed shell. The present result is consistent with a modest increase in g-factor between 130 Te and 132 Te.

4 Conclusions This experiment has shown that the RIV method can provide a good-quality g-factor measurement for 132 Te RIB. The result further indicates the possibility of performing similar experiments with beams that are at least one order of magnitude weaker than in this work. Since RIV attenuations are available for study whenever Coulombexcited states recoil from and decay beyond a thin target, this method is expected to be generally useful for g-factor determinations of short-lived excited states using RIBs. To maximize the potential of the method requires short calibration experiments with stable beams of nuclei having known g-factors, suitable lifetimes and the same spin as the RIB nuclei. More meaningful a priori modeling of the RIV process should emerge as further results become available. We acknowledge valuable discussions with G. Goldring and J. Billowes at the early stages of this work. Financial support came from US DOE grants DE-AC05-00OR22725 (ORNL), DE-FG02-96ER40983 (UT), DE-FG02-94ER40834 (JRS) and the US National Science Foundation (RU).

Ref.

[14] [15]

References 1. G. Goldring, in Heavy Ion Collisions, edited by R. Bock Vol. 3 (North Holland, Amsterdam, 1982) p. 484. See also Treatise on Heavy-Ion Science, edited by D.A. Bromley Vol. 3 (Plenum, New York, 1984) p. 539. 2. C.J. Gross et al., Nucl. Instrum. Methods Phys. Res. A 450, 12 (2000). 3. N.V. Zamfir et al., private communication, 2004. 4. K. Alder, A. Bohr, T. Huus, B. Mottelson, A. Winther, Rev. Mod. Phys. 28, 432 (1956). 5. K. Alder, A. Winther, in Coulomb Excitation (Academic Press, New York and London, 1966) p. 303. 6. A.E. Stuchbery, M.P. Robinson, Nucl. Instrum. Methods Phys. Res. A 485, 753 (2002). 7. A. Abragam, R.V. Pound, Phys. Rev. 92, 943 (1953). 8. F. Bosch, H. Spehl, Z. Phys. A 280, 329 (1977). 9. R. Brenn et al., Z. Phys. A 281, 219 (1977) and references therein. 10. C.L. Timlin, Project Report, Oxford 2004 (unpublished). 11. S. Raman et al., At. Data Nucl. Data Tables 78, 1 (2001). 12. N.J. Stone, Nuclear Moment Table, Nuclear Data Center, www.nndc.bnl.gov. 13. D.C. Radford et al., Phys. Rev. Lett. 88, 222501 (2002). 14. B.A. Brown et al., Phys. Rev. C 71, 044317 (2005), arXiv:nucl-th/0411099v1. 15. J. Terasaki et al., Phys. Rev. C 66, 054313 (2002); J. Teresaki, private communication (2004).

Eur. Phys. J. A 25, s01, 209–212 (2005) DOI: 10.1140/epjad/i2005-06-088-x

EPJ A direct electronic only

Anomalous magnetic moment of 9C and shell quenching in exotic nuclei Y. Utsunoa Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-1195, Japan Received: 20 October 2004 / c Societ` Published online: 30 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We discuss a mechanism of the anomalous spin expectation value of the 9 C-9 Li mirror pair in relation to the shell structure of exotic nuclei. In a similar way to the N = 20 shell gap for neutron-rich nuclei, the N = 8 shell gap should be rather narrow toward smaller Z from an empirical determination of the shell gap. The resulting ground state of 9 Li is still dominated by the normal configurations, whereas that of the mirror nucleus 9 C can be mixed with the intruder configurations triggered by the Thomas-Ehrman effect. This asymmetry of the ground state accounts for the experimental anomaly. PACS. 21.10.Ky Electromagnetic moments – 21.60.Cs Shell model – 27.20.+n 6 ≤ A ≤ 19

1 Introduction

2 Knowledge from previous calculations

The magnetic moment carries much information on the distribution of the total angular momentum among spin and orbital parts of protons and neutrons, since the g factor of each part is quite different from one another. Thus, the magnetic moment is of great help in understanding the single-particle structure, deformation, configuration mixing, etc. From magnetic moments of mirror nuclei, one can directly deduce the isoscalar spin expectation value [1] as

The shell model with an appropriate effective interaction successfully describes low-lying structure of nuclei in a systematic way. Good examples are found in the p-shell calculation by the Cohen-Kurath interaction [3], the sd-shell calculation by the USD [4], and the pf -shell calculations by the KB3 [5] and the GXPF1 [6]. These shell-model calculations give good magnetic moments, too. The spin expectation value of the 9 C-9 Li pair is calculated by available realistic p-shell model interactions, all of which give a value close to the single-particle estimate, 1, almost independently of the effective interaction. We now mention the nucleon g factors adopted in the calculation of the magnetic moment. Brown and Wildenthal [7] examined empirically optimum g factors and their effect on the magnetic moment within the full sd-shell framework. It was found in [7] that the free nucleon g factors give a good magnetic moment as a whole, but a certain improvement of the isoscalar spin expectation value is attained with effective g factors. Namely, the absolute value of the spin expectation value by the free nucleon g factors is somewhat larger than the experimental value typically by ∼ 0.1. This probably means that the effective g factors include renormalization of the second-order configuration mixing, whose effect is less than the first-order one but does work to reduce the spin expectation value. Namely, the use of the effective g factors does not explain the anomalous value for the 9 C-9 Li pair. In the shell-model, the mirror symmetry between the pair nuclei is assumed by using the isospin-conserving interaction. In ref. [8], the spin expectation value was calculated including the isospin-nonconserving process. The

σz  =

μ(Tz = +T ) + μ(Tz = −T ) − J , 0.38

(1)

where the mirror symmetry between the pair is assumed. In general, the absolute value of this spin expectation value for odd nuclei does not exceed a single-particle estimate [1] because of the strong pairing correlation. The configuration mixing decreases the absolute value of the spin expectation value due to the mixing with the spinorbit partner. However, it has turned out that the spin expectation value of the 9 C-9 Li pair has an extraordinary large value, 1.44, from the magnetic moment of 9 C measured for the first time by Matsuta et al. [2]. In the present paper, we discuss the shell structure varying from stable to unstable nuclei, and point out that it can lead to this anomalous spin expectation value. In the next section, we first survey results of previous theoretical studies on this problem, and indicate the need for inclusion of something not explored in depth so far. a

Conference presenter; e-mail: [email protected]

The European Physical Journal A

value was improved by 0.09 in [8], but there still remains a certain deviation. In models describing the clusterization [9, 10], the isospin symmetry is not assumed. The values by those models exceed the single-particle value by about 0.1, but are still rather short of the experimental one. This similar results between the shell model and the cluster models probably reflect the resemblance of the wave functions between those models. In order to go beyond the previous results, it may be essential to include configurations not only within the p shell but also involving excitations into the sd shell. In this situation, it is of importance to investigate the shell gap between the p to sd shells. In the next section, we summarize recent knowledge about the shell structure in exotic nuclei.

3 Shell evolution Since much information on the structure of neutron-rich nuclei has been recently accumulated owing to experimental developments, the shell structure of unstable nuclei has emerged gradually. This context is well investigated in the N ∼ 20 region in relation to the disappearance of the magic structure. In the so-called “island of inversion” picture [11], the disappearance of the magic structure occurs in some of N = 20 isotones, 30 Ne, 31 Na and 32 Mg, confirmed by several experiments. On the other hand, this picture predicts that the disappearance of the magic number does not occur in any N < 20 nuclei. We shall now define the shell gap as the difference of the so-called effective-single-particle energies (ESPE) (see, e.g., [12]) of the relevant orbits, including effects of the two-body interaction in the form of the monopole interaction. The N = 20 shell gap by the “island of inversion” picture is only weakly dependent on the proton and neutron numbers, and a somewhat constant ∼ 6 MeV gap persists from stable to unstable nuclei. Detailed structure of N < 20 nuclei has recently been accessible (see [13, 14] for the magnetic moment). Experimental results [13, 14] show that the boundary of the “island of inversion” must be extended from the original [11]. In relation to the shell structure, this extension indicates that the N = 20 shell gap should be narrower than that of stable nuclei. Indeed, a Monte Carlo shell-model study [15] shows that at N = 19 the intruder state is superior to the normal state with an interaction giving narrowing N = 20 shell gap toward smaller Z [12]. This varying shell gap has been discussed from a more general viewpoint of the effective interaction by Otsuka et al. [16] including the author of the present paper. Following this argument, referred to as the “shell evolution”, the N = 8 shell gap should be changed as the proton number varies.

4 Effect of shell quenching on the anomalous spin expectation value 4.1 Empirically determined N = 8 shell gap To calculate the ground state of 9 Li (i.e., the mirror nucleus of 9 C), it is desirable to fix the N = 8 shell gap for

effective shell gap (MeV)

210

10

WBP’

d5/2 0.5

5

s1/2 2.0

0

3

4

5

6

N Fig. 1. N = 8 shell gap as a function of the proton number. The thin lines are those of the original WBP interaction, while the marks guided by thick lines indicate the empirically determined one. The open circle is the shell gap at Z = 3 extrapolated from the Z = 4–6 data.

this nucleus. For Li isotopes, however, direct experimental information to determine the gap is missing. On the other hand, the shell gap for Z = 4–6 can be empirically determined by adjusting positive- and negative-parity energy levels of N = 7 isotones, which can be made use of to fix the shell gap at Z = 3. In this study, we perform p-sd shell model calculations. As the effective interaction we start with the WBP interaction [17] giving a good description of the abnormalparity states, mainly of near-stable nuclei, in this region. The original WBP interaction is designed to be used in the pure 0¯ hω and 1¯ hω model spaces, while in the present study (see ref. [18] in detail), the mixing with the higher excited configurations is included. The inclusion of the mixing plays an essential role particularly in the case that the normal and intruder states compete with each other. Since the mixing may have different effects between the 0¯ hω and 1¯ hω states, we should re-examine the shell gap suitable for this model space. In fig. 1, we compare the shell gap by the original WBP interaction with the empirical shell gap reproducing levels of abnormal-parity states of the N = 7 isotones. The empirical shell gap is rather similar to the original for Z = 6, whereas the difference between them increases as Z decreases. Namely, the evolution of the N = 8 shell gap more transparently develops in the extended model space than that in the small space. The reason for the difference is given in the following. The 0¯ hω states couple mainly hω states do with the 3¯hω with the 2¯ hω ones, while the 1¯ ones. Since in general the n¯ hω states are rapidly located higher as n increases, the coupling with the 2¯ hω states in the normal parity is stronger than that with the 3¯hω states in the abnormal parity. Thus, it is likely that the mixing favors the normal parity state, which in fact accounts for about half of the difference of the shell gap at Z = 4. The other half is accounted for by the difference of hω and 1¯hω the treatment of the 4 He core: in the pure 0¯ calculation, the breaking of the core is allowed only for the 1¯ hω state. This means that only the negative-parity states have room for the gain of the correlation energy through the breaking of the 4 He core. On the other hand,

Y. Utsuno: Anomalous magnetic moment of 9 C and shell quenching in exotic nuclei

in the present p-sd shell calculation the core breaking is not allowed for both parity states, equally. As a result, the shell gap for Z = 3 extrapolated from the empirical ones of Z = 4–6 is much narrower than that of the original interaction as shown in fig. 1.

4.2 Phenomenological treatment of the Thomas-Ehrman effect We move the ESPE of the sd orbits for Z = 3 to be the same as the extrapolated one in fig. 1, simply shifting the relevant bare single-particle energies. Even with this narrowing shell gap, the ground state of 9 Li calculated by the shell model is still dominated by the normal configurations. Consequently, the spin expectation value is calculated to be a normal one, also, under the assumption of the mirror symmetry for the 9 C-9 Li pair. While 9 Li is a sufficiently bound nucleus, its mirror pair, 9 C, is a very loosely bound one having Sp = 1.3 MeV due to the repulsive Coulomb force. In this situation, single-particle orbits above the Fermi level can be lowered from those of the mirror nucleus owing to the ThomasEhrman effect. In this study, the Thomas-Ehrman effect is incorporated in a phenomenological way, i.e., just by shifting the relevant single-particle energies in the shell-model calculation (see ref. [18] in more detail). In many cases, the Thomas-Ehrman effect emerges as the shift of energy levels involving the relevant orbit, whereas the component of the many-body wave function barely changes. In the present case, on the other hand, the ground state is gradually mixed with the intruder state once the ThomasEhrman effect is switched on. As a result, the magnetic moment of 9 C is shifted from that of the mirror wave function of 9 Li, and the spin expectation value calculated by eq. (1) becomes close to the experimental value with a reasonable shift of the single-particle energy. We stress that this softness of the ground-state configuration is most attributed to the narrow N = 8 shell gap as fixed in sect. 4.1. It is worthwhile to discuss how the mixing with the intruder configurations accounts for the experimental spin expectation value. Table 1 compares the expectation values of the angular-momentum operators, l and s, in the ground state of 9 C between different calculations. For the 0¯ hω, i.e., p-shell calculation, the distribution of the total angular momentum, 3/2, is rather similar to the pure single-particle value. On the other hand, most of the orbital angular momentum, carried by neutrons in the 0¯ hω ground state, moves to valence protons in the 2¯hω ground state. To be intuitive, since a large (prolate) deformation is favored in this intruder state as the Nilsson model predicts, it is very likely that the proton orbital angular momentum is large as a consequence of the collective rotation. It should be noted that once the mixing occurs by the lowering of the 0s1/2 orbit, the d orbits are involved, too, producing the present angular momentum distribution. In a well mixed wave function, the distribution is in between as shown table 1. Because the g-factor of the proton orbital angular momentum is positive, the magnetic

211

Table 1. Expectation value of the angular-momentum operators for the ground state of 9 C, compared between the singleparticle ν(0p3/2 )1 state (SP), the 0¯ hω and 2¯ hω shell-model calculations without the mixing, and the (0 + 2)¯ hω calculations. For the (0 + 2)¯ hω calculations, the values with/without the Thomas-Ehrman (TE) effect are shown. Note that the experimental magnetic moment is (−)1.3914(5)μN [2] or (−)1.396(3)μN [8].

SP

lzp 

lzn 

spz 

snz 

0 1 0 0.5

μ

−1.91

0¯ hω

2¯ hω

0.14 0.84 0.02 0.50

0.83 0.15 0.02 0.50

−1.66

−0.95

(0 + 2)¯ hω w/o TE w/ TE

0.24 0.75 0.02 0.49

0.44 0.56 0.01 0.49

−1.54

−1.38

moment is shifted positively, which pulls the calculated spin expectation value toward the experimental one.

5 Some other possible clues At present, there is no direct experimental information indisputably indicating the large breaking of mirror symmetry in the 9 C-9 Li pair. In order to obtain clues which can be related to the breaking, the followings would give some hints, although they may be rather subtle effects to be treated delicately. 5.1 Asymmetry of the β decay between the mirror nuclei From recent measurements of the β decay from the 9 Li and 9 C [19, 20], there is a large difference in their B(GT ) values for the decays having the largest B(GT ) value. This indicates that the mirror symmetry must be broken for either (or both) the parent ground states or the daughter states of this pair. 5.2 Deviation from the IMME It has been known that masses of the T = 3/2 isobaric quartet well follow the so-called the isobaric multiplet mass equation (IMME) [21]. For A = 9, however, the deviation from the IMME is larger than a theoretical estimate [22]. It is possible that this deviation is caused by a large energy gain due to the mixing with the intruder configurations in 9 C. 5.3 Energy levels Only one excited state has been reported for 9 C. It is located at 2.22 MeV, whereas the known first excited state of 9 Li lies at 2.69 MeV [23]. The spin/parity of neither

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state has been measured yet. If they are the mirror levels involving the excitation of the last odd nucleon, i.e. 1/2− , as expected by the p-shell model, this energy difference appears much larger than that seen in typical ones. This difference may be a signature of the large mirror asymmetry.

6 Summary We examined the shell structure of unstable nuclei in detail and discussed its effect on the anomalously large isoscalar spin expectation value known for the 9 C-9 Li mirror pair. Similarly to the variation of the N = 20 shell gap from stable to unstable nuclei, it turned out that the N = 8 shell gap should also become rather narrow toward smaller proton numbers, obtained from an empirical determination of the shell gap by a p-sd shell-model calculation. In the present shell-model calculation, we included the mixing between different ¯hω configurations. With this narrow shell gap, although the normal configurations still dominate the ground state of 9 Li, this state is softly mixed with the intruder state, which would occur in 9 C due to the Thomas-Ehrman effect. Some other viewpoints were suggested, possibly related to the breaking of the mirror symmetry in the 9 C-9 Li pair. The work was supported in part by Grant-in-Aid for Young Scientists (14740176) and that for Specially Promoted Research (13002001) from the Ministry of Education, Culture, Sports, Science and Technology.

References 1. K. Sugimoto, J. Phys. Soc. Jpn. Suppl. 34, 197 (1973). 2. K. Matsuta et al., Nucl. Phys. A 588, 153c (1995); K. Matsuta et al., Hyperfine Interact. 97/98, 519 (1996).

3. S. Cohen, D. Kurath, Nucl. Phys. 73, 1 (1965); Nucl. Phys. A 101, 1 (1967). 4. B.A. Brown, B.H. Wildenthal, Annu. Rev. Nucl. Part. Sci. 38, 29 (1988). 5. A. Poves, A. Zuker, Phys. Rep. 70, 235 (1981). 6. M. Honma, T. Otsuka, B.A. Brown, T. Mizusaki, Phys. Rev. C 65, 061301(R) (2002); 69, 034335 (2004). 7. B.A. Brown, B.H. Wildenthal, Nucl. Phys. A 474, 290 (1987). 8. M. Huhta et al., Phys. Rev. C 57, R2790 (1998). 9. Y. Kanada-En’yo, H. Horiuchi, Phys. Rev. C 54, R468 (1996). 10. K. Varga, Y. Suzuki, I. Tanihata, Phys. Rev. C 52, 3013 (1995). 11. E.K. Warburton, J.A. Becker, B.A. Brown, Phys. Rev. C 41, 1147 (1990). 12. Y. Utsuno, T. Otsuka, T. Mizusaki, M. Honma, Phys. Rev. C 60, 054315 (1999). 13. M. Keim, in Proceeding of the International Conference on Exotic Nuclei and Atomic Masses (ENAM98), edited by B.M. Sherrill, D.J. Morrissey, C.N. Davis, AIP Conf. Proc. 455, 50 (1998); M. Keim et al., Eur. Phys. J. A 8, 31 (2000). 14. G. Neyens, these proceedings. 15. Y. Utsuno, T. Otsuka, T. Mizusaki, M. Honma, Phys. Rev. C 70, 044307 (2004). 16. T. Otsuka, R. Fujimoto, Y. Utsuno, B.A. Brown, M. Honma, T. Mizusaki, Phys. Rev. Lett. 87, 082502 (2001). 17. E.K. Warburton, B.A. Brown, Phys. Rev. C 46, 923 (1992). 18. Y. Utsuno, Phys. Rev. C 70, 011303(R) (2004). 19. U.C. Bergmann et al., Nucl. Phys. A 692, 427 (2001). 20. Y. Prezado et al., Phys. Lett. B 576, 55 (2003). 21. W. Benenson, E. Kashy, Rev. Mod. Phys. 51, 527 (1979). 22. E. Kashy, W. Benenson, J.A. Nolen jr., Phys. Rev. C 9, 2102 (1974). 23. R.B. Firestone, V.S. Shirley (Editors), Table of Isotopes, 8th edition (Wiley, New York, 1998).

3 Moments and radii 3.2 Nuclear matter distribution

Eur. Phys. J. A 25, s01, 215–216 (2005) DOI: 10.1140/epjad/i2005-06-156-3

EPJ A direct electronic only

Investigation of nuclear matter distribution of the neutron-rich He isotopes by proton elastic scattering at intermediate energies O.A. Kiselev1,2,a , F. Aksouh1,b , A. Bleile1 , O.V. Bochkarev3 , L.V. Chulkov3 , D. Cortina-Gil1,c , A.V. Dobrovolsky2 , atos1 , F.V. Moroz2 , G. M¨ unzenberg1 , P. Egelhof1 , H. Geissel1 , M. Hellstr¨om1 , N.B. Isaev2 , B.G. Komkov2 , M. M´ 4 2 1 3 2 2 M. Mutterer , V.A. Mylnikov , S.R. Neumaier , V.N. Pribora , D.M. Seliverstov , L.O. Sergueev , A. Shrivastava1,d , K. S¨ ummerer1 , H. Weick1 , M. Winkler1 , and V.I. Yatsoura2 1 2 3 4

Gesellschaft f¨ ur Schwerionenforschung, D-64291 Darmstadt, Germany Petersburg Nuclear Physics Institute, RU-188300 Gatchina, Russia Kurchatov Institute, RU-123182 Moscow, Russia Institut f¨ ur Kernphysik, TU Darmstadt, D-64289 Darmstadt, Germany Received: 12 November 2004 / c Societ` Published online: 4 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Absolute differential cross-sections for elastic p6 He and p8 He scattering were measured in inverse kinematics with secondary beams. In order to supplement data taken for small-angle scattering, differential cross-sections for higher momentum transfer were measured using liquid hydrogen target. Both data sets were analyzed together. They have permitted to deduce the radial shape of the nuclear matter distributions and the root-mean-square radii with the help of Glauber theory. In addition to a phenomenological analysis, used already in the previous work, a model-independent analysis with a help of a Sum-Of-Gaussians (SOG) method has been performed. The experimental p6,8 He elastic scattering cross-sections have also been compared with the predictions from various theoretical nuclear models. PACS. 21.10.Gv Mass and neutron distributions – 24.50.+g Direct reactions – 25.10.+s Nuclear reactions involving few-nucleon systems – 25.40.Cm Elastic proton scattering

1 Introduction The study of neutron-rich light nuclei near the drip line has attracted much attention as they exhibit a particular nuclear structure, namely an extended distribution (socalled halo) of the valence neutrons surrounding a compact core. Elastic proton scattering at intermediate energies is known as a suitable technique for exploring the nuclear matter distributions in the stable nuclei. It was successfully applied at GSI also for the radioactive nuclei 6,8 He [1,2] and 8,9,11 Li [3] with beam energies close to 700 MeV/u in inverse kinematics. The method has been proven to be very effective for measuring the differential a

Conference presenter; Present address: Institut f¨ ur Kernchemie, Johannes Gutenberg Universit¨ at Mainz, D-55128 Mainz, Germany; e-mail: [email protected] b Present address: Instituut voor Kern- en Stralingsfysika, K. U. Leuven, B-3001 Leuven, Belgium. c Present address: Departamento de Fisica de Particulas, Universidade de Santiago de Compostela, E-15706 Santiago de Compostela, Spain. d Present address: Nuclear Physics Division, Bhabha Atomic Research Centre, IN-400085 Mumbai, India.

cross-sections and deriving the nuclear matter distributions in the halo nuclei, such as 6 He, 8 He and 11 Li, with the aid of the Glauber multiple scattering theory.

2 Motivation and experimental method Previous measurements performed in the small momentum transfer region have yielded valuable information on the nuclear sizes and radial structure of the overall nuclear matter density distributions. A high-pressure hydrogenfilled ionization chamber was used as the target and the detector for the recoiling protons. Theoretical estimations have shown that in case of higher momentum transfer the experimental data more sensitively probe the density of the inner part of the nuclei and thus generally improves the accuracy of the total matter distribution [4]. Recently, a novel experimental approach has been accomplished with the aim to deduce the differential p6,8 He cross-sections at a higher momentum transfer close to the first diffraction minimum. The major difference with respect to the previous experiments was that instead of the active gaseous target a liquid hydrogen target was used, combined with a proton recoil detector [5].

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Fig. 1. Nuclear matter density distribution deduced from the experimental cross-section for 6 He using a Sum-Of-Gaussians method. The shaded area represents the resulting error band.

Fig. 2. Experimental differential cross-section dσ/dt versus the four momentum transfer squared −t for p8 He and comparison with calculations based on predictions of various theoretical models for the nuclear matter density.

3 Analysis and results The differential cross-sections obtained in both experiments have been evaluated using several phenomenological parameterizations for the nuclear matter distribution. Details of this part of the analysis are described in [2]. In addition, a model-independent analysis with the help of a Sum-Of-Gaussians (SOG) method has been performed, which is a standard method for the investigation of nuclear charge distributions from electron scattering data [6]. Figure 1 shows, as an example, the radial shape of the total nuclear matter distribution in 6 He derived from the SOG analysis. The deduced values of the nuclear matter radii Rm of 6 He 2.37(5) fm and 8 He 2.49(4) fm are consistent with the results of the phenomenological analysis and confirm the existence of an extended neutron halo in these nuclei. The nuclear charge radius of 6 He has been recently measured for the first time using the method of isotope shift based on laser spectroscopy technique [7]. It was found to be 2.054(14) fm, and the corresponding value for the point-proton radius is 1.912(18) fm. The obtained value is in good agreement with the present value of Rcore = 1.97(9) fm (expected when assuming to have an α-particle core + 2n halo structure) that assures the consistency of both measurements. The analysis of the experimental cross-sections confirms the structure of 6 He as a three-body system. The core size of 8 He has been found to be Rcore = 1.86(8) fm and within the phenomenological approach, the nuclear matter density has been parameterized as an α-particle core and four valence neutrons and a 6 He core and two valence neutrons. Both parameterizations permit the same quality description of the experimental cross-sections. A possible explanation is that a ground state of 8 He is a mixture of these two configurations. This fact is supported by the analysis of the inelastic scattering of 8 He on protons, measured also in the present experiment [8].

Precise data on the differential cross-sections may provide a sensitive test for theoretical predictions on nuclear matter density distributions. Density distributions obtained from various theoretical approaches: relativistic mean field calculations [9], microscopic cluster model using the refined resonating group method [10], microscopic quantum Monte Carlo calculations [11], variational Monte Carlo [12], Fermionic Molecular Dynamics [13]. The crosssections dσ/dt for p6,8 He elastic scattering have been calculated using nuclear matter density distributions. Figure 2 shows the comparison of the data with the latest calculations for 8 He. The best agreement has been obtained using densities from [10] and [12]. A similar comparison has been also made for p6 He. In this case the best agreement between the experimental data and theory was archived with densities from [11] and [13].

References 1. 2. 3. 4. 5.

6. 7. 8. 9. 10. 11. 12. 13.

S.R. Neumaier et al., Nucl. Phys. A, 712, 247 (2002). G.D. Alkhazov et al., Nucl. Phys. A, 712, 269 (2002). P. Egelhof et al., Phys. Scr. T104, 151 (2003). L.V. Chulkov et al., Nucl. Phys. A, 587, 291 (1995). O.A. Kisselev et al., Procedings of ENAM2001 (Springer Verlag, 2003) p. 186; F. Aksouh, PhD Thesis, Universit´e de Paris XI, Orsay, France, 2002. I. Sick, Nucl. Phys. A, 218, 509 (1974). L.-B. Wang et al., Phys. Rev. Lett. 93, 142501 (2004). L.V. Chulkov et al., to be published in Nucl. Phys. A. S. Typel, H.H. Wolter, Nucl. Phys. A, 656, 331 (1999). J. Wurzer, H.M. Hofmann, Phys. Rev. C, 55, 688 (1997); J. Wurzer, H.M. Hofmann, private communication. B.S. Pudliner et al., Phys. Rev. C, 56, 1720 (1997). S. Karataglidis et al., Phys. Rev. C 71, 064601 (2005); K. Amos et al., Adv. Nucl. Phys., 25, 275 (2000). T. Neff, H. Feldmeier, Nucl. Phys. A, 738, 357 (2004).

Eur. Phys. J. A 25, s01, 217–219 (2005) DOI: 10.1140/epjad/i2005-06-078-0

EPJ A direct electronic only

Reaction cross-sections for stable nuclei and nucleon density distribution of proton drip-line nucleus 8B M. Takechi1,a , M. Fukuda1 , M. Mihara1 , T. Chinda1 , T. Matsumasa1 , H. Matsubara1 , Y. Nakashima1 , K. Matsuta1 , T. Minamisono2 , R. Koyama3 , W. Shinosaki3 , M. Takahashi3 , A. Takizawa3 , T. Ohtsubo3 , T. Suzuki4 , T. Izumikawa5 , S. Momota6 , K. Tanaka7,b , T. Suda7 , M. Sasaki8 , S. Sato9 , and A. Kitagawa9 1 2 3 4 5 6 7 8 9

Department of Physics, Osaka University, Osaka 560-0043, Japan Fukui University of Technology, Fukui, 910-0034, Japan Department of Physics, Niigata University, Niigata 950-2102, Japan Department of Physics, Saitama University, Saitama 338-3570, Japan RI Center, Niigata University, Niigata 951-8510, Japan Kochi University of Technology, Kami, Kochi 782-8502, Japan RIKEN, Wako, Saitama 351-0106, Japan Ritsumeikan University Shiga 525-8577, Japan National Institute of Radiological Sciences, Chiba 263-8555, Japan Received: 2 December 2004 / c Societ` Published online: 17 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The optical limit of the Glauber theory with zero-range approximation, which is successfully used at high energies to connect the nucleon density distribution with reaction cross-sections (σ R ), gives somewhat smaller values of σR by 10–20% at intermediate energies. We have precisely measured the σR for 12 C on Be, C, and Al at 30A–200A MeV, and for 9 Be on Be at 70A–100A MeV to investigate the enhancement of σR compared to the optical-limit calculation. From the enhancements, we deduced the nucleon-nucleon range as a function of energies. We deduced the density distribution of 8 B analyzing the known experimental σR for 8 B with an enhancement correction or with the finite range effect as a test. PACS. 25.60.Dz Interaction and reaction cross-sections

1 Introduction The measurement of reaction cross-sections (σR ) allows one to deduce the nucleon density distribution using the Glauber calculation (optical limit of the Glauber theory with zero-range approximation). Especially, σR at intermediate energies of several tens MeV/nucleon are considered to be quite sensitive to dilute nucleon densities, like a halo, because of the large σN N at those energies. However, it is known that the Glauber calculation underestimates σR by 10–20% at intermediate energies and this disagreement causes a relatively large systematic error in the deduced density distribution. In order to clarify the problem and to correct for the disagreement, we measured the σR of stable nuclei precisely, and investigated the enhancement of the experimental σR compared to the Glauber calculation. As a test, we deduced the density distribution of 8 B analyzing the a b

e-mail: [email protected] Conference presenter; e-mail: [email protected]

known experimental σR [1] with the enhancement correction or with the finite range effect.

2 Experiment We have precisely measured the σR for 12 C beams on Be, C and Al targets and 9 Be beams on Be target in the energy region of 30A–200A MeV, where there was a lack of precise and systematic σR data for stable nuclei. The primary beams of 12 C with energies of 75A, 100A, 180A, and 230A MeV were used, which were provided from the HIMAC [2] synchrotron. 9 Be beams were produced through the projectile fragmentation process in 12 C + 9 Be collision. The transmission method was employed to measure the σR . The schematic view of the experimental setup is shown in fig. 1. The nuclei produced in a production target were separated by magnetic rigidity analysis and identified by time of flight and ΔE. Two thin plastic scintillators (0.2 and 0.1 mm thick) placed upstream of the target were used for the identification of incoming particles to count the number of incident nuclei (N0 ). Four

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ε = σ R(Expt.) / σ R(Calc.)

1.20

(a)

1.15

1.10 12

C on Be C on C 12 C on Al 9 Be on Be

1.05

12

1.00

50

100

Fig. 1. Schematic view of the experimental setup.

150

200

E / A (MeV) 1.0

1600

12

12

12

C on C [3] C on Al [3]

(b)

0.8

1400

β (fm )

σR (mb)

12

C on Be C on C 12 C on Al 9 Be on Be

1800

1200

0.6 12

C on Be C on C 12 C on Al 9 Be on Be

1000

800

600

12

0.4

50

100 150 E / A (MeV)

200

0.2

150

200

Fig. 3. (a) Deduced ε and (b) deduced NN range. 10 10 10

0

ε(E)

10 10 10

Error

Error

Finite Range Analysis HF Calc.

-1

-2

8

-3

Density (fm )

1 N1 , σR = − ln t N0

100

E / A (MeV)

Fig. 2. Experimental results.

Si ΔE counters (400 or 500 μm thick) and a NaI(Tl) energy counter (76.2 mm φ, 60 mm thick) placed downstream of the target composed a counter telescope, for the identification of A and Z of outgoing particles to count the number of events without any nuclear reactions in the target (N1 ). The σR is determined as,

50

B

-3

-4

-5

where t is the target thickness. However, the ratio N1 /N0 must be corrected for nuclear reactions in the detectors. For this purpose, the measurement without the reaction target was also carried out in the same condition.

10

3 Results and discussion

Fig. 4. The deduced density distribution of 8 B.

In fig. 2, experimental results on the reaction cross-section σR are plotted as functions of beam energy. We also plot the σR reported by Kox et al. [3] with the open symbols. The present data agree with their data within the errors, while the accuracy is improved. We compared our experimental σR with the Glauber calculations, and the enhancement factor is defined by the ratio of the experimental value over the calculation as ε ≡ σR (Expt.)/σR (Calc.). In fig. 3(a), we plotted the obtained ε as a function of beam energy. Experimental σR exceed the calculations by ∼ 15% at 40A MeV, and ∼ 5% at 200A MeV. The ε data seem to be independent of the combination of projectile and target nuclides. We fitted a line to the ε data as shown in fig. 3(a) [ε(E)]. We used ε(E) as a correction factor to the Glauber calculation in the analysis for the density distribution of 8 B.

10

-6

-7

0

2

4

6 r (fm)

8

10

12

In the above analysis, we assumed zero-range approximation. However, this approximation may not be appropriate at intermediate energies. We deduced the range of nucleon-nucleon interaction (NN range) from our data, assuming the enhancement of σR is due to the finite range effect. In fig. 3(b), the deduced NN ranges (β) are plotted as a function of beam energy. The NN ranges should be the same for any nuclides. However, the deduced values seem to have a slight dependence on the combination of projectile and target nuclides. We fitted a polynomial function to the obtained ranges (solid line). Using this range function [β(E)], we analyzed density distribution of 8 B with the finite range Glauber calculation. Figure 4 shows the deduced density distribution of 8 B using the ε(E) (solid line) and using the finite range

M. Takechi et al.: Reaction cross-sections for stable nuclei and nucleon density distribution . . .

Glauber calculation (broken line). The error of the density distribution is shown with the shaded area. The error of the density distribution obtained by the finite range analysis is relatively large due to the slight target dependence of the effective NN range. It is seen that both density distributions are consistent with the Hartree-Fock (HF) calculation [4] (dotted line) at the tail part.

219

References 1. M. Fukuda et al., Nucl. Phys. A 656, 209 (1999). 2. HIMAC: Heavy Ion Medical Accelerator in Chiba, National Institute of Radiological Sciences, Chiba 263-8555, Japan. 3. S. Kox et al., Phys. Rev. C 35, 1678 (1987). 4. H. Sagawa, H. Kitagawa, private communication.

Eur. Phys. J. A 25, s01, 221–222 (2005) DOI: 10.1140/epjad/i2005-06-182-1

EPJ A direct electronic only

Nucleon density distribution of proton drip-line nucleus

17

Ne

K. Tanaka1,a , M. Fukuda1 , M. Mihara1 , M. Takechi1 , T. Chinda1 , T. Sumikama1 , S. Kudo1 , K. Matsuta1 , T. Minamisono1 , T. Suzuki2,b , T. Ohtubo2 , T. Izumikawa2 , S. Momota3 , T. Yamaguchi4,b , T. Onishi4 , A. Ozawa4,c , I. Tanihata4 , and Zheng Tao4 1 2 3 4

Department of Physics, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan Department of Physics, Niigata University, Niigata 950-2181, Japan Kochi University of Technology, Tosayamada, Kochi 782-8502, Japan RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Received: 12 January 2005 / c Societ` Published online: 2 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. 17 Ne is one of the candidates for proton halo nuclei. To study the halo structure of 17 Ne, we measured the reaction cross-sections (σR ) and deduced the density distribution of 17 Ne through the energy dependence of σR . From the deduced density, it is found that 17 Ne has a long density tail which is consistent with the picture of two valence protons of 17 Ne occupying the 2s1/2 orbital. PACS. 25.60.Dz Interaction and reaction cross-sections

1 Introduction It is interesting to study the proton halo structures that are less known compared to the neutron halo structures, in order to obtain a detailed understanding of the mechanism of halo formation in loosely bound nuclei. While several neutron halo nuclei have been found and well studied in the p-shell (e.g. 11 Li [1] ) and sd -shell (e.g. 14 Be, 17 B [2]) regions, only one proton-halo nucleus, namely 8 B, has been reported [3]. The ground state of proton drip-line nucleus 17 Ne(I π = 1/2− ) was suggested to have a proton halo structure, on the basis that the interaction crosssection (σI ) for 17 Ne at relativistic energies are larger than those for the mirror nucleus 17 N [4]. Several experiments have been performed to verify the hypothesis but the results conflict with each other [5]. If, indeed, 17 Ne has a proton halo structure, it will be the first proton-rich nucleus in the sd-shell region to have a two-proton halo structure. Another intriguing question that could be answered by the study on 17 Ne concerns the possibility of existence of a new magic number Z = 16. The new magic number N = 16 has been discovered for some neutron-rich nuclei [6]. The orbital that two valence protons could occupy is either the 1d5/2 or the 2s1/2 , and it is not easy to a Conference presenter; Present address: RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan; e-mail: [email protected] b Present address: Department of Physics, Saitama University, Saitama, Saitama, 338-8570, Japan. c Present address: Department of Physics, Tsukuba University, Tsukuba, Ibaragi, 305-8571, Japan.

discriminate the two possibilities in an experiment. If the two valence protons mainly occupy 2s1/2 , for which the centrifugal barrier becomes low, the proton density distribution for 17 Ne will have a long tail. In this case, the level energy of 2s1/2 should be lower than 1d5/2 , which can lead to the occurrence of magic number 16 [6]. To study the structure of 17 Ne, we have measured the reaction cross-sections (σR ) at several tens of A MeV to deduce the density distribution of 17 Ne. In this energy range, the nucleon-nucleon total cross-section (σN N ) becomes large [7], therefore σR becomes sensitive to the dilute-density at the nuclear surface.

2 Experiment The experiment was carried out at the RIKEN Accelerator Research Facility. A primary beam of 135 A MeV 20 Ne provided by the RIKEN Ring Cyclotron was impinged on a 9 Be production target to produce a 17 Ne beam. The 17 Ne secondary beam was separated from other reaction products through the RIKEN Projectile fragment Separator. The σR for 17 Ne on 9 Be, 12 C and 27 Al targets at 64 A MeV and 42 A MeV were measured by means of the transmission method to within 2% accuracy.

3 Density distribution In this study, the σR is related to a density distribution through the optical limit of the Glauber theory (OL). We

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10 0

Table 1. Reaction and interaction cross-sections for 17 Ne used in the fitting procedure.

Energy (A MeV)

σI (mb) [4]

Be

700 64 42 680 620 64 42 670 64 43

968 ± 45

C

Al

1090 ± 76 1044 ± 31 1412 ± 224

1249 ± 25 1467 ± 33 1331 ± 27 1541 ± 31 1795 ± 36 2012 ± 40

Bestfit Error Hartree_Fock s-wave Hartree_Fock d-wave Core

10 -1

σR (mb)

Density (fm-3)

Target

10 -2 10 -3 10 -4

17

Ne

10 -5 10 -6

0 deduced the density distribution of Ne via a fitting procedure using the present σR data and the σI data at high energies [4]. The fitting procedures are as follows. First, a calculation is performed to obtain an initial value for calc ), using the OL with an assumed density distriσR (σR calc bution. Next, the σR is compared with the experimental σR . If σR deviates from the experimental σR , the assumed density distribution is adjusted, and the calculation is recalc . Repeating these procedures, peated to obtain a new σR the best-fit density distribution of 17 Ne was obtained. In our calculation, we assumed the harmonic-oscillator (HO) type function plus single-particle densities as a functional form of the proton density. The single-particle density was calculated with the Woods-Saxon potential, the Coulomb and centrifugal barriers. The HO function with the same width was assumed for the neutron density. The free parameters were the width of the HO function, the separation energy of valence protons, and the fractions of 1d5/2 and 2s1/2 orbitals. Table 1 shows the σI and σR for 17 Ne used in the present fitting. In deducing the density distribution, we have considered the following three corrections. First, we corrected the σR calculated with the OL. In the lower energy region, as in the case of the present experiment, there is a discrepancy between the experimental σR and the one calculated with the OL even for stable nuclei. This discrepancy was corrected by using the ratio of the experimental σR to that obtained with the OL calculation for stable nuclei. In the present analysis, the σR calculated with the OL were always corrected by multiplying by this ratio [8]. Secondly, we considered the effect of the few-body approximation of Glauber theory (FB), which was proposed by Ogawa et al. and Al-Khalili et al. [9], because the FB is more appropriate than the OL for dilute densities. Since it is difficult to apply FB, instead of OL, directly to the fitting procedure, correction for the FB effect was done as follows. The experimental σR were multiplied by the ratio of σR with the FB to that calculated with the OL. Here, both σR were calculated using the same density distribution deduced through the OL fitting to the experimental FB ) were used in σR . Then these few-body corrected σR (σR the fitting with the OL again. Repeating this procedure,

2

4

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8

10

12

14

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Fig. 1. Density distribution of 17 Ne. The error indicated contains the experimental and also the ambiguity of the fitting method. FB σR and the density distribution converged into the final results. Lastly, correction for the effect of the Fermi motion was also taken into account in the FB calculation, which is considered to be important at low energies because of a finite reaction time neglected in the Glauber theory. Figure 1 shows the deduced density distribution of 17 Ne. For comparison, the theoretical densities calculated by Kitagawa et al. [10] with the Hartree-Fock model, in which two valence protons occupy the 2s1/2 orbital or 1d5/2 orbital, are also shown in this figure. The deduced density distribution of 17 Ne has a long density tail, consistent with the theoretical one for which two valence protons are in the 2s1/2 orbital. This fact implies the level inversion of 2s1/2 and 1d5/2 , and therefore, the possible occurrence of the magic number 16 on the proton-rich side.

References 1. I. Tanihata et al., Phys. Rev. lett. 55, 2676 (1985). 2. T. Suzuki et al., Nucl. Phys. A 658, 313 (1999). 3. W. Schwab et al., Z. Phys. A 350, 283 (1995); J.H. Kelly et al., Phys. Rev. Lett. 77, 5020 (1996); M. Fukuda et al., Nucl. Phys. A 656, 209 (1999). 4. A. Ozawa et al., Phys. Lett. B 334, 18 (1994). 5. R.E. Warner et al., Nucl. Phys. A 635, 292 (1998); R. Kanungo et al., Phys. Lett. B 571, 21 (2003). 6. A. Ozawa et al., Phys. Rev. Lett. 84, 24 (2000). 7. Particle Data Group Phys. Lett. B 592, 1 (2004). http://pdg.lbl.gov/xsect/contents.html. 8. M. Takechi et al., these proceedings; M. Takechi et al., in Proceedings of the International Symposium A New Era of Nuclear Structure Physics, 19-22 November 2003, Niigata, Japan (World Scientific, 2004) p. 367. 9. Y. Ogawa, et al., Nucl. Phys. A 543, 722 (1992); J.S. AlKhalili, et al., Phys. Rev. C 54, 1843 (1996). 10. H. Kitagawa et al., Z. Phys. A 358, 381 (1997).

Eur. Phys. J. A 25, s01, 223–226 (2005) DOI: 10.1140/epjad/i2005-06-185-x

EPJ A direct electronic only

Reaction cross-sections and reduced strong absorption radii of nuclei in the vicinity of closed shells N = 20 and N = 28 A. Khouaja1,2,3,a , A.C.C. Villari1,4,b , M. Benjelloun2 , G. Auger1,5 , D. Baiborodin6 , W. Catford7 , M. Chartier8 , C.E. Demonchy1,8 , Z. Dlouhy6 , A. Gillibert9 , L. Giot1,10 , D. Hirata11 , A. L´epine-Szily12 , W. Mittig1 , N. Orr10 , Y. Penionzhkevich13 , S. Pitae1,5 , P. Roussel-Chomaz1 , M.G. Saint-Laurent1 , and H. Savajols1 1 2 3 4 5 6 7 8 9 10 11 12 13

GANIL, BP 55027, F-14075 Caen Cedex 5, France LPTN Faculty of Sciences, El Jadida BP 20, 24000 El Jadida, Morocco LNS-INFN, 44 S. Sofia, 95129 Catania, Italy Physics Division, Argonne National Laboratory, 9700 S. Cass Av., Argonne, IL 60439, USA Coll`ege de France, 11 Place Marcelin Berthelot, F-75231, Paris Cedex 05, France Nuclear Physics Institute ASCR, 25068, Rez, Czech Republic University of Surrey, Nuclear Physics Department, Guilford, GU27XH, UK University of Liverpool, Department of Physics, Liverpool, L69 7ZE, UK CEA/DSM/DAPNIA/SPHN, CEN Saclay, F-91191 Gif-sur Yvette, France LPC - ISMRA and University of Caen, F-6704 Caen, France The Open University, Department of Physics and Astronomy, Walton Hall, Milton Keynes, MK6 2HL, UK University of S˜ ao Paulo IFUSP, C.P. 66318, 05315-970 S˜ ao Paulo, Brazil FLNR, JINR Dubna, P.O. Box 79, 101000 Moscow, Russia Received: 10 January 2005 / Revised version: 29 April 2005 / c Societ` Published online: 14 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Energy integrated reaction cross-section measurements of around sixty neutron-rich nuclei covering the region of closed shells N = 20 and N = 28 were performed at intermediate energy (30–65 A·MeV) using direct method. In this experiment, silicon detectors were used as active targets. The reduced strong absorption radii, r02 , for 19 new nuclei (27 F, 27,30 Ne, 33 Na, 28,34–35 Mg, 36–38 Al, 38–40 Si, 41–42 P, 42–44 S and 45 Cl) are deduced for the first time. An additional 60 radii, also measured in this experiment, are compared to results from literature. A new quadratic parametrization is proposed for the nuclear radius as a function of the isospin in the region of closed shells N = 8 and N = 28. According to this parametrization, the skin effect is well reproduced and anomalous behaviour on the radii are observed in 23 N, 29 Ne, 33 Na, 35 Mg, 44 S, 45 Cl and 45 Ar nuclei. PACS. 21.10.Gv Mass and neutron distributions – 25.60.Dz Interaction and reaction cross-sections

1 Introduction Radioactive nuclear beams (RNB) have provided a powerful tool for nuclear physics in the study of nuclear structure for exotic nuclei far from β-stability. For example, Coulomb excitation and mass measurements show evidences of magic shell breaking at N = 20 and N = 28 for exotic nuclei 32 Mg [1] and 44 S, respectively [2,3]. Moreover, recent measurements of reaction cross-sections (σR ) at high energy, revealed the existence of a new magic number at N = 16 [4] which appears only in very neutron-rich nuclei close to the drip-line. Historically speaking [5, 6], the measurement of reaction or interaction cross-sections involving fast-RNB launched what we could call today fast radioactive ion beam physics [7] a b

e-mail: [email protected] Conference presenter; e-mail: [email protected]

and continues to be responsible for major discoveries in this field. Total reaction cross-sections experiments can provide important hints of unexplored areas of the nuclear chart since this quantity can be measured with relatively low production yields. Experimentally, the quantity of data obtained up to now is remarkable, but no clear systematic studies have been carried out and no evaluation of the available data exists at present. In this contribution, we present new intermediate energy measurements of mean energy integrated reaction cross-sections performed at GANIL for neutron rich nuclei in the region defined by (5 < N < 28 ; 7 < Z < 18). These data correspond to the most exotic nuclei presently attainable in this region. We also investigate systematically the isospin dependence of the squared reduced strong ¯R and absorption radii r02 obtained from the measured σ we propose a new parametrization between r02 and isospin.

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12 13 14 15 16 17

Fig. 1. a) Total energy spectra for 25 F. b) Gamma coincidence spectra for the same isotope.

This relationship helps to localize anomalous behaviour of the nuclear radius, pointing out where further interesting studies could be performed.

2 Experimental setup The nuclei of interest were produced via the fragmentation of a 60.3 A · MeV 48 Ca primary beam, on a 181 Ta production target, placed between the two superconducting solenoids (SISSI) of GANIL [8]. Rotating at 2000 rpm, the production target was composed of three different sectors with thickness of 550 mg/cm2 (89%), 450 mg/cm2 (10%) and 250 mg/cm2 (1%). This ensured a sufficient production of both very and less exotic nuclei, allowing to measure new cross-sections while improving significantly known ones. The secondary beam was, after production, selected in flight by the α-shaped spectrometer and transported to the focal plane of SPEG (see refs. [9,10]). At the focal plane, all produced particles were stopped and detected by a stack of four cooled (about −10 ◦ C) silicon detectors with thicknesses of 50 μm (ΔE), 300 μm and 6700 μm. The first thin detector was used for identification of the produced beam while the second and third ¯ acted as active targets. A fourth detector (6700 μm (E)) was mounted downstream and served eventually as target for light nuclei or as detector of light charged particles produced in the reactions with the first three detectors. The Silicon detector-stack was surrounded by a 4π array of 14 NaI γ-detectors to identify quasi-elastic (Q close to zero) reactions. To limit the transmission of an undesired large number of light nuclei, a 25 μm Be-degrader was installed between the two dipoles of the α-shaped spectrometer. During the experiment, two different magnetic rigidities were selected in order to enhance the production of different regions of the nuclear chart. The incident nuclei could be unambiguously identified by correlating time of flight (TOF) between the production and the detection and energy loss (ΔE), event-by-event. For the measurements of reaction cross-sections we used a direct method, developed by Villari [11], which is a variant of the known transmission method. This technique is based on the total energy deposited by the incident particles in the silicon-stack. If the energy detected does not correspond to the total kinetic energy of the particle, it is

Fig. 2. Representation of the nuclei chart where the yellow region marks nuclei where mass measurements are available, grey are stable nuclei and the other colours and symbols denote nuclei where radii were evaluated in this paper.

a reaction event (fig. 1). This is easily identified in the energy spectrum of the silicon-stack by a queue towards low energy. There are a few percent quasi-elastic reactions that are not resolved directly in the energy spectrum. These are identified and added to the reaction events via the gamma detector coincidences. The cross-section measured by this method is represented by the following relationship: Emax σR (E)(dR/dE)dE m ln (1 − PR ) , (1) =− σ ¯R = 0 Rmax dNA Rmax dR 0

where m = 28 is the molecular-weight of silicon target with density d (g/cm2 ), NA is Avogadro’s number, and Rmax is the range of incident particles, calculated using the table of Hubert et al. [18]. The reaction probability PR is determined for each colliding isotope by the ratio of reaction events to the incoming ones. More details on the experimental procedure can be found in ref. [11].

3 Strong absorption radius Assuming that the energy dependence of the reaction cross-section is well described by the parametrization of S. Kox [19, 11], the reaction cross-section can be expressed as a function of the squared reduced strong absorption radius, r02 , as  σR (E) =

πr02



1/3 AP

+

B × 1− Ecm

1/3 AT

 ,

+a

(AP AT )1/3 1/3

1/3

AP + AT

2 − C(E)

(2)

A. Khouaja et al.: Reaction cross-sections and reduced strong absorption radii . . .

225

Fig. 3. Squared reduced strong absorption radii as a function of the isospin for masses from A = 12 to A = 46. The different colours refer to different authors (see fig. 2). The solid line represents the result of the parametrization given in eq. (3).

where AP and AT are the projectile and target numbers, a = 1.85 is the mass asymmetry related to the overlap volume between projectile and target. C(E) is the energy dependent transparency function which can be linearly evaluated, at energy range of 30–70 A MeV, by C(E) = 0.31 + 0.014 E/AP and at high energy by C(E) = 1.0. B and Ecm are the Coulomb barrier and incident energy. From eqs. (1) and (2), the squared reduced strong absorption radius r02 is extracted as a function of the reaction probability (PR ) of the measured mean energy integrated reaction cross-section. For a wide variety of target and

stable projectile systems, the squared reduced strong absorption radius, at different energies, is a constant and its value is r02 = 1.21 fm2 [19]. Previous measurements have already shown an increase of reduced radii r02 as a function of proton/neutron excess [6,16]. For Z ≤ 13 neutron-rich isotopes, Mittig et al. [6], have indicated that the reduced strong absorption radius has a linear isotopic dependence as a function of the neutrons excess, as, r02 = 1 + 0.06(N − Z). Later on, Assaoui et al. [16] presented a similar linear trend for Z ≥ 13 neutron-rich isotopes with r02 = 32/30 + (N − Z)/30.

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These two parametrizations have been built from a limited number of neutron-rich nuclei with reaction cross-sections measured at intermediate energies; they do not take into account the weight effect of mass number A for each isotope. Here, we propose a general relationship for this effect, valid for neutron and proton rich nuclei in a wider range of masses, i.e. A ≤ 50. Figure 2 shows the nuclei used in the search of this parametrization. The following equation has been obtained by a χ-square fitting of available intermediate- and high-energy data: r02 = 1.164 − 0.2819

T2 TZ + 4.628 Z2 . A A

(3)

From this equation, the reduced strong absorption radius for N = Z nuclei is r02 = 1.164 fm2 , in perfect agreement with r02 = 1.166 fm2 obtained from charge distribution of stable nuclei [20,21]. Importantly, we observe that the minimum radius is found at TAZ = 0.03, which also indicates that the minimum radius for an element deviates from N ∼ Z with increasing of A. In fig. 3, the squared reduced strong absorption radii obtained in this work are plotted as a function of the isospin for mass from 14 to 46, together with values deduced from reaction cross-sections obtained at high and intermediate energies using targets of Si, C and Be. The solid line represents the result of r02 using the new parametrization obtained from eq. (3). We observe that for each mass the isospin dependence of the nuclear radius is well reproduced by our parametrization: larger radius for larger isospin, which is more important for lighter masses than for heavier ones. Any anomalous behaviour of the nuclear radius can, therefore, be easily identified by a deviation from the solid line. A typical example can be observed for the larger radii of 23 Al and 27 P, already suggested by Zhang et al. [13] as one-proton halo nuclei. We also observe larger radii for the nuclei: 23 N, 29 Ne, 33 Na, 35 Mg, 44 S, 45 Cl, 41 Ar and 45 Ar. However, for 22 N, 24 F and 23 O, our results do not deviate from the parametrization, which is not in agreement with the observations of Ozawa et al. [14] at high energies, where neutron halo structures have been proposed. Our parametrization cannot disentangle the effects of halo and strong deformations, both allowing anomalous enhancement of the nuclear radius. For 33 Na, our experimental result is compatible with a large r.m.s. radius previously calculated via relativistic mean field theory [22], where a 1n-halo structure has been suggested. Moreover, the existence of large deformations of 45 Cl and 45 Ar were already proposed from mass and coulomb excitation measurements [3, 23]. We remark that for the nucleus 41 Ar, two results, mainly measured at intermediate energy, are inconsistent: one, obtained by Aissaoui et al. [16], is very close to the new parametrization while the one obtained by Licot et al. [17], is well above the systematics. 35 Mg and 44 S, as stated above, reveal important deviations from the systematic; both neutron-halo effect and strong deformation could be suggested.

4 Summary and conclusions In this work, the direct method —where a silicon telescope acts as an active target— is used to measure the mean energy integrated reaction cross-sections σ ¯ R for a variety of neutron-rich exotic nuclei in the range of closed shells N = 20 and N = 28. Assuming that the energy dependence of the reaction cross-section is well described by the parametrization of Kox, the square of the reduced strong absorption radius r02 is extracted and compared with results from the literature; from which 19 radii (obtained from the reaction cross-sections) are presented for the first time. The evolution of reduced the strong absorption radius is studied as a function of the excess of neutrons, independent of the mass number, incident energy and for both proton- and neutron-rich nuclei, in the region of 7 ≤ Z ≤ 18 and 14 ≤ A ≤ 46. A new quadratic parametrization is proposed for the evolution of nuclear radius as a function of the isospin. This parametrization reproduces well the skin effect and permits one to give indications of the existence of structure anomalies such as halo effects and large deformations. The existence of anomalous structure is proposed for the first time in the nuclei 35 Mg and 44 S. The authors would like to thank Jerry A. Nolen for discussions and help in preparing this manuscript. This work was partially supported by the U.S. Department of Energy, Office of Nuclear Physics, under contract W-31-109-ENG-38.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

15. 16. 17. 18. 19. 20. 21. 22. 23.

T. Motobayashi et al., Phys. Lett. B 346, 9 (1995). T. Glasmacher et al., Phys. Lett. B 395, 163 (1997). O. Sorlin et al., Phys. Rev. C 47, 2941 (1993). A. Ozawa et al., Phys. Rev. Lett. 84, 5493 (2000). I. Tanihata et al., Phys. Lett. B 160, 380 (1985). W. Mittig et al., Phys. Rev. Lett. 59, 1889 (1987). A.C.C. Villari, J.R.J. Bennett, C. R. Phys. 4, 595 (2003). R. Anne, Nucl. Instrum. Methods Phys. Res. B 126, 279 (1997). F. Sarazin et al., Phys. Rev. Lett. 84, 5062 (2000). G.F. Lima et al., Nucl. Phys. A 735, 303 (2004). A.C.C. Villari et al., Phys. Lett. B 268, 345 (1991). T. Suzuki et al., Nucl. Phys. A 616, 286c (1997); 658, 313 (1999). H.Y. Zhang et al., Nucl. Phys. A 707, 303 (2002). A. Ozawa et al., Phys. Lett. B 334, 18 (1994); Phys. Lett. A 583, 807c (1995); 608, 63 (1996); Nucl. Phys. A 691, 599 (2001); 693, 32 (2001); 709, 60 (2002). L. Chulkov et al., Nucl. Phys. A 603, 219 (1996). N. Aissaoui et al., Phys. Rev. C 60, 034614 (1999). I. Licot et al., Phys. Rev. C 56, 250 (1997). F. Hubert et al., Ann. Phys. (Paris) 5, 1 (1980). S. Kox et al., Phys. Rev. C 35, 1678 (1987). C.W. De Jager et al., At. Data Nucl. Data Tables 14, 479 (1974). H. De Vries et al., At. Data Nucl. Data Tables 36, 495 (1987). J.S. Wang et al., Nucl. Phys. A 691, 618 (2001). H. Scheit et al., Phys. Rev. Lett. 77, 3967 (1996).

Eur. Phys. J. A 25, s01, 227–230 (2005) DOI: 10.1140/epjad/i2005-06-115-0

EPJ A direct electronic only

Anomalous behaviour of matter radii of proton-rich Ga, Ge, As, Se and Br nuclei A. L´epine-Szily1,a , G.F. Lima1,2 , A.C.C. Villari3,4 , W. Mittig3 , R. Lichtenth¨ aler1 , M. Chartier5 , N.A. Orr6 , 6 7 3 8 9 J.C. Ang´elique , G. Audi , J.M. Casandjian , A. Cunsolo , C. Donzaud , A. Foti8 , A. Gillibert10 , D. Hirata11 , M. Lewitowicz3 , S. Lukyanov12 , M. MacCormick9 , D.J. Morrissey13 , A.N. Ostrowski3,14 , B.M. Sherrill13 , C. Stephan9 , T. Suomij¨arvi9 , L. Tassan-Got9 , D.J. Vieira15 , and J.M. Wouters15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Instituto de F´ısica-Universidade de S˜ ao Paulo, C.P. 66318, 05315-970 S˜ ao Paulo, Brazil FACENS-Faculdade de Engenharia de Sorocaba, C.P. 355, 18001-970 Sorocaba-SP, Brazil GANIL, IN2P3-CNRS/DSM-CEA, BP 55027, 14076 Caen Cedex 5, France Physics Division, Argonne National Laboratory, 9700 South Cass Ave., Argonne, IL 60439, USA University of Liverpool, Department of Physics, Liverpool, L69 7ZE, UK LPC, IN2P3-CNRS, ISMRA et Universit´e de Caen 14050 Caen Cedex, France CSNSM (IN2P3-CNRS&UPS), Bˆ atiment 108, 91405 Orsay Campus, France INFN, Corso Italia 57, 95129 Catania, Italy IPN Orsay, BP1, 91406 Orsay Cedex, France CEA/DSM/DAPNIA/SPhN, CEN Saclay, 91191 Gif-sur-Yvette, France Department of Physics and Astronomy, The Open University, Milton Keynes, MK7 6AA, UK FLNR, JINR, Dubna, P.O. Box 79, 101000 Moscow, Russia NSCL, Michigan State University, East Lansing, MI 48824-1321, USA Institut f¨ ur Physik, Universit¨ at Mainz, D-55099, Germany Los Alamos National Laboratory, Los Alamos, NM 87545, USA Received: 13 January 2005 / c Societ` Published online: 29 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Proton-rich isotopes of Ga, Ge, As, Se and Br had their total reaction cross-sections (σ R ) measured. Root-mean-squared matter radii were determined from Glauber model calculations, which reproduced the experimental σR values. For all isotopic series a decrease of the rrms with increasing neutron number and a correlation with deformation was observed. PACS. 21.10.Gv Mass and neutron distributions – 25.60.Dz Interaction and reaction cross-sections

1 Introduction Reaction cross-section measurements have been a very useful tool for the determination of nuclear matter radii. Since the discovery of extended neutron distributions [1], also called neutron halo, in light neutron dripline nuclei using reaction cross-section measurements, the method has gained even more interest. Effective rootmean-squared matter radii could be deduced from these measurements for unstable p and s-d shell nuclei [2]. The matter and charge radii of the Na and Ar isotopic chains were compared, and the increase of neutron skin with isospin was observed for the Na isotopes [3]. For the Ar isotopic chain [4] the increase of the proton skin thickness was observed with decreasing neutron number. Recent charge radius measurements [5] of the neutron-deficient a

Conference presenter; e-mail: [email protected]

Ti isotopes also show radial increase with decreasing neutron number. We have recently measured the root-meansquared matter radii of proton-rich isotopes of Ga, Ge, As, Se and Br [6]. The radii were obtained from the reaction cross-sections σR measured at intermediate energies (50–60 A MeV), where the reaction cross-section is higher and thus more sensitive to surface phenomena as skin or halo. In this contribution we compare the matter radii of the proton-rich isotopes with nuclear structure information about these nuclei and also with existing proton radius values of stable isotopes.

2 Experimental method The radioactive ions were produced at GANIL (Grand Acc´el´erateur National d’Ions Lourds, Caen, France), through the fragmentation of a 73 A MeV primary beam of 78 Kr, hitting a 90 mg/cm2 thick nat Ni target. Details

The European Physical Journal A Z=31 (Ga) Z=32 (Ge) Z=33 (As) 1/3 0.96A

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of the experiment were described in a recent paper [6]. The reaction products, a cocktail of many different secondary beams, were delivered after a first selection in the α-spectrometer, to the high-resolution energy-loss magnetic spectrometer SPEG. They were detected in the focal plane of SPEG by a cooled silicon telescope formed by three transmission detectors followed by a thick Si(Li) detector, where all ions of interest were stopped. Particle identification was obtained by combining the energy-loss measurement in the first Si detector with the time-of-flight information obtained between a fast micro-channel plate (MCP) detector located after the α-spectrometer and the second Si detector. The reaction target was the whole Si telescope behind the first thin ΔE detector, used for particle identification. The spectrum of the energy deposited in the target/detector system has a large peak corresponding to events that have not undergone any nuclear reaction and a low energy tail due to nuclear reactions with energy loss (Q ≤ 0) in any of the three Si target/detectors. We used two methods in our measurement: one based only on reactions in the second thin ΔE detector at a well defined energy E0 , thus allowing the determination of the reaction cross-section at this energy. The other method is based on reactions in any of the three Si target/detectors. In this case the energy integrated average reaction cross-section is determined.



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33

Z

Fig. 1. On the left panel the matter radii of different isotopic chains are compared as a function of N − Z, while on the right panel the matter radii of isotonic series are compared as a function of Z. On the lower panels the same comparison is performed for stable isotopes, where the usual A1/3 behaviour can be observed.

3 Data analysis The reaction cross-section was obtained from the reaction probability (ratio between the number of reaction events in the low energy tail and the total number of events in the energy spectrum) for the thin ΔE detector and also for the whole target/detector system. A phenomenological formula was developed by Kox et al. [7], which relates the reaction cross-section σR with a reduced strong absorption radius r0 . For stable nuclei the formula gives a good description of a wide variety of target and projectile systems at different energies with a constant value of r0 = 1.1 fm [7]. We have deduced two independent sets of values for the reduced strong absorption radii r0 using the reaction cross-sections measured in the thin ΔE detector and the energy integrated reaction cross-sections measured in the whole target/telescope system. The agreement between the r0 values obtained from both methods is good within the uncertainties, indicating that the Kox formula is also adequate to describe σR for these radioactive nuclei. In order to improve the accuracy, the weighted average values of the reduced strong absorption radii r0 were used together with the Kox formula to obtain reaction crosssections at energy E0 . 3.1 Glauber model calculations We used the Glauber theory in the optical limit to deduce r.m.s. matter radii from the measured σR reaction cross-

Fig. 2. Comparison between r.m.s matter radii together with the point proton r.m.s. radii calculated from r.m.s. charge radii for the Na and Ar isotopic chains and for our Se data, as a function of TZ .

sections. In this approximation the elementary N-N crosssection is folded over the static point proton and neutron density distributions of the projectile and target nuclei. The point proton distributions can be deduced from measured charge distributions, deconvoluting the proton size 2 2  − rchp , where or by using the formula [3] rp2  = rch the more recent value for the r.m.s. charge radius of the 2 1/2 = 0.8791(88) fm [8] was used. For the staproton rchp ble 28 Si target nucleus (N = Z) equal proton and neutron distributions were assumed and were determined by the procedure indicated above. However, for the proton-rich radioactive projectiles of this work neither the charge nor the proton or neutron distributions are known.

A. L´epine-Szily et al.: Anomalous behaviour of matter radii of proton-rich Ga, Ge, As, Se and Br nuclei

229

Fig. 3. Lower panel: The r.m.s. matter radii (full squares) of the Ga, Ge, As isotopes as a function of the neutron number N . We also show the r.m.s. proton radii (stars) of the stable isotopes. Upper panel: the excitation energies of the first 2 + or J = Jgs + 2 state as a function of N .

We adopted a procedure [3] with two extreme assumptions: In the first assumption the half-density proton radius Rp (obtained from charge density measurement of stable isotopes) is constant for the entire isotopic chain; the neutron radii Rn = Rp for TZ = 0, 1/2 isotopes and Rn increases with N 1/3 . The diffusenesses are free parameters to fit the reaction cross-sections. In the second assumption the diffusenesses (obtained from systematics or the measurement of stable isotopes) of the proton and neutron distributions are assumed equal, and Rp and Rn are varied independently in order to reproduce the reaction cross-sections. The Glauber model calculation was included in a search routine, where the parameters were varied between given limits and the reaction cross-section was calculated for every ensemble of parameters. The reaction cross-sections were reproduced in many searches with several, fairly different proton or neutron distributions. However, the r.m.s. matter radii, which were calculated from these different distributions using a simple 2  = (Z/A) rp2 +(N/A) rn2 , were averaging formula [3], rm very similar. The uncertainties in the r.m.s. matter radii were scaled by the uncertainties of the total reaction crosssections, adopting the same relative errors for both quantities. The r.m.s. matter radii obtained from the Glauber calculations are presented in fig. 1. On the left panel the matter radii of different isotopic chains are compared as a function of N − Z, while on the right panel the matter radii of isotonic series are compared as a function of Z. We also show on this figure, presented by dotted lines, the values of the nuclear radius given by the usual mass dependence R = 0.95A1/3 . A quite anomalous and surprising

behaviour can be observed on this figure: the matter radii of the proton-rich isotopes decrease with increasing neutron number N − Z. On the other hand, when protons are added, the matter radii increase much more rapidly than predicted by the A1/3 behaviour. The same comparison is also performed for stable isotopes, where the usual A1/3 behaviour can be observed. The r.m.s. matter radii obtained from the Glauber calculations are calculated from point distributions and before comparing them with measured r.m.s. charge distributions they should be folded with the nucleon matter distribution. However they can be directly compared to the r.m.s. point proton radii (assuming the proton as a point particle). We present on fig. 2 the comparison between r.m.s matter radii obtained from Glauber calculations together with the point proton r.m.s. radii calculated from r.m.s. charge radii for the Na and Ar isotopic chains [3, 4,8] and for our Se data, as a function of TZ . For all three cases and also for all our data (see figs. 3 and 4) the proton radii seem to be larger than the matter radii on the proton-rich side, even for quite high Z values, where no proton halo or skin is expected. This result persists for r.m.s. matter radii measured at very different energies. In order to better understand the correlation of the matter radii with neutron and proton number, we also compare them with deformation. Instead of using deformation parameters or quadrupole moments, not known for all isotopes of interest, we will compare with the excitation energy of the first 2+ state for even-even nuclei, or with the excitation energy of the first excited state with J = Jgs + 2 for odd-even nuclei. It is well known that, the

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Fig. 4. Lower panel: The r.m.s. matter radii (full squares) and the r.m.s. proton radii (stars) of the Se, Br and Kr isotopes as a function of the neutron number N . Upper panel: the excitation energies of the first 2 + or J = Jgs + 2 state as a function of N .

higher this excitation energy, the less collective or the less deformed is the nucleus. In figs. 3 and 4 we present three panels each, respectively the Ga, Ge and As isotopic series on fig. 3 and the Se, Br and Kr on fig. 4: on the lower part 2 1/2  r.m.s matter radii are shown, toof the panels the rm gether with the point proton r.m.s. radii calculated from r.m.s. charge radii, as a function of the neutron number N . The comparison is very revealing for the r.m.s. charge radii of the Kr isotopes [9]. The excitation energy presents a strong peak at the magic number N = 50, where the radii have a minimum. The increase in radii with decreasing N between N = 50 and 40 is correlated with the deformation effect, the excitation energies decrease and the radii increase, the maximum of deformation ocurring for N = 40. For N ≤ 40 the excitation energies again increase and the radii decrease. Unfortunately, there is no overlap between the proton radii and matter radii for the Ga, Ge, As, Se and Br isotopic chains, however the proton radii (measured for stable isotopes) are larger and with the exception of Se, they follow the A1/3 behaviour. The matter radii seem to be strongly correlated with deformations mainly for the Ga, Ge and Se isotopic chains. They present a strong minimum at the N values (respectively N = 37, 37 and 38), where the excitation energies present a strong maximum. For lower N values the excitation energies decrease very little (Ga, Ge) or even increase (Se), while the radii increase strongly. Thus this increase in radial extension for the very proton-rich isotopes cannot be attributed to an increase in deformation.

4 Conclusion In summary, we have measured the reaction cross-sections (σR ) of proton-rich nuclides of the Ga, Ge, As, Se and Br isotopic chains. We used Glauber model calculations to obtain r.m.s. matter radii from the measured reaction cross-sections. A clear correlation of the total r.m.s. matter radii with neutron number N and with proton number Z was verified. The radii decrease with increasing N , and increase strongly with increasing Z. Around N = 37, 38 the Ga, Ge and Se isotopic chains present a maximum in excitation energy and thus a minimum in deformation, which is correlated with a minimum in the matter radii. For lower N values the excitation energies decrease very little (Ga, Ge) or even increase (Se), while the radii increase strongly as was also observed in the Ti isotopes. This can possibly indicate the presence of a proton skin. A.C.C.V. acknowledges partial support by the US DOE, Off. Nucl. Phys, contract W-31-109-ENG-38.

References 1. I. Tanihata et al., Phys. Lett. B 160, 380 (1985). 2. A. Ozawa, T. Suzuki, I. Tanihata, Nucl. Phys. A 693, 32 (2001). 3. T. Suzuki et al., Phys. Rev. Lett. 75, 3241 (1995). 4. A. Ozawa et al., Nucl. Phys. A 709, 60 (2002). 5. Yu.P. Gangrsky et al., J. Phys. G 30, 1089 (2004). 6. G.F. Lima et al., Nucl. Phys. A 735, 303 (2004). 7. S. Kox et al., Phys. Rev. C 35, 1678 (1987). 8. I. Angeli, At. Data Nucl. Data Tables 87, 185 (2004). 9. M. Keim et al., Nucl. Phys. A 586, 219 (1995).

4 Reactions 4.1 Fusion

Eur. Phys. J. A 25, s01, 233–238 (2005) DOI: 10.1140/epjad/i2005-06-118-9

EPJ A direct electronic only

Fusion studies with RIBs W. Lovelanda Oregon State University, Corvallis, OR 97331-4501, USA Received: 12 September 2004 / c Societ` Published online: 29 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Recent developments in fusion studies with radioactive beams are reviewed critically from the perspective of an experimentalist. Typical available radioactive beam intensities and purities are shown along with the methods used to study evaporation residues and fission fragments. The fusion of halo and other loosely bound nuclei, i.e., 6 He, 11 Be, 17 F, is discussed. Fusion studies with intermediate mass beams such as 29 Al and 38 S are reviewed. Recent studies with n-rich fission fragments such as 132 Sn are shown. A discussion of fusion hindrance is presented and the use of radioactive beams in studying heavy nuclei is examined. PACS. 28.52.-s Fusion reactors – 25.70.Jj Fusion and fusion-fission reactions

1 Introduction Despite many years of study, fusion at energies near the Coulomb barrier is interesting to study because of the possibility of observing large enhancements in sub-barrier reactions that are related to nuclear structure and dynamics. These processes have been described as “coupling assisted tunneling”. Studies with radioactive ion beams (RIBs) are especially interesting due to the unusual situations posed in fusion studies with halo nuclei (with their large radii that might enhance fusion and their weakly bound valence nucleons which may produce breakup). Also fusion studies with very n-rich RIBs may allow us to study neutron “flow” or transfer. I also include, in this review, fusion studies with radioactive targets (RTs). These RT studies represent a high luminosity extension of the RIB studies and in the heaviest nuclei, offer us the opportunity to study fusion phenomena under the influence of large Coulomb forces with a resulting complex dynamics. This review will be cursory and the reader is encouraged to look at more extensive reviews for details [1,2,3, 4].

2 Experimental tools In table 1, I show typical intensities of radioactive beams at Coulomb barrier (208 Pb) energies used in current studies of fusion. The beam intensities range from 103 –106 particle/s. These low beam intensities preclude the usual “distribution of barriers” measurements [1] that typically require measurement of fusion cross sections to within 1% a

e-mail: [email protected]

Table 1. RIB intensities.

Projectile

Intensity (p/s)

Facility

6

105 –5 × 106 4 × 104 104 1.5 × 106 5 × 103 4 × 103 5 × 104

Notre Dame RIKEN ISAC2 ORNL MSU MSU ORNL

He Be 11 Li 17 F 38 S 46 Ar 132 Sn 11

uncertainty in 1–2 MeV steps in excitation energy. Similarly the use of sweepers and other low efficiency experimental devices to detect evaporation residues is precluded. In all studies with RIBs, the issue of beam purity must be addressed. In my experience at a PF facility, MSU [5], or an ISOL facility, ORNL [6], beam contaminants of 10% of the total beam intensity can occur and must be tagged as part of a beam tagging system or tolerated because their reactions do not interfere with the primary measurement. In fig. 1, I show a typical plot of time of flight vs. energy for a near barrier 38 S beam at MSU showing a 10% contamination that was removed by tagging. A non-trivial aspect of RIB experiments is the so-called “misery coefficient”, i.e., the ratio of (number of hours spent waiting for beam due to accelerator problems)/(number of hours of useful beam on target). Regretably this quantity may significantly exceed unity. In detecting the products of fusion reactions, the most definitive quantity to be measured is the evaporation residue (EVR) production cross section as it is an unambiguous signature of fusion. For studies involving the

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Fig. 1. Time of flight vs. energy for 38 S beam and impurities. The main peak at an energy of 260 MeV represents the 38 S beam, while the other peaks are those of contaminant beams. From Zyromski [5].

Fig. 3. Summary of theoretical predictions for the fusion excitation function for the 11 Li + 208 Pb reaction. From [9].

arise in inverse kinematics with n-rich fission fragment beams, especially if one wants to separate fusion-fission from quasifission and/or deep inelastic scattering [8].

3 Loosely bound nuclei

Fig. 2. Energy loss of beam and EVRs in two ion chamber segments. From Liang [6].

use of Pb or Bi targets, one can make the targets thick enough to stop the EVRs and detect their characteristic alpha-decay with the beam off. Shapira et al. [7] have constructed a high quality ion chamber that allows detection of evaporation residues emerging at zero degrees in a sea of scattered and direct beam particles (fig. 2). In some studies of fusion leading to heavier ERs, one chooses to detect fission fragments. They are relatively easy to detect with high efficiency and distinguish from scattered beam in asymmetric reactions in normal kinematics. Problems

In studying the fusion of halo nuclei or other loosely bound nuclei, one is trying to assess the relative effects of any fusion enhancement due to the larger radii or any decrease in fusion due to projectile breakup. For the “Rosetta Stone” of such reactions, 11 Li + 208 Pb, there is a remarkable disagreement among theorists [9] as to what will happen, with estimates of the fusion cross section varying by several orders of magnitude at near barrier energies (fig. 3). The 6 He + 209 Bi reaction has been extensively studied by Kolata and co-workers [10, 11, 12,13,14, 15,16,17]. The fusion cross section for 6 He+ 209 Bi is substantially enhanced at sub-barrier energies compared to the 4 He+209 Bi reaction and reduced above the barrier (fig. 4). A similar result is seen for the 4,6 He + 238 U reaction [18,19] if one takes into account non complete fusion-fission reactions above the barrier. Alamanos et al. [20] were able to reproduce the excitation functions for these reactions using a coupled channels calculation where breakup of the 6 He projectile was simulated by reducing the real part of the entrance channel optical potential. Breakup processes were identified by direct detection of the incomplete fusion products by Dasgupta et al. [21] in the 6,7 Li + 209 Bi reaction resulting in a suppression of complete fusion by 66–74%. For the reaction of the halo nucleus 11 Be with 209 Bi a complication arises in that the stable nucleus 9 Be used

W. Loveland: Fusion studies with RIBs

Fig. 6. Reduced excitation function for Zyromski [5].

235

32,38

S + 181 Ta. From

Fig. 4. Fusion excitation functions for loosely bound nuclei. The open circles indicate the RIB data while the closed circles indicate the stable beam data. From Alamanos [20].

Fig. 7. Reduced excitation function for From Watanabe [26].

Fig. 5. Measured excitation functions for the reaction [22, 23].

9,10,11

Be + 209 Bi

for comparison with the radioactive beam is very fragile itself, being one neutron outside of a 8 Be core and being deformed. The experimental data [22,23] show similar fusion excitation functions for the 9,10,11 Be + 209 Bi reaction, with no sub-barrier enhancement with 11 Be (fig. 5). (This is somewhat surprising given the halo structure of 11 Be and maybe due to a partial cancellation of enhancement and breakup effects.) Detailed calculations of the 11 Be fusion excitation functions considering breakup processes [20] do reproduce the observed cross sections. The interaction of the single proton halo nucleus 17 F with 208 Pb was studied by Rehm et al. [24] who showed the excitation functions with 17 F and 19 F reactions to be identical when scaled by the differing reaction barriers. Breakup processes were deduced to be small, a conclusion verifed in a subsequent measurement by Liang et al. [25]. In summary of the data with light loosely bound nuclei,

27,28,29

Al +

197

Au.

while there are experimental and theoretical points to be clarified, one concludes that, in the most well-studied system, there is fusion enhancement below the barrier due to couplings to transfer channels as well as bound states and suppression of fusion above the barrier due to breakup.

4 Intermediate mass neutron-rich nuclei Zyromski et al. [5] found no fusion enhancement, other than the expected lowering of the fusion barrier for the nrich 38 S, when comparing the fusion excitation functions of 32,38 S with 181 Ta (fig. 6). These measurements did not extend below the fusion barrier. In a similar study of the 27,28,29 Al + 197 Au reaction, Watanabe et al. [26] were able to make sub-barrier measurements. They also found that a reduced excitation function plot for the three systems studied showed no differences, apart from the expected barrier shift with the n-rich projectiles (fig. 7). Coupled channel calculations were not able to reproduce the subbarrier cross sections, but the use of the Stelson model [27]

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Fig. 9. Reduced excitation functions for 112–132 Sn+64 Ni. From Liang [6].

Fig. 8. Comparison of the measured fusion excitation functions with Stelson model calculations. The dashed lines show the barrier distributions, the vertical solid lines those calculated in CCDEF. From [26].

to simulate neutron transfer processes was shown to reproduce the 27,28,29 Al + 197 Au and 38 S + 181 Ta data (fig. 8). (The Stelson model assumes a flat distribution of barriers and introduces the concept of an isospin dependent neutron flow in the collisions proceeding through neck formation in fusion.) In summary, the data on the fusion of intermediate mass, n-rich projectiles shows no evidence for unusual fusion enhancements apart from the expected barrier shifts, but does require neutron transfer or flow to explain the sub-barrier cross sections.

5 Heavy neutron-rich fission fragments Liang et al. [6] studied the fusion of the n-rich fission fragment 132 Sn with 64 Ni in measurements of EVRs that went below the fusion barrier. When compared with previous measurements [28] of the fusion excitation functions for the 112–124 Sn + 64 Ni reaction, a substantial subbarrier fusion enhancement was observed that could not be explained by a simple shift of the fusion barriers with increasing isospin (fig. 9). Coupled channel calculations could not reproduce the 132 Sn excitation functions below the barrier although the inclusion of n-transfer channels did substantially improve the fit. A possibly relevant observation is that Wang et al. [29] were able to describe a similar situation in the 40,48 Ca + 90,96 Zr reaction using

Fig. 10. Schematic illustration of the energies and reaction types involved in fusion hindrance. From Bjørnholm and Swiatecki [30].

QMD calculations that included dynamical isospin effects on fusion. Extensions of these measurements to measure the fission exit channel in the 132 Sn + 64 Ni reaction and to study flow effects in the 134 Sn + 64 Ni reaction are underway [7,8].

6 Fusion hindrance Z1 Z2 ≥ 1600 When the charge product of the fusing nuclei Z1 Z2 is greater than 1600, one observes fusion hindrance with the “missing” cross section going into quasifission (“fast fission”). This effect increases in importance with increasing values of Z1 Z2 and is a very important limiting factor in fusion reactions to produce heavy nuclei. This effect was explained by Swiatecki and co-workers [30] in terms of the energetics of the collision (fig. 10). A certain amount of energy is needed to have the reacting nuclei come into contact (the “normal” reaction threshold) where neck growth between the nuclei starts. This results in elastic and quasielastic scattering and in some fusion models, fusion is defined as reactions proceeding beyond this point. An additional “extra push” energy is required to get the colliding nuclei to pass a conditional mass asymmetric saddle point, giving rise to deep inelastic events. Another energy, “the extra-extra push energy”, is required to drive the system from the contact configuration inside the fission

W. Loveland: Fusion studies with RIBs

Fig. 11. DNS model calculations of PCN .

saddle point where true complete fusion occurs. Systems that pass the conditional mass-asymmetric saddle but do not go inside the fission saddle point result in quasifission reactions. Reaction studies where Z1 Z2 ≥ 1600 in which one detects EVRs show an upward shift in fusion barrier (fusion hindrance) compared to unhindred systems. There is no doubt about the occurrence of fusion hindrance in heavy systems but there are difficulties in characterizing it from both experimental and theoretical viewpoints. Two differing, mutually exclusive theoretical approaches have been used. In dynamical approaches [31] the reacting nuclei form a mononucleus which evolves past the fission saddle point (or fissions) that largely neglects the shell structure of the nascent fragments. An alternative approach [32] using the di-nuclear system (DNS) model proposes the reacting nuclei retain their identities well into the collision process with the reaction proceeding by nucleon transfer until the lighter nucleus transfers all of its nucleons to the heavier nucleus (compound nucleus formation) or re-separation before that happens. (Zagrebaev [33] has suggested a hybrid model.) The underlying problem is the data used to check these predictions largely consists of EVR measurements in heavy nuclei where σfusion = σcapture PCN Wsur ,

(1)

where σcapture is the capture cross section (touching configuration), PCN represents the probability that the nucleus will evolve from the contact configuration to inside the fission saddle point and Wsur is the survival probability (against fission) of any compound nuclei that are formed. It is difficult to unambiguously untangle PCN and Wsur . (PCN is expected [32] to vary from 1 to 10−7 as Z1 Z2 varies from 1200 to 2800 (fig. 11).) As a consequence, Zagrebaev et al. [34] have concluded that the fusion cross sections for reactions forming elements with Z ≥ 112 can be estimated only within two orders of magnitude, at best. Nonetheless semiempirical treatments of PCN exist with self-consistent evaluations of Wsur that allow one to describe heavy element formation cross sections for Z ≤ 112 within an order of magnitude [35,36]. For example about 20 years

237

Fig. 12. Comparison of the Armbruster formalism with the measured EVR cross sections for the synthesis of elements 102– 112.

ago, Armbruster [35] suggested a semi-empirical equation that defined PCN as PCN (E, J) = 0.5[exp(c(xeff − xthr ))],

(2)

where the coefficient c has the value of 106 and the constant xthr is 0.72 for actinide-based reactions and 0.81 for Pb or Bi targets. This equation describes the fusion reactions used to synthesize heavy nuclei (fig. 12). The experimental signatures of quasifission involve an enhanced angular anisotropy [37] and large widths of the mass distributions. In systems where quasifission is the dominant process, complete fusion-fission events may be isolated as symmetric mass splits although that identification is not unambiguous. Measurements of the properties of quasifission, while interesting and informative in characterizing models of fusion, are unlikely to be executed with sufficient accuracy/precision to allow deduction of PCN when that number  10−2 .

7 RIBs and heavy nuclei The use of neutron-rich RIBs to synthesize new heavy nuclei is a topic of interest to the nuclear science community. There are interesting opportunities for the use of neutron-rich RIBs, particularly in connection with the RIA project [38]. However there are some critical limiting factors. For production of new heavy nuclei in fusion reactions with ∼ 1 pb cross sections requires beam intensities ≥ 1011 particles/s. That limits the radioactive projectile nuclei for a facility like RIA to be within 5–10 neutrons from stability. A more vexing, and as of yet, unresolved issue is that of the isospin dependence of fusion hindrance. Work done at GSI [39, 40] indicates the more neutron-rich projectiles show a greater fusion hindrance (larger extraextra push energies) than the more neutron-poor projectiles. For example, in fig. 13, one sees the extra-extra push energies in the 124 Sn+ X Zr reactions increase with increasing neutron number. Work is underway to study fusion hindrance in the 132 Sn + 90,96 Zr reaction [41].

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Fig. 13. Extra-extra push energies as a function of effective fissility. From Sahm [39].

8 Future developments Some areas of possible progress in the next few years might include a) the full development and use of fission fragment RIBs to study fusion that will allow the use of normal kinematics and a wider variety of fused systems b) the development and use of 11 Li beams at the fusion barrier of nuclei like 208 Pb to resolve the questions posed by fig. 3 and c) more sophisticated measurements of fusion with high efficiency auxiliary detectors, such as neutron and gamma-ray arrays, allowing the detailed study of breakup processes and the identification of individual evaporation residues. This work was supported in part by the U.S. Department of Energy, Office of High Energy and Nuclear Physics through Grant No. DE-FG06-97ER41026.

References 1. M. Dasgupta et al., Annu. Rev. Nucl. Part. Sci. 48, 401 (1998). 2. C. Signorini, Nucl. Phys. A 693, 190 (2001). 3. R. Vandenbosch, http://livingtextbook.oregonstate. edu/advanmat/nureactn/vandenbo.html.

4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38.

39. 40. 41.

V.I. Zagrebaev, http://nrv.jinr.dubna.ru/nrv. K.E. Zyromski et al., Phys. Rev. C 63, 024615 (2001). J.F. Liang et al., Phys. Rev. Lett. 91, 152701 (2003). D. Shapira, these proceeding. J.F. Liang, these proceedings. C. Signorini, Nucl. Phys. A 616, 262c (1997). J.J. Kolata et al., Phys. Rev. C 57, R6 (1998). P.A. De Young et al., Phys. Rev. C 58, 3442 (1998). J.J. Kolata et al., Phys. Rev. Lett. 81, 4580 (1998). P.A. De Young et al., Phys. Rev. C 62, 047601 (2000). E.F. Aguilera et al., Phys. Rev. Lett. 84, 5058 (2000). J.J. Kolata, Phys. Rev. C 63, 061604(R) (2001). D. Lizcano et al., Rev. Mex. Fis. 47, 78 (2001); 46, 116 (2000). J.J. Kolata et al., Eur. Phys. J. A 13, 117 (2002). M. Trotta et al., Phys. Rev. Lett. 84, 2342 (2000). J.L. Sida et al., Nucl. Phys. A 685, 51c (2001). N. Alamanos et al., Phys. Rev. C 65, 054606 (2002). M. Dasgupta et al., Phys. Rev. C 66, 041602(R) (2002). C. Signorini et al., Eur. Phys. J. A 2, 227 (1998). C. Signorini et al., Nucl. Phys. A 735, 329 (2004). E. Rehm et al., Phys. Rev. Lett. 81, 3431 (1998). J.F. Liang et al., Phys. Rev. Lett. 67, 044603 (2003). Y.X. Watanabe et al., Eur. Phys. J. A 10, 373 (2001). P.H. Stelson et al., Phys. Rev. C 41, 1584 (1990). W.S. Freeman et al., Phys. Rev. Lett. 50, 1563 (1983). N. Wang et al., Phys. Rev. C 67, 024604 (2003). S. Bjørnholm, W.J. Swiatecki, Nucl. Phys. A 391, 471 (1982). Y. Abe et al., Nucl. Phys. A 722, 241c (2003). G.G. Adamian et al., Phys. Rev. C 68, 034601 (2003). V. Zagrebaev, Phys. Rev. C 64, 034606 (2001). V.I. Zagrebaev et al., Phys. Rev. C 65, 014601 (2001). P. Armbruster, Annu. Rev. Nucl. Sci. 35, 135 (1985). W.J. Swiatecki et al., Acta Phys. Pol. B 34, 2049 (2002). B.B. Back, Phys. Rev. C 31, 2104 (1985). W. Loveland, in Proceedings of the Sixth International Conference on Radioactive Nuclear Beams (RNB6), Argonne, Illinois, USA, 22-26 September 2003, Nucl. Phys. A 746, 108 (2004). C.C. Sahm et al., Nucl. Phys. A 441, 316 (1985). A.B. Quint et al., Z. Phys. A 346, 119 (1993). A.M. Vinodkumar et al., private communication.

Eur. Phys. J. A 25, s01, 239–240 (2005) DOI: 10.1140/epjad/i2005-06-117-x

EPJ A direct electronic only

Sub-barrier fusion induced by neutron-rich radioactive

132

Sn

J.F. Liang1,a , D. Shapira1 , C.J. Gross1 , R.L. Varner1 , H. Amro2 , J.R. Beene1 , J.D. Bierman3 , A.L. Caraley4 , A. Galindo-Uribarri1 , J. Gomez del Campo1 , P.A. Hausladen1 , K.L. Jones5 , J.J. Kolata2 , Y. Larochelle6 , W. Loveland7 , P.E. Mueller1 , D. Peterson7 , D.C. Radford1 , and D.W. Stracener1 1 2 3 4 5 6 7

Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA b Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA Physics Department AD51, Gonzaga University, Spokane, WA 99258, USA Department of Physics, State University of New York at Oswego, Oswego NY 13126, USA Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854, USA Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37966, USA Department of Chemistry, Oregon State University, Corvallis, OR 97331, USA Received: 15 January 2005 / c Societ` Published online: 11 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Evaporation residue cross-sections measured with short-lived 132 Sn on 64 Ni at energies near and below the Coulomb barrier were found to be enhanced as compared to those measured with stable Sn isotopes on 64 Ni. Subsequent measurements of fission following fusion of 132 Sn with 64 Ni and extending the measurement of evaporation residues to higher energies were carried out. PACS. 25.60.-t Reactions induced by unstable nuclei – 25.60.Pj Fusion reactions – 25.70.-z Low and intermediate energy heavy-ion reactions – 25.70.Jj Fusion and fusion-fission reactions

1 Introduction Study of fusion induced by radioactive nuclei is a topic of current interest [1]. We have measured evaporation residue cross-sections using neutron-rich radioactive 132 Sn beams incident on a 64 Ni target in the vicinity of the Coulomb barrier. This is the first experiment using accelerated 132 Sn beams to study nuclear reaction mechanisms. The average beam intensity was 2×104 particles per second and the smallest cross-section measured was less than 5 mb. A large sub-barrier fusion enhancement was observed compared to evaporation residue cross-sections for 64 Ni on stable even Sn isotopes [2]. The enhancement cannot be accounted for by a simple barrier shift due to the change in nuclear sizes [3]. Coupled-channels calculations including inelastic excitation and neutron transfer with input parameters obtained from stable Sn and Ni reactions underpredicted the measured cross-sections at low energies where the evaporation residue cross-sections were taken as fusion cross-sections [4]. In the previous measurement, the compound nucleus decays by particle evaporation at energies below the barrier. At energies near the barrier fission starts to compete a

Conference presenter; e-mail: [email protected] b Research at the Oak Ridge National Laboratory is supported by the U.S. Department of Energy under contract DEAC05-00OR22725 with UT-Battelle, LLC.

with particle evaporation. In order to study fusion it is important to measure fission cross-sections.

2 Experimental method The measurement was carried out at the Holifield Radioactive Ion Beam Facility at the Oak Ridge National Laboratory. The secondary 132 Sn was produced by the ISOL technique and accelerated to energies from 530 to 620 MeV to bombard a 64 Ni target. The evaporation residues were detected in the apparatus described in ref. [5]. The fission fragments were detected in a large area annular Si strip detector. The detector has 48 annular strips and 16 radial sectors which cover an angular range of 15◦ to 40◦ . Figure 1 presents the setup of the measurement.

3 Data reduction The procedures for obtaining the evaporation residue cross-sections are described in ref. [3, 5]. The fission fragments were identified by requiring a coincidence hit on the Si strip detector and from the kinematics. Figure 2 displays the calculated energy as a function of scattering

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defining beam time−of−flight Fig. 1. Apparatus for measuring evaporation residues and fission fragments (not drawn in scale).

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Fig. 2. Calculated particle energy as a function of angle in 560 MeV 132 Sn on 64 Ni. The elastically scattered Sn and Ni are shown by dashed and dotted curves, respectively, and the fission fragments are shown by the solid curve.

References 1. 2. 3. 4.

W. Loveland, these proceedings. W.S. Freeman et al., Phys. Rev. Lett. 50, 1563 (1983). J.F. Liang et al., Phys. Rev. Lett. 91, 152701 (2003). J.F. Liang et al., Prog. Theor. Phys. Supp. 154, 106 (2004). 5. D. Shapira et al., these proceedings.

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angle for fission fragments and elastically scattered particles. This can be compared with the coincidence data taken by the strip detector at 560 MeV as shown in the bottom panel of fig. 3. The top panel of fig. 3 presents results of Monte Carlo simulations for coincident events in the strip detector from the same reaction. The fission fragments are located in the marked regions and the elastically scattered Ni and Sn events are shown by the labels. As can be seen, the fission fragments can be distinguished from particles originated from other reactions. Detailed analysis of the data is underway.

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Fig. 3. Top panel: results of Monte Carlo simulation for particles from 560 MeV 132 Sn on 64 Ni detected in coincidence in the strip detector. Bottom panel: coincidence data from the same reaction measured by the strip detector. The fission fragments are shown in the marked area.

Eur. Phys. J. A 25, s01, 241–242 (2005) DOI: 10.1140/epjad/i2005-06-190-1

EPJ A direct electronic only

Measurement of evaporation residue cross sections from reactions with radioactive neutron-rich beams D. Shapira1,a , J.F. Liang1 , C.J. Gross1 , R.L. Varner1 , J.R. Beene1 , A. Galindo-Uribarri1 , J. Gomez Del Campo1 , P.E. Mueller1 , D.W. Stracener1 , P.A. Hausladen1 , C. Harlin2 , J.J. Kolata3 , H. Amro3 , W. Loveland4 , K.L. Jones5 , J.D. Bierman6 , and A.L. Caraley7 1 2 3 4 5 6 7

Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Department of Physics, University of Surrey, Guildford GU2 7XH, UK Physics Department University of Notre Dame, Notre Dame, IN 46556-5670, USA Chemistry Department, Oregon State University, Corvallis, OR 97331, USA Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08856, USA Physics Department AD51, Gonzaga University, Spokane, WA 99258-0051, USA Department of Physics, SUNY at Oswego, Oswego, NY 13126, USA Received: 14 February 2005 / c Societ` Published online: 26 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Evaporation residue cross sections for 132 Sn, 134 Te and 124 Sn with 64 Ni were measured. A compact system to measure these cross sections to values as low as 1 mb is described and a sample of data acquired with this system is shown. PACS. 25.60.-t Reactions induced by unstable nuclei – 25.60.Pj Fusion reactions – 25.70.-z Low and intermediate energy heavy-ion reactions – 25.70.Jj Fusion and fusion-fission reactions

A diagram of the experimental setup used to study the evaporation residues from collisions of accelerated fission products from uranium produced at HRIBF [1] with a secondary 64 Ni target, is shown in fig. 1. The setup depicted allows beam rates of up to 105 counts/s (limited by the gas-filled ionization chamber). The efficiency for detecting evaporation residues is very high, especially under conditions where inverse kinematics are employed. The fast timing detectors allow us to apply a fast pre-trigger that selects events associated with particles slower than the beam (e.g. evaporation residues). These timing detectors also allow for continuous monitoring of beam intensity and the beam profile is monitored using the position signals from the third timing detector. Counting of incident beam particles and continuous monitoring of the beam position can yield accurate cross section data. A full description of this setup will appear in a forthcoming publication [2]. Figure 2 displays rescaled cross sections for 132 Sn and 124 Sn on 64 Ni. Part of the 132 Sn data shown here were measured in a separate experiment [3] with the same setup. The 124 Sn data were taken in a separate stable beam run, for comparison with data from ref. [4] as well as to extend these measurements to lower bombarding energy. Figure 3 contains similar data comparing evapa

Conference presenter; e-mail: [email protected]

oration residue cross sections for 134 Te + 64 Ni (A = 134 beam purity ≥ 95%) and for 124 Sn + 64 Ni. All cross section shown are plotted in a manner that removes any expected difference in cross section that are due to trivial variation in nuclear sizes and barrier heights (rescaled). The barrier height, Vb , used in these figures is the calculated barrier height of the combined nuclear [5] potential and the Coulomb potential of two charged spheres. The interaction radius, R, used in these figures is the radius corresponding to the top of the calculated interaction barrier (Vb ). The data in fig. 2 provide evidence for a large enhancement in the evaporation residue cross section of 132 Sn compared to the less neutron-rich 124 Sn case at energies below the Coulomb barrier. Note that for all the systems shown here fissilities are almost identical, and that fission competition is predicted by statistical model calculations to be very small at sub-barrier energies. Coupled-channel calculations which include coupling to inelastic excitation of target and projectile, twophonon excitation, mutual excitation and transfer of up to three neutrons describe, successfully, the 124 Sn + 64 Ni fusion cross sections [6] but could not reproduce the enhancement observed in the 132 Sn + 64 Ni system [7]. The 134 Te data in fig. 3 show a very different behavior. No enhancement of sub-barrier evaporation residue cross sections in 134 Te + 64 Ni is observed beyond what is seen

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in 124 Sn + 64 Ni. One could only speculate at this point whether the paucity of neutron transfer channels with positive Q-value is at play, or maybe fission is more important in 134 Te + 64 Ni after all. This work is supported by DOE contract DE-AC0500OR22725 with UT-Battelle. H.A. and J.J.K. are supported by NSF grant PHY02-44989. W.L. is supported by the USDOE grant No. DE-FG06-97ER41026.

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References 1. D. Stracener, Nucl. Instrum. Methods B 204, 42 (2003). 2. D. Shapira et al., A high efficiency compact setup to study evaporation residues formed in reactions induced by low intensity radioactive ion beams, to be published in Nucl. Instrum. Methods A. 3. J.F. Liang et al., Phys. Rev. Lett. 91, 152701 (2003). 4. W.S. Freeman et al., Phys. Rev. Lett. 50, 1563 (1983). 5. R. Bass, Phys. Rev. Lett. 39, 265 (1977). 6. H. Esbensen et al., Phys. Rev. C 57, 2401 (1998). 7. J.F. Liang et al., Prog. Theor. Phys., Suppl. No. 154, 106 (2004).

4 Reactions 4.2 Direct reactions

Eur. Phys. J. A 25, s01, 245–250 (2005) DOI: 10.1140/epjad/i2005-06-171-4

EPJ A direct electronic only

First experiments on transfer with radioactive beams using the TIARA array W.N. Catford1,a , R.C. Lemmon2 , M. Labiche3 , C.N. Timis1 , N.A. Orr4 , L. Caballero5 , R. Chapman3 , M. Chartier6 , M. Rejmund7 , H. Savajols7 , and the TIARA Collaboration 1 2 3 4 5 6 7

Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK Nuclear Structure Group, CCLRC Daresbury Laboratory, Daresbury, Warrington WA4 4AD, UK University of Paisley, Paisley, Scotland PA1 2BE, UK Laboratoire de Physique Corpusculaire, IN2P3-CNRS, ISMRA and Universit´e de Caen, F-14050 Caen, France Instituto de Fisica Corpuscular, CSIC-Universidad de Valencia, E-46071 Valencia, Spain Department of Physics, The University of Liverpool, Liverpool L69 7ZE, UK GANIL, BP 55027, 14076 Caen Cedex 5, France Received: 22 October 2004 / c Societ` Published online: 11 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Results from a study in inverse kinematics of the 24 Ne(d, pγ)25 Ne reaction, using a radioactive beam of 24 Ne from the SPIRAL facility at GANIL, are reported. First, a brief overview is given of several methods using radioactive beams to study the classic single-nucleon transfer reactions such as (d, p) or (d, t)/(d, 3 He), where the experimental design is strongly influenced by the extreme inverse kinematics. A promising approach to deliver good energy resolution is to combine a high geometrical efficiency for kinematically complete charged particle detection with a high efficiency array for gamma-ray detection. One of the first dedicated set-ups for this type of experiment is the TIARA silicon strip array combined with the EXOGAM segmented germanium array. Together they comprise a highly compact, position-sensitive particle array with 90% of 4π coverage, mounted inside a cubic arrangement of four segmented gamma-ray detectors in very close geometry with 67% of 4π active coverage. Using this setup, the structure of 25 Ne has been studied via the (d, p) reaction. A pure ISOL beam of 105 s−1 of 24 Ne at 10 MeV/A was provided by SPIRAL and bombarded a CD2 target of 1 mg/cm2 . The 25 Ne was detected at the focal plane of the VAMOS spectrometer where the direct beam was separated and intercepted. Reaction protons were detected in coincidence with little background. Four resolved peaks were recorded between E x = 0 and 4 MeV. The data confirm and extend the results from a multinucleon transfer study using the ( 13 C,14 O) reaction. Further information has been obtained using the energies of coincident gamma-rays. The reactions 24 Ne(d, dγ)24 Ne, 24 Ne(d, t)23 Ne and 24 Ne(d, 3 He)23 F were recorded simultaneously and analysis of these is also underway. PACS. 25.60.-t Reactions induced by unstable nuclei – 25.60.Je Transfer reactions – 27.30.+t Properties of specific nuclei listed by mass ranges: 20 ≤ A ≤ 38

1 Introduction Nucleon transfer reactions provide a valuable means to identify and study nuclear levels, and in particular to identify the levels that have a simple single-particle structure close to closed shells. Experiments using single-nucleon transfer become technically feasible with intensities of typically > 1000 or > 104 pps, depending on the experimental approach. The present work concentrates on light-ion– induced transfer, and in particular reactions such as (d, p) a

Conference presenter; e-mail: [email protected]

and (d, t) or (p, d) induced by hydrogen isotopes. The experiments are performed in inverse kinematics with a radioactive beam incident on hydrogen target nuclei. A major aim is to measure the angular distribution characterizing the transferred angular momentum, and this results in choosing to measure the light particles that come from the target. This, in turn, places a limit on the target thickness that is compatible with the desired energy resolution (of order 0.5 MeV). As discussed below, these various criteria have led to an approach using triple coincidences between the two charged products of the binary reaction, plus any de-excitation gamma-ray emitted by the heavy product.

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2 The experimental perspective The experimental design is determined largely by the properties of the extreme inverse kinematics [1,2]. A characteristic feature is that the light particles from reactions such as (d, t) or (p, d) —in which the radioactive beam loses a nucleon— are focussed to come within a cone of angles forward of typically 40◦ . In contrast, protons from (d, p) emerge at backward angles and typically require to be detected between 90◦ and 180◦ in the laboratory frame. The energies have a relatively minor dependence on the mass and velocity of the projectile, and thus a dedicated array with general utility can be envisioned. It can be remarked that there is some dependence that remains, on the beam velocity, which does have some experimental implications for detecting the light particles. Whilst the overall form of the velocity vector diagrams [2] is essentially independent of the beam mass or velocity, the size of the diagram scales with these quantities. With the notation of ref. [2],the velocities ve and vcm have lengths  MR /Me and 1/ MP /(q × MT ), respectively (where q is between 1.0 and 1.5 in most cases and the labels R, e, P and T refer to the heavy recoil, light ejectile, projectile and target). Since MP ≈ MR (because only one nucleon is transferred, and the projectile is assumed to have a large mass compared to √ the target) then the lengths of ve and vcm both scale as MP to a first approximation. Also, the unit of length  for the velocity vectors in this analysis is given [3] by 2qE cm /(MR + Me ) which is approximately proportional to (E/A)beam /MP assuming again that MP ≈ MR and that each of these masses is large compared to the light-particle masses. Combining these two length factors, the overall  scaling of the vector diagram varies approximately as (E/A)beam and hence the kinetic energies of backward or forward going light particles, or indeed the rate of energy increase with angle for elastically scattered particles near 90◦ , are roughly proportional to (E/A)beam . One of the earliest experiments of the type discussed here was a study of the (d, p) reaction on a 56 Ni projectile, for astrophysical interest [4]. The experimental set-up included a silicon array that covered the backward angular range that is important for (d, p) in inverse kinematics. The data from that experiment highlight the challenges faced by this type of work, in terms of limited statistics and resolution, but also they serve to demonstrate how a useful angular distribution can be obtained with only a limited number of counts. An alternative approach was used in a study of (p, d) induced by a 11 Be beam [5]. In this case, the angular information was obtained from the beam-like particle 10 Be as measured in a magnetic spectrometer. It was essential to tag reactions induced by the hydrogen rather than the carbon in the (CH2 ) target, using light-ion coincidences. A pure cryogenic target can avoid that problem but the coincidence is still required to avoid any ambiguity over the transfer reaction mechanism. In any case, a general feature of the kinematics is that the angular resolution required in the measurement of the beam-like particle be-

comes too demanding for beams that are somewhat heavier than beryllium. For this reason and others [6], in search of a more general technique, the method using triple coincidences (with gamma-rays) was selected for the present experiment and its related programme. A method that relies on triple coincidences places very demanding requirements on the efficiencies of each detection system. The TIARA array was constructed so as to achieve the maximum possible gamma-ray detection efficiency with the available detectors. Germanium clover detectors with additional electronic segmentation were chosen, where the segmentation was required so as to minimise the Doppler broadening introduced by the emitting nuclei, which have velocities essentially equal to that of the incident beam. At the same time, the idea was to have the capability of using quite intense radioactive beams up to 108 –109 pps, in which case gamma-ray detectors would need to be shielded from scattered beam, which can give subsequent gamma-rays from radioactive decay. These conflicting goals were achieved by using a very close geometry for the gamma-ray detectors and an open-ended barrel around the target for the charged particles. In turn, this placed strong limitations on the size and hence complexity of the charged particle detection system, and in the first version of TIARA there is no ΔE-E particle identification for the light particles, so reliance is placed instead on identifying the beam-like particles. Other recent light-ion–induced single-nucleon transfer studies, performed in inverse kinematics with radioactive beams, are reported at this conference. For example, several (d, p) studies using a similar technique but without gamma-ray detection are reported using beams of 82 Ge and 84 Se [7] and also 124 Sn [8]. A study of (α, t) with a beam of 22 O is also reported, using the method of measuring just the beam-like particle [9].

3 Experimental details The first radioactive beam experiment using the TIARA array was performed at GANIL using a pure 24 Ne beam of 1×105 pps, provided by the SPIRAL facility. The beam was limited in emittance to 8π mm.mrad so as to restrict the size of the beam spot on target to approximately 1.5–2.0 mm diameter. No beam tracking was employed. The energy was 10.6 MeV/A. The target was deuterated polythene (CD2 )n with a thickness of 1.0 mg/cm2 and this thickness was the limiting factor in the excitation energy resolution that was achieved using just the charged particles. A summary of the experimental setup is shown in fig. 1. The TIARA array [10] in its present configuration [11] has the active area of silicon strip detectors spanning 85% of 4π. The detectors have intrinsic thicknesses (without allowing for angle of incidence) of 400–500 μm. The main feature is an octagonal shaped barrel made from 8 silicon detectors, each approximately 100 mm in length and comprising 4 resistive strips, position sensitive along the beam direction. This barrel by itself spans approximately 80% of 4π, from 35◦ to 145◦ . Further, it has a radius of

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only 35 mm and there is a reduced radius for the vacuum chamber in the region of the barrel so that gamma-ray detectors can be placed as close as 50 mm from the target to maximize their efficiency. Beam and reaction particles coming forward of 4◦ relative to the beam escaped the most forward part of TIARA and entered into the VAMOS spectrometer [12] which was operated in momentum-dispersive mode. The direct beam was intercepted with an active scintillator finger mounted in front of the standard focal plane detector system. The kinematics were such that the finger did not intercept any of the 25 Ne products from (d, p) reactions for which the proton emerged at a laboratory angle of 100◦ or greater. Reaction products from the reactions (d, t) and (d, 3 He), leading to 23 Ne and 23 F respectively, were on the focal plane and well clear of the finger. At the focal plane, the angle and position were measured in two dimensions, and the energy loss, total energy and time of flight were also measured for each ion. Gamma-rays were recorded using four detectors from the EXOGAM array [13,14] mounted so that their square front faces almost touched, forming four sides of a cube. This put the front faces at 50 mm from the target. For the 24 Ne experiment, the segmentation information from the detectors was not available and only the central contact energy signal in each clover leaf was recorded. Segmentation would reduce the energy resolution, which is limited by Doppler broadening, by a factor of two. In the present work, this resolution was 50 keV (fwhm) at 1 MeV. The full energy peak efficiency in this configuration is approximately 17% at 1.332 MeV, but the effective efficiency was 1 or 2 percent in the present experiment due to an intermittent discriminator fault. The whole of the TIARA and EXOGAM array response has been modelled in a simulation using GEANT4 [15], including a verification of the algorithm employed for add-back of EXOGAM signals in the very close TIARA geometry. Here, “add-back” refers to the summing in software analysis of the two energy signals obtained when two leaves of a clover are triggered in the same event, and also the assignment of the primary in-

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teraction for Doppler calculations. Such events comprised approximately 20% of the data.

4 Results When a two-dimensional plot is made of particle energies (recorded in TIARA) as a function of scattering angle, gated on the requirement that a beam-like particle reaches the focal plane, it is found to be free of any significant background —especially backward of 90◦ . Such a plot (omitted due to space) highlights the loci in the backward hemisphere corresponding to different states populated in (d, p). The overall spectrum is dominated by the elastic scattering of deuterons from the target. This produces a kinematic line that rises in energy rapidly with decreasing angle, just forward of 90◦ . The kinematic loci from (d, t) reactions are discernible in the forward annular detectors and in the forward part of the barrel. The data for each of these other channels will require proper particle identification using the VAMOS focal plane parameters to identify the beam-like particles. This work is still in progress. The analysis reported here requires simply that there is a particle at the focal plane, in coincidence with TIARA. The angular range of interest for the (d, p) reaction, backward of 100◦ in the laboratory frame, corresponds simultaneously to the angles for which the proton is completely stopped by the barrel detector and the coincident particle at the focal plane avoids the active beam stopper. From the calibrated energy and angle of the detected particles in TIARA, the excitation energy of the corresponding 25 Ne nucleus can be calculated. Figure 2 shows the spectrum corresponding to events recorded in the annular array at backward angles, behind the barrel. The resolution in excitation energy is 500 keV (fwhm). The

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data from the barrel are consistent in terms of the peak centroid positions, but show a poorer average resolution of 1100 keV. An analysis of the contributions to the resolution using the approach of ref. [6] is consistent with these results and reveals that two angle-dependent terms become important and dominate the resolution in the barrel region. These terms arise firstly from the kinematics, whereby the calculated excitation energy is more critically dependent on the angle in the region closer to 90◦ , and secondly from the effects of multiple angular scattering which is accentuated when the particle exits from the target through more material, at a shallow angle to the surface. Proton angular distributions dσ/dΩ were extracted for the d(24 Ne, p)25 Ne reaction by selecting events in the ground-state peak and in the peak shown at an excitation energy of 2 MeV in fig. 2. Figure 3 shows these angular distributions, together with preliminary reaction calculations employing global optical potential parameters and the Johnson-Soper prescription [16] to account for deuteron breakup to the continuum. The transferred angular momentum for the ground state is assigned as  = 0, which implies a spin and parity of 1/2+ . For the group at 2 MeV, the angular distribution is clearly different. It shows quite good agreement with the calculation for  = 2 and this implies a state or states with spin and parity (3/2, 5/2)+ . Angular distributions for the incompletely resolved peaks at 3.3 and 4.0 MeV are still under analysis.

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The events in fig. 2 corresponding to the peak spanning the ground-state region are all removed from the spectrum when a coincidence with gamma-rays is required. Thus, the peak corresponds simply to population of the ground state. The remainder of the peaks in fig. 2 are in coincidence with gamma-rays. Figure 4 shows the summed spectrum

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Fig. 5. Energy levels in 25 Ne and their excitation energies in keV. The column “other reactions” refers to previous work (see text). Shell model results are labelled with spin and parity and are from ref. [17] with selected spectroscopic factors as calculated in ref. [18]. The present results show the observed gamma-ray transitions and an indication of the effective fwhm resolution in energy.

of these gamma-rays for all of the states between 2 and 5 MeV in 25 Ne. The gamma-ray energy for each event has been corrected for the Doppler shift imparted by the 25 Ne, which always has a velocity of magnitude approximately 0.15c and is always aligned within two degrees of the beam direction. The precise value of β cos θγ  required for the Doppler correction can be inferred from the data by comparing spectra from the elements of the clover situated forward and backward of the target position. In addition, an add-back procedure has been applied, as discussed in sect. 3. The energy resolution was measured to be 100 keV (fwhm) at 1.9 MeV using data from the d(24 Ne, d )24 Ne∗ reaction. This is consistent with the limitation imposed by Doppler broadening due to the finite size of each Ge detector crystal. The gamma-ray energy spectrum is displayed in fig. 4 and shows several clear peaks. The origin of the general increase in counts below 0.5 MeV is still being investigated. At higher energies, the spectrum abruptly drops to zero above about 4 MeV. A maximum gamma-ray energy of 4.03 MeV is inferred, which is consistent with the excitation energy of the highest particle group observed. Exclusive gamma-ray energy spectra have been extracted for each of the three excited state peaks seen in fig. 2, and show clear differences despite the limited statistics. In particular, the gamma-ray at 1.69 MeV is only clearly evident in association with the 4.03 MeV peak in the particle spectrum. Any direct population of a 1.68 MeV state in 25 Ne must be quite weak relative to the 2.03 MeV state. The gamma-ray decay scheme inferred from the data is included in fig. 5.

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5 Discussion The energy levels observed in the present work are displayed in fig. 5, along with previous information from the literature and the predictions for positive parity states according to the shell model within a full sd-shell basis [17]. The shell model levels are not explicitly labelled in energy, but rather the spin and parity are given, along with the single neutron spectroscopic factors for selected levels as calculated in ref. [18]. The previous data come from two heavy ion transfer studies and also a study of β-delayed gamma-rays in 25 Ne following the decay of 25 F [19]. The two heavy ion reaction studies each involved the removal of two protons from 26 Mg and the addition of a neutron. The selectivity of the (7 Li,8 B) reaction [20] and the (13 C,14 O) reaction [18] are slightly different, probably due to the cluster structure of 7 Li. Some further considerations are mentioned in ref. [18] and in the discussion below. The β-decay data give one rather clear result, namely a more precise energy than the transfer experiments for the state at 1.703 MeV. The present data indicate that the level at 2.03 MeV is populated much more strongly in the (d, p) reaction than the level seen at 1.68 MeV, and hence that the  = 2 assignment from fig. 3 rightly refers to the 2.03 MeV level. It seems likely that the level measured to be at 1.68 MeV can be associated with the level measured more precisely to be at 1.703 MeV in the β-decay work. It is not entirely clear from the gamma-ray spectrum to what extent the 1.68 MeV level is populated directly, or whether it is populated at all; this uncertainty is due to counts in the compton edge of the 2.03 MeV gamma-ray. However, it is clear that the relative strengths between the levels at 1.68 MeV and 2.03 MeV in (d, p) is exactly opposite to that observed using the (13 C,14 O) reaction. Insofar as both reactions involve the addition of a neutron to an N = 14 nucleus, this is perhaps surprising, but the reaction mechanism is much more complex in the case of (13 C,14 O). Woods [18] used the larger spectroscopic factor of the J π = 3/2+ state to argue that the peak observed at 1.7 MeV in (13 C,14 O) corresponded to this state. By the same criteria, it could be argued from the (d, p) result that the 2.03 MeV state is in fact the 3/2+ . Further study of this question is underway. It may be remarked that the population of the 5/2+ state in (13 C,14 O) can proceed by the transfer of a neutron to the vacant s1/2 orbital, accompanied by the removal of an  = 2 di-proton cluster from the 26 Mg target. The neutron step is the same as the transfer that produces the ground state strongly. It is a general feature of such reactions (see, for example, the discussion in ref. [21]) that higher  transitions are favoured by the reaction dynamics and this would enhance the  = 2 pathway relative to its amplitude according to simple structure considerations. This provides at least the possibility that the (13 C,14 O) reaction may actually favour the 5/2+ state over the 3/2+ state. Additional information about which states are likely to be populated in 25 Ne by the (d, p) reaction can be inferred from the results [22] of a (d, p) study performed using a target of 26 Mg, an isotone of 24 Ne. That study indicated in particular that significant strength is to be expected for

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the population of negative parity states in the region of 3 to 4 MeV. Thus, it seems likely that the levels seen here at 3.33 MeV and 4.03 MeV in 25 Ne represent transfer to the 0f7/2 and 1p3/2 orbitals. In summary, the present data indicate clearly that the ground state in 25 Ne is populated by  = 0 transfer in the (d, p) reaction, and hence that it has spin and parity 1/2+ which is consistent with the prediction of the simple shell model and also a full USD calculation [17]. The state seen at 2.03 MeV has a distribution that is well described by a transfer of two units of angular momentum. This is consistent with both of the states predicted near 1.7 MeV in the USD calculation. Further interpretation of these results and further analysis of the results for the two levels observed above 3 MeV (likely to be negative parity levels) is expected to give interesting information about the changing shell structure for neutrons in the N = 14 to N = 16 region. This is currently a topic of great research interest [23, 24,25]. The results of this first experiment using the TIARA array are also very encouraging in terms of what they demonstrate should be possible with transfer reaction studies in the future.

References 1. W.N. Catford, Acta Phys. Pol. B 32, 1049 (2001). 2. W.N. Catford, Nucl. Phys. A 701, 1 (2002). 3. W.N. Catford et al., Nucl. Instrum. Methods A 247, 367 (1986).

4. K.E. Rehm et al., Phys. Rev. Lett. 80, 676 (1998). 5. J.S. Winfield et al., Nucl. Phys. A 683, 48 (2001). 6. J.S. Winfield, W.N. Catford, N.A. Orr, Nucl. Instrum. Methods A 396, 147 (1997). 7. J.S. Thomas et al., these proceedings. 8. K.L. Jones et al., these proceedings. 9. S. Michimasa et al., these proceedings. 10. W.N. Catford, C.N. Timis, M. Labiche, R.C. Lemmon, G. Moores, R. Chapman, in CAARI 2002, edited by J.L. Duggan, I.L. Morgan, AIP Conf. Proc. 680, 329 (2003). 11. W.N. Catford, R.C. Lemmon, C.N. Timis, M. Labiche, L. Caballero, R. Chapman, in Tours Symposium V, edited by M. Arnould et al., AIP Conf. Proc. 704, 185 (2004). 12. H. Savajols et al., Nucl. Instrum. Methods B 204, 146 (2003). 13. W.N. Catford, J. Phys. G 24, 1377 (1998). 14. J. Simpson et al., Acta Phys. Hung. A: Heavy Ion Phys. 11, 159 (2000). 15. S. Agostinelli et al., Nucl. Instrum. Methods A 506, 250 (2003). 16. R.C. Johnson, P.J.R. Soper, Phys. Rev. C 1, 976 (1970). 17. B.A. Brown, on-line database “sd-shell USD energies”, http://www.nscl.msu.edu/∼brown/resources/SDE.HTM. 18. C.L. Woods et al., Nucl. Phys. A 437, 454 (1985). 19. A.T. Reed et al., Phys. Rev. C 60, 024311 (1999). 20. K.H. Wilcox et al., Phys. Rev. Lett. 30, 866 (1973). 21. W.N. Catford et al., Nucl. Phys. A 503, 263 (1989). 22. F. Meurders, A. Van Der Steld, Nucl. Phys. A 230, 317 (1974). 23. A. Ozawa et al., Phys. Rev. Lett. 84, 5493 (2000). 24. T. Otsuka et al., Phys. Rev. Lett. 87, 082502 (2001). 25. M. Stanoiu et al., Phys. Rev. C 69, 034312 (2004).

Eur. Phys. J. A 25, s01, 251–253 (2005) DOI: 10.1140/epjad/i2005-06-177-x

EPJ A direct electronic only

Spectroscopic factors in exotic nuclei from nucleon-knockout reactions A. Gade1,a , D. Bazin1 , B.A. Brown1,2 , C.M. Campbell1,2 , J.A. Church1,2 , D.-C. Dinca1,2 , J. Enders1,b , T. Glasmacher1,2 , P.G. Hansen1,2 , Z. Hu1 , K.W. Kemper3 , W.F. Mueller1 , H. Olliver1,2 , B.C. Perry1,2 , L.A. Riley4 , B.T. Roeder3 , B.M. Sherrill1,2 , J.R. Terry1,2 , J.A. Tostevin5 , and K.L. Yurkewicz1,2 1 2 3 4 5

National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA Department of Physics, Florida State University, Tallahassee, FL 32306, USA Department of Physics and Astronomy, Ursinus College, Collegeville, PA 19426, USA Department of Physics, School of Electronics and Physical Sciences, Guildford, Surrey GU2 7XH, UK Received: 10 January 2005 / Revised version: 27 April 2005 / c Societ` Published online: 2 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. One-neutron knockout at intermediate beam energies, an experimental approach sensitive to the single-particle structure of exotic nuclei, has been applied to the well-bound N = 16 isotones 34 Ar, 33 Cl and 32 S as well as to the N = 14 nucleus 32 Ar where the knockout residue 31 Ar is located at the proton drip line. The reduction of single-particle strength compared to USD shell-model calculations is discussed in the framework of correlation effects beyond the effective-interaction theory employed in the shell-model approach. PACS. 24.50.+g Direct reactions – 21.10.Jx Spectroscopic factors

1 Introduction The shell model pictures deeply-bound nuclear states as fully occupied by nucleons. The mixing of configurations leads to occupancies that gradually decrease to zero in the vicinity of the Fermi energy. These correlation effects [1] —short-range, soft-core, long-range, and coupling to vibrational excitations— are beyond the effectiveinteraction theory employed in the shell model. The situation described above will be modified depending on the strength of these correlations. In stable nuclei, a reduction of Rs = 0.6–0.7 with respect to the independent-particle shell model has been established from (e, e p) data [2]. At rare-isotope accelerators, very deeply as well as weakly bound nuclear systems become accessible to experiments. One approach to assess the occupation number of singleparticle orbits in exotic nuclei is the one-nucleon removal reaction at intermediate beam energies [3]. Following [4], the measured spectroscopic factor C 2 S relates to the occupation number of the single-particle orbit involved. Experiments probing very deeply as well as more loosely bound nuclei [5, 6] have been performed at the Coupled Cyclotron Facility of the National Superconducting Cyclotron Laba

Conference presenter; e-mail: [email protected] Present address: Institut f¨ ur Kernphysik, TU Darmstadt, D-64289 Darmstadt, Germany. b

oratory (NSCL) at Michigan State University (MSU) and will be discussed. Gamma-ray spectroscopy was used to identify the final states in the knockout reactions. The array SeGA [7], consisting of fifteen 32-fold segmented high purity germanium detectors, was used in conjunction with the highresolution S800 spectrograph [8] to identify γ-rays and reaction residues in coincidence. The two position-sensitive cathode readout drift counters of the S800 focal-plane detector system [9] in conjunction with the known optics setting of the spectrograph served to reconstruct the longitudinal momentum of the knockout residues on an eventby-event basis, providing information on the l-value of the knocked-out nucleon.

2 One-neutron knockout on well-bound N = 16 nuclei The single-particle properties of the proton-rich N = 15 isotones with Z = 16, 17 and 18 have been studied at the Coupled Cyclotron Facility of the NSCL at MSU using the one-neutron knockout reactions 9 Be(32 S,31 S + γ)X, 9 Be(33 Cl,32 Cl + γ)X and 9 Be(34 Ar,33 Ar + γ)X in inverse kinematics and at intermediate beam energies [10]. Gamma-rays and knockout residues detected in coincidence tagged the one-neutron removal leading to excited

252

The European Physical Journal A 33Ar

a)

l=0 l=2

1.0

b)

300

l=0. l=2

0.8

150 200

100 50

100

0

0

Rs

.

Counts/(36.2 MeV/c)

200

31

S

Cl

0.6

33

0.4

11.2 11.4 11.6 p|| (GeV/c)

d 3/2 uncertainty (expt.) uncertainty (expt. + theo.)

s1/2

1n removal N=16 −> N=15

40

σ inc (mb)

Fig. 1. Momentum distribution for the one-neutron knockout from 34 Ar to 33 Ar compared to calculated line shapes for different possible l values. (a) Momentum distribution for the knockout to the ground state of 33 Ar. (b) Momentum distribution for the knockout to excited states. The s1/2 character of the ground state is indicated by the consistency of the data points with the l = 0 line shape while the excited states, as expected from the USD shell model, are populated by the knockout of a neutron out of d5/2 and d3/2 orbits (l = 2). For more details see [10] (figure taken from this reference).

50

d5/2

Ar

inc

0.2 11.2 11.4 11.6 p|| (GeV/c)

32

30

S

20

Cl

Ar

17

18

10 16

Z final states in the reaction residues. The momentum distributions observed in the experiment were used to identify the angular momentum l carried by the knocked-out neutron in comparison to calculations based on a black-disk approach introduced in [11]. The momentum distributions for the knockout to the ground state of 33 Ar and to excited states, respectively, are shown in fig. 1. The inclusive knockout cross section is given by the number of knockout residues per incoming projectile accounting for the number density of the Be target. From the γ-ray intensities, the knockout cross sections to individual final states can be deduced. Spectroscopic factors C 2 S are then obtained by comparison to the single-particle cross sections from reaction theory [3]. The use of intermediate beam energies allowed a theoretical description of the reaction process within the sudden approximation and assuming straight-line trajectories. The dependency of the theoretical singleparticle cross sections on the Woods-Saxon parameters and the rms radius of the core was studied and, compared to weakly bound systems, found to be rather pronounced [10]. A reduction of the experimental spectroscopic strength with respect to a USD shell-model calculation has been observed and extends the systematics established so far for stable and near-magic systems from (e, e p) and (d, 3 He) reactions and for deeply-bound light nuclei around carbon and oxygen from one-nucleon knockout experiments [10]. The reduction factor Rs for the knockout to the N = 15 isotones is shown in the upper part of fig. 2. The reduction factor is defined as the ratio of the experimental cross section and the theoretical ones, based on a structureless reaction cross section from eikonal theory and spectroscopic factors from a many-body USD shell-model calculation. The lower part of the figure shows the inclusive cross sec-

Fig. 2. Reduction factor Rs and inclusive cross section for the one-neutron knockout reactions on proton-rich N = 16 isotones [10] (see this reference for details).

tion for the one-neutron removal reactions at beam energies above 60 MeV/nucleon.

3 One-neutron knockout to the proton-dripline nucleus 31 Ar —a comparison to weakly bound systems In the proximity of the proton drip line, the 9 Be(32 Ar, 31 Ar)X reaction, leading to the 5/2+ ground state of the most neutron deficient Ar isotope known to exist, was found to have a cross section of 10.4(13) mb at a midtarget beam energy of 65.1 MeV/nucleon [5]. This cross section to the only bound state of 31 Ar translates into a spectroscopic factor that is only 24(3)% of that predicted by many-body shell-model theory. Refinements to the eikonal reaction theory used to extract the spectroscopic factor were introduced to stress that this very strong reduction represents an effect of nuclear structure [5]. In summary, the 9 Be(32 Ar,31 Ar)X reaction with a neutron separation energy of 22.0 MeV leads to a nucleus situated at the proton drip line with only one bound state. The empirical reduction factor Rs is unexpectedly small, which may be linked to the very asymmetric nuclear matter in 31 Ar [5]. This is visualized in fig. 3. The left part of the figure shows that the reduction of the occupancy with respect to the USD shell-model prediction might correlate with the binding energy of the knocked-out nucleon. The right panel of fig. 3 displays the differences of radial distributions and potential depths for the isotones 21 O and 31 Ar

A. Gade et al.: Spectroscopic factors in exotic nuclei from nucleon-knockout reactions

15

253

C 22

O

B. Jonson, priv. comm.

32

Ar

Fig. 3. Reduction in occupancy with respect to shell model predictions as a function of nucleon separation energy (left panel) and differences in the radial distributions for isotones with widely different proton numbers (right panel). We note that 22 O and 32 Ar have the same neutron configuration but strikingly different reduction factors R s . Figures taken from [5].

to illustrate the pronounced proton-neutron asymmetry for the Ar isotopes at the proton drip line. The reduction factors for the two systems, (22 O,21 O) and (32 Ar,31 Ar), are very different. On the contrary, there is evidence from several experiments that nucleon knockout from a halo-like state shows a reduction factor Rs closer to unity. The radioactive nuclei 8 B and 9 C [4, 12] have been studied in one-proton knockout (proton separation energies of 0.14 and 1.3 MeV, respectively) giving reduction factors above 0.8 [4,12]. Recently, the one-neutron knockout from 15 C to the ground state of 14 C has been measured with high precision [6] and the reduction factor Rs is with 0.90(4)(5) close to unity and in line with the previous observations for weakly bound systems. This work was supported by the National Science Foundation under Grants No. PHY-0110253, PHY-9875122, PHY0244453 and PHY-0342281 and by the UK Engineering and Physical Sciences Research Council (EPSRC) under Grant No. GR/M82141.

References 1. W. Dickhoff, C. Barbieri, Prog. Nucl. Part. Sci. 52, (2004) 377. 2. V.R. Pandharipande et al., Rev. Mod. Phys. 69, 981 (1997). 3. P.G. Hansen, J.A. Tostevin, Annu. Rev. Nucl. Part. Sci. 53, 219 (2003). 4. B.A. Brown et al., Phys. Rev. C 65, 061601(R) (2002). 5. A. Gade et al., Phys. Rev. Lett. 93, 042501 (2004). 6. J.R. Terry et al., Phys. Rev. C 69, 054306 (2004). 7. W.F. Mueller et al., Nucl. Instrum. Methods Phys. Res. A 466, 492 (2001). 8. D. Bazin et al., Nucl. Instrum. Methods Phys. Res. B 204, 629 (2003). 9. J. Yurkon et al., Nucl. Instrum. Methods Phys. Res. A 422, 291 (1999). 10. A. Gade et al., Phys. Rev. C 69, 034311 (2004). 11. P.G. Hansen, Phys. Rev. Lett. 77, 1016 (1996). 12. J. Enders et al., Phys. Rev. C 67, 064301 (2003).

Eur. Phys. J. A 25, s01, 255–258 (2005) DOI: 10.1140/epjad/i2005-06-110-5

EPJ A direct electronic only

First experiment of 6He with a polarized proton target M. Hatano1,2 , H. Sakai1,2,3,a , T. Wakui3 , T. Uesaka3 , N. Aoi2 , Y. Ichikawa1 , T. Ikeda4 , K. Itoh4 , H. Iwasaki1 , T. Kawabata3 , H. Kuboki1 , Y. Maeda1 , N. Matsui5 , T. Ohnishi2 , T.K. Onishi1 , T. Saito1 , N. Sakamoto2 , M. Sasano1 , Y. Satou5 , K. Sekiguchi2 , K. Suda3 , A. Tamii6 , Y. Yanagisawa2 , and K. Yako1 1 2 3 4 5 6

Department of Physics, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-0033, Japan RIKEN, Hirosawa 2-1, Wako, Saitama 351-0198, Japan Center for Nuclear Study, University of Tokyo, Hirosawa 2-1, Saitama 351-0198, Japan Department of Physics, Saitama University, Shimo-Ohkubo 255, Saitama 338-8570, Japan Department of Physics, Tokyo Institute of Technology, Ohokayama 2-12-1, Meguro, Tokyo 152-0033, Japan Research Center for Nuclear Physics, Osaka University, Mihogaoka 10-1, Ibaraki, Osaka 567-0047, Japan Received: 15 November 2004 / c Societ` Published online: 30 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We have constructed a new type of spin polarized solid proton target which can be operated under a low magnetic field of 0.08 T and a high temperature of 100 K. We have measured for the first time the polarization asymmetry of an unstable beam of 6 He at an energy of 71 MeV/u. Optical potential analyses have been carried out. PACS. 24.70.+s Polarization phenomena in reactions – 25.40.Cm Elastic proton scattering – 27.20.+n 6 ≤ A ≤ 19

1 Introduction Radio-isotope (RI) beam experiments have extended the horizon of research to nuclei far from the stability line. Nuclear reactions with a spin polarized beam have been continuously giving us precious information both on nuclear structure and on reaction mechanisms. In order to apply such polarization measurements to the RI beam experiments, a polarized proton target is necessary. The first choice would be a polarized gas proton target type since it has been established technically. However a low density of the gas target coupled with a low intensity of RI beam, i.e. low luminosity, makes the RI beam experiment very difficult. Inevitably the second choice would be a polarized solid proton target (PSPT) system. A conventional PSPT system which requires a high magnetic field (≥ 2.5 T) and a very low temperature (≤ 1 K) is inconvenient for the RI beam experiments. This is because the RI beam experiments utilize inverse kinematics. Therefore it involves detection of low energy protons or deuterons which are emitted to large angles (> 50◦ in the lab. system). The detection of such low energy particles is very difficult under such severe environment. We have constructed a PSPT which overcomes those drawbacks and allows us to pursue various spin polarized experiments with RI beams. a

Conference presenter; e-mail: [email protected]

2 Construction OF PSPT Our target material is a crystal of naphthalene (host) doped with pentacene (guest). It was first reported by Henstra that a proton in this aromatic material can be polarized under a low magnetic field and at a high temperature [1]. The basic principle to polarize a proton is a pulsed dynamic nuclear polarization (DNP) method. First, an alignment of electron population which appears in the lowest triplet state of pentacene is produced by means of optical pumping by a laser. Maximum magnetic substate populations are |m = 0 = 76% and |m = ±1 = 12%. This electron alignment is subsequently transferred to a proton polarization by using the integrated solid effect (ISE). The maximum proton polarization is expected to be 72.8%, if the polarization transfer is perfect and relaxation of polarization is negligible. We first constructed a PSPT system for the off-line test which consisted of a C-type magnet, the laser system with an Ar-ion laser operated at 514 nm and the cylindrical cavity with a microwave generator with 9.1 GHz. By using this system we have achieved a proton polarization of about 37% under the magnetic field of 0.3 T and the temperature of 100 K with a naphthalene crystal size of 4 × 5 × 2 mm3 [2]. The relaxation time was measured to be about 22 hours.

The European Physical Journal A

Based on this experience gained in off-line tests we designed a PSPT system which could operate under the experimental conditions required by the RI beam [2,3]. Firstly, we needed to produce a large and thin target crystal made of naphthalene doped with pentacene to cope with a large size of the RI beam due to the secondary beam. Secondly, a completely new design was needed for the resonator system of microwave, to keep minimum material along the recoil proton trajectory to avoid energy loss. We introduced a loop-gap resonator which is made of a Teflon thin film of 25 μm on both sides of which copper stripes with a thickness of 4.4 μm are printed [4]. Finally, special care was taken for the target chamber design to cool down the target. The target chamber has another small chamber nesting inside it. The small chamber in which the target crystal and the devices for polarizing the target such as the loop-gap resonator are equipped is cooled by cold nitrogen gas. The volume between the two chambers is evacuated and connected to the beam pipe. Each chamber has a glass window for the laser light input and three exit windows with thin Kapton foils (50 μm), one for the beam and two for the recoil particles at left and right sides of the chambers with respect to the beam direction.

3 Polarization measurement The first polarization asymmetry measurement [3] was performed with the unstable beam of 6 He with 71 MeV/u produced by the RIKEN Projectile-fragment Separator (RIPS). We chose elastic scattering since the event identification is relatively easy. Moreover, the cross-section data existed for the scattering angle of θcm = 20◦ – 50◦ [5]. The cross-section and the polarization asymmetry (= target polarization × analyzing power) were measured for θcm = 40◦ –80◦ which covers the second diffraction peak of cross-sections. This angle region is very interesting since all optical model predictions based on a microscopic folding model [6, 7] or a phenomenological model [8] show a large positive polarization asymmetry, i.e. positive analyzing powers. The PSPT system was operated under a magnetic field of 0.08 T and a temperature of 100 K. The target crystal had a thickness of 1 mm with a diameter of 14 mm. The spot size of the 6 He beam was about 10 mm in diameter (FWHM) and its intensity was on the average 1.7 × 105 particles/s. The proton polarization during the measurement was monitored by a pulsed NMR method. The NMR amplitude as a function of time is shown in fig. 1. The direction of the polarization was reversed during the experiment to minimize the systematic uncertainties associated with geometry. The scattered 6 He were detected by a multi-wire drift counter (MWDC) and three planes of plastic scintillator hodoscopes. The recoil protons were detected by the multistripped position sensitive silicon detectors backed by the plastic scintillation counters on left and right sides with respect to the beam.

NMR amplitude [arb. unit]

256

200 0 -200

0

10

20

30

40

50

60

Time [hours] Fig. 1. NMR amplitudes during the measurement.

The polarization asymmetry  can be derived from the measurement by √ Y −1 , (1) = √ Y +1

Y =

NL↑ · NR↓

NL↓ · NR↑

,

(2)

↑(↓)

where NL(R) is the count detected by the left(right) L(R) detector with the target polarization state “up”(“down”) ↑ (↓).  is related to the target polarization Pt and the analyzing power Ay for the elastic scattering as  = P t × Ay .

(3)

To derive Ay we need to know Pt . Unfortunately, we could not perform the calibration of Pt during the experiment and we thus made our best guess on the Pt value. We assumed Pt = 0.21. Systematic uncertainty of Pt could be as large as 50%. Note that this brings a large ambiguity in the magnitude of Ay but never changes its sign. Figure 2 shows the cross-sections and the analyzing powers for the p + 6 He scattering at 71 MeV/u as a function of c.m. scattering angles. Present results are plotted by solid circles and previous results by Korsheninnikov [5] are plotted by open circles. Only statistical errors are shown in this figure. Errors for the cross-section are smaller than the size of the symbol in most cases. Systematic error for the cross-section is estimated to be ±9%. For the analyzing powers, the horizontal bar indicates the bin width of the angle integrated. It might be very interesting to compare our p+ 6 He results to those of p + 6 Li at the similar bombarding energy by Henneck [9]. The p + 6 Li data are plotted by the open square symbols in fig. 2. It is surprising to find that the magnitude and the angular dependence of cross-sections are almost identical. This indicates that both nuclei have a

M. Hatano et al.: First experiment of 6 He with a polarized proton target

257

Table 1. Optical potential parameters for p + 6 He and p + 6 Li reactions at 71 MeV/u and 72 MeV/u. Vi is in unit of MeV and ri and ai are in unit of fm. See text for detail.

Nucleus 6

6

6

6

He Li

He Li

VR

rR

aR

Wv

rwv

awv

−20.2 −31.7

1.27 1.10

0.57 0.75

−19.2 −14.1

0.92 1.15

0.64 0.56

Vs

rs

as

−3.36 −3.36

1.30 0.90

0.94 0.94

Table 2. Root mean square radius.

Nucleus 6

6

He Li

1

2 (fm)

r 2 pot

2.76(10) 3.18(28)

Fig. 2. Cross-sections and analyzing powers. See text for detail.

Fig. 3. Shape of the spin-orbit potential. See text for detail.

similar potential strength, i.e. radius and depth. However, it is even more surprising to find that the observed polarization asymmetry shows a remarkable difference between the p+ 6 He and p+ 6 Li scatterings. The polarization asymmetry changes the sign from positive to negative values for p + 6 He, while it increases rapidly from the small positive value to the large positive value for the same angular range in case of p + 6 Li. This feature of the negative values contradicts largely with the optical model predictions [6, 7, 8].

4 Analysis and discussion We have carried out the optical model analysis by using the cross-section data. The standard Wood-Saxon shape is assumed for real and imaginary central potentials (VR and WR ). The cross-sections are easily reproduced by the calculation as shown in the upper panel of fig. 2. Obtained parameters are shown in table 1. For a comparison purpose, those by Henneck [9] for the p + 6 Li reaction at 72 MeV/u are included in table 1 and plotted in fig. 2 with the dashed curve.

From the real central part of the optical potential, the mean square radius of the potential r 2 pot can be evaluated by   2 2 3 (4)

r pot = r VR (r)d r/ VR (r)d3 r. The root mean square radii for 6 He and 6 Li are shown in table 2. The root mean square radius of 6 Li is slightly larger than that of 6 He. This could be due to a d-α cluster structure of 6 Li. It should be noted that the mean square radius is related with the mean square matter distribution r 2 matt and the mean square interaction radius r 2 int as

r2 pot = r2 matt + r2 int ,

(5)

for a nucleus with a rotationally symmetric density distribution. A Glauber based analysis of the experimental elastic scattering of the p + 6 He scattering at 0.7 GeV 1 2  2.3 − 2.4 fm [10] which is smaller than gives r 2 matt

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the present result by the mean square interaction radius 1 2  1.5 fm. of r2 int Since the polarization asymmetry data are poor in statistics and only 4 angles exist, it is difficult to make an automatic parameter search for the spin-orbit potential V s . Here the Thomas type is used for V s . Thus we changed parameters (V s , r s , a s ) by hand and tried to get a better fit by eyes! The peculiar behavior of the sign change of Ay can be better reproduced when r s is set to be larger compared to the standard value in this mass region. One example of such fit is shown in the lower panel of fig. 3 by the solid curve. In fig. 3 the shapes of the spin-orbit potential are shown for 6 He (solid curve) and 6 Li (dashed curve), respectively. The spin-orbit potential for 6 He seems to locate outside further by about 0.8 fm compared to that for 6 Li. It is interesting to note that the angular behavior of the present polarization asymmetry of p + 6 He at 71 MeV/u is very similar to that of p + 4 He at 72 MeV/u [11].

5 Summary A polarized solid proton target which works under the condition of a low magnetic field of 0.8 T and a high temperature of 100 K has been built and used, for the first time, for the polarization asymmetry measurement with the 6 He beam at 71 MeV/u. The asymmetry shows an unexpected behavior which disagrees with the optical model predictions. The present work has demonstrated the usefulness of the polarization measurement for exploring a new aspect of unstable nuclei.

We would like to thank I. Tanihata and T. Suda for their continuous support on this work. We are indebted to M. Iinuma and K. Takeda for helpful suggestions in the early stage of this work. We also wish to thank the RIKEN accelerator group for their excellent work. This work has been supported in part by the Grant-in-Aid for Scientific Research No. 15740139 of the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

References 1. A. Henstra, T.-S. Lin, J. Schmidt, W.Th. Wenckebach, Chem. Phys. Lett. 165, 6 (1990). 2. T. Wakui, M. Hatano, H. Sakai, A. Tamii, T. Uesaka, AIP Conf. Proc. 675, 911 (2003); T. Wakui et al., Nucl. Instrum. Methods A 526, 182 (2004). 3. M. Hatano, PhD Thesis, University of Tokyo, unpublished (2004). 4. T. Uesaka et al., Nucl. Instrum. Methods A 526, 186 (2004). 5. A.A. Korsheninnikov et al., Nucl. Phys. A 616, 45 (1997). 6. S.P. Weppner, O. Garcia, Ch. Elster, Phys. Rev. C 61, 044601 (2000). 7. K. Amos, private communication. 8. D. Gupta, C. Samanta, R. Kanungo, Nucl. Phys. A 674, 77 (2000). 9. R. Henneck et al., Nucl. Phys. A 571, 541 (1994). 10. G.D. Alkhazov et al., Nucl. Phys. A 712, 269 (2002). 11. J. Campbell et al., Phys. Rev. C 39, 56 (1989).

Eur. Phys. J. A 25, s01, 259–260 (2005) DOI: 10.1140/epjad/i2005-06-014-4

EPJ A direct electronic only

Isobaric analog states of neutron-rich nuclei. Doppler shift as a measurement tool for resonance excitation functions P. Boutachkov1,a , G.V. Rogachev1 , V.Z. Goldberg2 , A. Aprahamian1 , F.D. Becchetti3 , J.P. Bychowski4 , Y. Chen3 , G. Chubarian2 , P.A. DeYoung4 , J.J. Kolata1 , L.O. Lamm1 , G.F. Peaslee4 , M. Quinn1 , B.B. Skorodumov1 , and A. Wohr1 1 2 3 4

Physics Department, University of Notre Dame, Notre Dame, IN 46556, USA Texas A&M University, College Station, TX 77843, USA Physics Department, University of Michigan, Ann Arbor, MI 48109, USA Physics Department, Hope College, Holland, MI 49422, USA Received: 1 October 2004 / c Societ` Published online: 21 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We present a new approach for the measurement of resonance excitation functions of neutronrich nuclei using Doppler shift information. Preliminary data from the first application of the method is presented in the spectroscopy studies of 7 He isobaric analog states in 7 Li. PACS. 25.60.-t Reactions induced by unstable nuclei – 25.40.Kv Charge-exchange reactions – 27.20.+n 6 ≤ A ≤ 19

11.22 3/2-;T=3/2

b) n

J-Detector

n+6Li0+;T=1

p

10.81

CH2

9.98

6He

p +6He

p

9.52

d +5He

9.09 1/2-;T=1/2 8.75 3/2-;T=1/2

Time

Radioactive beams provide new opportunities for spectroscopy studies of drip line nuclei. Neutron-rich beams can populate high isospin states which are isobaric analogs of even more exotic neutron-rich systems [1]. We propose a method in which high isospin states are populated in resonance interaction of protons with neutron-rich beams. A γ-ray is then detected from the daughter nucleus created in a subsequent neutron decay. Information about the total and differential cross-sections of the created high isospin states can be extracted from the shape of the observed Doppler shifted γ-spectrum.

a)

3.56 MeV

1 Introduction

CH2

E` 6Li

n 7.45 5/2-;T=3/2

7.25

n+6Li1+;T=0

2 The method The thick target inverse geometry technique [2] was successfully used to study proton-rich nuclei [3,4]. Recently it has been used in studies of exotic neutron-rich systems [5, 6]. In the latter experiments, the differential crosssection for (p, p) and (p, n) reactions populating high isospin states was measured at backward angles. The method presented here is a further development of the idea to study exotic neutron-rich nuclei through their isobaric analog states populated in well understood simple reactions [1]. We describe the technique using spectroscopy of 7 He isobaric analog states in 7 Li as an example. In 6 He + p scattering, one can populate states with isospin T = 3/2 in 7 Li. These states are isobaric analogs of a

Conference presenter; e-mail: [email protected]

7Li

Fig. 1. a) Decay scheme for T = 3/2 resonances in 7 Li and b) kinematic scheme of the experiment.

the levels in 7 He. The populated T = 3/2 states have only two open isospin allowed channels: proton decay back to 6 He or neutron decay to T = 1 states of 6 Li, see fig. 1a. As follows from the wave function of the populated T = 3/2 $ states,  2 6 1 6  √ Ψ He Ψ (p) + Ψ Li, T = 1 Ψ (n), (1) 3 3

the neutron decay is dominant and the reduced decay √ widths for the open channels are related as γn /γp = 2. The T = 1 state of 6 Li populated via the (p, n) reaction can decay only by isospin forbidden channels. Therefore,

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the probability for γ transition is enhanced with respect to the particle decays. For the specific case of the first T = 1 state in 6 Li, particle decay also violates the parity conservation law and therefore only γ decay is allowed. Thus, measuring the characteristic 3.56 MeV γ-ray from the decay of the first T = 1 state in 6 Li is a clear signature that a T = 3/2 state in 7 Li was populated. This chain of transmutations is typical for the isobaric analog states of neutron-rich nuclei close to the line of stability. What is special for the described example is the 100% probability for γ decay of the first T = 1 state in 6 Li. Suppose that a thick proton target ((CH2 )n ) is used to stop the 6 He beam. Interaction of 6 He with protons can take place at any energy from the maximum (beam energy) to zero populating T = 1/2 and T = 3/2 resonances in 7 Li. When a T = 3/2 resonance is populated, it will decay with highest probability to neutron and 6 Li(0+ , T = 1) state (see fig. 1). Velocity of 6 Li will depend on the velocity of 7 Li and the angle at which the neutron was emitted. The excited 6 Li nucleus decays by γ emission before it loses any energy in the target (the width of 0+ , T = 1 resonance is 8 eV) and information on the velocity of 6 Li is preserved in the Doppler shift of the γ-ray. Therefore a γ-detector placed at a fixed angle will observe a Doppler shifted and broadened peak. The shift comes mainly from the velocity of 7 Li while the broadening will depend on the angular distribution of the emitted neutron. The magnitude of the peak will depend on the reaction yield. Therefore by using a detector at fixed angle with known absolute efficiency, one can extract information about the total and the differential cross-sections as a function of energy and angle in one run without changing the experimental conditions. In addition, the measurement is insensitive to the energy resolution of the beam.

20000 15000 10000 5000 0 -5000 -10000 3700

3750

3800

3850

3900 Eγ [keV]

Fig. 2. Final spectrum of the Doppler shifted 3.56 MeV γ-rays obtained by subtraction of the carbon contribution form the CH2 target, a linear Compton background and dividing by the absolute detector efficiency. Solid line shows the contribution of the known g.s. resonance T = 3/2, J = 3/2− in 7 Li. Dotted line was obtained by taking into account the narrow low-lying 1/2− state proposed in [8].

of this resonance in 7 Li (T = 3/2 1/2− ) revealed no narrow resonances in this region [6]. The results obtained in ref. [6] are confirmed by the data presented here. The isobaric analog of a low-lying narrow 1/2− resonance in 7 He is not observed. The expected shape of the γ spectrum in case of population of a resonance with parameters from ref. [8] is shown with a dotted line in fig. 2. It is clearly seen from the figure the magnitude and the shape of the data is not reproduced. The present results and these of [6] are completely independent since different techniques were used to measure different quantities. Therefore, the existence of the state with parameters proposed in [8] can be reliably excluded.

3 Isobaric analog states of 7 He

4 Conclusion The method described above was first applied to the study of 7 He isobaric analog states. Figure 2 shows part of the spectrum from HPGe Clover detector placed at 0◦ with respect to the beam velocity. The continuous curve corresponds to the population of the isobaric analog of the 7 He ground state in 7 Li. The curve was obtained by folding the cross-section from a two channel R-matrix calculation and all kinematic effects, see sect. 2. There is no arbitrary normalization in the above calculation. The resonance parameters used for the g.s. were taken from ref. [6]. The contribution of the direct charge-exchange process was estimated with the code TWAVE [7] and was found to be negligible. Based on this calculation, one can see that the first peak in the spectrum is related to the g.s. and that there is a clear excess of counts at higher γ-ray energies which corresponds to 6 Li(0+ , T = 1) nuclei with higher velocity (higher excitation energies of 7 Li). In the spectroscopic studs of 7 He an interesting finding was made by M. Meister et al. [8]. Evidence was obtained for a very low-lying 1/2− state (spin-orbit partner of the ground state) with essentially single-particle (6 He(g.s.) + n) structure. An attempt to find the analog

We propose a new method for spectroscopic studies of neutron-rich nuclei close to the border of stability. As an example, the 7 He isobaric analog states of 7 Li were studied. The measured γ-ray spectra show clear evidence that isobaric analog states of 7 He were excited. The existence of a narrow low-lying 1/2− state in 7 He is ruled out. We present evidence for higher-lying resonances in 7 He. We believe that the presented technique will be very useful in the future for studies of nuclei at the drip line.

References 1. V.Z. Goldberg, in ENAM98: Exotic Nuclei and Atomic Masses, AIP Conf. Proc. 455, 319 (1998). 2. K.P. Artemov et al., Sov. J. Nucl. Phys. 52, 408 (1990). 3. L. Axelsson et al., Phys. Rev. C 54, R1511 (1996). 4. V.Z. Goldberg et al., JETP Lett. 67, 1013 (1998). 5. G.V. Rogachev et al., Phys. Rev. C 67, 041603 (2003). 6. G.V. Rogachev et al., Phys. Rev. Lett. 92, 232502 (2004). 7. S. Barua, private communication. 8. M. Meister et al., Phys. Rev. Lett. 88, 102501 (2002).

Eur. Phys. J. A 25, s01, 261–262 (2005) DOI: 10.1140/epjad/i2005-06-183-0

EPJ A direct electronic only

A new view to the structure of

19

C

R. Kanungo1,a , M. Chiba1 , B. Abu-Ibrahim2 , S. Adhikari3,4 , D.Q. Fang5 , N. Iwasa6 , K. Kimura7 , K. Maeda6 , S. Nishimura1 , T. Ohnishi1 , A. Ozawa8 , C. Samanta3,4 , T. Suda1 , T. Suzuki9 , Q. Wang10 , C. Wu10 , Y. Yamaguchi1 , K. Yamada1 , A. Yoshida1 , T. Zheng10 , and I. Tanihata1,b 1 2 3 4 5 6 7

8 9 10

RIKEN, 2-1, Hirosawa, Wako-shi, Saitama 351-0198, Japan Department of Physics, Cairo University, Giza 12613, Egypt Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700064, India Virginia Commonwealth University, Richmond, VA 23284, USA Sanghai Institute of Nuclear Research, Chinese Academy of Sciences, Shanghai 201800, PRC Department of Physics, Tohoku University, Miyagi 980-8578, Japan Department of Electric, Electronics and Computer Engineering, Nagasaki Institute of Applied Science, Nagasaki 851-0193, Japan Institute of Physics, University of Tsukuba, Ibaraki, 305-8571, Japan Department of Physics, Saitama University, Saitama 338-8570, Japan Department of Technical Physics, Peking University, Beijing 100871, PRC Received: 15 February 2004 / Revised version: 23 March 2004 / c Societ` Published online: 3 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The observation of longitudinal momentum distribution (P|| ) from two-neutron removal in 19 C with a Be target at 64 A MeV is reported. Analysis in terms of Glauber model considering 19 Cgs (J π = 1/2+ ) shows that neutron evaporation is necessary to explain the data. PACS. 25.60.Dz Interaction and reaction cross-sections – 25.60.Gc Breakup and momentum distributions

1 Introduction The existence of one-neutron halo structure has been well established in two nuclei, namely, 11 Be [1] and 15 C [2], having abnormal ground-state spin J π = 1/2+ . Such structures have been described by the core + n halo model. The “core” nucleus in these examples are nuclei whose valence neutron orbital is filled. For sd-shell nuclei close to dripline, the “core” is a more complex nucleus. It is therefore a question of a core + n decoupling is possible for them. One way to investigate this is the study of two-neutron removal from the nucleus of interest. The isotopic chain of carbon nuclei interestingly shows an abrupt increase in interaction cross-section for two isotopes, namely 15 C and 19 C [3]. This feature, together with the relatively narrow momentum distribution [4, 5,6] for one-neutron removal suggested this nucleus to have a one-neutron halo structure. The large Coulomb dissociation cross-section [7] also favoured the halo nature. These investigations suggested a ground-state spin of J π = 1/2+ for 19 C which is supported by shell model a

Conference presenter; Present address: TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada; e-mail: [email protected] b Present address: Argonne National Laboratory, 9700S Cass Avenue, Argonne, IL 60439, USA.

(WBP interaction) predictions [5]. The deformed Skyrme Hartree-Fock calculations however suggest 19 C to have an oblate deformed structure with a ground-state spin of 3/2+ [8], “nearly degenerate” with the 1/2+ excited state (320 keV). In this article, we present a different view to the structure of 19 C by measuring the P|| from two-neutron removal. Interestingly, it appears that the distribution cannot be explained by a J = 1/2+ spin with 18 C core primarily in its ground state, a structure necessary to form a halo.

2 Experiment The experiment was performed at the RIKEN Ring Cyclotron facility. The secondary beam of 19 C was produced by fragmentation of 22 Ne primary beam on a 2.5 mm thick Be target. The 19 C beam further interacted with a 2 mm Be target placed at the first achromatic focus of the fragment separator. The momentum of the 17 C fragment after the reaction target was derived from time-of-flight (TOF) measured using ultra-fast timing plastic scintillators. The momentum resolution was 10 MeV/c (σ). The particle identification was done using ΔE-TOF-E with ionisation chamber (for ΔE) and NaI(Tl) (for E) in addition to the scintillators. The details are described in ref. [6].

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2+

(a) s+d d+ d d+ s d+ s

0.29 1/2+

17C+n threshold

3/2+ 18C

0+

19C

1/2+

18C

0+

+ 19C 1/2

450

500

(b)

19 C  17C

Counts

350

300

250

200

150

100

50 -400

-400 -300 -200

(b)

19C  17C

400

Counts

s-wave d-wave p-wave

4.4 2-

4.18

0.03 5/2+

17C

(a)

7.7 0+ 5.3 2+ 1-

(19C  18C )+ (18C  17C)

-100 0 P|| [MeV/c]

100

200

Fig. 1. (a) The possible paths for emitting two neutrons from 19 C through the ground state and bound excited states of the “core” nucleus 18 C. (b) The P|| data (filled circles) for 19 C → 17 C. The different curves show the Glauber model calculations for the respective emission paths shown in (a).

3 Results and analysis Figure 1 shows the P|| data from two-neutron removal having a width (Γ ) of 203 ± 10 MeV/c. The data is analysed in the framework of the few-body Glauber model [9]. Two different kinds of neutron removal processes have been considered. In the first approach, we consider neutron emission through bound states of the “core” 18 C. The possible emission paths with J π (19 C) = 1/2+ are shown in fig. 1a. The states of 17 C are based on shell model predictions. The resultant P|| are shown, normalized to the peak of the data in fig. 1b. All the emission paths lead to distributions which are wider than the data. The solid curve has a width Γ = 300 MeV/c while the others have widths around Γ = 240 MeV/c. Another process of two-neutron emission is by neutron evaporation, i.e. through unbound excited states of the 18 C core. The resonances of 18 C have not yet been observed. They have thus been considered based on shell model predictions [10] (fig. 2a). Figure 2 shows the paths and the P|| (normalised to the peak of data) for the different evaporation paths. It is observed that processes involving emission of d-wave neutrons lead to much wider (Γ = 260 MeV/c) distributions than the data. The s-wave emission (Γ = 182 MeV/c) and p-wave emissions (Γ = 165 MeV/c for p3/2 ) are in agreement with the higher momentum side of the data. The emission from p1/2 (Γ = 115 MeV/c) is narrower than the data. The above discussion suggests that the configuration of 19 C having a ground-state spin of 1/2+ with the 18 C

-300

-200

-100

0

100

200

300

P|| [MeV/c]

300

Fig. 2. (a) The possible paths for emitting two neutrons from 19 C by neutron evaporation through unbound resonances of the intermediate nucleus 18 C. (b) The P|| data (filled circles) for 19 C → 17 C. The different curves show the Glauber model calculations for the respective emission paths shown in (a).

core in the ground state and/or bound excited states only, cannot explain the P|| from two-neutron removal. The explanation of the data is possible with the neutron evaporation process through unbound excited states of the 18 C core. Thus, in the core + n model for 19 C(J π = 1/2+ ), the 18 C core needs to be placed in unbound excited states too. This probably suggests that 18 C is not a good “core” for 19 C. That maybe expected, since the ground state of 18 C nucleus (J π = 0+ ) itself has quite a complex structure. In a 17 C + n model, the 17 C core must be mainly in the excited states (5/2+ or 1/2+ ) with the neutron in d5/2 or 2s1/2 orbitals respectively, because the ground-state spin of 17 C is known to be 3/2+ . It must be mentioned that the data might also be explained by other ground-state spin considerations for 19 C whose investigation is underway.

References 1. I. Tanihata et al., Phys. Lett. B 206, 592 (1988); S. Fortier et al., Phys. Lett B 461, 22 (1999). 2. E. Sauvan et al., Phys. Lett. B 491, 1 (2000); A. Ozawa et al., Nucl. Phys. A 693, 32 (2001); J.D. Goss et al., Phys. Rev. C 12, 1730 (1975). 3. A. Ozawa et al., Nucl. Phys. A 601, 599 (2001). 4. T. Baumann et al., Phys. Lett. B 439, 256 (1998). 5. V. Maddalena et al., Phys. Rev. C 63, 024613 (2001). 6. M. Chiba et al., Nucl. Phys. A 741, 29 (2004). 7. T. Nakamura et al., Phys. Rev. Lett. 89, 1112 (1999). 8. H. Sagawa et al., Phys. Rev. C 70, 054316 (2004). 9. Y. Ogawa et al., Nucl. Phys. A 543, 722 (1992). 10. B.A. Brown, private communication.

Eur. Phys. J. A 25, s01, 263–266 (2005) DOI: 10.1140/epjad/i2005-06-138-5

EPJ A direct electronic only

Reactions induced beyond the dripline at low energy by secondary beams W. Mittig1,a , C.E. Demonchy1,5 , H. Wang1,b , P. Roussel-Chomaz1 , B. Jurado1,c , M. Gelin1 , H. Savajols1 , no4 , M. Chartier5 , and A. Fomichev2 , A. Rodin2 , A. Gillibert3 , A. Obertelli3 , M.D. Cortina-Gil4 , M. Caama˜ 6,d R. Wolski 1 2 3 4 5 6

GANIL (DSM/CEA, IN2P3/CNRS), BP 5027, 14076 Caen Cedex 5, France FLNR, JINR, P.O. Box 79, 101 000 Dubna, Moscow region, Russia CEA/DSM/DAPNIA/SPhN, Saclay, 91191 Gif-sur-Yvette Cedex, France University of Santiago de Compostela, E-15706 Santiago de Compostela, Spain University of Liverpool, Department of Physics, Oliver Lodge Laboratory, Liverpool L69 7ZE, UK Institute of Nuclear Physics PAN, Radzikowskiego 152, PL-31-342, Cracow, Poland Received: 15 January 2005 / c Societ` Published online: 12 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Reactions induced on protons at low incident energy (3.5 MeV/n) were measured with a 8 He beam accelerated by Spiral at Ganil. The particles were detected in the active target Maya, filled with C4 H10 gas. The beam was stopped in the detector, so energies from incident beam energy down to detector threshold were covered. Proton elastic scattering, one neutron pick-up (p, d) and (p, t) reactions were observed. In the (p, d) reaction very high cross-sections of the order of 1barn were observed, that could be reproduced using a direct reaction formalism. This is the first time that this strong increase of transfer reaction cross-sections at very low energy predicted for loosely bound systems was observed. Spectroscopic factors are in agreement with a simple shell model configuration. No evidence for a low lying excited state in 7 He was found. PACS. 24.50.+g Direct reactions – 29.40.-n Radiation detectors

1 Introduction Since 1989 low energy reaccelerated secondary beams are available at LLN, and in more recent years at Ganil-Spiral, ORNL, Triumf-Isac and Rex-Isolde with energies typically in the 0.1–10 MeV/n domain. These energies are ideally suited for the study of resonant reactions, among them those of astrophysical interest, and direct transfer or pickup reactions. Elastic and inelastic scattering are other reactions of interest at this energy, especially near or below the Coulomb barrier. In most of these studies the interaction with simple target nuclei, such as protons, deuterons, 3 He and 4 He is preferred in order to obtain quantitative results. A recent review on this subject can be found in ref. [1]. A detector, in which the detector gas is the target, this is, an active target, has in principle a 4π solid angle of detection, and a big effective target thickness without loss of resolution, and is thus ideally suited for the study of a

Conference presenter; e-mail: [email protected] Present address: IMP Lanzhou, PRC. c Present address: CENBG Bordeaux, France. d Partially supported by the IN2P3-Poland cooperation agreement 02-106. b

reactions induced by reaccelerated secondary beams from Spiral at Ganil in the energy domain of 2–25 MeV/n. The detector developped, called Maya, used isobutane C4 H10 as gas in the first experiments, and other gases such as D2 . The multiplexed electronics of more than 1000 channels allows the reconstruction of the events occurring between the incoming particle and the detector gas atoms in 3D. Here we will present mainly reactions induced by 8 He on protons at 2–3.5 MeV/n. The design of the detector is shown, and some first results are discussed.

2 The Maya detector Active targets, such as bubble chambers were developped since a long time in high energy physics. In the domain of secondary beams, the archetype is the detector IKAR [2]. A discussion of the use of this detector for elastic scattering at GSI energies can be found in ref. [3]. The use of IKAR was limited to H2 at a pressure of 10 atm. Another example can be found in ref. [4], where a flash ADC readout of wedge signals was used. For the domain of low energies, and for the use of various gases, we developped a new detector called Maya [5,6] that we will describe here. The detector is shown schematically in fig. 1.

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Fig. 2. Typical event matrix as read out for the Maya detector. The calibrated amplitude (in channels/10) from the Gassiplex matrix is printed out for the 32 rows, and the first 20 lines. The beam particle is coming from the left, identified as 23 F, and makes a (d, 3 He) reaction after about one third of the length of the detector. The signal amplitudes in the wire lines and the respective times are printed out on the right. Fig. 1. The scheme of the detector Maya. The secondary beam is incident from the left, the electrons produced by ionising reaction products in the detector gas drift down, and induce a signal after amplification in the honeycomb like anode pattern. These signals are read out by Gassiplex electronics below this anode.

For a two body reaction, scattered and recoiling particles are in a plane. The electrons from the ionisation of the gas by the particles are drifting down in the electric field to the amplifying wires. The wires are parallel to the beam. Therefore their diameter can be different in the region of the beam, to adjust for different ionisation densities of beam and recoil particles. In an experiment with 8 He, we obtained a gain of 1/10 in this central region by the use of 20 μm instead of 10 μm amplifying wires. The spacing of the wires should be quite small, in principle less than the drift straggling of the electrons in order to avoid digitalisation. We used a distance of 3 mm. The wires corresponding to a line of pads are connected to the same preamplifier. The angle of the reaction plane can be determined by the drift time to the wires. The amplified signal is induced in the pads below. The distance between the wires and the pads determines the width of the induction pattern. A distance of 10 mm was chosen in order to have the best position resolution that is obtained when the signal of the two nearby lateral pads have about half the amplitudes of a central pad. A hexagonal structure was chosen for these strips, in order to have best conditions for the reconstruction of the trajectory, independant of the direction. This results in a honeycomb structure. A matrix of 35 by 34 pads, this is 1190 pads, constitutes this anode. The pads are arranged in rows below the wires, in order to have a precise time relation between the wire signal and the pad signal. The pads are connected to Gassiplex. The Gassiplex chip is a 16 analogical multiplexed channel ASIC developed at CERN. The multiplexed readout limits the number of connections from the detector to the outside. The Gassiplex are mounted on the back of the anode. The Gassiplex need a track and hold signal, provided by the wire signal, treated by classical electronics. The detector can be characterized as a CPC: Charge Projection Chamber in analogy with time projection chambers TPC.

A typical event read-out matrix is shown in fig. 2. It was observed with a cocktail beam around 26 F at about 30 MeV/nucleon. In this case the detector was filled with pure D2 to observe the (d, 3 He) reaction. The last column gives the drift times from TDC’s, and as can be seen, the 3 He particle is going down, the drift times at the end of the trace being smaller than at the beginning. The number 16383 means that the corresponding TDC had not fired. The determination of the trajectories in 3 dimensions from readout matrices as shown in fig. 2 needed a quite important development of software [6]. As pointed out above, inverse kinematics generate recoil particles in a large energy domain. High energy light particles such as protons cannot be stopped in a reasonable gas volume. For escaping particles, we added a Si-CsI wall of 20 × 25 cm2 , covering about 45 degrees around the beam for events in the middle of the detector. The detectors have an area of 5 × 5 cm2 . The thickness of the Si detectors is 500 μ and 1 cm for the CsI. For particles stopping in the gas, identification is obtained by the total charge-range correlation. For events stopping in the Si, the energy loss in the gas is used for dE-E identification. For elastic scattering a matrix for the correlation of the range of the heavy reaction partner and the energy in one of the Si-detectors is shown in fig. 3. From the width of this correlation and the distance between the two kinematic lines we obtain an excitation energy resolution of 160 keV(FWHM). Note that in the case of a standard thick target, only the projection on the Si-energy axis would be available, and thus would correspond to a complete loss of the information on excitation energy.

3 Results for the 8 He(p, d)7 He reaction We present mainly results from an experiment run in july 2004 with a beam energy of 3.5 MeV/n and the detector filled with 0.5 atm of isobutane. With this gas density and this energy, the beam was stopped in the detector, and thus the energy domain covered is between the incident energy and zero energy. First results are given below, and we will show some results of the 8 He(p, d) reaction.

W. Mittig et al.: Reactions induced beyond the dripline

Fig. 3. Scatter plot for particles leaving the gas volume, conditioned by the identification of protons, of the energy deposited in one of the Si-detectors, as a function of the range of the heavy reaction partner measured inside the gas. The two lines represent kinematical calculations for elastic scattering of 8 He on protons, and a (hypothetical) excited state at 1 MeV above the ground state.

3.1 Analysis of the energy spectrum of the He(p, d)7 He reaction

8

The ground state of 7 He is known [7] to be unbound by 440 keV, with a width of 150 keV. Thus 7 He disintegrates in 6 He plus neutron, and the remaining 6 He has a variable kinetic energy due to recoil. The broadening of the resolution function as compared to the elastic scattering (see fig. 3), and as observed for the 8 He(p, t)6 Hegs (not shown), is evident in fig. 4. This broadening is due to the intrinsic width of the unbound states in 7 He. In a fragmentation reaction at GSI [8], evidence for a state at (0.6±0.1) MeV above ground state was found with a width of (0.75 ± 0.08) MeV. Such a state would be of great interest, since it could be the p− 1/2 spin-orbit partner of the p− ground state, and would indicate a strong quenching 3/2 of the spin-orbit strength far from stability. In ref. [9] an excited state at 2.9 ± 0.3 MeV (Γ = 2.2 ± 0.3 MeV) was observed. In heavy ion transfer reactions [10], only the ground state of 7 He was observed. In a more recent experiment [11], in the 9 Be(15 N, 17 F)7 He reaction excited states were observed at 2.95 ± 0.1 MeV (Γ = 1.9 ± 0.3 MeV), in very good agreement with ref. [9], and (5.8 ± 0.3) MeV (Γ = 4 ± 1 MeV). Very recently [12], the authors concluded that this low lying state does not exist in an experiment on the isobaric analogue state of 7 He. In an analysis using the recoil corrected continuum shell model [13], it was argued that at the experimental angle of 180 degrees of ref. [12] the effect of such a res-

265

Fig. 4. Scatter plot for particles leaving the gas volume, conditioned by the identification of deuterons, of the energy deposited in one of the Si-detectors, as a function of the range of the heavy reaction partner measured inside the gas. The three lines represent kinematical calculations for the (p, d) leading to the unbound groundstate of 7 He and to excited states at 0.5 and 1 MeV above the ground state. As can be seen by comparison with fig. 3, the width of the distribution is essentially due to the finite width of the states in 7 He.

onance would be very small. Theoretical models, such as nocore SM, QMC, resonating group model, or shell model with different configuration spaces predict a p1/2− state at typically 2–4 MeV above ground state. The extraction of information on excited states in 7 He from experimental spectra is complicated by the fact that the widths are large, and the width and the population cross-section are strongly energy dependent. We treated the energy dependance of the decay width in two ways with very similar results. One was the energy dependance as cited in ref. [11], the other was the calculation of single particle resonance width by the code Fresco [14]. The result can be described to a good approximation by the simple formula Γ (E) = Γr ∗ E/Er . In fig. 5 this relation was used. The population cross-section was calculated as a function of excitation energy using the code Fresco. We included in the fit the following resonances: Er = 0.44 MeV with Γr = 0.15, Er = 1.00 MeV with Γr = 0.75 MeV, and Er = 3.3 MeV with Γr = 2.0. The energy of the center of the last resonance is below threshold for the present experiment, however the tail extends to low excitation energies. The energy spectrum, as projected from fig. 4 on the Si-energy axis, was simulated in a Monte-Carlo method. The experimental energy resolution being much better than the observed structure, it was not necessary to take it into account in the simulation. The individual contributions for these 3 resonances are shown, with arbitrary normalization, in fig. 5. The final fit is shown as solid line. In this fit the contribution relative to the ground

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Fig. 5. Projected energy spectrum for the (p, d) reaction. The experimental count rate/energybite are compared to a MonteCarlo simulation of this spectrum, including the effect of the energy dependant decay width, recoil broadening, energy dependance of the population cross-section. The individual contribution, with arbitrary normalisations, are shown for the ground state, a hypothetical state at 1 MeV separation energy, and a state at 3.3 MeV separation energy. The fitted sum of these contributions is shown, too. For details see text.

state for the state at Er = 1 MeV was (−0.015 ± 0.082). This means no contribution of such a state is seen, and the upper limit is far below the 30% contribution of ref. [8]. 3.2 Reaction cross-sections of the 8 He(p, d)7 Hegs reaction The angular distributions were obtained for maximum energy down to about 2 MeV/n. They were analysed using the code Fresco, with an optical potential taken from CH89 [15]. Experimental uncertainties of the absolute cross-section are of the order of 30% due to efficiency of the reconstruction algorithm. The optical model introduces another uncertainty in the evaluation of this reaction. Nonetheless, the angular distributions agree well, and a spectroscopic factor C 2 S = 3±1 is obtained in the analysis. This is close to a simple shell model estimation where one expects C 2 S = 4 for 4 nucleons in the p3/2 shell. A similar result was obtained at much higher energy [9]. Large transfer reaction cross-sections have been predicted at low energy for loosely bound systems [16]. This results from the very low Fermi momentum of the loosely bound last nucleons in these systems, which implies highest overlap at very low velocity. To our knowledge this effect has not yet been observed. In fig. 6 the angle integrated cross-section as a function of energy is shown. The experimental data were integrated using the Fresco angular distributions renormalized on the experimental data. As can be seen, the cross-section is very high, reaching 1barn in the energy domain of the present experiment.

Fig. 6. Angle integrated cross-section for the 8 He(p, d)7 Hegs reaction. The theory is given for C 2 S = 4.

The good agreement between the theory and experiment shows that even at this low energy the direct reaction mechanism may account for the observed cross-sections. The results shown here, and results on elastic scattering and the (p, t) reaction that were observed simultaneously and which will be discussed elsewhere, illustrate the interest of secondary beams at low energy. An active target as the MAYA detector presented is a powerful tool in this domain.

References 1. P. Roussel Chomaz et al., Nucl. Phys. A 693, 495 (2001). 2. A.A. Vorobyov et al., Nucl. Instrum. Methods 119, 509 (1974); Nucl. Instrum. Methods A 270, 419 (1988). 3. P. Egelhof, Proceedings of the International Workshop on Physics with Unstable Nuclear Beams, Serra Negra, Sao Paulo Brazil, edited by C.A. Bertulani et al. (World Scientific, 1997) p. 222. 4. Y. Mizoi et al., Nucl. Instrum. Methods A 431, 112 (1999); Phys. Rev. C 62, 065801 (2000). 5. P. Gangnant et al., report Ganil 27.2002. 6. C.E. Demonchy, thesis T 03 06, December 2003, University of Caen, France. 7. D.R. Tilley et al., TUNL Manuscript, Energy levels of light nuclei A = 7, and Energy levels of light nuclei A = 9. 8. M. Meister et al., Phys. Rev. Lett. 88, 102501 (2002). 9. A.A. Korsheninnikov et al., Phys. Rev. Lett. 82, 3581 (1999). 10. W. von Oertzen et al., Nucl. Phys. A 588c, 129 (1995). 11. H.G. Bohlen et al., Phys. Rev. C 64, 024312 (2001). 12. G.V. Rogachev et al., Phys. Rev. Lett. 92, 232502 (2004). 13. D. Halderson, Phys. Rev. C 70, 041603R (2004). 14. I.J. Thompson, Comput. Phys. Rep. 7, 167 (1988). 15. R.L. Varner et al., Phys. Rep. 201, 57 (1991). 16. H. Lenske, G. Schrieder, Eur. Phys. J. A 2, 41 (1997).

Eur. Phys. J. A 25, s01, 267–269 (2005) DOI: 10.1140/epjad/i2005-06-021-5

EPJ A direct electronic only

Study of the ground-state wave function of 6He via the 6 He(p, t)α transfer reaction L. Giot1,a , P. Roussel-Chomaz1,b , N. Alamanos2 , F. Auger2 , M.-D. Cortina-Gil3 , Ch.E. Demonchy1 , J. Fernandez3 , A. Gillibert2 , C. Jouanne2 , V. Lapoux2 , R.S. Mackintosh4 , W. Mittig1 , L. Nalpas2 , A. Pakou5 , S. Pita1 , E.C. Pollacco2 , A. Rodin6 , K. Rusek7 , H. Savajols1 , J.L. Sida2 , F. Skaza2 , S. Stepantsov6 , G. Ter-Akopian6 , I. Thompson8 , and R. Wolski6,9 1 2 3 4 5 6 7 8 9

GANIL (DSM/CEA, IN2P3/CNRS), B.P. 5027, 14076 Caen Cedex 5, France CEA/DSM/DAPNIA/SPhN, Saclay, 91191 Gif-sur-Yvette Cedex, France Departamento de Fisica de Particulas, Universidad Santiago de Compostela, 15706 Santiago de Compostela, Spain Department of Physics and Astronomy, The Open University, Milton Keynes, MK76AA, UK Department of Physics, The University of Ioannina, 45110 Ioannina, Greece FLNR, JINR, Dubna, P.O. Box 79, 101 000 Moscow, Russia Department of Nuclear Reactions, The Andrzej Soltan Institute for Nuclear Studies, Hoza 69, PL-00-681 Warsaw, Poland Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK Department of Nuclear Reactions, The Henryk Niewodniczanski Institute of Nuclear Physics, PL-31-342, Cracow, Poland Received: 15 December 2004 / c Societ` Published online: 20 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We have measured the 6 He(p, t)α transfer reaction in inverse kinematics at 25 MeV/nucleon. The data were compared to DWBA calculations in order to extract the spectroscopic amplitudes for α + 2n and t + t configurations in the ground state of 6 He. PACS. 24.50.+g Direct reactions – 25.60.Je Transfer reactions – 24.10.Eq Coupled-channel and distortedwave models – 21.10.Jx Spectroscopic factors

1 Motivation The 6 He nucleus is now currently used as one of the benchmark nuclei to study the halo phenomenon and 3-body correlations [1], especially because the alpha-core can very well be represented as inert. However, in order to have a complete and detailed description of the 6 He wave function, the question arises whether the only contributions are the cigar and di-neutron configurations, where only 4 He and 2n clusters intervene, or if some t + t clustering is also present. In the case of the 6 Li nucleus, it was shown that it was possible to have considerable α + d and 3 He + t clustering at the same time, and the importance of both configurations was studied by analyzing angular distributions of the 6 Li(p, 3 He)4 He reactions [2].

2 Experiment Following the same ideas, we measured recently at GANIL the complete angular distribution for the 6 He(p, t)4 He a b

e-mail: [email protected] Conference presenter; e-mail: [email protected]

with the SPEG spectrometer [3] and the MUST array [4], with a special emphasis on the most forward and backward angles which could not be measured in a previous experiment performed at JINR Dubna [5]. The 25 A MeV 6 He secondary beam was produced by fragmentation of a 60 A MeV 13 C beam on a 1040 mg/cm2 thick carbon target. After selection with magnetic dipoles and an achromatic Al degrader, it was transported to the SPEG reaction chamber where it impinged on a (CH2 )3 target, 18 mg/cm2 thick. The average intensity of the secondary beam was 1.1 · 105 pps, with only one contaminant, 9 Be, at the level of 1%. Due to the large emittance of the secondary beam, the incident angle and the position on the target of the incoming nuclei were monitored event by event by two low pressure drift chambers. The most forward and backward angles of the angular distribution for the 6 He(p, t)4 He reaction were measured in the SPEG spectrometer by detecting respectively the highenergy 4 He and the high-energy triton at forward laboratory angles. The particles were identified in the focal plane by the energy loss measured in an ionization chamber and the residual energy measured in plastic scintillators. The momentum and the scattering angle after the

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3 Analysis of the data

1

d σ/dΩ(mb/sr)

10

2n et t transfert 2n transfert t transfert 0

10

−1

10

−2

10

Salpha-2n=1. St-t=0.0625

−3

10

0

20

40

60

80

100

120

θcm(deg)

140

160

180

Fig. 1. Experimental angular distribution measured in the present work for the 6 He(p, t)4 He reaction, compared to DWBA calculations (see text for details).

target were obtained by track reconstruction of the trajectory as determined by two drift chambers located near the focal plane of the spectrometer. For center-of-mass angles between 20 and 110 degrees, the 4 He and triton from 6 He(p, t)4 He reaction were detected in coincidence by the eight telescopes of the MUST detector array. Each of these telecopes is composed of a 300 μm double-sided silicon strip detector backed by a Si(Li) and a CsI crystal which all give an energy measurement. These detectors were separated in two groups of four arranged in squared geometry on each side of the beam, one covering an angular range between 6 and 24 degrees, and the other one between 20 and 38 degrees with respect to the beam direction. The angular coverage in the vertical direction was 9 degrees. The angular distribution is presented in fig. 1. To extract differential cross-sections, data were corrected for the geometrical efficiency of the detection in SPEG or MUST. This efficiency was determined through a Monte Carlo simulation whose ingredients are the detector geometry, their experimental angular and energy resolutions, the position and width of the beam on the target. The error on the MUST detection efficiency deduced from the Monte Carlo simulation is estimated to 5%. The absolute normalisation for the transfer reaction was obtained from the elastic scattering which was measured in the same experiment with the SPEG spectrometer. Indeed elastic-scattering calculations for the system 6 He + 12 C using different potentials showed that the angular distribution at forward angles is dominated by Coulomb scattering and is rather insensitive to the potential used. Therefore the absolute normalisation of the data was obtained from the measured cross-section on the first maximum of the 6 He(12 C, 12 C)6 He angular distribution. The uncertainty on the absolute normalisation is of the order of 10%. The same normalisation was applied to the transfer data measured with the SPEG spectrometer. In the overlap domain between 19 degrees c.m. and 27 degrees c.m. where the transfer data were obtained with both SPEG and MUST, the agreement was good.

We have performed DWBA calculations including both 2n and t transfer. In the entrance channel, the coupling to the continuum of 6 He was taken into account via an effective dynamical potential derived by an iterative inversion method [6, 7]. A special care was taken in the choice of the exit channel potential. Indeed no data exist for α + t elastic scattering in the energy range considered presently. Therefore we used elastic scattering data for the system α + 3 He [8] to obtain the potential for the exit channel. Several potentials were considered. First, the process of one neutron transfer, which is not distinguishable experimentally from elastic scattering, was explicitely taken into account in a DWBA analysis of the 3 He(α, α)3 He reaction. However, the calculations performed for the 6 He(p, t)4 He reaction with the exit potential obtained with this procedure did not allow to reproduce simultaneously the forward and backward angles of the experimental angular distribution. Secondly, we used the potential B obtained in ref. [9] which was fitted, within a simple optical model approach, on the complete differential cross-section of the 3 He(α, α)3 He elastic scattering at Ecm = 28.7 MeV [10]. This potential gave the best simultaneous description of both α + 3 He elastic scattering and 6 He(p, t)4 He reaction. The data are compared to the DWBA calculation in fig. 1. The dashed line corresponds to the DWBA calculation where only the 2n transfer is taken into account, with a spectroscopic amplitude equal to 1. The crosses correspond to the triton transfer with a spectroscopic amplitude equal to 0.25. The solid line corresponds to the coherent sum of both processes with these values of their spectroscopic amplitudes. From this analysis, the value of the spectroscopic factor extracted for the t + t configuration is between 0.06 and 0.09, which is much less than predicted by shell model or microscopic three-body cluster model [11, 12]. However, it is important to include it in order to reproduce simultaneously the forward and backward angles of the angular distribution. It should be noted that the present result does not include several effects that could modify this conclusion. For example the sequential transfer of 2 neutrons or of one proton and 2 neutrons (in the case of the triton transfer) was not considered and is presently under study. Also an attempt to include transfer from the continuum states in a full Coupled Reaction Channel calculation did not give satisfactory results in the present stage of the analysis. Finally the exit channel potential should be investigated more deeply, since it was shown to strongly influence the angular distribution. This will be the subject of a forthcoming publication [13].

References 1. M. Zhukov et al., Phys. Rep. 231, 151 (1993). 2. M.F. Werby et al., Phys. Rev. C 8, 106 (1973). 3. L. Bianchi et al., Nucl. Instrum. Methods A 276, 509 (1989). 4. Y. Blumenfeld et al., Nucl. Instrum. Methods A 421, 471 (1999).

L. Giot et al.: Study of the ground-state wave function of 6 He . . . 5. 6. 7. 8. 9.

R. Wolski et al., Phys. Lett. B 467, 8 (1999). S.G. Cooper et al., Nucl. Phys. A 677, 187 (2000). R.S. Mackintosh et al., Phys. Rev. C 67, 034607 (2003). O.F. Nemets et al., Yad. Fiz. 42, 809 (1985). K. Rusek et al., Phys. Rev. C 64, 044602 (2001).

10. 11. 12. 13.

P. Schwandt et al., Phys. Lett. B 30, 30 (1969). Yu.F. Smirnov, Phys. Rev. C 15, 84 (1977). K. Arai et al., Phys. Rev. C 59, 1432 (1999). L. Giot et al., submitted to Phys. Rev. C.

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4 Reactions 4.3 Reaction mechanism

Eur. Phys. J. A 25, s01, 273–275 (2005) DOI: 10.1140/epjad/i2005-06-077-1

EPJ A direct electronic only

Effect of halo structure on

11

Be +

12

C elastic scattering

M. Takashina1,a , Y. Sakuragi2 , and Y. Iseri3 1 2 3

RIKEN, Wako, Saitama 351-0198, Japan Department of Physics, Osaka City University, Osaka 558-8585, Japan Department of Physics, Chiba-Keizai College, Chiba 263-0021, Japan Received: 14 October 2004 / c Societ` Published online: 17 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The 11 Be → 10 Be + n breakup effect on 11 Be + 12 C elastic scattering at E/A = 49.3 MeV is studied by continuum-discretized coupled-channels (CDCC) method based on the 10 Be + n + 12 C threebody model. The CDCC calculation well reproduces the experimental data of the elastic scattering, and the breakup effect of the 11 Be nucleus is found to be significant. Furthermore, the reaction dynamics of the 11 Be → 10 Be + n breakup process is investigated and a dynamical polarization potential (DPP) is evaluated. PACS. 25.60.-t Reactions induced by unstable nuclei – 24.10.Eq Coupled-channel and distorted-wave models – 25.60.Bx Elastic scattering

Nuclear reactions involving neutron-rich nuclei have been one of the most important subjects in nuclear physics. Particularly in light neutron-halo nucleus induced reactions, it is very interesting to investigate how the halo structure affects the reaction mechanism. Due to the weakly-bound nature, the projectile halo nucleus would be easily excited into core-plus-neutron breakup states by the nuclear and Coulomb fields of target nucleus. Therefore, the breakup process is expected to play an important role in the halo nucleus induced reaction. One of the practical and reliable methods to study the three-body reaction process is the continuumdiscretized coupled-channels (CDCC) method [1]. In this paper, we apply the CDCC method to investigate the 11 Be → 10 Be + n breakup effect on the elastic scattering of 11 Be by 12 C at E/A = 49.3 MeV. Our aim is to study the dynamical effect of the halo structure on the nuclear reaction mechanism in the full quantum mechanical framework. In the present calculation, the 10 Be + n internal wave functions are calculated by the Woods-Saxon form potential with geometry r0 = 1.00 fm and a0 = 0.53 fm. The depths V0 is adjusted -dependently to reproduce the binding energy of the ground state (2s, −0.503 MeV) for s-wave, the first excited state (1p, −0.183 MeV) for p-wave, and the resonance energy (1.275 MeV) for d-wave, respectively. The potential depth for f -wave is taken to be the same as that for p-wave. Here, the spin-orbit interaca

Conference presenter; e-mail: [email protected]

tion is neglected for simplicity. The continuum states of 10 Be + n relative motion up to 1.2 fm−1 are taken into account and are discretized into momentum bins of widths Δk = 0.133 fm−1 for s-, p- and f -waves, while for dwave Δk = 0.157 fm−1 , which is determined not to divide the resonance peak at Er (11 Be) = 1.275 MeV into two bins. The discretized states are treated as usual discrete excited states in the same manner of the ordinary coupled-channels theory. The diagonal and coupling potentials of the 11 Be + 12 C system are calculated by folding the 10 Be-12 C and n-12 C optical potentials with the bound-state and discretized-continuum-state wave functions of the 10 Be + n system. The parameters of optical potentials are taken from ref. [2]. Figure 1 shows differential cross-section angular distributions (ratio to Rutherford) of the 11 Be + 12 C elastic scattering at E/A = 49.3 MeV. The solid curve shows the result of the CDCC calculation, and the dotted curve shows the result of the single-channel calculation using the folding-model interaction. The experimental data [3] represented by the solid circles are found to be well reproduced by the CDCC calculation. The difference between the single-channel and CDCC calculations indicates that the breakup effect on the elastic scattering is significant. From further analysis, it is found that the couplings to the ˆx = 0.954 MeV, where E ˆx represents the mean second (E ˆ energy of the bin) and third (Ex = 2.592 MeV) bins of the p-wave continuum state as well as the d-wave resonance state have important contribution to the breakup effect. The large effect of resonance state is reasonable because of the large overlap of the resonance wave function with

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0.5

R = 5 fm

(r,R) ] Re [ Fp2, gs

λ=1

σ/σR

10

0

E/A = 49.3 MeV CDCC folded pot. (single–channel) exp. data

0

c −T

−0.5

n −T

–1

10 0

10 θ (degree)

20

0

Fig. 1. Angular distribution for 11 Be + 12 C elastic scattering at E/A = 49.3 MeV. The solid circles are the experimental data, and the dotted and solid curves represent the results of the single-channel and CDCC calculations, respectively.

the ground-state one. However, the overlap integral of the continuum wave function with the ground-state one is not so large in general. To clarify the reason why the p-wave continuum breakup state has a large contribution, we investigate the coupling potential. Here, we discuss only the second bin of the p-wave continuum state (p2). First, we define a funcλ=1 (r, R) as tion Fp2,g.s. λ=1 Fp2,g.s. (r, R) = Φp2 (r) V1 (r, R) Φg.s. (r),

(1)

where V1 (r, R) represents the potential between core (10 Be) and target (c-T), or that between neutron and target (n-T) with multipolarity λ = 1. r and R represent the separation between core and neutron, and that between the center-of-mass of 11 Be and target nucleus, respectively. Φα (r) is the 10 Be + n wave function in state λ=1 (r, R) over α (α represents g.s. or p2). Integrating Fp2,g.s. r and summing the c-T and n-T components, we obtain the coupling potential between the ground state and the second bin of p-wave continuum state as a function of R. λ=1 (r, R) as a funcFigure 2 shows the real part of Fp2,g.s. tion of r. R is fixed at 5.0 fm. It is found that the cT component represented by the solid curve has a large amplitude in the long-range region, while the n-T components represented by the dotted curve is localized in the short-range region. Since these two components are summed up in the calculation of the coupling potential, the short-range parts cancel each other. However, the longrange part of the c-T component survives, resulting in comparable magnitude of coupling potential with that between the ground state and the d-wave resonance breakup state. This large amplitude of the c-T component is due to the long-range tail of the valence neutron wave function of the ground state. Namely, the large contribution from the p-wave breakup state reflects the characteristic of the weakly bound halo structure of the 11 Be nucleus. In order to see the breakup effect of 11 Be shown in fig. 1 in the potential form, we evaluate dynamical polar-

10 r (fm)

20

λ=1 Fig. 2. The real part of Fp2,g.s. (r, R) defined in eq. (1) as a function of the separation r between neutron and core nucleus. R represents the separation between the center-of-mass of 11 Be and target nucleus, and is fixed at R = 5.0 fm. The solid and dotted curves represent the core-target (c-T) and neutron-target (n-T) components, respectively.

0.4

ΔW / WF ΔV / VF

0.2

0

5

10

15

R (fm)

Fig. 3. Ratio of a dynamical polarization potential to the folded potential. The solid and dashed curves represent the real and imaginary parts, respectively.

ization potential (DPP). We search effective potential of the form Ueff = UF + ΔU , which reproduces the result of the CDCC calculation in the single-channel framework and, consequently, simulates the breakup effect. Here, UF denotes the folded potential for the elastic channel, which is the same as used in the CDCC calculation. We assume the Woods-Saxon derivative form for both the real (ΔV ) and imaginary (ΔW ) parts of ΔU and their parameters are searched by using a computer code ALPS [4]. The evaluated DPP is shown in fig. 3 as ratio to the folded potential. The DPP has a weakly repulsive real part (solid curve) and a long-range imaginary part of absorptive nature (dashed curve). These results also show a characteristic of the weakly-bound neutron-halo structure of the projectile nucleus.

M. Takashina et al.: Effect of halo structure on

References 1. Y. Sakuragi, M. Yahiro, M. Kamimura, Prog. Theor. Phys. Suppl. 89, 136 (1986).

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Be +

12

C elastic scattering

275

2. J.S. Al-Khalili, J.A. Tostevin, J.M. Brooke, Phys. Rev. C 55, R1018 (1997). 3. P. Roussel-Chomaz, private communication. 4. Y. Iseri, computer code ALPS, unpublished.

Eur. Phys. J. A 25, s01, 277–278 (2005) DOI: 10.1140/epjad/i2005-06-009-1

EPJ A direct electronic only

Observation of pre-equilibrium alpha particles at extreme backward angles from 28Si + nat Si and 28Si + 27Al reactions at E < 5 MeV/A Chinmay Basu1,a , S. Adhikari1 , P. Basu1 , B.R. Behera2 , S. Ray3 , S.K. Ghosh1 , and S.K. Datta4 1 2 3 4

Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata-700064, India Physics Department, Utkal University, Bhubaneswar, Orissa-751004, India Physics Department, Kalyani University, Kalyani, West Bengal-741325, India Nuclear Science Center, New Delhi-110067, India Received: 12 September 2004 / c Societ` Published online: 15 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. α clusters are measured in 28 Si + nat Si and 28 Si + 27 Al reactions at E(28 Si) < 5 MeV/A. Though forward angle data is explained well by the statistical model for compound nuclear emissions, the backward angle data indicate presence of pre-compound emissions. PACS. 25.70.Gh Compound nucleus – 25.70.-z Low and intermediate energy heavy-ion reactions

1 Introduction In heavy ion collisions at low incident energies (E ∼ 4–7 MeV/A) a dominant reaction mechanism is evaporation of light charged particles (LCP). The spectra of evaporation LCPs are generally explained well by the statistical model. However, there are many papers which report that the spectra of α-particles emitted from compound nuclei at high spin and excitation energy are not explained well by the statistical model calculations assuming a spherical compound nucleus [1]. It has been also observed that the entrance channel affects the equilibrium α-spectra to some extent [2]. These conclusions are however based on forward angle measurements only. On the other hand, the pre-equilibrium effects are considered to be negligible at these energies. In the light of these controversies we carried out an experiment where α-particles were measured at both forward and backward angles to have a more complete understanding of the reaction mechanism. The forward angle data was explained well in the framework of the statistical model for compound nuclear emissions. At extreme backward angles however, the data shows underpredictions in comparison to compound nuclear calculations.

2 Experiment The experiment was carried out at the Nuclear Science Centre Pelletron facility, New Delhi. 28 Si9+ beam at in

Conference presenter Dr Rituparna Kanungo; e-mail: [email protected] a e-mail: [email protected]

cident energy of 130 MeV was bombarded on 1 mg/cm2 of nat Si and 27 Al self-supporting targets. Standard twodetector Si telescopes were used for particle identification. Protons, deuterons, tritons, helions and alpha particles could be well separated. We, however, concentrate only on the alpha particles in this paper. The LCPs were detected in the telescopes at laboratory angles of 54◦ , 66◦ , 78◦ , 114◦ , 126◦ and 138◦ .

3 Results and discussion Figure 1(a)-(d) shows the inclusive α-spectra measured from this experiment at forward and backward angles. We carried out statistical model calculations using the code ALICE91 [3] (the full Hauser-Feshbach calculations are not very different from ALICE91 results). The forward angle data is not reproduced well unless the excited compound nucleus is considered to be highly deformed. The deformations are calculated by using the rotating liquiddrop model. This observation reconfirms the earlier conclusions of [1, 2]. However, at extreme backward angles the compound nucleus calculations fail to reproduce the data. This clearly indicates the contribution from noncompound effects, which has not been reported earlier as all the previous data were recorded at forward angles. As for mass symmetric systems the PEQ angular distributions are symmetric about 90◦ c.m. angle [4] there is a possibility that PEQ emissions become more prominent at extreme backward angles, even at such low energies. However one should determine which of the two laboratory angles is further away from 90◦ in the center of mass

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Fig. 1. Inclusive α-spectra for (a), (b) 28 Si + nat Si and (c), (d) 28 Si + 27 Al at the specified laboratory angles. The solid lines are ALICE91 calculations including RLDM deformation. In (a) and (c) also shown are ALICE91 calculations without deformation (dash-dotted lines). In (a), (b) the dotted lines are Hauser-Feshbach calculations.

Fig. 2. The plot of Δθcm (=| θcm − 90◦ |) against the alpha-particle energy in the laboratory frame (α ). In (a) the range of θcm is between 82.56◦ and 73.03◦ and in (b) between 151.36◦ and 154.85◦ .

frame. In the present case, the c.m. angles corresponding to the tail part of the spectrum at 138◦ (α = 10–20 MeV) (fig. 2(b)) is further away from 90◦ c.m. angle than the higher energy part (α = 20–40 MeV) of the 54◦ spectrum (fig. 2(a)). However, the effect of pre-equilibrium is not very strong compared to that seen at the higher energies. Detailed study in this direction is in progress for a better understanding of this interesting effect.

References 1. I.M. Govil et al., Phys. Rev. C 62, 064606 (2000). 2. I.M. Govil et al., Phys. Rev. C 66, 034601 (2002). 3. M. Blann, UCRL-JC-10905, LLNL, California, USA (1991). 4. C. Basu, S. Ghosh, Phys. Lett. B 484, 218 (2000).

Eur. Phys. J. A 25, s01, 279–280 (2005) DOI: 10.1140/epjad/i2005-06-105-2

EPJ A direct electronic only

Yield of low-lying high-spin states at optimal charge-particle reactions T.V. Chuvilskayaa and A.A. Shirokova Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119992, Moscow, Russia Received: 30 October 2004 / c Societ` Published online: 9 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Isomeric cross-section ratios (ICSR) σg /σm for the 4,6,8 He-induced reactions of Sr isotopes giving (g) (m) rise to 89mg Zr isomeric pair (J π = 9/2+ , T1/2 = 3.27 d; J π = 1/2− , T1/2 = 4.18 min) are calculated using 86 89mg Zr and 87 Sr(α, 2n)89mg Zr measured by a statistical model approach. ICSR of the reactions Sr(α, n) us earlier in the energy range E = 17–29 MeV are used as a test. Calculations and analysis of ICSR of reactions produced by unstable projectiles are performed for the first time. The dependence of obtained values on the projectile neutron number is discussed. PACS. 25.60.-t Reactions induced by unstable nuclei

At the moment the development of investigations of nuclear isomers (NI) is expected in the context of the use of unstable nuclear beams. In the present paper we discuss the probability of low-lying high-spin states production in the reactions with light neutron-rich (halo) projectiles. The ratio of cross-sections of a certain pair of isomeric states (high-spin and low-spin respectively) in one and the same nucleus allows to obtain an information on angular momentum dynamics of a preceding reaction and spin dependence of nuclear level density. This dynamics depends on the properties of a target, projectile, and emitted particles. It is important to find out optimal reaction parameters to populate high-spin isomer. In the present work we investigate the dependence of its yield on the projectile neutron number and the bombarding energy. Measurements of isomeric cross-section ratios in the reactions 86 Sr(α, n)89mg Zr and 87 Sr(α, 2n)89mg Zr in the energy range 17–29 MeV were carried out by us earlier using off-beam measurements of induced activity of the isomeric pair [1]. The activation method is a reliable tool for identification of reaction products. Here we present for the first time our results improved through the handling of the activation data with the use of the optimal extraction formula from [2]. Calculations of ICSR for the indicated reactions are performed using the upgraded program EMPIRE-II-18 [3]. This code is based on Hauser-Feshbach version of the statistical theory of nuclear reactions [4]. The field of application of the model is placed over the area of 10–50 MeV excitation energy of a compound nucleus, where the widths of resonances are greater than the distances between them. a

e-mail: [email protected]

Table 1. Values of the cross-section of population σ p in the reaction 86 Sr(α, n)89 Zr at Eα = 25.0 MeV.

E (MeV)

Jπ

σ p (mb)

0.0 0.59 1.09 1.45 1.51 1.62 1.71 1.83 1.86 1.94 2.01 2.10 2.10 2.12

9/2+ 1/2− 3/2+ 5/2− 9/2+ 5/2+ 3/2+ 5/2+ 3/2+ 13/2+ 9/2+ 5/2− 7/2+ 13/2−

7.245 0.184 0.292 0.45 1.25 0.34 0.127 0.259 0.107 4.761 0.557 0.184 0.318 3.513

Properties of nuclei involved in the discussed reactions are taken from the table [5]. ICSR is calculated using the formula: σg /σm = σt /σm − 1, where  σpt is the total cross-section of the re- the sum of partial cross-sections action, σm = p σm of the processes which result in population of the levels corresponding the condition J ≤ 5/2. According to [5] γ-transitions to low-spin member J π = 1/2− of the pair of 89 Zr nucleus dominate for such levels. Deexcitation of other levels results mainly in the high-spin state J π = 9/2+ population. Let us exemplify typical σ p values. For lower levels of the 89 Zr nucleus populated in the reaction 86 Sr(α, n)89 Zr

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Fig. 1. The excitation function (triangles-line) and isomeric cross-section ratios (squares-line: the calculation, circles: the experiment) for the reaction 86 Sr(α, n)89mg Zr.

Fig. 2. The excitation function (triangles-line) and isomeric cross-section ratios (squares-line: the calculation, circles: the experiment) for the reaction 87 Sr(α, 2n)89mg Zr.

at Eα = 25.0 MeV they are given in table 1, which is the fragment of population data produced by the EMPIRE code. In fact the list of the levels contributing the σm value is exhausted by this fragment. The list of high-spin levels contributing σg is very broad and extends far beyond table 1. As it is seen from table 1 the values of partial cross-sections for these levels are essentially larger than for presented low-spin ones. For high-spin levels which are not presented in table 1 that is also true. That is why ICSR are so large in the reaction. The experimental data and the results of calculations are represented in figs. 1 and 2 together with the excitation functions σt (E). As is shown on fig. 1 for the reaction 86 Sr(α, n)89mg Zr experimental values of ICSR up to energy Epr = 23 MeV are in agreement with calculated ones with an accuracy of 20–30%. At higher energy of α-particles calculated isomeric ratios exceed experimental ones, this is evidence of mechanisms of (α, n)-reactions other than statistical ones (preequilibrium, direct). For the reaction 87 Sr(α, 2n)89mg Zr a good agreement of the experimental and calculated values of ICSR is observed in the energy range of α-particles Epr = 19–27 MeV (fig. 2).

Fig. 3. The excitation function (triangles-line) and calculated isomeric cross-section ratios (squares-line) for the reaction 84 Sr(6 He, n)89mg Zr.

Calculations of isomeric ratios produced by the reactions 84 Sr(6 He, n)89mg Zr and 84 Sr(8 He, 3n)89mg Zr are carried out by us for the first time. As is shown in fig. 3, the value of the total cross-section of the reaction (6 He, n) falls down as the projectile energy increases. Isomeric ratios increase with the growth of the energy of 6 He-particles. Comparing ICSR values of the (α, n)- and (6 He, n)-reaction (figs. 1 and 3) calculated in the statistical model in the energy region E = 17–23 MeV (where the theoretical results are in agreement with measured ones for the (α, n)-reaction) one can conclude that the greater angular momentum contributing by 6 He is strongly reflected in ICSR. Is this tendency realized in the planning experiment with the 6 He beam? This depends on the contrbution of the competing reaction mechanisms there. ICSR calculated for the reaction with 8 He (another compound nucleus) is approximately fixed at the value σg /σm  12 in the energy region E = 25–29 MeV (we omit the respective figure for brevity). Thus experimental investigation of ICSR produced by halo projectiles such as 6(8) He seems to be very interesting because these values are sensitive to the relative contribution of direct and compound mechanisms as it was demonstrated above for 4 He-induced reactions. For heavier helium projectiles probability of a halo neutron to be ejected in a direct reaction is expected to be much higher.

References 1. V.D. Avchukhov et al., Izv. Akad. Nauk SSSR, Ser. Fiz. 44, 155 (1980). 2. R. Vanska, R. Rieppo, Nucl. Instrum. Methods 179, 525 (1981). 3. M. Herman, www-nds.iaea.org/empire/. 4. W. Hauser, H. Feshbach, Phys. Rev. 87, 366 (1952). 5. R.B. Firestone, Table of Isotopes CD-Rom Edition, Version 1.0., edited by V.S. Shirley, S.Y.F. Chu (J. Wiley & Sons, Inc., N.Y., 1996) p. 2372.

4 Reactions 4.4 Techniques and detectors

Eur. Phys. J. A 25, s01, 283–285 (2005) DOI: 10.1140/epjad/i2005-06-112-3

EPJ A direct electronic only

Developing techniques to study A ∼ 132 nuclei with (d, p) reactions in inverse kinematics K.L. Jones1,a , C. Baktash2 , D.W. Bardayan2 , J.C. Blackmon2 , W.N. Catford3 , J.A. Cizewski1 , R.P. Fitzgerald4 , U. Greife5 , M.S. Johnson6 , R.L. Kozub7 , R.J. Livesay5 , Z. Ma8 , C.D. Nesaraja2,8 , D. Shapira2 , M.S. Smith2 , J.S. Thomas1 , and D. Visser4 1 2 3 4 5 6 7 8

Department of Physics and Astronomy, Rutgers University, New Brunswick, NJ 08903, USA Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Department of Physics, University of Surrey, Guildford, Surrey, GU2 7XH, UK Department of Physics and Astronomy, University of NC, Chapel Hill, NC 27599, USA Department of Physics, Colorado School of Mines, Golden, CO 80401, USA Oak Ridge Associated Universities, Oak Ridge, P.O. Box 117, TN 37831, USA Physics Department, Tennessee Technological University, Cookeville, TN 38505, USA Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA Received: 11 October 2004 / c Societ` Published online: 22 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A measurement of the (d, p) reaction in inverse kinematics at energies near the Coulomb barrier using a stable beam of 124 Sn has been performed at ORNL’s Holifield Radioactive Ion Beam Facility (HRIBF). The sensitivity of proton angular distributions to the transferred angular momentum has been demonstrated. Spectroscopic factors have been extracted for three states and are in agreement with previous measurements made in normal kinematics. PACS. 25.60.Je Transfer reactions – 27.60.+j 90 ≤ A ≤ 149

Neutron-transfer reactions on stable targets have been used extensively to study the spectroscopy of both ground and excited states of nuclei close to stability. By utilizing this technique in inverse kinematics with rare isotope beams (RIBs), it is possible to study the evolution of single-particle structure away from the valley of stability. This is of importance to the understanding of both effective interactions and the synthesis of heavy elements in the r-process. Of particular interest is the region close to the double shell closure at 132 Sn. The first (d, p) measurement in inverse kinematics was made in GSI using stable Xe beams at 5.87 A MeV [1]. Reaction measurements with weak RIBs are technically challenging, and although (d, p) reactions in inverse kinematics have been performed with RIBs in the A ∼ 80 region [2,3] close to the Coulomb barrier, it was not clear that the technique would work well for heavier nuclei at these low bombardment energies. Hence it was decided to first make a test measurement using a stable beam of 124 Sn as the reaction has been well studied in normal kinematics [4,5,6, 7,8]. In one study [8] the center of mass energies were similar to those which are available at the HRIBF, where a 132 Sn(d, p) measurement will be performed. a

Conference presenter; e-mail: [email protected]

The single-neutron transfer reaction 2 H(124 Sn, p) has been measured at 4.5 A MeV using a deuterated polyethylene target with an effective thickness of 200 μg/cm2 [9]. Protons were detected in two position sensitive silicon telescopes and the silicon detector array SIDAR [10], covering angles θlab = 70◦ –160◦ (θC.M. = 7◦ –61◦ ). Particle identification was possible in the telescopes, where elastically scattered target constituents were detected as well as protons from the reaction. Data were collected for about 18 hours with a beam rate of 107 124 Sn particles per second. Angular distributions of elastically scattered deuterons were used to obtain absolute normalization of the cross sections. Comparisons of the data with calculations made with the DWUCK5 [11] code indicate that the deviations from Rutherford scattering for the measured deuterons were at most 5% for angles foward of 40◦ in the centerof-mass system owing to the close vicinity of the beam energy to the Coulomb barrier. This method allows normalization of the data independently of target thickness and beam fluctuation effects as it is a direct measure of the total number of beam ions incident on target atoms, and reduces the uncertainties to about 10%. The angle and energy of reaction protons were measured and used to determine the excitation energies in 125 Sn. States populated in 125 Sn were measured with a

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2.5

2

dσ/dΩ (mb/sr)

Table 1. Spectroscopic factors from this work and previous works. The quoted uncertainties include statistical, DWBA fitting effects and systematic errors due to the normalization.

sum s + d l=0 DWBA l=2 DWBA l=1 DWBA

1.5

Ex (MeV)

Jπ

This work

Ref. [8]

Ref. [7]

0.028 0.215 2.8

3/2+ 1/2+ 7/2−

0.44(6) 0.33(4) 0.46(5)

0.53 0.32 0.52

0.44 0.33 0.54

1

0.5 0

15

30

45 θC.M. (deg.)

60

75

90

Fig. 1. Angular distribution for the group of states below Ex = 300 keV in 125 Sn. The solid curve is the combined DWBA calculation for the 3/2+ state (dot-dashed) and the 1/2+ state (dashed). A 3/2− DWBA calculation (dotted) is shown for comparison.

dσ/dΩ (mb/sr)

3

l=3 DWBA

2

1

0 0

15

30

45 θC.M. (deg.)

60

75

90

Fig. 2. Angular distribution for the 2.8 MeV in 125 Sn. The solid curve is the DWBA calculation for an  = 3 transfer. All the small angle data from SIDAR have been binned into one data point.

resolution ΔE ≈ 200 keV FWHM, hence the 3/2+ state at 28 keV and the 1/2+ state at 215 keV could not be resolved in this measurement. The resolution was limited primarily by target thickness effects, specifically, the energy loss incurred by the heavy beam particle and the resulting uncertainty in the reaction energy. A slightly enlarged beam spot also affected the resolution. The combined angular distribution for the two lowlying states populated in 125 Sn and the angular distribution for the 2.8 MeV state are shown in figs. 1 and 2, respectively. Distorted Wave Born Approximation (DWBA) calculations using the TWOFNR code [12] with the optical model parameters given in [8] were performed. The calculations were fitted to the data and it was found that for the states below Ex = 300 keV both the 3/2+ state (dot-dashed) and the 1/2+ state (dashed) were needed in order to reproduce the data. Calculations including either a 3/2− state (as shown by the dotted line) or the 11/2− ground state did not improve the fit. The state at 2.8 MeV shows a considerably different shape to any of the low angular momentum transfer calculations shown in fig. 1 and is well described by a calculation assuming  = 3 transfer, in agreement with the known f7/2 assignment of this state.

Spectroscopic factors were extracted from the DWBA fits for  = 2 transfer to the 3/2+ state (dot-dashed) at 28 keV and the  = 0 transfer to the 1/2+ state (dashed) at 215 keV as well as for f7/2 state at 2.8 MeV, as shown in table 1. These values are compared with those measured in normal kinematics at the same effective deuteron energy [8] and at a higher beam energy Ed = 33 MeV [7]. Considering the 15–30% uncertainty normally assigned to spectroscopic factors, our results are in good agreement with those made in normal kinematics. In summary, the 124 Sn(d, p) reaction has been measured in inverse kinematics at 4.5 A MeV. The resolution in Q-value was found to be 200 keV, limited mostly by the target thickness, but also by a slightly enlarged beam spot. It should also be noted that level densities around 132 Sn are expected to be low due to the vicinity to the double shell closure, hence the resolution obtained here should be adequate. The data presented here show sensitivity of proton angular distributions to the -value of the transferred neutron in this mass region, with beam energies close to the Coulomb barrier. It is encouraging to note that even where states are not resolvable, it is still possible to extract both -values and spectroscopic factors, as for the 3/2+ and 1/2+ states in this work. Similar levels of statistics would be required to resolve -values with radioactive beams. With currently available beam intensities at the HRIBF, this equates to ten days of 132 Sn beam. This work was funded in part by the NSF under contract No. NSF-PHY-00-98800; the U.S. DOE under contract Nos. DE-FC03-03NA00143, DE-AC05-00OR22 725, DE-FG02-96ER40955, and DE-FG03-93ER40789; and the LDRD program of ORNL. K.L.J. would like to thank the Lindemann Trust Committee of the ESU.

References 1. G. Kraus et al., Z. Phys. A 340, 339 (1991). 2. J.S. Thomas et al., Radioactive Nuclear Beams (RNB6) proceedings, Nucl. Phys. A 746, 178c (2004); J.S. Thomas et al., Phys. Rev. C 71, 021302 (2005). 3. J.S. Thomas et al., Nuclei in the Cosmos (NIC8) proceedings, to be published in Nucl. Phys. A. 4. Bernard L. Cohen, Robert E. Price, Phys. Rev. 121, 1441 (1961). 5. E.J. Schneid, A. Prakash, B.L. Cohen, Phys. Rev. 156, 1361 (1967). 6. P.L. Carson, L.C. McIntyre jr., Nucl. Phys. A 198, 289 (1972).

K.L. Jones et al.: Developing techniques to study A ∼ 132 nuclei with (d, p) reactions in inverse kinematics 7. C.R. Bingham, D.L. Hillis, Phys. Rev. C 8, 729 (1973). 8. A. Str¨ omich, B. Steinmetz, R. Bangert, B. Gonsior, M. Roth, P. von Brentano, Phys. Rev. C 16, 2193 (1977). 9. K.L. Jones et al., Phys. Rev. C 70, 067602 (2004). 10. D.W. Bardayan et al., Phys. Rev. Lett. 83, 45 (1999).

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11. DWUCK5, P.D. Kunz, http://spot.colorado.edu/ ∼kunz/. 12. University of Surrey modified version of the code TWOFNR of M. Igarashi, M. Toyama, N. Kishida, private communication.

Eur. Phys. J. A 25, s01, 287–288 (2005) DOI: 10.1140/epjad/i2005-06-162-5

EPJ A direct electronic only

MUST2: A new generation array for direct reaction studies E. Pollacco1,a , D. Beaumel2 , P. Roussel-Chomaz3,b , E. Atkin1 , P. Baron1 , J.P. Baronick2 , E. Becheva2 , Y. Blumenfeld2 , A. Boujrad3 , A. Drouart1 , F. Druillole1 , P. Edelbruck2 , M. Gelin3 , A. Gillibert1 , Ch. Houarner3 , V. Lapoux1 , L. Lavergne2 , G. Leberthe3 , L. Leterrier2 , V. Le Ven1 , F. Lugiez1 , L. Nalpas1 , L. Olivier3 , B. Paul1 , B. Raine3 , A. Richard2 , M. Rouger1 , F. Saillant3 , F. Skaza1 , M. Tripon3 , M. Vilmay2 , E. Wanlin2 , and M. Wittwer3 1 2 3

CEA/DSM/DAPNIA/SPhN, Saclay, 91191 Gif-sur-Yvette Cedex, France IPN Orsay, 91405 Orsay Cedex, France GANIL (DSM/CEA, IN2P3/CNRS), BP 5027, 14076 Caen Cedex 5, France Received: 15 December 2004 / c Societ` Published online: 8 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We have developed a new telescope array, dedicated to the study of direct reactions of exotic nuclei on light targets in inverse kinematics. This device, called MUST2, is briefly described, and the results of the first tests performed with an alpha source and Ni beams at 10 and 75 MeV/u on a CDH target are presented. PACS. 29.30.Ep Charged-particle spectroscopy – 29.40.Wk Solid-state detectors – 29.40.Gx Tracking and position-sensitive detectors – 25.60.-t Reactions induced by unstable nuclei

1 Description of the array A new and innovative array, MUST2, based on silicon strip technology and dedicated to the study of reactions induced by radioactive beams on light particles, is presently under construction. The detector will consist of 6 silicon stripsSi(Li)-CsI telescopes (see fig. 1). The thickness of these detectors is respectively 300 μm, 5mm and 4 cm, corresponding to a maximum energy deposition for protons of 6 MeV, 25 MeV and 150 MeV. Compared to the existing MUST array [1], the innovation comes from the new Si strip detectors (10×10 cm2 instead of 6×6), the number of strips/side on each of them (128 instead of 60), the compactness of the array (volume divided by 6) and above all, the electronics which is based on ASIC chips. Each BiCMOS 36 mm2 chip has 16 bipolar channels, with energy and time measurement [2]. Table 1 presents the ASIC characteristics and performances. The data are multiplexed and coded with VXI ADCs. When complete, the array will correspond to more than 3000 channels of electronics.

2 First results The results of the first tests performed with one complete telescope show that the energy resolution is excellent. Figure 2 presents the spectrum measured with a 3-peak alpha a b

e-mail: [email protected] Conference presenter; e-mail: [email protected]

Fig. 1. Schematic drawing of the future MUST2 array. Table 1. ASIC characteristics and performances.

Power consumption Capacitance of detector Current of detector Energy range Contribution to energy resolution TAC range Time resolution (FWHM) Threshold range Readout

28 mW/channel (+/ − 2.5 V) 65 pF 20 nA +/ − 50 MeV 16 keV FWHM 300 ns and 600ns 240 ps (proton 6 MeV) +/ − 1 MeV on 8 bits DAC 2 MHz serial

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4500

4000

3500

3000

2500

2000

1500

1000

500

0

4800

5000

5200

5400

5600

5800

Energy (keV) Fig. 2. Alpha souce spectrum measured with the Si strip detector of MUST2. The spectrum is obtained by superposition of the 128 horizontal strips, after calibration.

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102

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1

Fig. 3. Identification plot measured for the Si strip and Si(Li) detectors. The energy for Si strip is given in keV. The calibration for Si(Li) is 2 keV/channel.

source, composed of 239 Pu,241 Am, 244 Cm. The resolution obtained was 35 keV, when the 128 horizontal or 128 vertical strips were superposed. The telescope was also tested at GANIL by measuring the elastic scattering of 58 Ni at

Fig. 4. Identification plot measured for the Si(Li) and CsI detectors. The axis scale is 2 keV/channel for Si(Li) and 10 keV/channel for CsI detectors.

10 and 74.5 MeV/nucleon on a CDH target. Figures 3 and 4 present ΔE-E identification plots for the Si-strip versus the Si(Li) detectors measured at 10 MeV/nucleon and for the Si(Li) versus CsI detectors at 74.5 MeV/nucleon, when the MUST2 telescope was located at 70 degrees from the beam axis in the laboratory. In both plots the identification is straightforward: Z = 1 (proton, deuton and triton) and Z = 2 (3,4 He) in fig. 3 and Z = 1 hyperbolas in fig. 4 are clearly distinguished. The present set-up of MUST2, as shown in fig. 1 has a large angular coverage with efficiencies of approximately 70% up to angles of 45 deg. This along with the additional measurement of time per channel and a large energy dynamic range makes the study of reactions leading to unbound states with several particles in the exit channel possible. The compactness of the array allows it to be installed inside a Ge multi-detector such as EXOGAM, allowing the γ-particles coincidences to be measured in the case of bound excited states. The first experiment with a large fraction of the final array is scheduled in the second half of 2005.

References 1. Y. Blumenfeld et al., Nucl. Instrum. Methods A 421, 471 (1999). 2. P. Baron et al., Conference IEEE NSS Portland, October 2003.

Eur. Phys. J. A 25, s01, 289–290 (2005) DOI: 10.1140/epjad/i2005-06-187-8

EPJ A direct electronic only

The EXODET apparatus: Features and first experimental results M. Romoli1,a , M. Mazzocco2 , E. Vardaci3 , M. Di Pietro1 , A. De Francesco1 , R. Bonetti4 , A. De Rosa3 , T. Glodariu2,5 , A. Guglielmetti4 , G. Inglima3 , M. La Commara3 , B. Martin3 , V. Masone1 , P. Parascandolo1 , D. Pierroutsakou1 , M. Sandoli3 , P. Scopel2 , C. Signorini2 , F. Soramel6 , L. Stroe5 , J. Greene7 , A. Heinz7 , D. Henderson7 , C.L. Jiang7 , E.F. Moore7 , R.C. Pardo7 , K.E. Rehm7 , A. Wuosmaa7 , and J.F. Liang8 1 2 3 4 5 6 7 8

INFN Napoli, Complesso Universitario MSA, Via Cintia, I-80126 Napoli, Italy University of Padova and INFN, Padova, Italy University “Federico II” and INFN, Napoli, Italy University of Milano and INFN, Milano, Italy INFN Laboratori Nazionali di Legnaro, Legnaro (PD), Italy University of Udine and INFN, Udine, Italy ANL, Argonne IL, USA ORNL, Oak Ridge TN, USA Received: 11 January 2005 / Revised version: 8 February 2005 / c Societ` Published online: 19 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The low intensity of the RIBs presently available at the first generation production facilities (105 –106 pps) and the necessity to reconstruct the event kinematics in RIB measurements require detection systems having both a large solid-angle coverage and a high granularity. The EXODET (EXOtic DETector) apparatus has been accomplished to respond to these requirements and the first experiment has been successfully performed studying the 17 F scattering on 208 Pb at 90.4 MeV. PACS. 87.66.Pm Solid state detectors – 25.60.-t Reactions induced by unstable nuclei

The EXODET (EXOtic DETector) consists of 16 large area silicon detectors (50 × 50 mm2 ), each of them having the front side segmented in 100 strips with a 0.5 mm pitch size and a 50 μm inter-strip distance. The detectors are arranged in 8 telescopes placed near the target both in the forward and backward hemispheres (see fig. 1), subtending a total solid angle of about 70% of 4π sr and covering the [26◦ , 82◦ ] and [98◦ , 154◦ ] theta-angle ranges [1]. The strips of the first-layer detectors (60 μm thick) are orthogonal to the beam direction and perpendicular to the strips of the second layer (500 μm thick), as shown in fig. 1, defining a position pixel of 0.5 × 0.5 mm2 for the particles passing through the first layer. For such particles, a Z identification is possible by using the usual ΔE-E technique, as well. The overall energy resolution, obtained with a standard electronic chain for the signals coming from the unsegmented rear side of the detectors, is about 1% for the E layer detectors, as it can be evinced from the spectrum reported in fig. 2, and about 3% for the ΔE ones. Due to the large number of channels (1600 for the whole apparatus) to be analyzed in order to get the position information, an innovative readout system based on highly integrated electronic circuitry (ASIC microchips) has been used. A chip originally developed for a

Conference presenter; e-mail: [email protected]

Fig. 1. Displacement of the EXODET telescopes around the target and assembling of the two layers.

high-energy experiments [2] was found suitable for the EXODET position readout and an appropriate detector-chip interface has been designed. Each chip is connected to the

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Fig. 2. E-detector energy spectrum for a three-peak alpha source.

Fig. 4. a) JT spectrum of the backward ΔE detector; b) and c) ToT spectrum for the same detector corresponding to the 17 F-peak and light particles, respectively.

Fig. 3. a) ΔE spectrum collected from the backward detector of the EXODET apparatus; b) ΔE spectrum gated by JT = 10 and ToT = 6; c) ΔE spectrum gated by JT = 10 and ToT ranging from 2 to 4.

strips of one EXODET detector. The signals outcoming from each strip are separately treated: they are amplified, shaped, sampled at a 15 MHz frequency, compared with an externally settable threshold, and stored in a 193 cells memory buffer. When a validated trigger command arrives to the chip the buffer is analyzed and, if a signal is present, a digitalized data stream is sent as output. It contains the identification number of the strips hit, the time spent by the signals over the threshold (ToT) and the time distance between the signals and the trigger (JT, Jitter Time), both measured in clock cycles. Front-end modules based on VME standard bus and an appropriate

acquisition system have been developed. The first successful experiment [3] has been performed, using a part of the EXODET apparatus, at the Argonne National Laboratory (USA). The scattering of a 17 F exotic beam by a 208 Pb target has been measured in the angular range θlab = 98◦ to 154◦ at an incident energy of 90.4 MeV. The data collected have been analyzed in terms of the optical model to find the best-fit parameter set of the nuclear potential and a comparison with the behavior for other stable nuclei in the same mass region has been discussed. The 17 F seems to behave more similarly to the oxygen stable isotopes (16 O and 17 O) than to the stable 19 F nucleus. The cross section for the 17 F −→ 16 O + p break-up process has been evaluated giving an average value of 2.6±1.2 mb/sr at backward angles. In fig. 3a) we report the energy spectrum of the collected events showing the peaks of the 17 F scattered ions, of the 17 O beam contaminant and of light particles. In fig. 4a) the JT spectrum of the strip signals is presented. The sharp peak at JT = 10 indicates that all events classified as “good ones” are correlated to the trigger within a 67 ns time window. In panels b) and c) of fig. 3 and fig. 4 is evidenced the correlation between ToT and energy and the system capability to disentangle different contributions by selecting the events with appropriate gates.

References 1. M. Romoli et al., AIP Conf. Proc. 704, 202 (2003). 2. A. Perazzo et al., BABAR Note 501 (1999) and references therein. 3. M. Romoli et al., Phys. Rev. C 69, 064614 (2004).

4 Reactions 4.5 Theory

Eur. Phys. J. A 25, s01, 293–294 (2005) DOI: 10.1140/epjad/i2005-06-002-8

EPJ A direct electronic only

Unbound exotic nuclei studied via projectile fragmentation reactions A. Bonaccorsoa INFN, Sezione di Pisa and Dipartimento di Fisica, Universit` a di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy Received: 1 February 2005 / Revised version: 10 February 2005 / c Societ` Published online: 17 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We present a time-dependent model for the excitation of a nucleon from a bound state to a continuum resonant state in the neutron-core potential. The final state is described by an optical model S-matrix so that overlapping resonances of any energy as well as deeply bound initial states can be considered. Due to the coupling between initial and final states the neutron-core free particle phase shifts are modified, in the exit channel, by a small additional phase. The model allows to extract structure information from data obtained in projectile fragmentation reactions of a borromean nucleus on a light target. Some results relative to the study of 13 Be are presented. PACS. 25.60.-t Reactions induced by unstable nuclei – 21.60.-n Nuclear structure models and methods

1 Introduction and reaction model Light unbound nuclei have recently attracted much attention [1, 2] in connection with exotic halo nuclei. A precise understanding of unbound nuclei is essential to determine the position of the driplines in the nuclear mass chart. A fundamental question to answer, in order to understand the structure of matter, is indeed what makes a certain number of neutrons and protons to bound together, while adding an extra neutron would lead to an unbound nucleus. Sometimes adding instead two neutrons leads to bound nuclei. Those are two-neutron halo nuclei such as 6 He, 11 Li, 14 Be, in which the two neutron pair is bound, although weakly, while each single extra neutron is unbound in the field of the core. In a three-body model these nuclei are described as a core plus two neutrons. The properties of core plus one neutron system are essential and structure models rely on the knowledge of angular momentum, parity, energies and spectroscopic strength for neutron resonances in the field of the core and the corresponding neutron-core effective potential. The neutron elastic scattering at very low energies on the “core” nuclei is not feasible as such cores, like 9 Li, 12 Be or 15 B are themselves unstable and cannot be used as targets. Indirect methods like projectile fragmentation, following which the neutron-core relative energy spectrum is reconstructed [2] have been used so far. Our model describes one neutron breakup probability from a halo projectile due to the interaction with the a

In collaboration with G. Blanchon, D.M. Brink, N. Vinh Mau; e-mail: [email protected]

target and including final-state interaction with the original core nucleus. It is appropriate to describe coincidence measurements in which the neutron-core relative energy spectrum is reconstructed. For two-nucleon breakup the complete process including the second nucleon breakup will be discussed elsewhere [3]. According to eq. (2.15) of [4] inelastic-like excitations can be described by a firstorder time-dependent perturbation theory amplitude  1 ∞ dt ψf (r, t)|V2 (r − R(t))|ψi (r, t), (1) Af i = i −∞

for a transition from an occupied nucleon bound state ψi to an unoccupied final state ψf . Here V2 is the interaction responsible for the neutron transition. The wave function ψi (r) for the initial state is calculated in a potential V1 (r) which is fixed in space. The final-state wave function ψf (r) can be a bound state or a continuum state. The potential V2 (r − R(t)) moves past on a constant velocity path with velocity v in the z-direction with an impact parameter bc in the x-direction in the plane y = 0. The first-order time-dependent perturbation amplitude can be put in a simple form by changing variables  (εf − εi )/v, and V2 (x−bc , y, q) = as ∞z = z −vt. Also q =iqz dzV (x−b , y, z)e . In order to obtain a simple ana2 c −∞ lytical formula we consider the special case in which V2 (r) is a delta function potential V2 (r) = v2 δ(x)δ(y)δ(z), with v2 ≡ [MeV fm3 ]. Then the integrals over x and y can be calculated and  ∞ v2 (2) dz ψf∗ (bc , 0, z)ψi (bc , 0, z)eiqz . Af i = iv −∞

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The initial state is the numerical solution of the Schr¨odinger equation which fits the experimental neutron separation energy and the final continuum state is given by

z   i  (+) (−) . hlf (kr) − Slf hlf (kr) Plf r 2 (3)  2mεf / is the neutron momentum in the final k = states and Cf is the asymptotic normalization constant. Slf is the S-matrix representing the final-state interaction of the neutron with the projectile core. The probability to excite a final continuum state of energy εf is an average over the initial state and a sum over the final states. Introducing the quantization condition and the density of final states [5] the probability spectrum reads ψf (bc , 0, z) = Cf k

2 v22 2 m dPin Σl (2lf + 1)|1 − S¯lf |2 |Ilf |2 , C = π 2 v 2 i 2 k f dεf

(4)

where |I| and α are the modulus and phase, respectively, of the integral in eq. (2). Here S¯ = ei2(δ+α) does not represent the free neutron-core scattering, since there is an additional contribution α to the free neutron phase δ. An absorption term 1 − |S¯lf |2 should be included if the neutron energy is higher than the core inelastic excitation energy threshold.

2 Application to

13

Be

One of the aims of this paper is to simulate the neutronBe relative energy spectra obtained from fragmentation of 14 Be or 14 B on a 12 C target at 70 A. MeV and to see whether they would show differences predictable in a theoretical model. In the case of 14 B the neutron is in a state combination of s and d components [2], and we assume the binding energy |εi | = 0.97 MeV. In 14 Be a combination of s, p and d components can be supposed and we take the binding energy |εi | = 1.85 MeV. Figure 1 shows results obtained including the s and d states according to eq. (4). The p-state is included only in the 14 Be case. In 12 Be the ground state wave function is a combination of such states with almost equal weight and none of them is fully occupied, then we assume that each of them has also components in the continuum. For each initial state a unit spectroscopic factor is taken. The result includes the transition bound to unbound from an s initial state to an s and d unbound states and from a bound d-state to unbound s and d states and from a bound p-state to an unbound p-state. In our model transitions with change of parity give no contribution. Keeping fixed binding energies and the resonance energies of the p and d states, we have varied the scattering length of the final s-state (given in the figure). The s-peak is dominant because of the well-known threshold effect. It does not have a Lorentzian shape because it receives contribution from both the s and d bound 12

Fig. 1. n-12 Be relative energy spectrum. Initial binding energy and final s-state scattering lengths are given in the figure.

components. In the case of a final bound s-state there is a very narrow peak close to threshold, while for as > 20 fm there is no peak at all. In this case the p-state contribution appears as a little bump at 0.5 MeV but the peak takes less strength than that of the d-state around 2 MeV. This is due to the concentration at threshold of the s-state, which has a less diffuse tail. When the s-state is unbound, the p-resonance peak disappears in the tail of the s-state, while the d-resonance peak can be clearly seen around 2 MeV because of the enhancement due to the 2lf + 1 factor in eq. (4). Finally we wanted to address the issue of possible core excitation effects in 14 Be. They can be modeled in the present approach by considering a small imaginary part in the neutron-core optical potential. A potential of WoodsSaxon derivative form has been taken with a −0.5 MeV strength. The result is shown in fig. 1 by the dashed line. The effect of the imaginary potential is to shift the s-state peak towards threshold and to wash out the d-resonance peak. It seems then that the spectrum of unbound nuclei would reflect the structure of the bound parent nucleus and that reaction mechanism models used to extract structure information should carefully include the effects discussed above. The model presented here seems to be promising in this respect. Details of potentials and physical parameters used will be given in a forthcoming publication [3].

References 1. G. Blanchon, A. Bonaccorso, N. Vinh Mau, Nucl. Phys. A 739, 259 (2004). 2. B. Jonson, Phys. Rep. 389, 1 (2004) and references therein. 3. G. Blanchon, A. Bonaccorso, D.M. Brink, N. Vinh Mau, IFUP-TH 29/2004. 4. A. Bonaccorso, D.M. Brink, Phys. Rev. C 43, 299 (1991). 5. A. Bonaccorso, D.M. Brink, Phys. Rev. C 38, 1776 (1988).

Eur. Phys. J. A 25, s01, 295–297 (2005) DOI: 10.1140/epjad/i2005-06-160-7

EPJ A direct electronic only

Progress on reactions with exotic nuclei F.M. Nunes1,a , A.M. Moro2 , A.M. Mukhamedzhanov3 , and N.C. Summers1 1 2 3

NSCL and Department of Physics and Astronomy, MSU, East Lansing, MI 48824, USA Departamento de FAMN, Universidad de Sevilla, Aptdo. 1065, 41080 Sevilla, Spain Cyclotron Institute, Texas A&M University, College Station, TX 77843 USA Received: 17 November 2004 / Revised version: 15 April 2005 / c Societ` Published online: 4 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Modelling breakup reactions with exotic nuclei represents a challenge in several ways. The CDCC method (continuum discretized coupled channel) has been very successful in its various applications. Here, we briefly mention a few developments that have contributed to the progress in this field as well as some pertinent problems that remain to be answered. PACS. 24.10.Ht Optical and diffraction models – 24.10.Eq Coupled-channel and distorted-wave models – 25.55.Hp Transfer reactions – 27.20.+n 6 ≤ A ≤ 19

1 Introduction Light nuclei on the drip lines can be studied through a variety of reactions. Models for nuclear reactions have been developed in recent years in order to incorporate the exotic features of these dripline nuclei. The real challenge for reaction theory lies in the low-energy regime where most approximations are not valid [1]. Three-body effects need to be carefully considered in the lower-energy regime. At energies close to the breakup threshold, Integral Faddeev Equations would be the appropriate choice. However, due to technical difficulties, the Continuum Discretized Coupled Channel Method (CDCC) [2] is the best working alternative. Here we consider specific features of breakup within CDCC, namely the continuum couplings in the usual breakup basis (sect. 2), and the alternative breakup mechanism consisting of transfer to the continuum of the target (sect. 3). Finally, in sect. 4, we briefly comment on remaining problems.

2 Continuum couplings Measurements of 8 B breakup are of importance to nuclear astrophysics. There have been several experiments performed at different facilities to provide the needed information on the S17 . Using our best understanding of the reaction mechanism, we assume the projectile can be represented by 7 Be(inert) + p. Within CDCC, the scattering states are binned up in energy (or momentum) labelled a

Conference presenter; e-mail: [email protected]

by an index α. When the projectile breaks up through the interaction with the target it can rearrange itself within the continuum. The relevant couplings, connect two continuum bins and have the form Vα;α (R) = φα (r)|VcT (Rc ) + Vf T (Rf )|φα (r) ,

(1)

where r is the projectile internal relative motion (c + f ), R is the relative motion between the projectile and the target and Rc (Rf ) is the vector connecting the center of mass of the core (fragment) to the center of mass of the target. The proximity to the breakup threshold has been shown to have important effects in the reaction mechanism. For instance, in the 8 B breakup around the Coulomb barrier [3] Coulomb multistep effects reduced the crosssection up to 20% but the most remarkable effect was related to the nuclear peak at larger angles which disappeared through continuum-continuum couplings. Continuum couplings are a way of looking into the effect of the final state interaction, integral part of CDCC. The properties of these continuum couplings and the influence they can have on breakup observables have been the object of a recent study [4]. Their long range behaviour is preserved throughout the multipole expansion, which slows down convergence: these couplings are shown to behave as 1/R2 for dipole transitions and 1/R3 for all higher multipoles. It was also found that continuum-continuum couplings have certain patterns with core-fragment relative energy and relative angular momentum. Monopole couplings are strongest when the initial and final relative energies are the same (represented in fig. 1 by the solid line), a simple consequence of the normalization of the bin wave function.

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7

7

Li

Li

n

Eα’ (MeV)

6.0

n 208

4.0

Pb

(a)

208

Pb

(b)

2.0

0.0

0.0

2.0

4.0

6.0

8.0

Fig. 2. Schematic diagram for the breakup of 8 Li on 208 Pb: (a) the standard breakup and (b) the transfer to the continuum of the target.

Eα (MeV)

Fig. 1. Representation of the relevant bins that need to be considered in a CDCC calculation: for a monopole transitions (solid), dipole transitions (dashed) and hexadecapole transitions (long-dashed). More details can be found in the text.

Dipole couplings are strongest when these energies differ by an amount comparable to the energy width of the bin, (represented in fig. 1 by the area in between the dashed lines). The higher the order of the couplings, the larger the region that needs to be taken into account. Tests on using this property for optimizing the large CDCC calculations have been performed. Optimization of lower partial waves is of little interest since the number of bins involved are typically small. It is for the larger partial waves (l > 2) that calculations become heavy. Our tests show that couplings with initial and final energies differing by several energy steps need to be considered in order to get convergence. This does not allow for significant improvement of the size and the time of the calculations.

3 Transfer to the continuum A variety of breakup models are presently in use and, when two different models are applied to the same problem, there is often a disparity in the predictions. In this sense, a generalized effort to bridge the various approaches is very much needed. One of the important issues lies in the choice of the coordinate representation of the continuum wave functions. We present results of a comparative study between the standard CDCC breakup approach and the so-called transfer to the continuum [5]. In the standard breakup approach, a projectile fragment is excited into the continuum, whilst keeping the correlation to the projectile core. There are cases where the correlation of the fragment with the target is more important, and then an expansion in terms of the standard breakup basis does not enable convergence within practical limits. Such was the case for the breakup studies of 6 He [6] and 8 Li [7] at energies around the Coulomb barrier. In fig. 2 we show the coordinate representation for the breakup of 8 Li on 208 Pb in the standard approach (a) and in the transfer to the continuum of the target approach (b). The differences between the two approaches are over-emphasized when resonances (in any particular channel) play a role in the dissociation process.

Typically, with an option of using an expansion based on the continuum of the projectile or the continuum of the target, one chooses the continuum of the more loosely bound nucleus, since it will be more prone to breaking up. However, there are some cases where this choice is not clear. For example, in the 7 Be(d,n)8 B reaction [8] one can immediately expect the 8 B continuum to be very important given the binding energy 0.137 MeV. However, the deuteron breakup is often very strong too. The inclusion of both continua, in the entrance channel and the exit channel raise some orthogonality issues that need to be addressed soon.

4 Remaining problems Even though the 8 B breakup application of CDCC has been extremely successful [9], low-energy Notre Dame data and high-energy NSCL/MSU data show a 60% inconsistency in the quadrupole excitation strength. This is an extremely severe problem from the point of view of direct capture [10]. Independently, accurate measurements have shown that 7 Be first excited state contributes to the ground state of 8 B [11]. It is possible that core excitation will help solve the puzzle. Major advances have been performed on microscopic approaches to reactions which include the treatment of one and two particle continuum (e.g., the Shell model embedded in the continuum model [12]). Although the variety of reactions that can be addressed through these microscopic models is rather limited, core excitation is much better treated than within the CDCC few-body approach. This work has been partially supported by National Superconducting Cyclotron Laboratory at Michigan State University, the Portuguese Foundation for Science (F.C.T.), under the grant POCTIC/36282/99, the Department of Energy under Grant No. DE-FG03-93ER40773 and the U.S. National Science Foundation under Grant No. PHY-0140343.

References 1. J. Al-Khalili, F. Nunes, J. Phys. G 29, R89 (2003). 2. M. Yahiro, N. Nakano, Y. Iseri, M. Kamimura, Prog. Theor. Phys. 67, 1464 (1982); Prog. Theor. Phys. Suppl. 89, 32 (1986).

F.M. Nunes et al.: Progress on reactions with exotic nuclei 3. 4. 5. 6. 7. 8.

F.M. Nunes, I.J. Thompson, Phys. Rev. C 59, 2652 (1999). F.M. Nunes, et al., Nucl. Phys. A 736, 255 (2004). A.M. Moro, F.M. Nunes, resubmitted to Phys. Rev. C. E. F. Aguilera et al., Phys. Rev. Lett. 84, 5058 (2000). A.M. Moro et al., Phys. Rev. C 68, 034614 (2003). Kazuyuki Ogata et al., Phys. Rev. C 67, 011602R (2003).

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9. J.A. Tostevin, F.M. Nunes, I.J. Thompson, Phys. Rev. C 63, 024617 (2001). 10. N.C. Summers, F.M. Nunes, arXiv:nucl-th/0410109v3. 11. D. Cortina-Gil et al., Phys. Lett. B 529, 36 (2002). 12. J. Okolowicz et al., Phys. Rep. 374, 271 (2003).

Eur. Phys. J. A 25, s01, 299–301 (2005) DOI: 10.1140/epjad/i2005-06-066-4

EPJ A direct electronic only

Entrance channel dependence in compound nuclear reactions with loosely bound nuclei S. Adhikari1 , C. Samanta1,2,a , C. Basu1 , S. Ray3 , A. Chatterjee4 , and S. Kailas4 1 2 3 4

Saha Institute of Nuclear Physics, 1/AF Bidhan nagar, Kolkata - 700 064, India Physics Department, Virginia Commonwealth University, Richmond, VA 23284, USA Department of Physics, University of Kalyani, Kalyani, West Bengal - 741 235, India Nuclear Physics Division, BARC, Mumbai - 400 085, India Received: 15 April 2004 / c Societ` Published online: 12 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The measurement of light charged particles evaporated from the reaction 6,7 Li + 6 Li has been carried out at extreme backward angle in the energy range 14–20 MeV. Calculations from the code ALICE91 show that the symmetry of the target-projectile combination and the choice of level density parameter play important roles in explaining the evaporation spectra for these light particle systems. In the above barrier energy region the fusion cross-section is not suppressed for these loosely bound nuclei. PACS. 25.70.Gh Compound nucleus – 25.70.-z Low and intermediate energy heavy-ion reactions

1 Introduction

2 Experiment

Study of fusion reactions with loosely bound stable nuclei like 6,7 Li, 9 Be etc. have gained importance in recent times as they provide a good analogue to investigations with halo nuclei. The effect of low break-up threshold of loosely bound nuclei on fusion reactions are not well understood [1, 2,3,4]. Most of the recent experiments with loosely bound nuclei investigate the behaviour of fusion excitation functions both in the above and below barrier regions. There are however fewer attempts to study the evaporation of light charged particles involving the reaction of such nuclei [5, 6]. In this work we report the inclusive measurement of α-particles emitted in the reactions of 6,7 Li projectile on 6 Li target at extreme backward angle for a range of energies above the Coulomb barrier. Statistical model calculations reproduce the experimental α-spectra (from other published works) nicely when emitted from a compound nucleus (CN) formed from an asymmetric target projectile combination. However in our case where the target-projectile combination is nearly symmetric, a large deformation (in terms of the rotating liquid drop model [7]) along with a structure-dependent level density parameter is required to properly explain the observed spectra.

The experiment was performed using 6,7 Li beams from the 14UD BARC-TIFR Pelletron Accelerator Facility at Mumbai, in the laboratory energy range 14 to 20 MeV. A 4 mg/cm2 thick rolled 6 Li target was used. Only light charged particles were detected. For particle identification standard two element ΔE-E telescopes with silicon surface barrier (ΔE = 10 μm) and Si(Li) detectors (E = 300 μm) were used. This telescope was placed at 175◦ to detect α-particles. The beam current was kept between 1–20 nA. Standard electronics and CAMAC based data acquisition system were used. Energy calibration was done using 7 Li elastic scattering data on Au and mylar targets each of thickness 500 μg/cm2 .



Conference presenter: Dr Rituparna Kanungo; e-mail: [email protected] a e-mail: [email protected]

3 Results and discussions Figures 1(a) and (b) show the inclusive α-spectrum measured at 175◦ from the reaction 7 Li + 6 Li at energies E(7 Li) = 14 and 16 MeV, respectively. The experimental spectra in general consists of a continuum part followed by some discrete peaks at higher energy. The discrete peaks are identified as due to α emission from 13 C and 23 Na (formed due to oxidation of 6 Li target) compound nuclei. As 6,7 Li are loosely bound nuclei, the continuum part may contain contributions from both break-up and compound nuclear reactions. However, the contribution of α emission from break-up process at this extreme

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Fig. 1. (a), (b) Inclusive α-spectrum measured at 175◦ from the reaction 7 Li + 6 Li at energies E(7 Li) = 14 and 16 MeV, respectively. Inclusive α-spectrum from (c) 28 Si + 6 Li scattering at E(6 Li) = 36 MeV, θ = 155◦ and (d) n + 12 C scattering at E(n) = 72.8 MeV, θ = 40◦ . Calculations (solid, dashed and dotted lines) are explained in the text.

backward angle is expected to be negligible. To evaluate the continuum part we use the statistical model code ALICE91 [8]. The dashed lines in fig. 1 indicate calculations with the Fermi gas level density parameter (a = A/9) assuming a spherical compound nucleus. As can be seen, the calculations grossly overpredict the experimental data. It is well known that the level density parameter a strongly influences the level density and hence the higher energy part of the evaporation spectra. We have found that in our case arbitrary change of a parameter does not help to improve the spectra, except for some change in slope. Instead of resorting to arbitrary adjustment of the parameters in the statistical model we try to consider a deformation in the excited CN as in the works [9, 10] for reactions with heavier nuclei. The dotted lines show the results of this calculation with the same level density parameter. The rotational energy is evaluated in terms of the Rotating Liquid Drop Model deformations [7]. These new calculations are now much reduced in comparison to the calculations assuming a spherical CN but they still overpredict the data. In the Fermi gas model a/A is simply a constant. However there are shell effects in a especially near the magic nucleon numbers. Therefore, instead of trying to adjust the parameter a, we now adopt the Gilbert Cameron prescription [11] for the shell-dependent level density parameter. The solid lines are calculations using shell corrected Gilbert-Cameron level density parameter and a deformed CN. This calculation agrees with the experimental data more satisfactorily. Similar results were observed for the reactions with 6 Li beam which will be discussed elsewhere. In order to verify the effect of target-projectile symmetry on the statistical calculations we have reanalyzed the published experimental data for 12 C(n, α) [12] and 28 Si(6 Li, α) [6] shown in figs. 1(c) and (d). In the reaction 12 C(n, α) the compound nucleus is 13 C, which is same as in our experiment but populated by an asymmetric combination of target and projectile. However, the excitation energy is much higher (72.15 MeV) (lower energy data is not available for this system). In case of 28 Si(6 Li, α) the α-particles were detected at backward angle (155◦ ) and the excitation of the compound nucleus

was 46.68 MeV. The excitation of the compound nucleus in our case is close to this value (32.34 to 35.1 MeV). ALICE91 calculations (dotted line) using Fermi gas level density parameter (a = A/9) in the Weisskopf-Ewing approximation (without any deformation) and comparison to the observed data is shown in figs. 1(c) and (d). The calculation reproduces the experimental data satisfactorily considering a spherical compound nucleus. In summary, the measurement of light charged particles evaporated from 6,7 Li + 6 Li has been carried out at extreme backward angle in the energy range 14–20 MeV. Calculations considering a deformed compound nucleus and shell-corrected Gilbert-Cameron level density parameter agree well with the experimental data. Interestingly, statistical model calculations require the excited compound nucleus to be deformed for 6,7 Li + 6 Li reaction, but spherical for asymmetric n + 12 C target-projectile combination. This indicates some target-projectile dependence for the light particle evaporation spectra. This phenomenon though known for heavier systems has not been reported earlier for such light loosely bound nuclei. For further verification of this phenomenon, additional experimental data leading to the same compound nucleus, excitation energy and angular momentum are needed in both the symmetric and asymmetric channels. Authors thank V. Tripathi, K. Mahata, K. Ramachandran and Pelletron personnel for their generous help during experiment and grant No. 2000/37/30/BRNS for funding.

References 1. 2. 3. 4. 5.

J.J. Kolata et al., Phys. Rev. Lett. 81, 4580 (1998). V. Tripathi et al., Phys. Rev. Lett. 88, 172701 (2002). C. Beck et al., Phys. Rev. C 67, 054602 (2003). J. Takahashi et al., Phys. Rev. Lett. 78, 30 (1997). Y. Leifels, G. Domogala, R.P. Eule, H. Freiesleben, Z. Phys. A 355, 183 (1990). 6. S. Kailas et al., Pramana J. Phys. 35, 439 (1990). 7. S. Cohen, F. Plasil, W.J. Swiatecki, Ann. Phys. (N.Y.) 82, 557 (1974).

S. Adhikari et al.: Entrance channel dependence . . . 8. M. Blann, UCRL-JC-10905, LLNL, California, USA (1991). 9. I.M. Govil et al., Nucl. Phys. A 674, 377 (2000). 10. C. Bhattacharya et al., Phys. Rev. C 65, 014611 (2001).

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11. A. Gilbert, A.G.W. Cameron, Can. J. Phys. 43, 1446 (1965). 12. I. Slypen, S. Benck, J.P. Meulders, V. Corcalciuc, At. Data Nucl. Data Tables 76, 26 (2000).

5 Clusters and drip lines 5.1 Clustering

Eur. Phys. J. A 25, s01, 305–310 (2005) DOI: 10.1140/epjad/i2005-06-035-y

EPJ A direct electronic only

Cluster structure in stable and unstable nuclei Y. Kanada-En’yo1,a,b , M. Kimura2,b , and H. Horiuchi3 1

2 3

Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan Institute of Physical and Chemical Research (RIKEN), Saitama 351-0198, Japan Department of Physics, Kyoto University, Kitashirakawa-Oiwake, Sakyo-ku, Kyoto 606-01, Japan Received: 24 September 2004 / c Societ` Published online: 25 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Cluster structure in stable and unstable nuclei has been studied. We report recent developments of theoretical studies on cluster aspect, which is essential for structure study of light unstable nuclei. We discuss negative-parity bands in even-even Be and Ne isotopes and show the importance of cluster aspect. Three-body cluster structure and cluster crystallization are also introduced. It was found that the coexistence of cluster and mean-field aspect brings a variety of structures to unstable nuclei. PACS. 21.60.-n Nuclear structure models and methods – 23.20.Lv γ transitions and level energies

1 Introduction Clustering is one of the essential features in nuclear dynamics. As already known, cluster structures appear in light stable nuclei such as 8 Be, 12 C and 20 Ne. Owing to recent developments of experimental and theoretical studies on unstable nuclei, cluster structures have been found also in light unstable nuclei. For instance, cluster states have been suggested in neutron-rich Be isotopes [1, 2,3,4,5,6,7,8,9,10,11, 12, 13, 14]. Furthermore, in the heavier nuclei, the importance of cluster aspect are found in such phenomena as molecular resonances, which has been observed in stable sd-shell and pf -shell nuclei. On the other hand, we should remind the reader that the mean-field nature is the other essential aspect. It is important that the coexistence of these two natures, the cluster and the mean-field aspects brings a variety of structure to unstable nuclei as well as stable nuclei. We can see the coexistence of cluster and mean-field aspects in such stable nuclei as 12 C, where the 3α-cluster structure plays an important role. The ground state is considered to contain the 3α-cluster and p3/2 sub-shell closure configurations [15]. In the excited states above the 3α threshold energy, developed 3α-cluster structures + + 12 C have are expected. The 0+ 2 , 03 and 21 states of been discussed in relation to the 3α structure for a long time [16,17, 15, 18, 19]. In unstable nuclei, a variety of cluster structure appears, and the coexistence of cluster and mean-field asa Conference presenter; e-mail: [email protected] b Present address: Yukawa Institute for Theoretical Physics, Kitashirakawa Oikawe-Cho, Kyoto 606-8502, Japan.

pects becomes further important. In halo nuclei, 6 He and 11 Li, the behavior of valence neutrons is described by a hybrid configuration of the independent single-particle motion and di-neutron structure [20,21,22,23,24,25]. The former is a kind of mean-field nature, and the latter is regarded as cluster aspect. In the neutron-rich Be isotopes, a molecular-orbital picture describes well the structure of low-lying states [4, 5,9, 26]. 2α core and valence neutron structure are found in many low-lying states of neutronrich Be. The molecular orbitals are formed in the meanfield of 2α-cluster system, and the valence neutrons are moving in the molecular orbitals around the 2α core. It means that a kind of mean-field nature is seen in the valence neutron behavior, and simultaneously the 2α-cluster core plays an important role to form the mean-field for the molecular orbitals. In the highly excited states of 12 Be, molecular resonant states with 6 He clusters have been suggested [12,13, 14]. As mentioned above, a variety of structure has been revealed and it motivates one to extend theoretical frameworks. In these years, the development of theoretical framework for cluster structure has been remarkable following the progress of physics of unstable nuclei. Such cluster models as core+neutrons models and multi-cluster models have been applied to unstable nuclei. These models are useful to describe the details of the relative motion between clusters and motion between core and valence neutrons. In addition to simple cluster models based on two-body or three-body calculations, extended models such as stochastic variational method (SVM) [6, 10, 20,27], molecular orbital method (MO) [4, 5,9, 28] and generator coordinate method (GCM) [24,29,30, 31] have been developed for structure study of unstable nuclei. We

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should give a comment on another important development of cluster models concerning studies of resonances in loosely bound systems. The complex scaling method (CSM) [21, 22, 25, 32, 33], method of analytic continuation in the coupling constant (ACCC) [34], and R-matrix theory [35] were applied to estimate widths of the resonances in cluster models. In most of cluster models, the existence of clusters is a priori assumed. However, the assumption of clusters is not necessarily valid for systematic study of unstable nuclei. Instead, it is important to take into account degrees of all single nucleons. In this sense, a method of antisymmetrized molecular dynamics (AMD) [15, 36,37, 38] is one of the powerful approaches which do not rely on the model assumption of cluster cores. The wave function of the AMD is similar to the Bloch-Brink model, but is based completely on single nucleons. Namely, an AMD wave function is given by a Slater determinant of singleparticle Gaussian wave functions, where all the centers of Gaussians are independent variational parameters. Therefore, the degrees of all single-nucleon wave functions are independently treated. Due to the flexibility of the AMD wave function, it can describe various cluster states as well as shell-model-like states. Similar model space has been adopted in a method of Fermionic molecular dynamics (FMD) [39]. One of the remarkable advantages of the recent version of FMD is that the effect of tensor force is incorporated based on realistic nuclear forces in this framework [40], while phenomenological effective nuclear forces are usually used in other cluster models. Owing to the progress of calculations with these models, the structure study of stable and unstable nuclei has been now extended to a wide mass number region up to sdand pf -shell region, and it reveals the importance of cluster aspect in ground and excited states of various nuclei. In this paper, we take some topics on cluster aspect in unstable nuclei. In the next sect. 2, we focus on the negativeparity bands in even-even nuclei. The excited states of Be and Ne isotopes are discussed in relation to cluster structure. In sect. 3, we report 3α structure in C isotopes and discuss the mechanism of rigid cluster structure. Finally, we give a summary in sect. 4.

2 Negative-parity bands in even-even nuclei As well known, 20 Ne has a 16 O+α-cluster structure, which − π was confirmed by parity doublets, K π = 0+ 1 and K = 01 rotational bands. The parity doublets arise from the reflection asymmetry of the intrinsic state, which is caused by 16 O + α clustering. Thus, negative-parity bands can be good probes for cluster structure. It is interesting that another type of negative-parity rotational band with cluster structure appears in neutron-rich nuclei based on singleparticle excitation of neutron orbitals. In such a state, the origin of the negative parity is the single-particle excitation. A typical example is the 1p-1h excitation of the valence neutron orbitals in the molecular orbital states. The negative-parity bands with the 1p-1h excitation have been suggested in low-lying states of neutron-rich Be isotopes.

(a) Be σ

π

+ α

+

α

α

-

α

+

-

(b) Ne

σ

+ 16O +

α

-

Fig. 1. Schematic figure of the molecular orbitals: the π- and σ-orbitals around 2α core (a) and σ-orbital around 16 O + α core (b).

One of the characteristics of those negative-parity bands is the quanta K π = 1− , which differs from the K π = 0− of the parity doublets. In this section, we discuss the negative-parity bands in neutron-rich Be and Ne isotopes.

2.1 Be isotopes The low-lying states of neutron-rich Be isotopes are well described by the molecular orbital picture based on the 2α core and valence neutron structure. In the 2α system, the molecular orbitals are formed by a linear combination of p-orbits around the 2α core. In neutron-rich Be, the valence neutrons occupy the molecular orbitals. The negative-parity orbitals are called as “π-orbitals” and the longitudinal orbital with positive parity is a “σ-orbital” (fig. 1). As a result of the formation of molecular orbitals in Be isotopes, a negative-parity K π = 1− band is constructed because of the one valence-neutron excitation of the molecular orbitals in the rotating cluster structure. In 10 Be, the K π = 1− band is regarded as such a molecularorbital band with the one-neutron excitation, which can be described by a π 1 σ 1 configuration in the molecularorbital picture [5, 8,9, 26]. In 12 Be, many rotational bands are theoretically suggested. Figure 2 shows the energy levels of 12 Be calculated by variation after spin-parity projection in the AMD framework. The energy variation is performed for the J π eigenstates projected from a single-Slater AMD wave function. For the k-th J π state, the wave function is obtained

Excitation Energy (MeV)

Y. Kanada-En’yo et al.: Cluster structure in stable and unstable nuclei

(8+)

20

7+ (6+)

6 He+ 6He

11Be+n

0

314-

5+ + 1 2 4

8 He+4 He

5 10Be+2n

5-

6+

1+ + (4+) 5+ 4 0+1+ 2+ + 6+ 3 2+

15 10

8+

1-

+

+0 2 + 0

EXP

+ 2+ 0 0+

23-

K=1- K=0

AMD

Fig. 2. Energy levels of 12 Be. The MV1 case 1 force (m = 0.65) + G3RS (uls = 3700 MeV) force is adopted. The details of the AMD calculations are explained in [12].

by the energy variation for the component orthogonal to π states. The energy variation is perthe lower J1π , · · · , Jk−1 formed by a frictional cooling method (a imaginary time method). After the variation, we superpose the 22 AMD wave functions of 12 Be determined by the variation for various spin and parity to obtain better wave functions. The adopted effective nuclear force is the MV1 (Modified Volkov) force [41], which contains a zero-range threebody repulsive term in addition to the two-range twobody central force, complemented by a two-range spinorbit force of G3RS [42] and Coulomb force. The details of the framework and calculations are given in [12] and references therein. The theoretical results obtained by the AMD calculations agree well to the experimental data. We + found three positive-parity rotational bands K π = 0+ 1 , 02 + and 03 . The ground band consists of the intruder states (2¯hω excited configurations), which are well-deformed states with the 2α core and the surrounding neutrons. On the other hand, the normal neutron-shell-closed states belong to the K π = 0+ 2 band. It means that the breaking of neutron magic number N = 8 occurs in 12 Be. In the K π = 6 6 0+ 3 band, He + He molecule-like states are predicted in the results. The experimentally measured 4+ and 6+ states are the candidates of these molecular resonant states. Next, let us analyze the negative-parity states of 12 Be. In the negative-parity states, two bands K π = 1− and K π = 0− are obtained by the AMD calculations. The lower one is the K π = 1− band which consists of 1− , 2− , 3− , 4− and 5− states. These states are the molecular-orbital states, which can be described by the π 3 σ 1 (three neutrons in the π-orbitals and one neutron in the σ-orbital) configuration of the valence neutrons in the 2α-cluster system. This K π = 1− band is consistent with the molecular-orbital band predicted by von

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Oertzen et al. [26]. On the other hand, we also obtain the higher negative-parity band (K π = 0− ). The K π = 0− band is formed by a parity asymmetric neutron structure of the 4 He + 8 He-like intrinsic state. This band is associated with the well-known parity doublet K π = 0− band in 20 Ne. Descouvemont and Baye performed GCM calculations of 12 Be [30], where 6 He + 6 He and 4 He + 8 He configurations are coupled and the relative distance between two He clusters is chosen as the generator coordinate. The effective two-body nucleon-nucleon interaction was chosen as the Volkov V2 force [43] (m = 0.45, b = −h = −0.2374) + zero-range spin-orbit force (S0 = 30 MeV fm5 ) + Coulomb. These interaction parameters are chosen so as to reproduce the 6 He + 6 He and 4 He + 8 He thresholds simultaneously. In the GCM calculations, they found the K π = 0− band with the 8 He + αlike cluster structure, which is consistent with the higher negative-parity band (K π = 0− ) found in the AMD results. It is concluded that the existence of two negativeparity bands K π = 1− and 0− is suggested in 12 Be. The K π = 1− band is the molecular orbital band, while the K π = 0− band is the parity doublet caused by the parity asymmetric intrinsic state. Both bands have developed cluster structure, however, there exists a remarkable difference between these two bands concerning the origin of negative parity. In the K π = 1− band, the negative parity originates from the one-particle excitation of the valence neutron in the molecular orbitals. On the other hand, the negative parity of the K π = 0− band arises from the parity asymmetric shape of the intrinsic state. Due to the collectivity, the E1 transition into the ground state is stronger − 2 4 π − as B(E1; 0+ 1 → 12 ) = 1.0 e fm from the K = 0 band + − 2 4 π than B(E1; 01 → 11 ) = 0.2 e fm from the K = 1− band. It is interesting that the lower one is the molecularorbital K π = 1− band which has a kind of mean-field nature in the valence neutron behavior. We consider that the experimentally observed K π = 1− state [44] corresponds to the band-head state of the K π = 1− band. 2.2 Ne isotopes In analogy to neutron-rich Be isotopes, von Oertzen proposed molecular orbital structure of Ne isotopes based on the 16 O + α-cluster core [26]. In the molecular-orbital picture, the cluster structure may develop when the valence neutrons occupy the molecular σ-orbitals, which correspond to longitudinal f p-like orbits (fig. 1). In 22 Ne, they proposed a developed cluster structure where two valence neutrons occupy the σ orbit. As a result of the development of cluster, the parity doublet K π = 0− band arise from the parity asymmetric structure of the 16 O + αcluster core. We performed the AMD + GCM calculations of 22 Ne with Gogny D1S force. The deformed-base AMD wave functions are used, and the constraint on the oscillator quanta of the deformed harmonic oscillator is applied in addition to the constraint on the deformation parameter β. We find that the parity doublet K π = 0+ and 0− bands arise from the developed 16 O + α core with two valence neutrons in the σ-like orbital in the excited states

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Fig. 3. Density distribution of 22 Ne. The density of the intrinsic states of the ground band is illustrated in panel (a). Panel (b) shows the density in the K π = 0− band with valence neutrons in longitudinal σ-like orbitals. The middle and top figures in each box show the density distribution of the singleneutron wave functions of the highest single-particle level. The matter density of the total system is displayed at the bottom of the box.

below the 18 O + α threshold energy. In fig. 3(b), we show the developed 16 O + α cluster and the single-particle orbit of the last valence neutron, which is consistent with the molecular σ-orbital around the 16 O + α core (fig. 1(b)). The details of the AMD calculations of 22 Ne will be published in a future paper. Recently, Rogachev et al. observed the α-cluster states in negative-parity bands which start from the 1− state at 12 MeV excitation energy of 22 Ne [45]. These negativeparity states above the 18 O + α threshold energy can be associated with the developed 18 O + α-cluster structure. The microscopic calculations of the excited states of 22 Ne were performed by Dufour and Descouvemont by using the GCM method within a 18 O + α-cluster model [46]. They chose the inter-cluster distance as the generator coordinate, and incoorporated many 18 O+α channels by defining the 18 O internal wave functions in the s, p, and sd shell-

model configurations. The effective interaction was chosen as the Volkov V2 force (m = 0.6259) + zero-range spinorbit force (S0 = 30 MeV fm5 ) + Coulomb. The negativeparity bands with the developed 18 O + α-cluster states are found in the results of the GCM calculations. These negative-parity states in the parity doublet band exist in the energy region above 18 O+α threshold energy (9.7 MeV excitation energy of 22 Ne), which is consistent with the observed α-cluster states [45]. These theoretical and experimental works suggest that the 18 O + α-cluster bands appear above the 18 O + α threshold, while the molecularorbital bands with the developed 16 O + α cluster and two neutrons in the molecular σ-orbital may exist in the lowerenergy region than the 18 O + α-cluster bands. Next, we discuss a further neutron-rich nucleus, 30 Ne. The AMD+GCM calculations of 30 Ne with the deformedbase AMD wave functions [38, 47] have been performed by Kimura et al. [47] The deformation parameter β was chosen as the generator coordinate. As is usually done in the GCM calculations of Hartree-Fock (HF) framework, the AMD wave functions obtained by the variation with the constraint on the β value were projected to the spin-parity eigenstates, and were superposed. The effective nuclear interaction was chosen as the Gogny D1S force [48] and Coulomb. In the results, many low-lying bands have been predicted. They found that the ground hω configuration, which band of 30 Ne is dominated by 2¯ indicates the breaking of magic number N = 20. The results suggest 4¯ hω state with a 4p-4h neutron configuration appear in the low-lying 0+ 3 band (the excitation energy ) = 4 MeV). The 4p-4h state has a parity asymmetEx (0+ 3 ric proton structure which indicates the developed 16 O+αcluster core. One of the striking results is the prediction of a low-lying K π = 1− band with a 3p-3h neutron configuration. The structure of the K π = 1− band is described by the excitation of neutrons in the deformed mean field. The excitation energy of the band-head 1− state of the K π = 1− band is predicted to be less than 3 MeV. It is surprising that such many-particle many-hole states may exist in low-energy region of 30 Ne. These results indicate the softness of neutron N = 20 shell, and point the importance of neutron excitation in the deformed mean-field in neutron-rich nuclei.

3 Three-center clustering and cluster crystallization As mentioned before, the 3α-cluster structure is known in 12 C. The 3α-cluster states with a triangular shape and linear-chain structure have been discussed for a long time. Recently, Tohsaki et al. proposed a gas-like dilute 3α state and succeeded to describe the properties of the 0+ 2 state of 12 C with Bose-condensed wave functions of 3 α-particles. In the experimental side, the broad resonances at 10 MeV + are recently assigned to be 0+ 3 and 22 states, which are candidates of 3α-cluster states. In neutron-rich C isotopes, three-center cluster structures with the 3α-cluster core are expected to exist

Y. Kanada-En’yo et al.: Cluster structure in stable and unstable nuclei

(a)

(b) 12C(0+) 2

C(3-2)

14

α

α α

α

α

(c)

(d) Ne

Be +

α

α

-

α

+

+ 16O +

α

-

Fig. 4. Schematic figures for cluster structure in 12 C(0+ 2 ) (a), C(3− 2 ) (b), neutron-rich Be with the molecular σ-orbitals (c), neutron-rich Ne with the σ-orbitals (d).

14

in the excited states. Possible linear chain structures were suggested to appear in highly excited states of 16 C and 15 C [26, 49, 50]. In 14 C, Itagaki et al. proposed an equilateral-triangular shape with 3α core in K π = 3− band which is stabilized by excess neutrons [51]. They performed molecular orbital model calculations of 14 C with 3α and excess neutrons. In the model, the molecular orbitals around the 3α core are introduced, and the excess two neutrons occupy them. With respect to the positions of 3α clusters and configurations of the valence neutrons, the spin-parity projected wave functions are superposed by the diagonalization of Hamiltonian as is done in the GCM method. The Volkov V2 force complemented by a two-range spin-orbit force of G3RS were used in the calculation of 14 C. In their calculations, it was found that the excess neutrons distribute in the gap space between α cores. As a result, the triangular configuration of 3α is stabilized, and the K π = 3− rotational band is formed due to the D3h symmetry. It should be noticed that the neutron configuration in the orbital given by the linear combination of the molecular orbitals on the α-α bonds is important in the K π = 3− band. The experimentally observed − − 3− 2 , 41 and 51 states are the candidates of the members of π − this K = 3 band. Comparing the gas-like 3α structure 12 C, the triangular shape of the 3α becomes in the 0+ 2 of more rigid due to the valence neutrons in 14 C. Itagaki et al. named this phenomenon as “α crystallization”. The mechanism of rigid cluster structure is understood as follows. In case of 12 C, 3α clusters are weakly bounded and can move freely in the cluster states above the 3α threshold energy (fig. 4(a)). When two neutrons are added into those 3α states, the valence neutrons move around the α cores and occupy the gap space between α cores (see

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fig. 4(b)). As a result, the α clusters cannot freely move because the motion of the α clusters are forbidden due to the Pauli blocking between the valence neutrons and the neutrons inside the α clusters. Thus, the 3α clusters are crystallized to form the triangular shape in 14 C. Itagaki’s idea of “cluster crystallization” can be also applied to two-body cluster states as well as the 3α-cluster states. As mentioned before, the developed cluster structures are suggested in neutron-rich Be and Ne isotopes which have α + α-cluster and 16 O + α-cluster cores, respectively. Especially, the remarkable enhancement of cluster structure is expected when the valence neutrons occupy the longitudinal molecular orbitals, namely, the σ-orbitals. The σ-orbitals have nodes along the longitudinal axis. It is important that the valence neutrons in σ-orbitals occupy the gap space between the core clusters (fig. 4(c) and (d)). As a result, when the core clusters approach to each other, they feel repulsion against the valence neutrons in the gap region because of Pauli blocking. In other words, due to the existence of the valence neutron in the gap space, the core clusters cannot move so freely and are kept away. Thus, the cluster structure is enhanced. It is concluded that the valence neutrons in molecular orbitals play important roles in the cluster states of neutron-rich nuclei. The valence neutrons bound the clusters more deeply, and may make the spatial configuration of clusters more rigid.

4 Summary The recent development of theoretical and experimental studies revealed that the cluster aspect is an essential feature in unstable nuclei as well as stable nuclei. The coexistence of cluster and mean-field aspects brings a variety of structure to unstable nuclei. We reported some topics concerning the cluster structure of unstable nuclei while focusing on the negative-parity bands of even-even nuclei. In the low-lying states of neutron-rich nuclei, the meanfield aspect of the valence neutron behavior is found to be essential. The negative-parity rotational bands appear in the low-energy region due to the particle-hole excitation in the deformed neutron mean-field. On the other hand, in high-energy region, there may exist negative-parity states in the parity doublet bands which are caused by asymmetric intrinsic shapes. In Be and Ne isotopes, developed cluster structures with 2α-cluster and 16 O+α-cluster cores were suggested, while 3α-cluster structures were predicted in C isotopes in many theoretical studies. The valence neutrons in the molecular orbitals play an important role to stabilize cluster structure. The computational calculations in this work were supported by the Supercomputer Projects of High Energy Accelerator Research Organization (KEK). This work was supported by the Japan Society for the Promotion of Science and Grant-inAid for Scientific Research of the Japan Ministry of Education, Culture, Sports, Science and Technology.

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References 1. A.A. Korsheninnikov et al., Phys. Lett. B 343, 53 (1995). 2. M. Freer et al., Phys. Rev. Lett. 82, 1383 (1999); M. Freer et al., Phys. Rev. C 63, 034301 (2001). 3. A. Saito et al., Proceedings of the International Symposium on Clustering Aspects of Quantum Many-Body Systems, edited by A. Ohnishi, N. Itagaki, Y. Kanada-En’yo, K. Kato (World Scientific Publishing Co.) p. 39. 4. M. Seya, M. Kohno, S. Nagata, Prog. Theor. Phys. 65, 204 (1981). 5. W. von Oertzen, Z. Phys. A 354, 37 (1996); 357, 355 (1997). 6. K. Arai, Y. Ogawa, Y. Suzuki, K. Varga, Phys. Rev. C 54, 132 (1996). 7. A. Dot´e, H. Horiuchi, Y. Kanada-En’yo, Phys. Rev. C 56, 1844 (1997). 8. Y. Kanada-En’yo, H. Horiuchi, A. Dot´e, Phys. Rev. C 60, 064304 (1999). 9. N. Itagaki, S. Okabe, Phys. Rev. C 61, 044306 (2000); N. Itagaki, S. Okabe, K. Ikeda, Phys. Rev. C 62, 034301 (2000). 10. Y. Ogawa, K. Arai, Y. Suzuki, K. Varga, Nucl. Phys. A 673, 122 (2000). 11. Y. Kanada-En’yo, Phys. Rev. C 66, 011303 (2002). 12. Y. Kanada-En’yo, H. Horiuchi, Phys. Rev. C 68, 014319 (2003) and references therein. 13. M. Ito, Y. Sakuragi, Y. Hirabayashi, Phys. Rev. C 63, 064303 (2001). 14. P. Descouvemont, D. Baye, Phys. Lett. B 505, 71 (2001). 15. Y. Kanada-En’yo, Phys. Rev. Lett. 81, 5291 (1998). 16. H. Morinaga, Phys. Rev. 101, 254 (1956); Phys. Lett. 21, 78 (1966). 17. Y. Fujiwara, H. Horiuchi, K. Ikeda, M. Kamimura, K. Kato, Y. Suzuki, E. Uegaki, Prog. Theor. Phys. Suppl. 68, 29 (1980). 18. A. Tohsaki, H. Horiuchi, P. Schuck, G. R¨ opke, Phys. Rev. Lett. 87, 192501 (2001). 19. Y. Funaki, A. Tohsaki, H. Horiuchi, P. Schuck, G. R¨ opke, Phys. Rev. C 67, 051306 (2003). 20. K. Varga, Y. Suzuki, R.G. Lovas, Nucl. Phys. A 571, 447 (1994). 21. A. Cs´ ot´ o, Phys. Rev. C 48, 165 (1993); A. Cs´ ot´ o, Phys. Rev. C 49, 3035 (1994). 22. S. Aoyama, S. Mukai, K. Kato, K. Ikeda, Prog. Theor. Phys. 93, 99 (1995). 23. Y. Tosaka, Y. Suzuki, K. Ikeda, Prog. Theor. Phys. 83, 1140 (1990). 24. P. Descouvemont, Nucl. Phys. A 626, 647 (1997).

25. S. Aoyama, K. Kato, K. Ikeda, Prog. Theor. Phys. Suppl. 142, 35 (2001). 26. W. von Oertzen, Nuovo Cimento. A 110, 895 (1997); W. von Oertzen, Eur. Phys. J. A 11, 403 (2001). 27. K. Varga, Y. Suzuki, I. Tanihata, Nucl. Phys. A 588, 157c (1995). 28. S. Okabe, Y. Abe, H. Tanaka, Prog. Theor. Phys. 57, 866 (1977); S. Okabe, Y. Abe, Prog. Theor. Phys. 59, 315 (1978); 61, 1049 (1979). 29. D. Baye, P. Descouvemont, N.K. Timofeyuk, Nucl. Phys. A 577, 624 (1994). 30. P. Descouvemont, D. Baye, Phys. Lett. B 505, 71 (2001). 31. P. Descouvemont, Nucl. Phys. A 699, 463 (2002). 32. A.T. Kruppa, R.G. Lovas, B. Gyarmati, Phys. Rev. C 37, 383 (1988); A.T. Kruppa, K. Kat, Prog. Theor. Phys. 84, 1145 (1990). 33. S. Aoyama, K. Kat, K. Ikeda, Phys. Rev. C 55, 2379 (1997). 34. S. Aoyama, Phys. Rev. C 68, 034313 (2003). 35. K. Arai, P. Descouvemont, D. Baye, W.N. Catford, Phys. Rev. C 68, 014310 (2003). 36. Y. Kanada-En’yo, H. Horiuchi, A. Ono, Phys. Rev. C 52, 628 (1995); Y. Kanada-En’yo, H. Horiuchi, Phys. Rev. C 52, 647 (1995). 37. Y. Kanada-En’yo, H. Horiuchi, Prog. Theor. Phys. Suppl. 142, 205 (2001). 38. Y. Kanada-En’yo, M. Kimura, H. Horiuchi, C. R. Phys. 4, 497 (2003). 39. H. Feldmeier, K. Bieler, J. Schnack, Nucl. Phys. A 586, 493 (1995). 40. T. Neff, H. Feldmeier, Nucl. Phys. A 713, 311 (2003). 41. T. Ando, K. Ikeda, A. Tohsaki, Prog. Theor. Phys. 64, 1608 (1980). 42. N. Yamaguchi, T. Kasahara, S. Nagata, Y. Akaishi, Prog. Theor. Phys. 62, 1018 (1979); R. Tamagaki, Prog. Theor. Phys. 39, 91 (1968). 43. A.B. Volkov, Nucl. Phys. 74, 33 (1965). 44. H. Iwasaki et al., Phys. Lett. B 491, 8 (2000). 45. G.V. Rogachev et al., Phys. Rev. C 64, 051302 (2001). 46. M. Dufour, P. Descouvemont, Nucl. Phys. A 738, 447 (2004). 47. M. Kimura, H. Horiuchi, Prog. Theor. Phys. 111, 841 (2004). 48. J.F. Berger, M. Girod, D. Gogny, Nucl. Phys. A 428, 23c (1984). 49. N. Itagaki, S. Okabe, K. Ikeda, I. Tanihata, Phys. Rev. C 64, 014301 (2001). 50. W. von Oertzen, M. Freer, Y. Kanada-En’yo, submitted to Rev. Mod. Phys. 51. N. Itagaki, T. Otsuka, K. Ikeda, S. Okabe, Phys. Rev. Lett. 92, 142501 (2004).

Eur. Phys. J. A 25, s01, 311–313 (2005) DOI: 10.1140/epjad/i2005-06-208-8

EPJ A direct electronic only

Multineutron clusters Perspectives to create nuclei 100% neutron-rich Fco. Miguel Marqu´es Morenoa For the DEMON-CHARISSA Collaborations Laboratoire de Physique Corpusculaire, IN2P3-CNRS, ENSICAEN and Universit´e de Caen, F-14050 Caen cedex, France Received: 12 September 2004 / c Societ` Published online: 9 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A new approach to the production and detection of multineutrons, based on breakup reactions of beams of very neutron-rich nuclei, is presented. The first application of this technique to the breakup of 14 Be into 10 Be and 4n revealed 6 events consistent with the formation of a bound tetraneutron. The description of these data by means of an unbound-tetraneutron resonance is also discussed. The experiments that have been undertaken at GANIL in order to confirm this observation with 12,14 Be and 8 He beams are presented. Details and illustrations related to this contribution can be found in the conference page at https://www.phy.ornl.gov/enam04/WebTalks/Mo-1.html. PACS. 21.45.+v Few-body systems – 25.10.+s Nuclear reactions involving few-nucleon systems – 21.10.Gv Mass and neutron distributions

1 Introduction Stable systems formed by few nucleons, such as 3 H and 3,4 He, have long played a fundamental role in testing nuclear models and the underlying N-N interaction. Their ground states, however, do not appear to be particularly sensitive to the form of the interaction. New perspectives should be provided by light nuclei exhibiting very asymmetric N/Z ratios. For example, among the N = 4 isotones one finds the two-neutron halo structure around the α-particle in 6 He, or the ground state of 5 H observed as a relatively narrow, low-lying resonance. Concerning the lightest isotone, 4 n, nothing is known. The existence of neutral nuclei has been a longstanding question in nuclear physics. Over the last forty years very different techniques have been employed in various laboratories for the search of multineutrons, mainly 3,4 n, without success [1]. All the techniques consisted of two stages, the formation and the detection of the multineutron, and the negative results were always interpreted as due to the extremely low cross-section of the reaction used to form the multineutron. Theoretically, ab initio calculations [2] suggest that neutral nuclei are unbound. However, the uncertainties in many-body forces, the already relatively poor knowledge of the two-body n-n interaction, and in general the lack of predictive power of these calculations, do not exclude the possible existence of a very weakly bound 4 n. a

e-mail: [email protected]

2 New experimental approach We have recently proposed a new approach to the production and detection of multineutron clusters [1]. The technique is based on the breakup of energetic beams of very neutron-rich nuclei and the subsequent detection of the liberated multineutron cluster in liquid scintillator modules. The detection in the scintillator is accomplished via the measurement of the energy of the recoiling proton (Ep ). This is then compared with the energy derived from the flight time (En ), possible multineutron events being associated with values of Ep > En . In light neutron-rich nuclei, components of the wave function in which the neutrons present a cluster-like configuration may be expected to appear [3]. Owing to pairing and the confining effects of any underlying α-clustering on the protons, the most promising candidates may be the dripline isotopes of helium and beryllium, 8 He (S4n = 3.1 MeV) and 14 Be (S4n = 5.0 MeV). As breakup reactions present realtively high cross-sections (typically ∼ 100 mb), even only a small component of the wave function corresponding to a multineutron cluster could result in a measurable yield with a moderate secondary beam intensity. Furthermore, the different backgrounds encountered in previous experiments are obviated in direct breakup. The method has been applied to data from the breakup of 11 Li, 14 Be and 15 B beams. In the case of 14 Be, some 6 events have been observed with characteristics consistent with the production and detection of a multineutron cluster, most probably in the channel 10 Be + 4 n (fig. 1). Special care was taken to estimate the effects of pileup; that

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the probability of some of them to enter the same module may increase. The simulations presented in [1] have therefore been modified in order to include the decay of a 4 n resonance [4]. The results of the simulations show the expected increase of the pileup probability towards low resonance energies. For a given resonance energy, the results do not depend much on the width. A significant increase of the pileup probability appears below E = 2 MeV, the resonance energy suggested in [2]. A resonance below 2 MeV may, therefore, be consistent with the events observed in [1]. We note that preliminary results of an experiment measuring the α transfer in the reaction 8 He(d, 6 Li)4n suggest a resonant structure about 2 MeV above threshold [5].

4 Attempts at confirmation

Fig. 1. Scatter plot, and the projections onto both axes, of the particle identification parameter versus Ep /En for the data from the reaction C(14 Be, X + n). The PID has been projected for all neutron energies. The dotted lines correspond to Ep /En = 1.4 and to the region centred on the 10 Be peak [1].

is the detection for a breakup event of more than one neutron in the same module. Three independent approaches were applied and it was concluded that at most pileup may account for some 10% of the observed signal. The most probable scenario was concluded to be the formation of a bound tetraneutron in coincidence with 10 Be [1].

3 Energy of the tetraneutron state Following the publication of [1], many theoretical papers have investigated the conditions needed for the binding of a four-neutron system [2]. The overall conclusion is that the present knowledge on the n-n interaction and the physics of few-body systems do not predict a bound 4 n. Interestingly, however, the calculations of Pieper suggested that it may be possible for the tetraneutron to exist as a relatively low-energy, broad resonance. In [1], two scenarios were confronted in order to explain the events observed: the scattering of a bound 4 n on a proton, and the detection of several neutrons in the same module (pileup). The hypotesis of a bound 4 n was found to be consistent with the experimental observations, while the estimates of pileup obtained, mainly through Monte Carlo simulations, were one order of magnitude too low. If the four neutrons, however, form a resonance at low energy, the decay in flight will lead to four neutrons with very low relative momentum, and one could expect that

The confirmation of the multineutron candidate events observed with a higher-intensity 14 Be beam and an improved charged-particle identification system, and the search for similar events in tyhe breakup of 8 He, were proposed to GANIL. Even if the intensity and quality of the 8 He beam, delivered by SPIRAL, should be much higher, structural effects may well lead to a stronger 4 n component in 14 Be g.s. than, say, in 8 He. For example, the configuration of the neutrons in a 4 n system, (1s)2 (1p)2 , is closer to that of the valence neutrons in 14 Be than to those in 8 He. Therefore, if no events were observed during the 8 He run the question whether the tetraneutron exists would remain open. Unfortunately, several problems concerning the cyclotron lead to null results after two different attempts with 14 Be beams, in 2001 and 2002. An analysis of the channel (14 Be, 8 Be), planned in order to search in parallel for the existence of the hexaneutron, could neither be performed. On the other hand, some data were acquired with a high-intensity 8 He beam from SPIRAL. Preliminary results [6] exhibit the same kind of signal observed in [1], an abnormal number of high-energy proton recoils in the −4n channel with respect to all other channels. Simulations and cross-check analyses are in progress. The reanalysis of data from a previous experiment on the breakup of 12 Be, specially the (12 Be, 8 Be) channel, was also undertaken [7]. No clear evidence of such events appeared.

5 Conclusion After four decades of experimental search for multineutrons, or neutral nuclei, the new approach described here has lead to the first observation of events that can, at present, be only explained through the existence of a 4n state. This state could be composed of very weakly bound (neutral) nuclei, as discussed in [1], or a broad low-energy resonance, as discussed in [4]. Following the most complete calculations to date [2], the most likely scenario should be the latter. It would, in addition, explain the preliminary signal observed by [5].

Fco. Miguel Marqu´es Moreno: Multineutron clusters

Among the different attempts at confirmation, only the one using an intense 8 He beam from SPIRAL was successful. The preliminary results, and the analyses in progress, seem to confirm the existence of the 4 n state [6]. A new experiment aiming to study the (14 Be∗ , 14 Be + 4 n) channel using one-proton knock-out from a more intense 15 Be beam will be undertaken at GANIL in 2005.

References 1. 2. 3. 4. 5. 6. 7.

F.M. Marqu´es et al., Phys. Rev. C 65, 044006 (2002). S.C. Pieper, talk given at the ENAM2004 conference. Y. Kanada-En’yo, these proceedings. F.M. Marqu´es et al., submitted to Phys. Rev. C. D. Beaumel, private communication. V. Bouchat et al., in preparation. G. Normand et al., in preparation.

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EPJ A direct electronic only

New insights into the resonance states of 5H and 5He G.M. Ter-Akopian1,a , A.S. Fomichev1 , M.S. Golovkov1 , L.V. Grigorenko1 , S.A. Krupko1 , Yu.Ts. Oganessian1 , A.M. Rodin, S.I. Sidorchuk1 , R.S. Slepnev1 , S.V. Stepantsov1 , R. Wolski1,2 , A.A. Korsheninnikov3,b , E.Yu. Nikolskii3,b , P. Roussel-Chomaz4 , W. Mittig4 , R. Palit5 , V. Bouchat6 , V. Kinnard6 , T. Materna6 , F. Hanappe6 , O. Dorvaux7 , L. Stuttge7 , C. Angulo8 , V. Lapoux9 , R. Raabe9 , L. Nalpas9 , A.A. Yukhimchuk10 , V.V. Perevozchikov10 , Yu.I. Vinogradov10 , S.K. Grishechkin10 , and S.V. Zlatoustovskiy10 1 2 3 4 5 6 7 8 9 10

Joint Institute for Nuclear Research, Dubna, 141980 Russia The Henryk Nievodnicza´ nski Institute of Nuclear Research, Cracow, Poland RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan GANIL, BP 5027, F-14076 Caen Cedex 5, France Gesellschaft f¨ ur Schwerionenforschung, D-64231 Darmstadt, Germany Universit´e Libre de Bruxelles, PNTPM, Brussels, Belgium Institut de Recherches Subatomique, IN2P3/Universit´e Louis Pasteur, Strasbourg, France Centre de Recherche du Cyclotron, UCL, Chemin du Cyclotron 2, B-1348 Louvain-La-Neuve, Belgium DSM/DAPNIA/SPhN, CEA Saclay, F-91191 Gif-sur-Yvette Cedex, France RNFC – All-Russian Research Institute of Experimental Physics, Sarov, Nizhni Novgorod Region, 607190 Russia Received: 10 December 2004 / Revised version: 18 February 2005 / c Societ` Published online: 27 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The 5 H system was produced in the 3 H(t, p)5 H reaction studied at small CM angles with a 58 MeV tritium ion beam. High statistics data were used to reconstruct the energy and angular correlations between the 5 H decay fragments. A broad structure in the 5 H missing-mass spectrum showing up above 2.5 MeV was identified as a mixture of the 3/2+ and 5/2+ states. The data also present an evidence that the 1/2+ ground state of 5 H is located at about 2 MeV. Then, the 5 H and 5 He systems were explored by means of transfer reactions occurring in the interactions of 132 MeV 6 He beam nuclei with deuterium. In the 2 H(6 He,3 H) reaction a T = 3/2 isobaric analog state of 5 H in 5 He was observed at an excitation energy of 22.0 ± 0.3 MeV with a width of 2.5 ± 0.3 MeV. PACS. 25.10.+s Nuclear reactions involving few-nucleon systems – 25.60.-t Reactions induced by unstable nuclei – 25.60.Je Transfer reactions – 27.10.+h Properties of specific nuclei listed by mass ranges: A ≤ 5

1 Introduction A number of experimental papers [1,2, 3,4,5] published recently presented rather contradictory data about the position and width of the J π = 1/2+ ground state (g.s.) resonance of the 5 H nuclear system. Controversy in results obtained to date on the 5 H system caused intense discussions (see a review in ref. [6]). Essentially, the question is whether the 5 H g.s. is located at 1.7–1.8 MeV above the t + 2n decay threshold [3,4], or at about 3 MeV [5] or even higher [1,2]. Consequently, new experiments must be carried out if this question is to be resolved. This is important also for planning future experiments aimed at the even heavier hydrogen nucleus 7 H [7]. a

e-mail: [email protected] On leave from the Kurchatov Institute, Kurchatov sq. 1, Moscow, 123182 Russia. b

We report here on a new study made for the 5 H system obtained in the same 3 H(t, p)5 H reaction as in ref. [4]1 . We also explored the 2 H(6 He,3 He)5 H and 2 H(6 He,3 H)5 He reactions to observe the g.s. in 5 H and the lowest T = 3/2 state in 5 He. These two reactions correspond to the transfer of either proton or neutron from the α core of 6 He to the deuterium target nucleus. The kinematics of these reactions is similar, and their relative yields are governed by the isospin selection rule.

2 Experimental conditions We studied the 3 H(t, p)5 H reaction using a 58 MeV beam of tritium ions accelerated by the U-400M (JINR, Dubna) cyclotron. The ACCULINNA separator [9] was used to 1

Since the time of the ENAM conference this material has been partly published in ref. [8].

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reduce the angular spread and energy dispersion of the primary triton beam to 7 mrad and 0.3 MeV (FWHM), respectively. Finally, the triton beam with intensity of 3 · 107 s−1 was focused in a 5 mm spot on a cryogenic tritium target [10]. The 4 mm thick target cell, having twofold 6 μm stainless steel windows on each side, was filled with tritium to a pressure of 860 mbar and cooled down to 25 K. The thickness of the tritium target was 2.2 × 1020 atoms/cm2 . The missing-mass energy spectrum of 5 H was derived from the energies and emission angles measured by means of an annular Si detector for the protons emitted to the backward direction. The measurements covered center-of-mass (CM) angles between 3.5◦ and 10.0◦ . Due to the kinematic focusing, the 5 H decay products (t + 2n) were detected in wide ranges of their emission angles. Tritons moving in the forward direction in laboratory system were detected by a telescope consisting of four annular Si detectors. Neutrons were detected by 48 scintillation modules of the time-of-flight neutron spectrometer DEMON [11]. Secondary 6 He beam from the ACCULINNA separator was used to study the reactions 2 H(6 He,3 He)5 H and 2 H(6 He,3 H)5 He. The beam intensity and energy were, respectively, 3 × 105 pps and 132 MeV. Angular and position resolutions of ±0.2◦ and 1.25 mm were achieved by tracking individual 6 He ions hitting the deuterium target. The kinetic energy of each 6 He was measured with accuracy 1.6% by means of a pair of time-of-flight detectors. The target cell was filled at 1 atm with a high purity deuterium gas and cooled down to 25 K. It had 6 μm stainless steel entrance and exit windows. The thickness of the deuterium target was 2.6×1020 atoms/cm2 . The missing-mass energy spectra of 5 H and 5 He nuclei were derived, respectively, from the energies and emission angles measured for the 3 He and 3 H nuclei formed in the reactions 2 H(6 He,3 He)5 H and 2 H(6 He,3 H)5 He. The first, trigger telescope detected relatively low energy 3 He and 3 H nuclei emitted at laboratory angles θlab = 25◦ ± 7◦ . In coincidence with these low energy 3 He and 3 H nuclei we detected charged particles emitted as the decay products of 5 H and 5 He. The second, slave telescope was used to detect these high energy 3 H nuclei originating from the t+2n decay of 5 H and high energy charged particles from different decay modes possible for the 5 He nucleus: 5 He → 3 He + n + n, 5 He → d + p + n, 5 He → α + n, 5 He → t + d. The measurements made for such coincidence events covered a CM angular range of 21◦ –40◦ for each of these reactions: 2 H(6 He,3 He)5 H and 2 H(6 He,3 H)5 He. Due to the difference in the energy of the reaction ejectiles and the decay products of 5 H and 5 He, the corresponding kinematical branches of these reactions were uniquely identified.

3 Results and discussion 3.1 Study of the 3 H(t, p)5 H reaction In the case of the 3 H(t, p)5 H reaction we discuss only the ptn coincidence data. Such coincidence events uniquely

Fig. 1. Missing-mass spectrum of 5 H. Diamonds show the experimental data points. The vertical dashed line shows the position of the 5 H g.s. deduced in refs. [3, 4]. The histogram is the result of Monte Carlo (MC) simulation and the solid curve is the input for MC simulation. Here and below, the data points show the real numbers of detected events. The statistical errors are not shown.

Fig. 2. Relative energy spectrum for two neutrons. The plot details are the same as in in fig. 1.

identify the p + 5 H outgoing channel and make possible a complete kinematic reconstruction. The 5 H missingmass spectrum measured with a 0.4 MeV resolution in energy is presented in fig. 1. We measured this spectrum up to 5 MeV. The 5.5 MeV limit is caused by the detection threshold for slow protons moving in the backward direction. The smooth, continuum nature of this high statistics spectrum do not leave any chance for a narrow resonance state which one could attribute to 5 H. However, much more informative are correlations revealed for the decay products of this nucleus. Figure 2 shows the distribution of the 5 H decay energy (E5 H ) between the relative motions in the t-nn and nn subsystems (presented in terms of the Enn /E5 H ratio). It shows a narrow peak corresponding to a strong n-n final-state interaction (FSI). The most

G.M. Ter-Akopian et al.: New insights into the resonance states of 5 H and 5 He

Fig. 3. Angular distributions of tritons in the 5 H frame for the two ranges of the 5 H energy: 3.5–5.5 MeV (upper panel) and 0–2.5 MeV (lower panel). θt is the triton emission angle taken in respect to Z-axis chosen to coincide with the direction of the momentum transfer kbeam − kp occurring in the reaction 3 H(t, p)5 H. The plot details here are the same as in fig. 1.

317

that arises from the fact that the light proton can not carry away as much angular momentum as the heavier triton projectile brings in. DWBA calculations confirm this idea indicating that the momentum transfers ΔL = 1, 2 dominate, whereas ΔL = 0 is suppressed by about one order of magnitude even at forward angles. The spin transfer is negligible in this reaction. ΔS = 1 is possible only if the two neutrons are in a negative parity state of relative motion. The previous experience shows that this is highly improbable in contrast to the “dineutron” transfer, which is known to be a good approximation valid in a broad range of transfer reactions. The 3/2+ and 5/2+ states can be considered as degenerate. Theory calculations (e.g., [14]) show that the expected energy split between these states is much less than their widths. To produce the strongly oscillating picture, the domination of the {L = 2, Sx = 0, lx = 0, ly = 2} component in the structure of the 5 H wave function is necessary (L is the total angular momentum, subscripts x and y refer to the spins and angular momenta of nn and t-nn subsystems). This is a reasonable expectation supported both by the analysis of experimental data [15] and theoretical calculations [16] made for the 6 He 2+ state. We employed the following procedure for data analysis. Correlations occurring at the 5 H decay are described as 

J  M  |ρ|JM  A†J  M  AJM , W = JM,J  M 

striking result is the observation of a sharp oscillating picture in the triton angular distribution shown in fig. 3. Such a sharp oscillating angular distribution can be obtained only for very specific conditions. To our knowledge, only one observation of oscillating pattern was reported for the reaction involving nuclei with non-zero spin: 13 C(6 Li, d)17 O∗ (α)13 Cg.s. [12]. It was shown in ref. [13] that the energy degeneracy and interference of (at least) two states are required to reproduce the observed correlations. Calculations were made with assumption that a single J π state (either 3/2+ or 5/2+ ) is populated in the 5 H system formed in the reaction 3 H(t, p)5 H. These calculations made us sure that the strongly oscillating distribution shown in fig. 3 can not be obtained for 5 H assuming the population of one selected J π state. At the same time it appeared that the bulk of data observed in the present experiment can be explained by the assumption that the direct transfer of two neutrons (ΔL = 2, ΔS = 0) dominates in the 3 H(t, p)5 H reaction leading to the population of the broad, overlapping 3/2+ and 5/2+ states. The idea is supported by the following arguments. The 5 H system could be considered as a “proton hole” in 6 He (e.g., [14]), so definite similarities can be expected between these systems. Theoretical predictions give J π = 1/2+ for the g.s. of 5 H. The low lying excited states are supposed to be a 3/2+ and 5/2+ doublet. One should expect a weak population of the 5 H g.s. in the 3 H(t, p)5 H reaction due to the statistical factor and also as a consequence of the “angular momentum mismatch”

where J, M are the total 5 H spin and its projection, AJM are the decay amplitudes depending on the 5 H decay dynamics. J  M  |ρ|JM  is the density matrix, which describes the polarization of the 5 H states populated in the 3 H(t, p) reaction and takes into account the mixing of the 3/2+ and 5/2+ states. It was parameterized assuming azimuthal symmetry with respect to the momentum transfer in the 3 H(t, p) reaction. This assumption is well confirmed by the experimental data and reduces to 5 the number of independent parameters. All elements of the density matrix were assumed to have the same energy dependence and were represented by splines. The amplitudes AJM were expanded over a limited set of hyperspherical harmonics (assumed to be the same for the 3/2+ and 5/2+ states). A similar approach has been used in ref. [17], where the non-isotropic three-particle decay of 6 Be(2+ ) state has been explored. The hyperspherical expansions of the decay amplitudes were also used for the analysis of A = 6 [15, 18] and 5 H [5, 6] decay data. Parameters of the ρ-matrix and hyperspherical expansion were treated as free in our analysis. A complete MC simulation of the experiment has been performed. In this way, analytical expressions were extracted for the decay probability in the multidimensional space, corrected for the setup efficiency. Projections of the extracted distributions (solid curves) and the results of MC simulations (histograms) are shown in figs. 1-3. The amplitudes and relative arguments obtained for the hyperspherical components are listed in table 1. Agreement obtained between the experimental data and the MC results is excellent at E5 H > 2.5 MeV (see

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Table 1. Hyperspherical decompositions of decay amplitudes AJM for the excited states of 5 H (E5 H = 2.5–5.5 MeV) (the squared moduli of the partial amplitudes are given in percents and relative arguments in degrees). The errors given for our fit are pure statistical; the other uncertainties discussed in ref. [15] are valid also for the present analysis.

K

L

lx

ly

Sx

mod2

arg

2 4 6 2 2

2 2 2 2 1,2

0 0 0 2 1

2 2 2 0 1

0 0 0 0 1

35 ± 2 37 ± 2 8.0 ± 1.5 20 ± 2 <3

0 58 ± 1 138 ± 6 180 ± 3

upper panel in fig. 3). Below this energy, we could not achieve an agreement assuming the interference of only 3/2+ and 5/2+ states. This can be well seen in fig. 3 (lower panel). The impact of this disagreement on the 5 H missing-mass spectrum is also seen in fig. 1 in the deviation of the MC results from the experimental data below 3 MeV. We can reproduce the correlations obtained at E5 H < 2.5 MeV by assuming the interference of the 1/2+ g.s. with the 3/2+ –5/2+ doublet. One can take this as an evidence for the population of the 5 H g.s. lying at about 2 MeV. Interference of the 1/2+ , 3/2+ , and 5/2+ states becomes possible in the 5 H missing-mass spectrum when the detection probability of the 5 H decay fragments depends on their emission angles. This dependence was strongly pronounced in ref. [4] and had a place in this work. Interference was considered in ref. [4] as a possible explanation for the too small width of the 5 H peak observed at 1.8 MeV. The interference of the 5 H g.s. with the 3/2+ – 5/2+ doublet, apparently showing up in the correlation patterns observed in the present work at E5 H < 2.5 MeV, supports this assumption of ref. [4]. Good quality description of data presented in fig. 2 and, especially, in fig. 3 supports the assumption that the 5 H states are populated in the reaction utilized in this study. A combination of direct processes with a pairwise FSI can hardly give such a result. 3.2 Resonance states of 5 H and 5 He in 6 He + 2 H collisions To identify the 2 H(6 He,3 He)5 H reaction we analyzed such events where relatively low energy 3 He nuclei (Tlab ≤ 20 MeV) were detected by the the trigger telescope in coincidence with tritons which were the 5 H decay products. The tritons were detected by the slave telescope. The obtained 5 H missing-mass energy spectrum is shown in fig. 4. Reaction 2 H(6 He,3 H)5 He became apparent when low energy tritons (Tlab ≤ 20 MeV) were detected by the trigger telescope in coincidence with charged particles originating from the 5 He decay. First of all we were interested in the 5 He decay modes which were expected for the T = 3/2 isobaric analog state. In order to satisfy the isospin selection rule, pure T = 3/2 states in 5 He

Fig. 4. Missing-mass energy spectrum of 5 H from the 2 H(6 He,3 He) reaction. The 5 H energy is presented relative to the t + n + n decay threshold. Curve 1 is the three-body decay curve with resonance energy Eres = 2.2 ± 0.3 MeV and width Γ obs  2.5 MeV (see text). Curve 2 shows the phase space spectrum with the n + n FSI. The solid curve is the sum of curve 1, folded with the resolution and weighted with the efficiency, and the phase space curve 2. The dotted curve shows the detection efficiency folded with the resolution (arbitrary units).

must decay by the emission of three particles, 3 He + n + n and t + p + n. For T = 1/2 states, there are the well known two-particle decays t + d and α + n. Thus, to build missing-mass energy spectra for 5 He nuclei formed in resonance states with isospin T = 3/2, we used events where the low energy tritons were detected in coincidence with 3 He, tritons or protons (we refer to these events as to the t-3 He, t-t and t-p coincidences). Due to the precise measurements made for the energies and trajectories of coincident particles we could separate the t-t coincidences originating from the 5 He → t + p + n decays from those t-t coincidence events which appeared due to the two-particle decay 5 He → t + d. The two spectra presented in fig. 5 were built for the tree-particle decay modes of 5 He using the t-3 He coincidences (upper panel) and the sum of the t-t and t-p coincidences (lower panel). Steep ascents setting in just near the decay thresholds and the overall similarity of the spectra shown in figs. 4, 5 are clear indications that we see similar nuclear resonance states in the systems with mass number A = 5 which decay into three particles. To describe these resonance states, showing the three-body decays, we used analytical expression obtained in ref. [19]. The spectra in figs. 4, 5 were fitted as sums of the resonance state and the three-body phase space spectra for t + n + n, 3 He + n + n and t + p + n with the n + n and n + p FSI. Data in fig. 4 can be described within two standard deviations assuming a single resonance with energy varied between 1.8 and 2.6 MeV and width Γ obs  2.5 MeV, alongside with the phase space. One can not more precisely estimate the 5 H g.s. resonance parameters as the acquired statistics prevents one from any accurate separation from the excited states of this nucleus presumably

G.M. Ter-Akopian et al.: New insights into the resonance states of 5 H and 5 He

319

Fig. 6. Missing-mass energy spectrum of 5 H, relative to the t + n + n decay threshold, derived from inclusive data obtained for 3 He ejectiles detected in the trigger telescope from the 2 H(6 He,3 He) reaction. The background obtained with the empty target cell is shown by the solid line histogram.

Fig. 5. Missing-mass excitation energy spectrum of 5 He from the 2 H(6 He, t) reaction. The excitation energy is presented relative to the 5 He g.s. resonance energy. The upper panel shows the spectrum obtained for t+ 3 He coincidences. The lower panel shows the spectrum obtained for the t+t and t+p coincidences. The vertical arrows indicate the 5 He → 3 He + n + n (upper panel) and the the 5 He → t + p + n (lower panel) decay thresholds. Curve 2 in upper and lower panels show the corresponding phase space spectra with n + n (upper panel) and n + p (lower panel) FSI. Other notations are as in fig. 4.

populated in the same reaction. Taking this consideration into account, we are inclined rather to say that the 5 H g.s. resonance energy and width inferred from fig. 4 do not contradict results presented in ref. [3]. In favor of this says also the 5 H spectrum derived from the inclusive 3 H ejectile data (see fig. 6). This agrees also with the 5 H g.s. resonance position presented in ref. [4]. From the fit shown in fig. 4 we estimated a value of about 0.3 mb/sr for the cross-section of the reaction 2 H(6 He,3 He)5 H populating the g.s. resonance in 5 H. The error of this value may amount to as much as 50% in magnitude because of the uncertainty from the contribution of the 5 H excited states. Data presented in fig. 5 indicate that we have observed a 5 He resonance state with isospin T = 3/2, located at an excitation energy E obs = 22.0 ± 0.3 MeV and having a width Γ obs = 2.5 ± 0.3 MeV. We found that this state showed up in the 5 He three-body decay modes allowed for the T = 3/2 state. The cross-sections were estimated to be, respectively, 0.10 ± 0.03 mb/sr and 0.2 ± 0.1 mb/sr for

Fig. 7. Missing-mass excitation energy spectrum of 5 He from the 2 H(6 He,3 H) reaction, obtained for t + d coincidences. The vertical arrow shows the 5 He → t+d threshold. Other notations are as in fig. 4.

the 5 He → 3 He + n + n and 5 He → t + p + n decay modes of the isobaric analog state. For this 22.0 MeV 5 He state we did not observe the t + d decay mode which is allowed only for a T = 1/2 state. However, we could measure the t + d decay of the T = 1/2, J π = 3/2− resonance state of 5 He located at about 20 MeV, according to ref. [20]. Figure 7 shows the missing-mass energy spectrum of 5 He derived from the t + d coincidence events associated with the t + d decay of 5 He nuclei produced in the 2 H(6 He,3 H) reaction. In fact, in the 5 He excitation energy region extending from 19 to 20 MeV there are four broad T = 1/2 states of 5 He with J π = 5/2+ , 3/2+ , 7/2+ and 3/2− derived in [20] in the framework of the extended R-matrix theory. The 3/2− state ought to be the most probably

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populated via the 2 H(6 He,3 H) reaction. Fitting the spectrum in fig. 7 with a single-level Breit-Wigner formula we found that this J π = 3/2− state of 5 He was located at Eres = 19.7 ± 0.3 MeV (curve 1 in fig. 7). This fit corresponds to a cross-section of 0.3 ± 0.1 mb/sr. The contribution from the energetically allowed three-body decays of this T = 1/2 state in the region of the 22.0 MeV isobaric analog T = 3/2 state was estimated to be less than 10%. We did not see the t + d decay mode of the well known 16.8 MeV (J π = 3/2+ ) state of 5 He as our detection efficiency was too low for this excitation energy (see the detection efficiency curve shown in fig. 7). We also could not see the α + n decay mode of this 5 H resonance state as well as the α + n decay mode of the observed 19.7 MeV resonance. This is well explained as due to the high background from the reaction 2 H(6 He, α) resulting in the formation of the 4 H nucleus in its ground state.

4 Conclusions Missing-mass spectrum obtained in the 3 H(t, p)5 H reaction shows a broad structure above 2.5 MeV. The observed strong correlation pattern allows us to unambiguously identify this structure as a mixture of the 3/2+ and 5/2+ states in 5 H. Such correlation is a rare phenomenon for transfer reactions involving particles with nonzero spin and means that the 3/2+ and 5/2+ states are either almost degenerate or the reaction mechanism causes a very specific interference of these states. Excited states observed in this 5 H energy range support the conclusion made in ref. [3] about the 5 H g.s. resonance position at 1.7 ± 0.3 MeV. The correlation picture obtained at E5 H < 2.5 MeV (see fig. 3) gives evidence for the interference of the 3/2+ –5/2+ doublet with the J π = 1/2+ g.s. in 5 H. This is consistent with the alternative explanation presented in ref. [4] for the small width of the observed 1.8 MeV g.s. peak of 5 H. Indeed, the interference can cause such a distortion of the 5 H g.s. resonance inherently having a sizeable width. Analysis made for angular and internal energy correlations in 5 H shows a reasonable agreement between the structure deduced for 5 H and the structure calculated or deduced from experimental data in the case of 6 He 2+ state (see refs. [15, 18]). By studying the three-body decay modes 5 He → 3 He+ n + n and 5 He → t + p + n we have identified for the first time the isobaric analog of the 5 H g.s. resonance in 5 He formed in the 2 H(6 He,3 H)5 He reaction. We have made sure that the 19.7 MeV (J π = 3/2− , T = 1/2) resonance state known for 5 He does not show these three body decay modes. The T = 3/2 isobaric analog state is located at a 5 He excitation energy of 22.0 ± 0.3 MeV and has a width of 2.5 ± 0.3 MeV. Simultaneously, we observed the g.s. resonance of 5 H populated in the reaction 2 H(6 He,3 He) Data obtained for this reaction allowed us to come to a conclusion that the 5 H g.s. resonance is located at about 2 MeV above the 5 H → t + n + n decay threshold. This does not contradict

the data on the energy of the 5 H g.s. resonance presented in refs. [3, 4]. Assuming the isospin invariance of nuclear forces the excitation energy of the isobaric analog state in 5 He can be estimated from the neutron-proton mass difference and Coulomb energy 0.6Z(Z − 1)/A1/3 [20]. For a 5 H g.s. at ∼ 2 MeV, the T = 3/2 analog state should exist in 5 He at an excitation energy of ∼ 21.7 MeV. Taking into consideration experimental errors assigned to the energy positions of the resonance states, we conclude that the energies observed for the 5 H g.s. resonance and its isobaric analog in 5 He are in mutual accord. Our data show that the cross-sections of the 1p/1ntransfers from the α core of the 6 He nucleus to deuteron resulting in the formation of the T = 3/2 states of 5 H/5 He are close to each other in their values. In the strict sense of the isospin selection rule, the cross-section ratio of the two reactions leading to the 5 H g.s. and to the lowest T = 3/2 state in 5 He should equal 3. However, isospin mixing and/or reaction dynamics could be a plausible reason of the approximate equality obtained for these crosssections. As a whole, the observation of the T = 3/2 isobaric analog state in 5 He with the energy and width given above presents an additional argument in favor of the conclusions drawn in refs. [3,4] about the 5 H g.s. resonance. Partial support of the work by the Russian Basic Research Foundation (grant No. 02-02-16550) and by the INTAS grant No. 03-51-4496 is acknowledged.

References 1. D.V. Aleksandrov et al., Proceedings of the International Conference on Exotic Nuclei and Atomic Masses, (ENAM95), Arles, France, 1995 (Editions Frontiers, Gifsur-Yvette, France, 1995) p. 329. 2. M.G. Gornov et al., JETP Lett. 77, 344 (2003). 3. A.A. Korsheninnikov et al., Phys. Rev. Lett. 87, 092501 (2001). 4. M.S. Golovkov et al., Phys. Lett. B 566, 70 (2003). 5. M. Meister et al., Phys. Rev. Lett. 91, 162504 (2003). 6. L.V. Grigorenko, Eur. Phys. J. A 20, 419 (2004). 7. M.S. Golovkov et al., Phys. Lett. B 588, 163 (2004). 8. M.S. Golovkov et al., Phys. Rev. Lett. 93, 262501 (2004). 9. A.M. Rodin et al., Nucl. Instrum. Methods B 126, 236 (1997). 10. A.A. Yukhimchuk et al., Nucl. Instrum. Methods A 513, 439 (2003). 11. I. Tilquin et al., Nucl. Instrum. Methods A 365, 446 (1995). 12. K.P. Artemov et al., Yad. Fiz. 28, 288 (1978). 13. G. Cardella et al., Phys. Rev. C 36, 2403 (1987). 14. N.B. Shul’gina et al., Phys. Rev. C 62, 014312 (2000). 15. B.V. Danilin et al., Sov. J. Nucl. Phys. 46, 225 (1987). 16. B.V. Danilin et al., Nucl. Phys. A 632, 383 (1998). 17. O.V. Bochkarev et al., Sov. J. Nucl. Phys. 55, 955 (1992). 18. O.V. Bochkarev et al., Nucl. Phys. A 505, 215 (1989). 19. S.N. Ershov et al., Phys. Rev. C 70, 054608 (2004). 20. D.R. Tilley et al., Nucl. Phys. A 708, 3 (2002).

5 Clusters and drip lines 5.2 Halo nuclei

Eur. Phys. J. A 25, s01, 323–324 (2005) DOI: 10.1140/epjad/i2005-06-152-7

EPJ A direct electronic only

Borromean nuclei and three-body resonances E. Garrido1 , D.V. Fedorov2,a , and A.S. Jensen2 1 2

Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark Received: 4 November 2004 / Revised version: 29 March 2005 / c Societ` Published online: 11 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The interconnection between the resonances and virtual states of a three-body system and the resonances and virtual states in its two-body subsystems is investigated using the Borromean halo nucleus 11 Li as a realistic example. The three-body core + neutron + neutron model is used, where the neutron-core interaction is fixed to reproduce a given s-wave virtual state and a p-wave resonance. The neutron-neutron interaction is then multiplied by a factor which is progressively changed from 0 to 1 and the resulting trajectories of the three-body states in the complex energy plane are investigated. PACS. 21.45.+v Few-body systems – 31.15.Ja Hyperspherical methods

a

Conference presenter; e-mail: [email protected]

0 +

s+s -0.5

EI=−ΓR/2 (MeV)

The properties of three-body systems are directly determined by the internal two-body structures. This statement is actually obvious as soon as only two-body interactions are involved in the three-body system. However, a direct and clean connection between the two-body and three-body properties has not been provided yet. In this work we compute the three-body states by the complex scaled hyper-spheric adiabatic expansion method [1, 2], which gives both bound states and resonances as (effectively) bound solutions of the Faddeev equations with energies independent of the scaling angle. Starting from a trivial system in which the core has infinite mass and the two light particles do not interact with each other, we can first test the method, since the numerical calculations must reproduce accurately the expected trivial result. Secondly, this simple system is used as starting point in the calculations, being then possible to trace the different three-body states when more and more realistic features are introduced in the numerical calculations (e.g. finite core mass, interaction between the two light particles, finite particle and core spins, Pauli principle, and others). In fig. 1 we show the three-body states for a system made by a zero-spin core with mass equal to 9 m (where m is the nucleon mass) and two neutrons with mass m. The neutron-core s- and p-wave interactions are tuned to reproduce correspondingly a virtual (anti-bound) state at −0.54 MeV and a resonance at 1.4 MeV with the width 2.8 MeV. Together with a realistic neutron-neutron interaction this parametrization of the neutron-core states gives an overall reasonable description of 11 Li within the

−

11

1 in Li

11

0 in Li

+

s-state m2=m3=m

-1

s,p -1.5

s+p

s,p

m1=9m

p-res. +

-2

11

2 in Li

11

0 in Li

+

V23≠0 (0 ) +

V23≠0 (2 ) −

-2.5

V23≠0 (1 )

p+p -3

-1

-0.5

0

0.5

1

1.5

2

2.5

3

ER (MeV) Fig. 1. Evolution of the complex energies of different states in 11 Li when the neutron-neutron interaction V23 is progressively introduced. The s- and p-wave neutron-core interaction is fixed to reproduce the virtual state and the resonance indicated in the figure. The real part of the energy, ER , is plotted along the horizontal axes and the imaginary part, EI , along the vertical axes. The core is assumed to have zero spin. The upper part of the lowest-energy 0+ trajectory, shown outside of the figure, corresponds to a virtual (anti-bound) state, that is located on another (unphysical) sheet of the complex energy. Also the horizontal part of the 1− trajectory is located on the unphysical sheet of the complex energy. 9

Li + neutron + neutron model and roughly corresponds to the spin-averaged structure of states in the neutron9 Li system [3,4]. The neutron-core states are marked with crosses in the figure.

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We use the neutron-neutron interaction from [5], which is a combination of central, spin-orbit, tensor, and spinspin terms with a double-Gaussian shape fitted to the low-energy experimental data on s- and p-wave scattering. The neutron-neutron interaction is multiplied by a factor which is progressively changed from 0 to 1. When the interaction between the neutrons is introduced, the different states (two 0+ , one 1− and one 2+ ) evolve as shown in the figure, such that the final points on each trajectory correspond to the states when the full neutron-neutron interaction is included. In particular, the lowest of the 0+ states is a Borromean state, that is a bound three-body state where none of the two-body subsystems have bound states. In the absence of the neutron-neutron interaction the lowest of the two 0+ core + neutron + neutron states is a virtual (anti-bound) state, marked as s + s in the figure. It is located on the unphysical complex energy sheet at approximately twice the energy of the neutron-core virtual s-state, and contains predominantly neutron-core s-waves. The neutron-neutron interaction introduces an admixture of p-waves which reaches about 30% at the end point of the trajectory. If the mass of the core were infinitely large, the threebody energy would have been precisely equal to the sum of the energies of the neutron-core virtual s-state. Since the mass of the core is finite the actual energy deviates from the sum. However, since the core is still much heavier than the neutrons this deviation is small and can hardly be seen in the figure. As the neutron-neutron interaction is progressively introduced, this three-body state moves on the unphysical complex energy sheet towards zero. Having reached zero it enters the physical complex energy sheet and thus becomes a bound state. It then moves on the physical sheet towards its final destination at about −0.4 MeV. The 1− state shows similar behavior —it starts on the unphysical sheet at an energy, marked as “s+p” in the figure, approximately equal to the sum of the energies of the neutron-core s-wave virtual state and p-wave resonance. At this point the state includes an equal admixtures of the neutron-core s- and p-waves. As the neutron-neutron interaction is introduced, it moves on the unphysical sheet towards the branching point at the energy of the p-wave neutron-core resonance, marked with a cross in the figure, where it enters the physical sheet and then moves on the physical sheet towards its final destination. The trajectories for the highest 0+ and the 2+ states starts at the energy, marked as “p + p” in the figure, approximately equal to twice the energy of the neutron-core p-wave resonance. At this point both these states are dominated by neutron-core p-waves.

The progressive introduction of the neutron-neutron interaction lifts the degeneracy of these states and makes them evolve along different trajectories on the physical complex energy sheet. It also introduces and admixture of s-waves into the 0+ state. For the sake of a cleaner picture we have assumed that only s-wave virtual states and p-wave resonances are present in the two-body subsystems. Thus the interactions in partial waves higher than s and p are assumed to be equal to zero. Since in Faddeev equations each partial wave of a Faddeev component is multiplied by a corresponding interaction [1], only s- and p-waves, where the interactions are nonzero, were included in each of the three Faddeev components. Again, to have a clean picture we have in these calculations assumed that the spin of the core is equal zero as it is in some other halo systems like 6 He and 12 Be. Had the spin of the core been included, there would have been more neutron-core states and more trajectories would appear on the plot. Those trajectories would correspond to different spin-parities of the total core + neutron + neutron system and to different possible combinations of the neutron-core states. However, the general behavior of the new trajectories should be similar to one of the trajectories for our simplified system. We leave the classification of the effects of the finite core spin for a separate investigation. Tracing the evolution of the three-body states permits one to visualize the features responsible for the existence of the different states, in particular the Borromean states. For a system like 11 Li the Borromean ground state is due to the neutron-neutron interaction, while other systems like two heavy particles and a light one can have a Borromean state produced only by center of mass effects, even if the two heavy particles do not interact with each other. Furthermore, an understanding of the contribution from the different “realistic” features permits the use of the very schematic case as a starting point and make crude estimates of the spectrum of realistic three-body systems.

References 1. E. Nielsen, D.V. Fedorov, A.S Jensen, E. Garrido, Phys. Rep. 347, 373 (2001). 2. Y.K. Ho, Phys. Rep. 99, 1 (1983). 3. E. Garrido, D.V. Fedorov, A.S. Jensen, Nucl. Phys. A 700, 117 (2002). 4. E. Garrido, D.V. Fedorov, A.S. Jensen, Nucl. Phys. A 708, 277 (2002). 5. E. Garrido, D.V. Fedorov, A.S. Jensen, Nucl. Phys. A 617, 153 (1997).

Eur. Phys. J. A 25, s01, 325–326 (2005) DOI: 10.1140/epjad/i2005-06-139-4

EPJ A direct electronic only

Breakup reactions of halo nuclei T. Nakamura1,a and N. Fukuda2 1 2

Department of Physics, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro, Tokyo 152-8551, Japan The Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Received: 19 January 2005 / c Societ` Published online: 10 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Coulomb and nuclear breakup of halo nuclei have been studied at RIKEN. In this contribution, we focus on the cases of Coulomb breakup of the one-neutron halo nucleus 11 Be at 69 MeV/nucleon with a lead target and the nuclear breakup of 11 Be at 67 MeV/nucleon with a carbon target. In these studies, we have extracted the angular distributions of 10 Be + n c.m. system (inelastic scattering) as well as the relative energy spectra. The angular distributions have been found very important to extract the pure E1 component in the breakup with Pb target, while it has been used to specify the angular momentum of two discrete levels observed for the breakup with C target. We also present preliminary results of Coulomb breakup of the two-neutron halo nucleus 11 Li. PACS. 25.60.-t Reactions induced by unstable nuclei – 21.45.+v Few-body systems

1 Coulomb breakup of the one-neutron halo nucleus 11 Be Breakup reactions have played an important role in the study of halo structures. Coulomb breakup of halo nuclei is characterized by its large cross-section of the order of 1 barn due to strong E1 excitation to the lowlying continuum just above the neutron-decay threshold. Our previous Coulomb breakup experiment on 11 Be [1] and 19 C [2] clearly showed that this large E1 strength is attributed to the direct breakup mechanism. Owing to this simple picture, the Coulomb dissociation of the halo nucleus can become a powerful tool to probe exclusively the halo ground state, whose wave function is related directly to the B(E1) spectrum. However, this simple reaction mechanism may require a revision due to the possible higher-order effects and the contribution of the nuclear breakup as pointed out by many theoretical papers [3,4, 5,6,7, 8, 9,10, 11]. In order to resolve these problems, we have recently revisited the Coulomb dissociation of 11 Be at 69 MeV/nucleon with about 30 times more statistics than the previous experiment [1]. In this study, we have adopted the analysis using the angle θ of 10 Be + n centerof-mass (c.m.) system, namely, that of the inelastic scattering. In the semi-classical Coulomb breakup picture, this angle θ is directly related to the impact parameter b as b = a cot(θ/2)  2a/θ, where a represents half the distance of the closest approach in the classical Coulomb head-on collision. Since the Coulomb breakup occurs at a

Conference presenter; e-mail: [email protected]

Fig. 1. Relative energy spectra for 11 Be + Pb at 69 MeV/nucleon for the whole acceptance region (open points), and for the selected forward angles (solid points). The data points are compared to the pure E1 direct breakup model calculation obtained with the ECIS code [12] with α2 (spectroscopic factor for the halo configuration) of 0.72 (solid lines).

large impact parameters, selection of data at forward angular regions is expected to be effective to extract the pure E1 Coulomb breakup component. Figure 1 shows the relative energy spectra for 11 Be on the Pb target for the whole acceptance (open points), and the data selected for θ ≤ 1.3◦ (solid points) corresponding to b ≥ 30 fm in the semi-classical approximation. Here no subtraction for the nuclear breakup contribution is made.

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subtracted. The angles are defined in the center-of-mass frame of the projectile and the target. From the comparison with the DWBA calculation (ECIS [12], solid curves), these two transitions were found to have both L = 2 property, which is consistent with the assignment of 5/2+ and 3/2+ , respectively, for these states predicted by the shell model. The detailed analysis and discussions are described in ref. [13].

3 Coulomb breakup of the two-neutron halo nucleus 11 Li

Fig. 2. Angular distributions of 11 Be into Ex = 1.79 MeV and 3.41 MeV states observed in the breakup reaction of 11 Be on C target. The angles are taken in the center-of-mass frame of the projectile and the target. Solid lines show calculations by the ECIS code for L = 2 transitions. Inset: excitation energy spectrum of 11 Be at θ = 6◦ in this reaction.

We can see clearly an excellent agreement with the firstorder perturbation theory with the direct breakup model when selecting the most forward angles (solid curve). The spectroscopic factor is thus extracted to be 0.72(4), which is consistent with the previous experiment. We have found that the higher-order effects can be well controlled by selecting the forward scattering angle, and that this effect is, in fact, very small. We could extract the spectroscopic factor of the ground state of 11 Be more precisely by this method. The details of the experiments and related discussions are seen in ref. [13].

2 Nuclear breakup of one-neutron halo nucleus 11 Be As seen in the previous section, the Coulomb breakup of halo nuclei is dominated by a strong direct breakup crosssection, which is suitable for extracting the information of halo structure in the ground state. However, this implies that the discrete states above the neutron decay threshold are hidden by the direct breakup component. Breakup reaction of halo nuclei on a light target is thus very important to observe such discrete states. The inset of fig. 2 shows the excitation energy spectrum for 11 Be on the carbon target at 67A MeV at θ = 6◦ . As clearly seen in the figure, we have observed two discrete peaks corresponding to the known excited state at Ex = 1.79 MeV and Ex = 3.41 MeV. The angular distributions corresponding to these peaks are shown in fig. 2, where backgrounds were estimated as in the inset and were

As shown in sect. 1, Coulomb breakup for the one neutron halo nucleus is now well established. On the other hand, that for the two-neutron halo case as in 11 Li has not been well understood, mainly due to discrepancies among previous three experimental results on the Coulomb dissociation obtained at MSU [14], RIKEN [15], and GSI [16]. We have thus studied the Coulomb dissociation of 11 Li on a Pb target at an incident energy of approximately 70 MeV/nucleon to obtain the data with much higher statistics and with much less ambiguities caused by cross talk events in detecting two neutrons. In the preliminary spectrum of the relative energy (Erel ) of the three outgoing particles, 9 Li and two neutrons, we have observed a huge bump with an asymmetric shape as in 11 Be. This bump peaks at Erel ∼ 0.3 MeV and its width is about 0.6 MeV (FWHM). The integrated cross-section at low relative energies amounts to 2.74±0.07 (stat.) barns for Erel ≤ 3 MeV (preliminary). The B(E1) strengths have then been obtained to be 1.5 ± 0.1 e2 fm2 for Erel ≤ 3 MeV using the conventional equivalent photon method. Further analysis is now in progress.

References 1. T. Nakamura et al., Phys. Lett. B 331, 296 (1994). 2. T. Nakamura et al., Phys. Rev. Lett. 83, 1112 (1999). 3. T. Kido, K. Yabana, Y. Suzuki, Phys. Rev. C 53, 2296 (1996). 4. V.S. Melezhik, D. Baye, Phys. Rev. C 59, 3232 (1999). 5. M.A. Nagarajan, C.H. Dasso, S.M. Lenzi, A. Vitturi, Phys. Lett. B 503, 65 (2001). 6. C.H. Dasso, S.M. Lenzi, A. Vitturi, Phys. Rev. C 59, 539 (1999). 7. S. Typel, G. Baur, Phys. Rev. C 64, 024601 (2001). 8. S. Typel, R. Shyam, Phys. Rev. C 64, 024605 (2001). 9. I.J. Thompson, J.A. Tostevin, F.M. Nunes, Nucl. Phys. A 690, 294c (2001). 10. J. Margueron, A. Bonaccorso, D.M. Brink, Nucl. Phys. A 703, 105 (2002). 11. J. Margueron, A. Bonaccorso, D.M. Brink, Nucl. Phys. A 720, 337 (2003). 12. J. Raynal, Coupled channel/DWBA code ECIS97, also Notes on ECIS94, unpublished. 13. N. Fukuda, T. Nakamura et al., Phys. Rev. C 70, 054606 (2004). 14. K. Ieki et al., Phys. Rev. Lett. 70, 730 (1993). 15. S. Shimoura et al., Phys. Lett. B 348, 29 (1995). 16. M. Zinser et al., Nucl. Phys. A 619, 151 (1997).

Eur. Phys. J. A 25, s01, 327–330 (2005) DOI: 10.1140/epjad/i2005-06-184-y

EPJ A direct electronic only

Observation of a two-proton halo in

17

Ne

R. Kanungo1,a , M. Chiba1 , B. Abu-Ibrahim2 , S. Adhikari3,4 , D.Q. Fang5 , N. Iwasa6 , K. Kimura7 , K. Maeda6 , S. Nishimura1 , T. Ohnishi1 , A. Ozawa8 , C. Samanta3,4 , T. Suda1 , T. Suzuki9 , Q. Wang10 , C. Wu10 , Y. Yamaguchi1 , K. Yamada1 , A. Yoshida1 , T. Zheng10 , and I. Tanihata1,b 1 2 3 4 5 6 7

8 9 10

RIKEN, 2-1, Hirosawa, Wako-shi, Saitama 351-0198, Japan Department of Physics, Cairo University, Giza 12613, Egypt Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700064, India Virginia Commonwealth University, Richmond, VA 23284, USA Sanghai Institute of Nuclear Research, Chinese Academy of Sciences, Shanghai 201800, PRC Department of Physics, Tohoku University, Miyagi 980-8578, Japan Department of Electric, Electronics and Computer Engineering, Nagasaki Institute of Applied Science, Nagasaki 851-0193, Japan Institute of Physics, University of Tsukuba, Ibaraki, 305-8571, Japan Department of Physics, Saitama University, Saitama 338-8570, Japan Department of Technical Physics, Peking University, Beijing 100871, PRC Received: 15 November 2004 / c Societ` Published online: 3 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The measurement of longitudinal momentum distribution for two-proton removal from the proton-drip line nucleus 17 Ne with a Be target at 64 A MeV is reported. The observed narrow momentum distribution and the large interaction cross-section suggests the formation of a two-proton halo. The data analyzed within the Few-body Glauber model suggests a significant probability of the two valence protons to abnormally occupy the 2s1/2 orbit, indicating its lowering in proton-rich nuclei. PACS. 25.60.Dz Interaction and reaction cross-sections – 25.60.Gc Breakup and momentum distributions

1 Introduction The first observations on neutron halos were for Borromean nuclei (6 He, 11 Li) [1] which have a two-neutron halo structure. A two-proton halo has however not been observed so far. It is thus interesting to search for their possible existence which is reported in this article. The investigation involved a simultaneous study of the longitudinal momentum distribution (P|| ) from twoproton removal and the interaction cross-section (σI ). A possible candidate seemed to be 17 Ne, the lightest borromean nucleus at the proton drip-line. It has a small two-proton separation energy (S2p = 0.96 MeV). A normal shell model places the valence protons in the d5/2 orbital giving rise to a wide momentum distribution and a small two-proton removal cross-section. An abnormal occupancy of the protons in the 2s1/2 orbital will lead to a narrow momentum distribution with a large cross-section.

The earliest studies on the nucleus observed a large asymmetry in the beta decay strength of 17 Ne and its mirror partner 17 N [2]. This asymmetry could be explained [3] through an enhanced s-wave component in the ground state of 17 Ne compared to 17 N. The amount of enhancement was however not significantly large and the ground state wave function of 17 Ne was considered to be dominated by the normal d-wave nature. The work on Coulomb energy [4] also reached similar conclusions. Some other recent theoretical investigation [5] however suggests a larger s-wave probability of the valence protons. A large s-wave strength is also expected from the observed large interaction cross-section [6] which requires detailed interpretation. The situation is thus unclear and new experimental information may help to shed more light on it.

2 Experiment and analysis

a

Conference presenter; Present address: TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada; e-mail: [email protected] b Present address: Argonne National Laboratory, 9700S Cass Avenue, Argonne, IL 60439, USA.

The experiment for P|| was performed using the new direct time-of-flight (TOF) technique [7]. The secondary beam of 17 Ne interacted with a secondary Be target, with an energy of 60 A MeV. The fragment 15 O after two-proton

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1.2

dσ/dp||(mb/MeV/c)

1 0.8 0.6 0.4 0.2

+0.1

•••••• •• •• -0.25 • • • • • • •• ••• •• •• •• • •• ••• • • • •• • •• •• • • • •• • ••• • • • • ••••• • ••••• • • • • • •• • • • ••• • •• •

5=0.9

0 -400 -300 -200 -100

0

100 200 300 400

P|| (MeV/c) Fig. 1. Longitudinal momentum distribution data of 15 O fragments from 17 Ne. The curves are Glauber model calculations for model-1 as explained in the text. The dash-dotted line is the data for 15 O → 13 O normalized to the peak of 17 Ne → 15 O data. The shaded region is the uncertainity from the twoproton removal cross-section.

removal was detected and its P|| distribution was measured converting to the projectile rest frame. The experimental details are described in ref. [8]. The P|| distribution of 17 Ne → 15 O shown in fig. 1 (black points) is found to have a very narrow width of 168 ± 17 MeV/c (FWHM) compared to the Goldhaber estimate of ∼ 290 MeV/c. A large two-proton removal crosssection of 191±48 mb is also observed. In comparison, the two-proton removal cross-section of 15 O is 54 ± 14 mb [9]. For a comparison on the change of valence proton P|| distribution we also measured the P|| distribution for twoproton removal from the core nucleus, i.e. 15 O → 13 O. The data (dash-dotted line in fig. 1) shows nearly two times wider distribution than 17 Ne [9]. This suggests a halo formation 17 Ne, showing the two valence protons in 17 Ne to have a significant probability of being outside the 15 O core. The data is analysed in the framework of the few-body Glauber model, considering two possibilities for fragmentation. In the first approach (model-1) we consider the fragmentation process to arise from the emission of two uncorrelated protons. 17 Ne has a model of 15 O core + two uncorrelated protons. The solid curve here shows the momentum distribution from such a fragmentation process considering the two valence protons to occupy only the 2s1/2 orbital. It agrees with the data within the error bars. The dashed line shows the distribution for condition where the two valence protons occupy the d5/2 orbital. This is both small in magnitude and wider than the data. We have considered the mixing of these s and d configurations where S1 is the probability of finding two protons in the s-orbital. S1 = 1 denotes a pure s-wave configuration while S1 = 0 denotes a pure d-wave configuration. The dotted line represents S1 = 0.65. It is seen that the data can be explained by a 65%–100% s-wave probability of

the valence protons. This is favorable for a halo formation in 17 Ne. In the second approach (model-2), we consider the possibility of proton evaporation from 17 Ne. In this process, first one proton is knocked out from the 17 Ne nucleus and this leads to a resonance in the unbound 16 F. It then decays to 15 O by another proton emission. In the first knockout step, the valence proton from the s or d orbitals can be removed. Besides, there exists some probability of proton removal from the deeply bound p orbitals populating much higher resonance states in 16 F. The individual contributions for proton removal from the s, p, d, orbitals are shown in fig. 2a by solid, dotted and dashed lines, respectively. They do not agree with the measured distribution. Next we consider a mixed probability of proton removal for the proton evaporation process. Here we have an additional spectroscopic factor S3 for the p-wave proton knockout. It assumes values from zero to 3 independent of S1 (because this is only the probability of knockout and not a part of the 17 Ne wave function description). S3 = 3 represents the conditions where a total of 6 p-wave protons can contribute to the two-proton knockout. Figure 2b summarizes the result of a mixed emission probability which can explain simultaneously the P|| width and the cross-section for two-neutron removal. The shaded region in fig. 2b shows the S1 and S3 values which are in agreement with these data. It is seen that S3 > 1.0 is needed for ovelap with the data, showing that emission of more than 2 protons is necessary. This means, that emission from the p3/2 orbital is needed. Thus, within this framework a 20%–50% s-wave probability of valence protons in 17 Ne is suggested. A 50% s-wave probability is suggestive of a moderate halo formation. To confirm on the structure of 17 Ne we need to now interpret the measured σI for this nucleus. Weighted average of data from ref. [6] when analysed in a Glauber model framework considering core + two-uncorrelated-proton structure for 17 Ne, suggest S1 = 0.75–1.0 [8]. The shaded band in fig. 3 shows that S1 = 0.7–1.0 is the region of swave which consistently explains both the P|| and σI data.

3 Discussion The narrow P|| distribution data from two-proton removal and the large interaction cross-section taken together are suggestive of a two-proton halo formation. A consistent description of these data in a core + p + p Glauber model requires a large s-wave probability of the protons. The extent of the two-proton halo is shown in fig. 4, which demonstrates the percentage of the two-proton density outside the distance “r” measured from the center of the nucleus. The boundary of the core is defined as the radial distance beyond which only 10% of the core density exists. The vertical shaded line shows this distance. The two-proton density is shown by dashed (solid) line for S1 = 0.0 (1.0). From the above analysis the s-wave probability in 17 Ne is S1 ∼ 0.7. It is then found that the valence protons have around 60% probability of residing outside

R. Kanungo et al.: Observation of a two-proton halo in

1.2

Ne

329

1

>

=

dσ/dp||(mb/MeV/c)

•••••• •• ••• •• • 0.8 • •• 0.6 • ••• •• • • •• 0.4 • •• • • • ••• •• 0.2 • • •• ••••• • ••• • • • • •• •••••••••••• • • •• • • 0 •••••••••••• • •••• -400 -300 -200 -100

0

100 200 300 400

0.8

Overlap region with experimental data 0.6

S1

1

17

0.4

0.2

0 0.5

0

1

1.5

2

2.5

3

3.5

S3

P|| (MeV/c)

Fig. 2. (a) The longitudinal momentum distribution of 15 O fragments from 17 Ne. The curves are results of proton evaporation as explained in the text. (b) The range of S1 and S3 which overlaps with both the P|| and σ−2p data.

σint

dσ dΡ|| uncorrelated proton emission

dσ dΡ||

0

proton evaporation

0.2

0.4

0.6

0.8

1

Percentage of density outside 'r'

100 80

2p in s-wave 60 40

2p in d-wave

20

15O-core

0

s-wave probability (S1) Fig. 3. Summary of s-wave probability of the two valence protons from the different analysis. The shaded vertical band shows the region of consistency between interaction crosssection and momentum distribution.

the core. A similar analysis for the two-neutron halo nucleus 11 Li [10] shows 73% of the two-neutrons being outside the 9 Li core (considering the 11 Li ground state to have an equal mixture of s and p wave configurations). In contrast, well-bound nuclei like 15 O or 17 N, show only 38% of the valence nucleon to be outside the core (the “core” nuclei here are 13 O and 15 N, respectively). It is certainly true that proton halos are far less pronounced than neutron halos. Nevertheless, that fact that despite the Coulomb barrier, the s-orbit is lowered even in proton-rich drip-line nuclei, causes them to have spatial extension compared to well-bound normal nuclei. Evidence for the lowering of the 2s1/2 orbit can also be noted in neighbouring nucleus 16 F.

17Ne

4

8

r

[fm]

1 2

Fig. 4. The probability of the two valence protons to be outside the 15 O core for 17 Ne. The dotted line shows the percentage of density of 15 O outside “r”. The dashed/solid line shows the percentage of two-proton density for protons in the d5/2 /2s1/2 orbit.

It may be mentioned here that further interpretation with a microscopic correlated wave function for 17 Ne maybe useful for obtaining deeper insights. In addition, some alternative experimental investigation would help to put further constraint on the s-wave probability.

References 1. I. Tanihata et al., Phys. Lett. B 160, 380 (1985); Phys. Rev. Lett. 55, 2676 (1985). 2. M.J.B. Borge et al., Phys. Lett. B 317, 25 (1993); A. Ozawa et al., J. Phys. G 24, 143 (1998).

330 3. 4. 5. 6.

The European Physical Journal A J.D. Millener, Phys. Rev. C 55, R1633 (1997). H.T. Fortune, R. Sherr, Phys. Lett. B 503, 70 (2001). L.V. Grigorenko et al., Nucl. Phys. A 713, 372 (2003). A. Ozawa et al., Phys. Lett. B 334, 18 (1994).

7. 8. 9. 10.

R. R. H. R.

Kanungo et al., Phys. Rev. Lett. 88, 142502 (2002). Kanungo et al., Phys. Lett. B 571, 21 (2003). Jeppesen et al., Nucl.Phys. A 739, 57 (2004). Kanungo, Nucl. Phys. A 738, 293 (2004).

5 Clusters and drip lines 5.3 Drip lines and beyond

Eur. Phys. J. A 25, s01, 333–334 (2005) DOI: 10.1140/epjad/i2005-06-001-9

EPJ A direct electronic only

Remarks about the driplines M. Thoennessena Department of Physics & Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Received: 12 September 2004 / Revised version: 3 November 2004 / c Societ` Published online: 7 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Reaching the limits of nuclear stability has been one of the driving forces of nuclear physics experiments. A few observations and remarks about the current status of the proton and neutron driplines will be presented. PACS. 21.10.-k Properties of nuclei; nuclear energy levels

1 Proton dripline The proton dripline itself is not clearly defined. Sometimes it is simply defined by the proton separation energy passing through zero (Sp = 0 MeV) [1]. Although this definition is unambiguous due to the Coulomb barrier especially in heavy nuclei, it is not identical with protons “dripping” from the nucleus. With this definition many nuclei “exist” beyond the dripline. An alternative definition of the dripline is to set it equal to the existence of a nucleus which can be defined as limited by the typical nuclear timescale of ∼ 10−22 s [2]. The dripline and the existence of a nucleus could also be related to the definition of radioactivity with a limit of ∼ 10−12 s [3]. Most of these discussions of different definitions are semantics. It is, however, important that especially in the interaction of theorists and experimentalist it is understood which definition is used. Assuming the above definition of the dripline as Sp = 0 MeV it is generally accepted that the dripline is relatively well delineated [4]. Compared to the neutron dripline this is certainly true. However, if one looks carefully at the location of the dripline, the exact location is experimentally known for only six elements beyond Mg and below Pb (Cl, K, Sc, Lu, Ta, and Au) [5]. Beyond Pb the dripline is known for the odd isotopes Bi, At, Fr, Ac, and Pa. An interesting possibility exists in the At isotopes, where 195 At is unbound by −234 ± 15 keV, while 194 At could potentially be bound 117 ± 189 keV [6]. 195 At could thus be an island of a proton unbound nucleus surrounded by bound nuclei. This would still only be a curiosity with no practical implications because even though 195 At is proton unbound it already has been measured to be an α-emitter [7]. However, if the limit can be pushed to even more proton unstable nuclei islands of proton emitters surrounded by β- and α-emitters could exist. a

e-mail: [email protected]

Although the exact location of the dripline is not well known, the dripline (Sp = 0 MeV) has been crossed for most (predominantly for the odd proton) elements. Nevertheless, with the current detection capabilities for the direct observation of isotopes (on the order of nanoseconds) many hundreds of isotopes beyond the dripline are still unknown. The proposed Rare Isotope Accelerator RIA [8] will be able to produce well over 200 new isotopes along the proton dripline [5]. The importance of the dripline for the astrophysical rp-process has been discussed extensively [9]. The exact location of the dripline itself is not really important. The crossing of Sp = 0 MeV has no special significance for the lifetimes of waiting point nuclei in stellar environments. These lifetimes have to be determined from the accurate knowledge of the binding energies. Again, because of the Coulomb barrier even unbound nuclei can have significant lifetimes and can have a large influence on the stellar lifetimes [9].

2 Neutron dripline It is generally accepted that the neutron dripline has been reached for all elements up to oxygen [8]. However, due to the strong odd-even effect of the binding energy, even if an odd isotope has been found to be unstable one still has to check if the next heavier even isotope is also unbound in order to know if the last bound isotope of a given element has been observed. For example, so far no experiments searching for the existence of 13 Li or 18 Be have been performed. Thus, strictly speaking the dripline is only known up to helium [5]. In order to avoid the odd even staggering of the neutron dripline, it should be handled equivalent to the proton dripline, i.e. in terms of isotones instead of isotopes [1,5]. Figure 1 shows the neutron dripline in this presentation.

The European Physical Journal A

20

protons

neutrons

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N BC

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20

measured uncertain

Ca K Ar

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calculated uncertain Cl S

measured dripline calculated dripline

A = 30

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calculated

H

N

stable bound unbound - meas.

C

10

stable bound

B

unbound - observed

Be Li

unbound - limit

He

unbound - limit 0

F O

A = 10

A = 10

0

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10

A = 20

20

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0 0

H

10

20

neutrons

Fig. 1. Light mass region of the chart of nuclei. Left: The neutron dripline presented in terms of isotones, i.e. the neutron numbers are plotted vs. the proton numbers. Right: The proton dripline for comparison in the normal presentation of proton numbers vs. neutron numbers. See text for more details about the notations.

The number of neutrons are plotted vs. the number of protons (left). The right side of the figure shows the proton dripline for comparison in the normal presentation, i.e. protons vs. neutrons. The figure indicates stable, bound and unbound isotopes. Unbound isotopes which have not been observed but where lifetime limits were established are also included (unbound - limit). In addition, the measured (solid lines) and calculated (dashed lines) driplines are shown. At the proton dripline, isotopes where the uncertainty for the binding energies includes Sp = 0 MeV are shown as solid hashed (measured uncertainty) and dashed hashed (calculated uncertainty) squares. In the isotone presentation, the dripline is known up to N = 9. It is unlikely that 13 Li, 18 Be or 30 O are bound, so effectively, the dripline is known up to N = 23 (34 Na) [10, 11,12]. The location of the dripline is typically calculated with a variety of mass models. It is often pointed out that these calculations deviate from each other significantly for extrapolations towards the driplines [13]. This is especially true for the neutron dripline. While the deviations of the proton dripline of the empirical model based on p-n interaction by Tachibana et al. [14], the finite-range droplet model [15], and the Hartree-FockBogolyubov model (HFB-2) [16] from the extrapolated masses of the AME2003 atomic mass evaluation [6] are on the order of 3-4 isotopes, the neutron dripline (defined as the occurrence of the first unbound isotope) differs just among the three calculations by up to 15 isotopes [5]. However, if the differences are displayed in terms of isotones the deviations of the models are not as large. Again, this representation avoids the difficulty to determine the dripline due to the odd-even staggering. The differences

between the models of about 3-4 isotones are comparable to the deviations along the proton dripline [5]. This work has been supported by the National Science Foundation grant number PHY01-10253.

References 1. P.G. Hansen, J.A. Tostevin, Annu. Rev. Nucl. Part. Sci. 53, 219 (2003). 2. A.C. Mueller, B.M. Sherrill, Annu. Rev. Nucl. Part. Sci. 43, 529 (1993). 3. J. Cerny, J.C. Hardy, Annu. Rev. Nucl. Part. Sci. 27, 323 (1977). 4. RIA Physics White Paper (2000), http://www.orau.org/ ria/ria-whitepaper-2000.pdf. 5. M. Thoennessen, Rep. Prog. Phys. 67, 1187 (2004). 6. G. Audi, A.H. Wapstra, C. Thibault, Nucl. Phys. A 729, 337 (2003). 7. M. Leino et al., Act. Phys. Pol. B 26, 309 (1995). 8. ISOL Task Force to NSAC (1999), http://www.orau.org/ ria/ISOLTaskForceReport.pdf. 9. H. Schatz et al., Phys. Rep. 294, 167 (1998). 10. H. Sakurai et al., Phys. Lett. B 448, 180 (1999). 11. M. Notani et al., Phys. Lett. B 542, 49 (2002). 12. S.M. Lukyanov et al., J. Phys. G 28, L41 (2002). 13. Scientific Opportunities with Fast Fragmentation Beams from RIA, Michigan State University (2000), http:// www.orau.org/ria/opportunitiesffbeam.pdf. 14. T. Tachibana, M. Uno, M. Yamada, S. Yamada, At. Data Nucl. Data Tables 39, 251 (1988). 15. P. M¨ oller, J.R. Nix, W.J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995). 16. S. Goriely, M. Samyn, P.H. Heenen, J.M. Pearson, F. Tondeur, Phys. Rev. C 66, 024326 (2002).

Eur. Phys. J. A 25, s01, 335–338 (2005) DOI: 10.1140/epjad/i2005-06-192-y

EPJ A direct electronic only

Discovery of

60

Ge and

64

Se

A. Stolz1,a , T. Baumann1 , N.H. Frank1,2 , T.N. Ginter1 , G.W. Hitt1,2 , E. Kwan1,2 , M. Mocko1,2 , W. Peters1,2 , A. Schiller1 , C.S. Sumithrarachchi1,3 , and M. Thoennessen1,2 1 2 3

National Superconducting Cyclotron Laboratory, East Lansing, MI 48824, USA Department of Physics & Astronomy, Michigan State University, East Lansing, MI 48824, USA Department of Chemistry, Michigan State University, East Lansing, MI 48824, USA Received: 17 January 2005 / Revised version: 24 April 2005 / c Societ` Published online: 15 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Very neutron-deficient fragments were produced by projectile fragmentation of a 140 MeV/ nucleon 78 Kr primary beam on a beryllium target. The secondary fragments were unambiguously identified after separation in the A1900 fragment separator. Three events of 60 Ge and four events of 64 Se have been observed for the first time, making 60 Ge the heaviest known isotone of the N = 28 neutron shell. No events of 59 Ga and 63 As have been observed providing very strong evidence that these nuclei are unbound with respect to proton emission. PACS. 25.70.Mn Projectile and target fragmentation – 27.50.+e 59 ≤ A ≤ 89 – 23.50.+z Decay by proton emission

1 Introduction The proton drip line, in contrast to the neutron dripline, is not a boundary of existence [1]. Due to the Coulomb barrier, nuclei beyond the proton dripline can have very long lifetimes depending on their nuclear charge and binding energy. They can decay by either β + or proton emission. The observation of new isotopes at and beyond the proton dripline yields important input for the understanding of the nuclear forces [2] and the formation of the elements [3]. The location of the proton dripline as defined as Sp = 0 is not a critical parameter itself. The contribution to the generation of heavier elements along the astrophysical rapidproton (rp) capture process depends on the lifetimes and binding energies of the nuclei involved. Even the pure observation or non-observation of nuclei produced in projectile fragmentation reactions yields important information about their lifetimes. Although the limits of current knowledge has already passed the region of interest for the rp-process the lifetime information of these nuclei can be used to constrain the mass models, because the proton decay lifetimes are correlated with the binding energies. It becomes increasingly more difficult to produce new isotopes the closer one approaches the dripline. The last observation of a new isotope below mass 100 was reported more than three years ago [4]. The predominant method to discover new neutron-deficient isotopes in this mass region has been projectile fragmentation. Previous experiments were able to map a large range of new isotopes a

Conference presenter; e-mail: [email protected]

simultaneously [5, 6,7]. The more exotic nuclei need to be specifically isolated in dedicated fragment separator settings [8]. Projectile fragmentation is also predicted to be the most efficient production method to extend the knowledge of neutron-deficient nuclei even further with the next generation rare isotope accelerators [9, 10,11]. Measuring the production rates of the most exotic nuclei with the existing facilities is crucial for the predictions of rates for the new facilities.

2 Experimental procedure A beam of 78 Kr34+ was accelerated to an energy of 140 MeV/nucleon at the Coupled Cyclotron Facility of the National Superconducting Cyclotron Laboratory at Michigan State University. The primary beam was fragmented in a 610 mg/cm2 thick 9 Be production target located at the object position of the A1900 fragment separator [12]. The experimental setup is shown in fig. 1. Secondary fragments of a single magnetic rigidity were selected in the first half of the A1900 (Bρ1 = 2.4486 Tm for 60 Ge, Bρ1 = 2.4935 Tm for 64 Se). A slit system at the central dispersive focal plane (image-2) of the separator limited the momentum acceptance to dp/p = 0.5%. A 240 mg/cm2 thick wedge-shaped aluminum energy degrader was also placed at this position. Setting the second half of the separator to the magnetic rigidity of the fragment of interest (Bρ2 = 1.7206 Tm and 1.7481 Tm for 60 Ge and 64 Se, respectively) allowed for further isotopic

336

The European Physical Journal A focal plane

production target

A1900 image-2 20 ft 10 m

PPAC

PIN (ΔE) PIN (Eres) PIN (veto)

SCI

focal plane

degrader

slit

image-2

Fig. 1. Schematic view of the experimental setup at the A1900 fragment separator. The detector systems for particle identification were placed at the dispersive focal plane (image-2) and at the achromatic focal plane: a timing scintillator (SCI), a position-sensitive PPAC, and 3 silicon detectors (PIN).

separation. The fragments were stopped in a telescope of three silicon detectors (Si PIN diodes with an active area 50×50 mm2 ) at the achromatic final focal plane of the A1900. A first detector (thickness 0.5 mm) provided an energy-loss signal for nuclear charge identification and a timing signal to start the time-of-flight (TOF) measurement. The fragments of interest were stopped in the second silicon detector (thickness 1 mm) which measured the residual energy. A third silicon detector served as veto detector to reject particles not being stopped. A 0.1 mm thick plastic scintillator (BC-400) was installed at the image-2 position. This detector was read out by two photomultiplier tubes on either end of the scintillator and provided two independent timing signals. Several parameters were used from this detector setup to unambiguously identify implanted fragments: energy loss signals from the first two silicon detectors, a veto signal from the last silicon detector, and position information from the PPAC detector (used to veto events implanted at the edges of the active area of the silicon detectors). Three independent TOF signals were obtained by recording the time differences between the signal from the silicon detector and signals from the cyclotron RF or each of the two timimg signals of the image-2 scintillator. The resolution σ of each signal was also determined. To be accepted as a valid event, all parameters were required to lie within a 3σ interval.

3 Results and discussion A two-dimensional identification plot of energy loss in the first silicon detector versus the TOF between that and the image-2 scintillator for the 60 Ge fragment separator set-

Fig. 2. Two-dimensional identification plot of energy loss in the first silicon detector versus the time-of-flight between the image-2 scintillator and the silicon detector at the focal plane. The fragment separator setting was optimized for 60 Ge.

ting is shown in fig. 2. During 60 hours of beam on target with an average primary beam current of 3.6 pnA a total of three events of 60 Ge were unambiguously identified. These events fulfill the conditions explained above. Other fragments shown in the identification plot are N = 28 and N = 27 isotones with masses A < 60. The group of events above 53 Fe are events with “pile-up” signals in the electronics of the energy loss detector. Due to the separation in time-of-flight, none of those background events can be found in the region of 60 Ge, The probability for random background was determined to be less than 2 × 10−9 in the vicinity of 60 Ge. The contribution of 58 Zn within the 60 Ge cut is even smaller. Therefore, we conclude that the new isotope 60 Ge has been observed for the first time. The analysis of this run is consistent with no observation of 59 Ga, which provides very strong evidence that 59 Ga is unbound with respect to proton decay. The right panel of fig. 3 shows a two-dimensional identification plot for the 64 Se separator setting. The left panel shows the 64 Se events in a plot of energy loss versus the total energy measured with the silicon detectors at the focal plane. Four events of 64 Se were observed during 32 hours of beam on target with an average primary beam current of 13.5 pnA. This measurement shows the first observation of 64 Se and the non-observation of 63 As. To investigate the production of neutron-deficient nuclei close to the dripline the production yields of germanium and selenium isotopes with isospin projections from Tz = 0 to Tz = −2 were measured. The maximum of the momentum distribution after the production target was determined experimentally for 64 Ge and compared with the prediction of the program LISE++ [13]. For other isotopes, yield measurements were perfomed at the maximum

A. Stolz et al.: Discovery of

60

Ge and

64

Se

337

2.2

energy loss [GeV]

2.0

1.8

64

Se

1.6

1.4 1.4

1.6

1.8 2.0 2.2 total kinetic energy [GeV]

2.4

2.6

Fig. 3. Two-dimensional identification plots for a 64 Se setting of the fragment separator. The left panel shows the energy loss in the first silicon detector versus the total energy measured in both silicon detectors. The right panel shows the energy loss signal versus the the time-of-flight between the image-2 scintillator and the silicon detector at the focal plane.

Figure 4 shows the experimental cross-section data in comparison with the predictions of EPAX2 [15], an empirical parametrization of projectile cross-sections. EPAX2 overpredicts the the krypton fragmentation cross-sections by more than one order of magnitude. This overprediction of all isotopes towards the dripline might have significant implications for next generation rare isotope accelerators like RIA [11], where part of the rare ion beam rate estimates are based on EPAX2.

102 EPAX2

100

exp. data

cross section [mbarn]

10-2

10-4

Ge

4 Conclusion

10-6

Se

10-8

10-10

10-12

60

61

62

63 64 65 mass number

66

67

68

Fig. 4. Measured cross-section for germanium and selenium isotopes as a function of the mass number. The experimental values are compared with EPAX2 parametrization.

of the momentum distribution as scaled from the measured 64 Ge value. The transmission for these isotopes was calculated with the simulation codes LISE++ and MOCADI [14] to determine the production cross-sections. The intensity of the primary beam was monitored by a BaF2 scintillation detector measuring secondary particles emitted from the production target.

The very neutron-deficient isotopes 60 Ge and 64 Se were observed for the first time. The non-observation of 59 Ga and 63 As provides very strong evidence that these nuclei are unbound with respect to proton emission. The experimental production cross-sections of germanium and selenium isotopes close to the proton drip-line were significantly lower than the predictions by parametric EPAX2 model. This result might have major implications for predicted rates for the next generation rare isotope accelerators. This work was supported by the National Science Foundation under Grant No. PHY-01-10253.

References 1. M. Thoennessen, Rep. Prog. Phys. 67, 1187 (2004). 2. D. Lunney, J. M. Pearson, C. Thibault, Rev. Mod. Phys. 75, 1021 (2003). 3. H. Schatz et al., Phys. Rep. 294, 167 (1998). 4. J. Giovinazzo et al., Eur. Phys. J. A 11, 247 (2001).

338 5. 6. 7. 8. 9.

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F. Pougheon et al., Z. Phys. A 327, 17 (1987). M. F. Mohar et al., Phys. Rev. Lett. 66, 1571 (1991). B. Blank et al., Phys. Rev. Lett. 74, 4611 (1995). B. Blank et al., Phys. Rev. Lett. 84, 1116 (2000). T. Motobayashi, Nucl. Instrum. Methods Phys. Res. B 204, 736 (2003). 10. W. F. Henning, Nucl. Instrum. Methods Phys. Res. B 204, 725 (2003). 11. B. M. Sherrill, Nucl. Instrum. Methods Phys. Res. B 204, 765 (2003).

12. D. J. Morrissey, B. M. Sherrill, M. Steiner, A. Stolz, I. Wiedenh¨ over, Nucl. Instrum. Methods Phys. Res. B 204, 90 (2003). 13. O. Tarasov, D. Bazin, M. Lewitowicz, O. Sorlin, Nucl. Phys. A 701, 661c (2002). 14. N. Iwasa et al., Nucl. Instrum. Methods Phys. Res. B 126, 284 (1997). 15. K. S¨ ummerer, B. Blank, Phys. Rev. C 61, 034607 (2000).

Eur. Phys. J. A 25, s01, 339–341 (2005) DOI: 10.1140/epjad/i2005-06-173-2

EPJ A direct electronic only

Studies of light neutron-rich nuclei near the drip line U. Datta Pramanik1,2,a , T. Aumann2 , K. Boretzky2 , D. Cortina3 , Th.W. Elze4 , H. Emling2 , H. Geissel2 , unzenberg2 , C. Nociforo5 , M. Hellstr¨om2 , K.L. Jones2 , L.H. Khiem5 , J.V. Kratz5 , R. Kulessa6 , Y. Leifels2 , G. M¨ ummerer2 , S. Typel2 , W. Walus6 , and H. Weick2 R. Palit2 , H. Scheit7 , H. Simon2 , K. S¨ 1 2 3 4 5 6 7

Saha Institute of Nuclear Physics, Kolkata, India Gesellschaft f¨ ur Schwerionenforschung (GSI), Darmstadt, Germany Universidad de Santiago de Compostela, Santiago de Compostela, Spain Institut f¨ ur Kernphysik, Johann-Wolfgang-Goethe Universit¨ at, Frankfurt, Germany Institut f¨ ur Kernchemie, Johannes-Gutenberg Universit¨ at, Mainz, Germany Instytut Fizyki, Uniwersytet Jagello´ nski, Krak´ ow, Poland Institut f¨ ur Kernphysik, Heidelberg, Germany Received: 14 February 2005 / Revised version: 6 May 2005 / c Societ` Published online: 4 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Coulomb breakup of neutron-rich Be, B, C, and O isotopes at relativistic energies (400– 600 A MeV) was studied with kinematically complete measurements. The ground-state properties of these nuclei were deduced by comparing experimental data for Coulomb-dissociation cross-sections with directbreakup model calculations. The dominant ground-state configurations of 15 C, 11 Be, 14 B, and 23 O were found to be 14 Cgs (0+ ) ⊗ νs ,10 Begs (0+ ) ⊗ νs , 13 Bgs (3/2+ ) ⊗ νs,d , and 22 Ogs (0+ ) ⊗ νs , respectively, and 16 C(2+ ) ⊗ νs,d for 17 C. The capture cross-section for 14 C(n,γ) 15 C relevant in astrophysical scenarios was measured indirectly through Coulomb dissociation. PACS. 21.10.Jx Spectroscopic factors – 25.40.Lw Radiative capture – 26.30.+k Nucleosynthesis in novae, supernovae, and other explosive environments

1 Introduction Recent developments in radioactive nuclear beam techniques have led to exciting discoveries in the field of nuclear structure. The neutron halo, the appearance of lowlying dipole strength, and the melting of closed shells are examples of new structural phenomena observed in light nuclei near the neutron drip line. Breakup reactions are an important source of information about the structure of exotic nuclei. Coulomb breakup is a particularly important mechanism due to its sensitivity to the tail of the wave function of loosely bound nuclei. In the present contribution we summarize the results of Coulomb-breakup measurements to study the single-particle ground-state properties of 15,17 C, 11 Be, 14 B, and 23 O, and an indirect measurements (through Coulomb dissociation) of the radiative-capture cross-section of the 14 C(n,γ)15 C reaction which is relevant in astrophysical scenarios.

tation of a 40 Ar beam. Those beams were separated in the FRS and transferred to a secondary-reaction target placed inside the LAND-ALADIN setup at GSI [1, 2,3]. The ions were identified event by event by means of energy-loss and time-of-flight measurements. Neutrons from the decay of reaction products were kinematically forward focussed and detected by the large-area neutron detector, LAND. Decay γ-transitions of the fragments were measured to identify the core-excited states. Coulomb-dissociation crosssections were obtained using a Pb target. Breakup data were also taken for a C target to determine the nuclear contribution, and for an empty target in order to deduce background reactions taking place in various detector materials. By measuring the momenta of all decay products after breakup, the excitation energies of the decaying nuclei were determined.

3 Results 2 Experimental details Secondary beams of neutron-rich Be, B, C, and O isotopes at energies of 400–600 A MeV were produced by fragmena

Conference presenter; e-mail: [email protected]

3.1 Single-particle structure of light neutron-rich nuclei The electromagnetic breakup of loosely bound nuclei in energetic heavy-ion collisions is dominated by dipole excitations. The non-resonant direct breakup cross-section

The European Physical Journal A Counts / (200 keV)

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16

C→ C+n+γ

1.76 MeV

40

17

4+, 4.14 MeV

27%

C

+

(0 ), 3.03 MeV

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20

2+, 1.76 MeV

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+

0 , 0.0 16

0

0

2000

4000

6000

C

8000

10000 γ

20

17

16

+

C → C(2 ) + n

dσ

/ dE

*

[mb/MeV]

Esum [keV]

10 l=0 l=2

0

2

4

6

8

10

12

14 E

*

[MeV]

Fig. 1. Top: Sum-energy spectrum of γ transitions in 16 C after Coulomb breakup of 17 C. Bottom: Differential CD crosssections as a function of excitation energy, E ∗ , of 17 C in coincidence with the 1.766 MeV γ transition (16 C(2+ → 0+ )). The smooth curves are the cross-sections calculated using a direct-breakup model in plane-wave approximation for l = 0 and l = 2 neutrons (solid lines) and their sum (heavy solid curve). The dashed curve shows the result using the distortedwave approximation [1]. ∗

(Icπ ),

due to the Coulomb interaction, dσ/dE can be expressed as    16π 3 dσ π NE1 (E ∗ ) C 2 S(Icπ , nlj) (I ) = c ∗ 9c dE nlj  | q|(Ze/A)rYm1 |ψnlj |2 , (1) × m

ψnlj represents the single-particle wave function of the valence neutron in the projectile ground state, and C 2 S(Icπ , nlj) its spectroscopic factor with respect to a particular core state, Icπ . The final-state wave function q | of the valence neutron in the continuum may be approximated by a plane wave, or, alternatively, by a distorted wave. The single-particle wave functions have been derived from a Woods-Saxon potential. NE1 (E ∗ ) is the number of equivalent dipole photons of energy E ∗ . For details see ref. [1]. Non-resonant low-lying dipole strength is observed in neutron-rich 15,17 C [1], 11 Be [3], 14 B and 23 O [2] isotopes which can be explained by the direct-breakup mechanism. Data analysis showed that after Coulomb dissociation (CD) of 15 C, 11 Be, 14 B, and 23 O, the respective cores are mainly populated in their ground states (to 90–70%), and that the valence neutrons occupy the s1/2 orbital (d5/2 in the case of 14 B). But the situation is very different in 17 C. Figure 1 (top) shows the partial CD cross-section of 17 C when different core states after Coulomb breakup are populated. The experimental data for CD [1] shows (fig. 1, bottom) that the predominant ground-state configuration of 17 C is 16 C(2+ )⊗νs,d . In 23 O, the analysis of the dipoletransition probability into the continuum allows us to infer a 22 O(0+ )⊗2νs1/2 ground-state configuration with a spectroscopic factor of 0.77(10) and thus a ground-state spin

Fig. 2. Differential CD cross-sections for 23 O breakup into 22 O(0+ ) and neutron. In panel (a) and (b), respectively, the full (dashed) line shows the direct-breakup calculation assuming plane waves and distorted wave using an optical potential for the outgoing neutron and adopting a ground-state spin of 1/2+ (5/2+ ) for 23 O. The dotted line in panel (b) is the result of the calculation within the effective-range approach for a groundstate spin of 1/2+ . For details see [2]. Table 1. Capture cross-section (in μb) at Ecm = 23 keV

This expt

Direct [7]

Indirect [8]

4.3(10)

1.1(3)

2.6(9)

I π (23 O) = 1/2+ , resolving earlier conflicting experimental findings [4, 5]. It is evident from fig. 2 that final-state interactions are of significant influence in the case of the more tightly bound 23 O nucleus; an effective reduced scattering length for low-energy p3/2 neutron scattering could be derived from the data [2].

3.2 Indirect measurement of capture cross-section The radiative-capture cross-section of the 14 C(n, γ)15 C reaction may play an important role in various astrophysical scenarios [6]. Beer et al. [7] measured this reaction cross-section directly at low energies and obtained a result different from the calculated one. However, a direct measurement of this reaction is very difficult due to the small cross-section (μb) and the use of a radioactive target. We measured the capture cross-section indirectly via CD and obtained an integrated cross-section of 360 ± 10 mb. Table 1 shows the (deduced) capture crosssection at Ecm = 23 keV for both direct and indirect measurements. Horvath et al. [8] also derived the same quantity from a CD measurement but at a much lower beam energy (35 A MeV); the dependence of their curve on relative energy appears to be different from our measurement. Both indirect measurements of capture cross-section at the astrophysical relevant energies were obtained from extrapolating the CD cross-sections. One of the authors (U. Datta Pramanik) is indebted to the Alexander-von-Humboldt foundation for partial support of the work presented in this article and is also thankful to the conference organizers of ENAM04 for partial financial support to attend the conference.

U. Datta Pramanik et al.: Studies of light neutron-rich nuclei near the drip line

References 1. 2. 3. 4.

U. C. R. R.

Datta Pramanik et al., Phys. Lett. B 551, 63 (2003). Nociforo et al., Phys. Lett. B 605, 79 (2005). Palit et al., Phys. Rev. C 68, 034318 (2003). Kanungo et al., Phys. Rev. Lett. 88, 142502 (2002).

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5. D. Cortina-Gil et al., Phys. Rev. Lett. 93, 062501 (2004). 6. M. Wiescher et al., J. Phys G 25, R133 (1999); M. Terasawa et al., Astro. Phys. J. 562, 470 (2001). 7. H. Beer et al., Astrophys. J. 387, 258 (1992). 8. A. Horvath et al., Astrophys. J. 570, 926 (2002).

Eur. Phys. J. A 25, s01, 343–346 (2005) DOI: 10.1140/epjad/i2005-06-149-2

EPJ A direct electronic only

One-neutron knockout of

23

O

D. Cortina-Gil1,a , J. Fernandez-Vazquez1 , T. Aumann2 , T. Baumann3 , J. Benlliure1 , M.J.G. Borge4 , L.V. Chulkov5 , U. Datta Pramanik2 , C. Forss´en6 , L.M. Fraile4 , H. Geissel2 , J. Gerl2 , F. Hammache2 , K. Itahashi7 , R. Janik8 , unzenberg2 , T. Ohtsubo2 , A. Ozawa9 , B. Jonson6 , S. Mandal2 , K. Markenroth6 , M. Meister6 , M. Mocko8 , G. M¨ Y. Prezado4 , V. Pribora5 , K. Riisager10 , H. Scheit11 , R. Schneider12 , G. Schrieder13 , H. Simon13 , B. Sitar8 , A. Stolz12 , ummerer2 , I. Szarka8 , and H. Weick2 P. Strmen8 , K. S¨ 1 2 3 4 5 6 7 8 9 10 11 12 13

Universidad de Santiago de Compostela, E-15706 Santiago de Compostela, Spain Gesellschaft f¨ ur Schwerionenforschung (GSI), D-64291 Darmstadt, Germany NSCL, Michigan State University, East Lansing, MI-48824, USA Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain Kurchatov Institute, RU-123182 Moscow, Russia Avd. f¨ or Experimentell Fysik, Chalmers Tekniska H¨ ogskola och G¨ oteborgs Universitet, SE-412 96 G¨ oteborg, Sweden Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan Faculty of Mathematics and Physics, Comenius University, 84215 Bratislava, Slovakia RIKEN, 2-1 Hirosawa Wako, Saitama 3051-01, Japan Institut for Fysik og Astronomi, Aarhus Universitet, DK-8000 Aarhus C, Denmark Max-Planck Institut f¨ ur Kernphysik, D-69117 Heidelberg, Germany Physik-Deptartment E12, Technische Universit¨ at, M¨ unchen, D-85748 Garching, Germany Institut f¨ ur Kernphysik, Technische Universit¨ at, D-64289 Darmstadt, Germany Received: 14 March 2005 / Revised version: 19 April 2005 / c Societ` Published online: 14 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Breakup reactions were used to study the ground-state configuration of the neutron-rich isotope 23 O. The 22 O fragments produced in one-nucleon removal from 23 O at 938 MeV/nucleon in a carbon target were detected in coincidence with de-exciting γ rays, allowing to discern between 22 O ground-state and excited-states contributions. From the comparison of exclusive experimental momentum distributions for the one-neutron removal channel to theoretical momentum distributions calculated in an Eikonal model for the knockout process, and spin and parity assignment of I π = 1/2+ was deduced for the 23 O ground state. This result solved the existent experimental discrepancy. PACS. 25.60.Gc Breakup and momentum distributions – 25.60.Dz Interaction and reaction cross-sections – 27.20.+n 6 ≤ A ≤ 19

1 Introduction Recent studies in neutron-rich oxygen isotopes near the neutron dripline have shown very exciting issues.22 O [1] with its first excited state at 3.17 MeV and 24 O [2] with no excited states below 4 MeV seem to be double magic nuclei. In addition, 24 O is today accepted to be the last bound oxygen isotope reinforcing the idea of the N = 16 magic number replacing the N = 20 gap for sd-shell dripline nuclei. In this context, 23 O is a key nucleus to understand the structure of light neutron-rich isotopes. Consequently, it has been subject of interest and several experiments have been dedicated to its study during the last years. a

Conference presenter; e-mail: [email protected]

The main experimental tool used in these investigations are high-energy knockout reactions of single neutrons from near-dripline nuclei. Brown et al. [3] have shown that the residue momentum distributions and the corresponding cross-sections can be analyzed in such a way that both the l-values and the single-particle occupation probabilities of the levels can be deduced.This, however, requires that the level from which the breakup occurred is identified uniquely by measuring γ-rays in coincidence with the residue [4, 5,6]. The first dedicated 23 O experiments could not profit from this γ-tagging and were limited to measure inclusive observables. Two experiments were performed. The first one, done at GANIL by Sauvan et al. [7,8] who measured a relatively narrow longitudinal momentum distribution of 22 O after one-neutron knockout from 23 O, led to a ground-state spin and parity of I π = 1/2+ for 23 O.

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production scintillator SC

target SCI1

ionization chamber IC

ToF 1 IC1

position detector TPC

SCI2

NaI array

ToF 2

breakup target dispersive mid−plane

IC2

SCI3

32 NaI array

F2

final focus F4

Fig. 1. A schematic view of the FRagment Separator (FRS) with the detection set-up. The complete identification was possible in both sections of the spectrometer by time-of-flight (TOF) measurements between scintillators (SCI) and energydeposition in ionization chambers (IC) measurements. Several position-sensitive detectors (TPC) allow tracking of projectiles and fragments and momentum measurements of the fragments. γ-rays coincident with fragments where measured with a NaIarray.

In contrast, the other performed at RIKEN by Kanungo et al. [9], attributed I π = 5/2+ to the 23 O ground state. If confirmed this would have significant implications on our understanding of the shell structure in the vicinity of N = 16. This controversy prompted a comment by Brown et al. [10] and calculations by Sauvan et al. [8]. Both papers give a consistent analysis of the available inclusive data in terms of a (d5/2 )6 (s1/2 )1 configuration for 23 O. This discrepancy was at the origine of the experimental study presented in this paper where an exclusive oneneutron knockout experiment of 23 O was performed. In this work, the individual levels are identified by measuring the deexciting γ-rays in coincidence with the inclusive observables.

2 Experimental set-up A 938 MeV/nucleon 23 O secondary beam was produced by fragmentation of a 40 Ar primary beam with an energy of 1.0 GeV/nucleon, delivered by the heavy-ion synchrotron SIS, in a 4 g/cm2 Be target. The Fragment Separator (FRS [11]) at GSI was used in its energy-loss mode to transmit the 23 O secondary beam to the breakup carbon target at the intermediate focal plane (F2) and the 22 O fragments to the final focal plane (F4). We used a special ion optics that ensured the measurement of the complete momentum distribution in one single setting. The average intensity of the primary beam was 1.5·1010 particles/spill, whereas only 50 23 O/spill and 1 22 O/spill reached the breakup target and final focus, respectively. The detector set-up at the FRS, shown in fig. 1, included position sensitive time projection chambers (TPC) for particle tracking and longitudinal momentum measurements, ionization chambers (IC) for determining the fragment charge, and scintillators (SC) that gave the time of flight between the different parts of the FRS. Using the magnetic rigidity

and the time-of-flight information together with the energy loss data from the ICs, a complete particle identification was available throughout the spectrometer. For the present experiment, the most significant addition to the set-up was an array of 32 NaI crystals for the detection of γ rays emitted by the fragments around the reaction target in F2. This array has an average energy resolution (ΔE/E) of (12.0±0.8)% and a total efficiency of (5.0±0.4)% for the case of γ-rays emitted by relativistic moving sources (obtained from a GEANT [12] simulation for Eγ = 3.2 MeV in the rest frame of the fragment [13]). The intrinsic momentum resolution for 23 O was evaluated to be 19±1 MeV/c (FWHM). This experimental value includes the ion optical properties of the FRS plus straggling in the target, optical misalignment and any other secondary effects.

3 Experimental results We measured in this experiment inclusive fragment longitudinal momentum distributions and cross-sections after one-neutron removal on a large number of neutron-rich oxygen isotopes. We only present in this paper results relative to 23 O. The inclusive one-neutron removal cross-section (σ−1n ) was measured by directly counting 23 O and 22 O in front of, and behind the carbon breakup target. This ratio was corrected for the experimental transmission evaluated with the code MOCADI [14] after adjusting the simulated fragment longitudinal momentum width to the measured one. The value obtained was σ−1n = 85±10 mb. The error includes statistical and transmission errors. This data does not show a significant increase when compared with the same quantity measured for other neutron-rich oxygen isotopes. In consequence, it does not support the idea of 23 O being a halo nuclei as it was proposed by Ozawa et al. [15]. The technique employed for fragment longitudinal momentum distributions measurements is described in ref. [6, 16]. The differential cross-section with respect to longitudinal momentum plong (in the projectile center-of-mass frame) is shown on the left frame of fig. 2 for the oneneutron removal reaction. The solid curve corresponds to a double Gaussian fit to the experimental data from which a width of 134±10 MeV/c (FWHM) was obtained. A minor correction for the intrinsic momentum resolution gives a final width of 133±10 MeV/c. This result can be directly compared to the corresponding value of 114±9 MeV/c (FWHM) obtained at 47 MeV/nucleon [7] and of 73±15 MeV/c at 72 MeV/nucleon [9]. The γ-rays emitted during de-excitation of 22 O were recorded with the NaI detectors described in sect. 2. The high-energy γ-rays and the emission of γ-rays in cascade made it necessary to apply add-back corrections. Subsequently we performed a Doppler shift correction. The analysis of the γ-ray spectrum reveals three γ-ray energies at 1.3, 2.6, and 3.2 MeV corresponding to the known transitions in 22 O [10, 1,2] (see the level scheme in ref. [17].) They correspond to de-excitation of the 2+ and 3+ states at 3.2 and 4.5 MeV, respectively, resulting from a 1d5/2

D. Cortina-Gil et al.: One-neutron knockout of

0.4

0.4 22

O e.s

0.2

0.3 0 0.2

l=2

0.3

mb

0.2

FWHM = 237 ± 20 MeV/c

345

0.4

dσ-1n/dp ( /MeV/c)

O g.s

O

0.6

mb

dσ-1n/dp (mb/MeV/c)

0.6

22

dσ-1n/dp ( /MeV/c)

FWHM = 127 ± 20 MeV/c FWHM = 134 ± 10 MeV/c

23

0.2

l=0

0.1

0.1 0

-200

0

200 -200

0

200

0

plong(MeV/c)

Fig. 2. Left: Inclusive longitudinal momentum distribution (plong ) for 22 O fragments after one-neutron removal from 23 O. Right top: Exclusive longitudinal momentum distribution for 22 O in its ground state. Right bottom: Longitudinal momentum distribution for 22 O in any excited state.

hole coupled to a 2s1/2 particle. The 5.8 MeV state could be due to the 0− or/and 1− states proposed in [10](see ref. [17] for details). The broad peak observed at higher energy is assumed to be due to the 3.2 MeV and the 2.6 MeV transitions that our NaI detectors cannot resolve. This peak is, therefore, used to gate the longitudinal momentum distribution in order to obtain the exclusive distribution. The result, after efficiency correction of the γ array evaluated with a GEANT simulation and proper background subtraction, is shown in the right-bottom part of fig. 2, where the solid line corresponds to the Gaussian fit performed to obtain the width of the distribution. This results in a FWHM of 236±20 MeV/c for the momentum distribution leaving the core in any excited state. The longitudinal momentum distribution for 22 O in its ground state could be obtained by subtracting from the inclusive measurement the exclusive one involving 22 O in any of its excited states. The resulting spectrum is shown in the upper part of fig. 1. We obtain a FWHM of 126±20 MeV/c (after correcting for the intrinsic momentum resolution). The corresponding integrated crosssection amounts to 50±10 mb. A summary of the experimental results obtained for 23 O is given in table 1 (third column). The associated error bars include statistical errors, assumptions for the level scheme of 22 O, and uncertainties in the γ-efficiency simulation. The relative weight of the exclusive one-neutron removal cross-section involving 22 O in any excited states to the inclusive measurement amounts to (41±10)%.

4 Discussion The experimental momentum distribution for the oneneutron removal-channel leaving the 22 O core in its ground state is compared in fig. 3 to theoretical momentum distributions calculated in an Eikonal model for the knockout

0 -200

-120

-40

40

120

200

plong(MeV/c)

Fig. 3. Ground-state exclusive momentum distribution for 22 O fragments after one-neutron knockout reaction from 23 O compared with calculations assuming l = 0 and l = 2 (see text).

process. Two calculations are shown for angular momenta l = 0 and l = 2. Clearly, the distribution assuming a 2s1/2 neutron coupled to the 22 O(0+ ) core is in much better agreement with the data. We can thus conclude that the ground-state spin of 23 O is I π = 1/2+ . This result has been recently confirmed in another exclusive experiment performed by C. Nocciforo et al. [18]. They have measured exclusive differential cross-sections dσ/dE ∗ for electromagnetic excitation of 23 O projectiles at 422 MeV/nucleon incident on a lead target, probing its ground-state configuration (I π = 1/2+ ) by an independent method. We note, however, that the experimental distribution is slightly wider than the prediction for l = 0. This might be due to a slightly incomplete subtraction of the excitedstate contribution. The large width of 237±20 MeV/c observed for the distribution involving excited states is in line with the expectation that in this case, most of the cross-section is related to knockout of neutrons from the d shell. We now turn to the one-neutron removal crosssections, which are calculated separately for the individual single-particle configurations adopting the Eikonal approach [19, 20], which is well justified at the high beam energy used in the present experiment. The neutroncore relative-motion wave functions are calculated for a Woods-Saxon potential with geometry parameters of r0 = 1.25 fm and a = 0.7 fm [4, 5]. Further input to the calculations are free nucleon-nucleon cross-sections and harmonic-oscillator density distributions for the target and the core, which were chosen to reproduce the measured interaction cross-sections at high energy [15]. Neutron-knockout cross-sections were calculated for the configuration (d5/6 )6 (s1/2 )1 , and are summarized in the fourth column of table 1. For the neutron knockout from the 2s shell the calculated cross-section is equal to 51 mb and thus in agreement with the experimental value of 50±10 mb. This result confirms the large spectroscopic factor for the s-neutron (C 2 S = 0.8) obtained by Brown et al. [10]. Another experimental confirmation to this result is provided by C. Nocciforo et al. [18] that have reported

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Table 1. The experimental one-neutron removal cross-sections are presented for 23 O → 22 O + n in the different final state configurations considered. Calculated cross-sections are shown for comparison.

E (MeV)

Iπ

σexp (mb)

σsp (mb)

0 3.2 4.5 5.8

0+ 2+ 3+ − − (1 ,0 )

50±10 10.5±4.5 14.0±5.0 10.5±4.5

51 20 18 15

85±10

104

Total

4

and would evidence that the knockout technique is an adequate tool to provide spectroscopic information [21]. We can observe a very good correlation for the 22 O(0+ ) configuration but an important discrepancy is observed for configurations involving 22 O excited states. This discrepancy might to a large extent be related to the fact that the experiment is only scanning the external part of the wave function, together with deficiencies related to the theoretical description used. Shell model calculations do not include short-range correlation and only many-body correlations within the reach of the basis are considered. These deficiencies point as well towards the need of more elaborate reaction models for calculating knockout crosssections from the deeply bound core states. This result is not fully understood and further theoretical and experimental investigations are certainly needed.

0+

C2S(Experiment)

+

2

3

5 Conclusion

+

3

(1-,0-)

2

1

0

0

1

2

2

3

4

C S(Theory)

Fig. 4. Experimental vs. theoretical spectroscopic factors for the particular cases studied in this experiment. The experimental values represent the measured partial cross-section divided by the single particle cross-section (eikonal model), whereas the theoretical values correspond to many-body shell-model calculation. The diagonal line indicates a correlation factor between both quantities equal to one.

a spectroscopic factor of 0.78(13) for the 2s1/2 ⊗22 O(0+ ) configuration. The knockout of a neutron from the 1d-shell in this calculation results in 22 O either in the 2+ state (20.0 mb), or in the 3+ state (18.3 mb). The contribution of knockout of neutrons from deeper p shells (1− , 0− state) amounts to 15 mb. A comparison with the experimental data shows that the contribution involving excited states is smaller by a large factor (see table 1). This fact is reflected in fig. 4, where we represent experimental versus theoretical spectroscopic factors for the particular cases studied in this experiment. The experimental spectroscopic factors are evaluated from the ratio between measured partial cross-section and singleparticle cross-section calculated in an eikonal model. The theoretical spectroscopic factors correspond to many-body shell-model calculation [10]. The diagonal line represent a perfect correlation between these quantities

We have measured the 22 O momentum distribution after one-neutron knockout from high-energy 23 O projectiles differentiated according to states populated in 22 O observed by a coincident measurement of the 22 O γ deexcitation. The experimental observations are evidence for a ground-state spin I π = 1/2+ for 23 O with a large spectroscopic factor for the s1/2 ⊗22 O(0+ ) single particle configuration, thus providing support for the existence of the N = 16 shell closure for Z = 8.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

P.G. Thirolf et al., Phys. Lett. B 485, 16 (2000). M. Stanoiu et al., Phys. Rev. C 69, 034312 (2004). B.A. Brown et al., Phys. Rev. C 65, 061601R (2000). T. Aumann et al., Phys. Rev. Lett. 84, 35 (2000). V. Maddalena et al., Phys. Rev. C 63, 024613 (2001). D. Cortina-Gil et al., Nucl. Phys. A 720, 3 (2003). E. Sauvan et al., Phys. Lett. B 491, 1 (2000). E. Sauvan et al., Phys. Rev C 69, 044603 (2004). R. Kanungo et al., Phys. Rev. Lett. 88, 142502 (2002). B.A. Brown et al., Phys. Rev. Lett 90, 159201 (2003). H. Geissel et al., Nucl. Instrum. Methods B 70, 286 (1992). GEANT, CERN Library Long Writeup W5013 (1994). J. Fernadez, Thesis, University of Santiago de Compostela (2003). N. Iwasa et al., Nucl. Instrum. Methods B 126, 284 (1997). A. Ozawa et al., Nucl. Phys. A 691, 599 (2001). T. Baumann et al., Phys. Lett. B 439 , 256 (1998). D. Cortina-Gil et al., Phys. Rev. Let. 93, 062501 (2004). C. Nocciforo et al., Phys. Lett. B 605, 79 (2005). J. Tostevin, J. Phys. G 25, 735 (1999). G.F. Bertsch et al., Phys. Rev. C 57, 1366 (1998). P.G.Hansen, B.M. Sherrill, Nucl. Phys. A 693, 133 (2001).

Eur. Phys. J. A 25, s01, 347–348 (2005) DOI: 10.1140/epjad/i2005-06-056-6

EPJ A direct electronic only

Inelastic proton scattering on

16

C

H.J. Ong1,a , N. Imai2 , N. Aoi2 , H. Sakurai1 , Zs. Dombr´adi3 , A. Saito4 , Z. Elekes2,3 , H. Baba4 , K. Demichi5 , Zs. F¨ ul¨op3 , J. Gibelin5,6 , T. Gomi2 , H. Hasegawa5 , M. Ishihara2 , H. Iwasaki1 , S. Kanno5 , S. Kawai5 , T. Kubo2 , K. Kurita5 , Y.U. Matsuyama5 , S. Michimasa2 , T. Minemura2 , T. Motobayashi2 , M. Notani4,b , S. Ota7 , H.K. Sakai5 , S. Shimoura4 , E. Takeshita5 , S. Takeuchi2 , M. Tamaki4 , Y. Togano5 , K. Yamada2 , Y. Yanagisawa2 , and K. Yoneda2,c 1 2 3 4 5 6 7

University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan ATOMKI, P.O. Box 51, Debrecen, H-4001, Hungary CNS, University of Tokyo, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan IPN, F-91406 Orsay Cedex, France University of Kyoto, Kitashirakawa, Kyoto 606-8502, Japan Received: 26 November 2004 / c Societ` Published online: 6 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 16 C via inelastic proton scattering in inverse kineAbstract. We have studied the 2+ 1 state in neutron-rich matics, using a 33 MeV/nucleon beam. From the angle-integrated cross-section, the deformation parameter βpp = 0.50(8) is obtained. This value is greater than the deformation parameter deduced from the lifetime measurement. With these two result combined, the ratio of the neutron and proton quadrupole matrix elements is deduced to be approximately 7, indicating a neutron-dominant quadrupole collectivity in 16 C.

PACS. 25.40.Ep Inelastic proton scattering – 23.20.Lv γ transitions and level energies

1 Introduction The E2 transition strength is a fundamental quantity of a nucleus and the reduced transition probability B(E2) + from the first 2+ (2+ 1 ) state to the ground (0gs ) state for an even-even nucleus reflects the proton contribution to the quadrupole collectivity. Recently, an anomalously small 16 C was highlighted via a lifeB(E2) for the 2+ 1 state in time measurement of this state [1]. The result indicates an unexpectedly weak proton contribution to the transition. On the other hand, as shown in table 1, the relatively small energy gap between the ground state and the + 2+ 1 state E(21 ), only 1766 keV, compared to the neighboring even-even C isotopes indicates a possible deformation in the 16 C nucleus. It is then of great interest to study the neutron contribution in order to disentangle this contradiction. A large difference in neutron and proton contributions has been reported by a recent study on 16 C + 208 Pb inelastic scattering [2]. Extended studies using simpler hadronic probes should be helpful in exploring the nature of this phenomenon. a

Conference presenter; e-mail: [email protected] b Present address: Argonne National Laboratory, Argonne, IL, USA. c Present address: Michigan State University, East Lansing, MI, USA.

+ Table 1. B(E2; 2+ 1 → 0gs ) and excitation energies of the first excited 2+ state of several even-even C isotopes. 1

10

B(E2) (e fm ) E(2+ 1 ) (keV) 2

4

C 12 [3] 3353

12

C 8.2 [3] 4439

14

C 3.8 [3] 7012

16

C 0.63(19) [1] 1766

We report inelastic proton scattering (p, p ) on 16 C in reversed kinematics incorporating the technique of inbeam γ-ray spectroscopy. To determine the neutron contribution to the quadrupole collectivity, we have combined the (p, p ) data with the lifetime measurement. At an intermediate energy of several tens of MeV, the inelastic proton scattering is about three times more sensitive to neutrons than to protons [4]. Thus, a combination of this (p, p ) data with the lifetime measurement [1] allows us to disentangle the proton and neutron quadrupole collectivities.

2 Experiment The experiment was performed at the RIKEN Accelerator Research Facility. A secondary 16 C beam was produced through fragmentation reaction by bombarding a 740 mg/cm2 9 Be target with a 94 MeV/nucleon 40 Ar primary beam. The 16 C was separated by the RIKEN Projectile Fragment Separator (RIPS) [5]. The flight times

The European Physical Journal A

of the secondary beams between the second focal plane F2 and the final focal plane F3 were measured using two 1 mm thick plastic scintillators (F2PL and F3PL) placed at F2 and F3. Particle identification was performed by combining the time-of-flight (TOF) and the ΔE information, measured with F3PL. The 16 C beam, the energy of which was measured to be 33 MeV/nucleon at the center of the target using the TOF information, bombarded a liquid hydrogen target placed 1.3 m downstream of the F3PL. The scattered particles were detected by a set of detector telescopes placed downstream of the secondary target. The telescope consisted of a parallel plate avalanche counter PPAC and a stack of Si detectors. The stack of Si detectors comprised four layers, each with four Si detectors of the same thickness arranged in a 2 × 2 matrix. The thicknesses of the four layers were 0.5 mm, 0.5 mm, 1.0 mm and 0.5 mm. Most of the 16 C nuclei were stopped in the third layer of the Si-telescope. The Si detectors provided information on ΔE and E. The PPAC provided the timing signals and was also used together with two upstream PPACs to measure the scattering angles of the 16 C particles. Particle identification was performed by means of the TOF-ΔE and ΔE-E methods. The acceptance of the Si-telescope was found to effectively cover 53(3)% of the angle-integrated cross-section of the inelastic scattering using a Monte Carlo simulation. The de-excitation γ-rays were detected by an NaI(Tl) array consisting of 105 scintillators, which form part of the DALI2 [6]. The total full-energy peak efficiency was calculated with the GEANT simulation code [7] to be 6.3(4)% for 1.77 MeV γ-rays emitted from the 16 C nuclei in flight.

3 Result and discussion To determine the angle-integrated cross-section, we evaluated the γ-ray yield associated with the 2+ → 0+ transition (see fig. 1), and obtained a value of 24.1(36) mb. To extract the deformation parameter βpp and the deformation length δpp (= βpp r0 A1/3 ), distorted-wave Born approximation calculations were performed. In the calculations, three sets of optical potential parameters, namely the global optical potential parameter set CH89 [8], and potential parameters obtained from elastic scattering on 12 C at 31 MeV and on 16 O at 34 MeV [9] were used. The βpp and the δpp obtained are shown in table 2. Since no significant preference between the three was found, we adopted the average values over the three sets of optical potential parameters. Hence, the deformation parameter and deformation length were determined to be 0.50(8) and 1.4(2) fm. This deformation length is larger than that of the lifetime measurement where only a small value of 0.41(6) fm was observed. To obtain the magnitude of neutron contribution, we have combined the δpp and the deformation length deduced from the lifetime measurement. Using the neutron and proton quadrupole matrix elements, Mn and Mp , defined in ref. [4], and applying the equation for the Mn /Mp ratio suggested therein, the Mn /Mp ratio was determined to be 6.6(15), assuming the same sign for the deformation

200

1.77 MeV C (21+

16

150

Count / 40 keV

348

+ ) 0 gs

100

50

0

1.0

1.5

2.0

2.5

3.0

Eγ [MeV]

Fig. 1. Doppler-shift corrected γ-ray energy spectrum measured by 105 NaI(Tl) scintillators in coincidence with the scattered 16 C particles. The full-energy peak corresponding to the + 2+ 1 → 0gs is clearly seen around 1.77 MeV. Table 2. Nuclear deformation parameter βpp and deformation length δpp deduced from DWBA calculations.

Optical potential CH89 [8] p + 12 C [9] p + 16 O [9]

βpp 0.493(41) 0.550(47) 0.456(38)

r0 (fm) 1.16 1.10 1.14

δpp (fm) 1.44(12) 1.52(13) 1.31(11)

lengths. This result is consistent with the recent measurement of 16 C + 208 Pb inelastic scattering where a value of 7.6(17) was reported [2]. The (Mn /Mp )/(N/Z) = 4.0(9) obtained for 16 C is by far the greatest value ever observed in any nucleus; it is about two times greater than the values for 20 O [10] and 48 Ca [11].

4 Conclusion We have performed an inelastic proton scattering on 16 16 C to study the 2+ C. From the angle1 state in integrated cross-section, determined to be 24.1(36) mb, the deformation parameter βpp = 0.50(8) is extracted. This result contrasts the result of the lifetime measurement where a small deformation parameter is observed. Combining these two results, a large value of 4.0(9) is obtained for the ratio of the neutron and proton quadrupole matrix elements (Mn /Mp )/(N/Z). This result, together with the similar result reported in ref. [2], suggests that 16 C is dominated by neutron excitations. the 2+ 1 state in

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

N. Imai et al., Phys. Rev. Lett. 92, 062501 (2004). Z. Elekes et al., Phys. Lett. B 586, 34 (2004). S. Raman et al., At. Data Nucl. Data Tables 78, 1 (2001). A.M. Bernstein et al., Commun. Nucl. Part. Phys. 11, 203 (1983). T. Kubo et al., Nucl. Instrum. Methods B 70, 309 (1992). S. Takeuchi et al., RIKEN Accel. Prog. Rep. 36, 148 (2003). GEANT3: Detector Description and Simulation Tool, CERN program library. R.L. Varner et al., Phys. Rep. 201, 57 (1991). C.M. Perey et al., At. Data Nucl. Data Tables 17, 1 (1976). J.K. Jewell et al., Phys. Lett. B 454, 181 (1999); E. Khan et al., Phys. Lett. B 490, 45 (2000). A.M. Feldman et al., Phys. Rev. C 49, 2068 (1994).

Eur. Phys. J. A 25, s01, 349–351 (2005) DOI: 10.1140/epjad/i2005-06-186-9

EPJ A direct electronic only

Experimental evidence of a ν(1d5/2 )2 component to the ground state

12

Be

S.D. Pain1,a , W.N. Catford1 , N.A. Orr2 , J.C. Angelique2 , N.I. Ashwood3 , V. Bouchat4 , N.M. Clarke3 , N. Curtis3 , M. Freer3 , B.R. Fulton5 , F. Hanappe4 , M. Labiche6 , J.L. Lecouey2,b , R.C. Lemmon7 , D. Mahboub1 , A. Ninane8 , G. Normand2 , N. Soi´c3,c , L. Stuttge9 , C.N. Timis1 , J.A. Tostevin1 , J.S. Winfield10 , and V. Ziman3 1 2 3 4 5 6 7 8 9 10

Department of Physics, University of Surrey, Guildford, Surrey, GU2 7XH, UK Laboratoire de Physique Corpusculaire, ISMRA and Universit´e de Caen, IN2P3-CNRS, 14050 Caen Cedex, France School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK Universit´e Libre de Bruxelles, CP 226, B-1050 Bruxelles, Belgium Department of Physics, University of York, Heslington, York, YO10 5DD, UK University of Paisley, High Street, Paisley, Scotland PA1 2BE, UK CLRC Daresbury Laboratory, Daresbury, Warrington, Cheshire, WA4 4AD, UK Institut de Physique, Universit´e Catholique de Louvain, Louvain-la-Neuve, Belgium Institut de Recherche Subatomique, IN2P3-CNRS/Universit´e de Louis Pasteur, BP 28, 67037 Strasbourg Cedex, France Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Sud, I-95123 Catania, Italy Received: 31 January 2005 / Revised version: 21 April 2005 / c Societ` Published online: 19 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Data have been obtained on exclusive single neutron knockout cross sections from 12 Be to study its ground state structure. Preliminary cross sections for the first (0.32 MeV, 1/2 − ) and second (1.78 MeV, 5 /2 + , unbound ) excited states in 11 Be have been obtained, giving evidence of significant admixtures of both ν(1p1/2 )2 and ν(1d5/2 )2 configurations in the ground state of 12 Be. PACS. 27.20.+n 6 ≤ A ≤ 19 – 24.10.-i Nuclear reaction models and methods – 25.60.-t Reactions induced by unstable nuclei – 25.70.-z Low and intermediate energy heavy-ion reactions

1 Introduction In stable nuclei, the N = 8 magic number corresponds to the shell gap between the ν(1p1 /2 ) and ν(1d5 /2 ) orbitals; for example, the stable nuclei 16 O and 14 C exhibit closed shell behaviour, corresponding to a predominantly ν(1p1 /2 )2 configuration. However, the ground state of 11 Be + is a J π = 1/2 intruder state (with a predominantly − 10 Be ⊗ ν(2s1 /2 ) structure); the 1/2 state lies 320 keV above, corresponding to a predominantly ν(1p1 /2 ) valence neutron. Consequently, the structure of 12 Be is not unambiguously inferred from the systematics of neighbouring nuclei. An experiment at MSU [1] to measure the 1 n knockout cross sections from 12 Be gave approximately − + equal spectroscopic factors for the 1/2 and 1/2 states a

Conference presenter; Present address: Rutgers University, Piscataway, NJ, USA; e-mail: [email protected] b Present address: NSCL, Michigan State University, MI 48824, USA. c Present address: Rudjer Boˇskovi´c Institute, Bijeniˇcka 54, HR-10000, Zagreb, Croatia.

in 11 Be, indicating breaking of the N = 8 magic num+ ber in 12 Be. A significant yield to the unbound 5/2 state at 1.78 MeV was suggested, indicating a ν(1d5 /2 )2 component to the 12 Be ground state. This was unobservable experimentally, as it results in breakup to 10 Be + n. The present experiment was focussed on measuring the cross + section to this 5/2 state in 11 Be, along with the bound − 1 /2 state to give an overlap with the MSU measurement. The yield to the ground state of 11 Be was not measurable without the reduction in background from a coincidence requirement.

2 Experimental configuration A fragmentation beam of 12 Be, (∼ 5000 pps) produced using the LISE3 spectrometer [2] at the GANIL laboratory, was incident on a 180 μg/cm2 carbon target at a midtarget energy of 39.3 MeV/A. Beam particle energies were determined from time-of-flight, which also allowed unique identification of 12 Be ions from the 5% contaminants in

The European Physical Journal A

the beam. Two drift chambers were employed to track beam particles onto the target. Beam-like residues were detected in a 3-stage telescope mounted at 0◦ , covering ±9◦ in both x and y directions, consisting of two 500 μm thick resistive-strip silicon detectors, mounted to allow resistive measurement in both x and y, and a close-packed array of 16 CsI detectors, in a 4×4 arrangement. Neutrons were measured in the D´eMoN array [3] of 91 liquid scintillation detectors, between 2.4 m and 6.3 m downstream of the target, spanning angles to 32◦ , with an efficiency of ∼ 10%. Neutron energies were derived from time-offlight, and neutrons were distinguished from γ rays via pulse shape discrimination. The target was surrounded by four NaI detectors, to detect the 320 keV γ rays from the 1 − /2 state in 11 Be with an efficiency of 3.5%. A result of using a 0◦ charged particle telescope is that the entire beam flux is incident on these detectors. Consequently, the number of beam particles that undergo nuclear reactions in the telescope is significant relative to the target-induced reactions. An effect of these reactions was to produce a CsI signal which overlaps with the 10,11 Be particles of interest. Additionally, these reactions were a source of neutrons with velocities close to that of the beam. Coupling these effects can give a neutron of approximately the expected energy, in coincidence with a false identification of a charged particle of interest. This background was measured separately by acquiring data with no target present, with the beam energy lowered to account for the average energy loss in the target, and was scaled and subtracted from the target-in data.

3 Analysis and results A cross section of 33.5(5.6)mb was extracted for the pro− duction of the 1/2 state in 11 Be, from the Dopplercorrected γ ray spectrum measured in coincidence with a detected 11 Be. Corrections were made for detector efficiencies, attenuation in the target, and the geometric effects of relativistic focussing of γ rays. For reactions leading to neutron unbound states in 11 Be*, the decay energy to 10 Be + n, along with a spread of momenta introduced via the neutron removal process, determines angular spread of the neutrons in the laboratory frame and hence their detection efficiency. To interpret the experimental data, detailed simulations were performed using a Monte Carlo simulation code [4]. The simulations included the effects of the geometrical acceptance of the D´eMoN array, energy and angular straggling of charged particles, beam divergence and energy spread, and detector acceptances, resolutions and efficiencies, along with the absorption of neutrons by the telescope. The momentum distribution induced by the neutron removal process was determined from the angular distribution of neutrons from a very low energy decay, where the neutron momentum distribution is dominated by the momentum distribution of the 11 Be* before decay. The measurement of a neutron diffracted from 12 Be, in coincidence with 10 Be from the subsequent decay of the

2000 Experimental Data 10

+

Simulated ~4 Mev -> Be(2 ) Simulated 1.78 MeV Simulated 2.69 MeV Simulated ~4 MeV Uncorrelated neutron

1500

Counts

350

1000

500

0

0

1

2

3 4 Relative Energy (MeV)

5

6

Fig. 1. Relative energy spectrum of 10 Be + n, where the stepped line represents the experimental data. The dotted and dashed lines depict the individual line-shapes of the simulation, which are dominated by the excitation energy resolution.

remaining 11 Be* was included, using a momentum distribution determined from diffracted neutrons only (those in coincidence with a bound 11 Be). Full kinematic reconstruction of unbound states in 11 Be was performed from the momentum vectors of coincident 10 Be ions and neutrons. Simulations were performed for the breakup of states in 11 Be below 4 MeV, including the decay from a state at ∼ 4 MeV to the first 2+ state in 10 Be (the efficiency for the detection of γ rays from this state was prohibitively small to separate this channel), and for the detection of neutrons diffracted from 12 Be in coincidence with 10 Be core. The simulated data were analyzed in the same manner as the experimental data. The simulated relative energy (Erel ) line-shapes were fitted to the experimentally measured distribution, shown in fig. 1. These weightings well reproduced the Erel spectrum, the reconstructed 11 Be* transverse momentum distribution, and the neutron angular distributions in coincidence with 10 Be (diffracted neutrons plus sequential decay neutrons) and 11 Be (diffracted neutrons only). The weighting for the diffraction component, whilst necessary to fit to the Erel spectrum, neutron angular distribution and the transverse momentum distribution of reconstructed 11 Be*, is too large to be assigned entirely to the diffraction process. Some of the events described by this curve could be due to other sources of uncorrelated neutrons, such as the direct three-body breakup of 12 Be into 10 Be + n + n, the Erel line-shape for which would be of a similar form to that of the diffracted neutrons. Furthermore, the measured form of such a broad distribution is partially determined by the form of the array efficiency, which decreases with increasing Erel . Using the geometric detection efficiency determined from the simulations, a (preliminary) + cross section for production of the 5/2 state was determined as 30.3(2.5) mb (statistical error). A further 30% is assigned to account for the uncertainty in precise form of the “uncorrelated” neutron distribution. That the cross + − section for the production of the 5/2 and 1/2 states in

S.D. Pain et al.: Experimental evidence of a ν(1d5/2 )2 component to the 11

Be are comparable suggests a strong ν(1d5/2 )2 component to the ground state of 12 Be. Further simulations and analysis are being performed to improve the quantitative interpretation of the data.

12

Be ground state

351

References 1. 2. 3. 4.

A. Navin et al., Phys. Rev. Lett. 85, 266 (2000). R. Anne et al., Nucl. Instrum. Methods A 257, 215 (1987). I. Tilquin et al., Nucl. Instrum. Methods A 365, 446 (1995). N. Curtis, RESOLUTION8 computer code (unpublished).

Eur. Phys. J. A 25, s01, 353–354 (2005) DOI: 10.1140/epjad/i2005-06-027-y

EPJ A direct electronic only

Stability island near the neutron-rich

40

O isotope

K.A. Gridnev1,2,a , D.K. Gridnev1,2 , V.G. Kartavenko2,3 , V.E. Mitroshin4 , V.N. Tarasov5 , D.V. Tarasov5 , and W. Greiner2 1 2 3 4 5

St. Petersburg State University, St. Petersburg, Russia J.W. Goethe University, Frankfurt/Main, Germany Joint Institute for Nuclear Research, Dubna, Russia Kharkov National University, Kharkov, Ukraine Kharkov National Scientific Center KIPT, Kharkov, Ukraine Received: 4 November 2004 / c Societ` Published online: 20 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Stability with respect to neutron emission is studied for nuclear isotopes 4–12 He, 14–44 O, 38–80 Ca in the framework of Hartree-Fock approach with Skyrme forces SLy4 and Ska. The data shows possible existence of stability island around 40 O. PACS. 21.60.Jz Hartree-Fock and random-phase approximations – 21.10.Dr Binding energies and masses

Here we present our first in series of results in searching for highly neutron-excessive stable nuclei within the HF framework, that are outdistanced from conventional nucleon stability line. The calculation method is HartreeFock approximation with Skyrme effective interaction [1].  Vij = t0 (1 + x0 Pσ )δ(r) + (1/2)t1 (1 + x1 Pσ ) k2 δ(r) +  δ(r)k2 + t2 (1 + x2 Pσ )k δ(r)k + (1/6)t3 (1 + x3 Pσ )    ρα (R)δ(r) + iW0 k × δ(r)k σi + σj − → − → where r = ri − rj , R = (ri + rj )/2, k = −i(∇i − ∇j )/2, ← − ← − k = i(∇i −∇j )/2, Pσ = (1+σi σj )/2. Parameters are given in table 1. We have used the set of parameters Ska and compared the results with the most widely used set SLy4. In [2] we have shown that for deformed nuclei 25 Mg and 29–31 Si the most satisfactory description of observed spectra comes with the set Ska. Pairing effects were included in the standard way with the pairing constant G = 19/A both for protons and neutrons and were restricted to the space of bounded one-particle states. Taking into account the continuous spectrum increases the pairing effects near the drip line [3] and thus may only increase the nucleon separation energy as well as stability with respect to nucleon emission. We have looked for stability islands around isotopes 4–12 He, 14–44 O and 38–80 Ca and analyzed how results depend on forces we have used. For isotopes 4–12 He our results on one- and two-neutron separation energies matched already known ones from [4]. For Helium the last stable isotope with respect to two-neutron emission is 8 He. a

Conference presenter; e-mail: [email protected]

Fig. 1. Calculated separation energies of one-neutron Sn for isotopes 14–44 O with different choices of Skyrme forces compared to the experimental data.

Comparison with experiment (see the figures) shows that both Ska and SLy4 equally well describe the known experimental data. The large separation energy of one and two neutrons in the stable isotope 24 O indicates the possible existence of heavier stable isotopes, yet presently it is in contradiction with the experimental data. Our calculations predict the existence of stable 26,28 O which are also predicted as stable in [4, 5]. In our calculations with forces Ska we have found that the oxygen isotope 40 O is stable. Its stability is seen in fig. 1, where we did not plot the two-neutron separation energy for 40 O because all its neighboring isotopes are unstable. With forces SLy4 this isotope appears to be unstable with respect to one-neutron

354

The European Physical Journal A Table 1. Parameters of the Skyrme forces.

Force

SLy4 Ska

t0 (MeV fm3 ) −2488.91 −1602.78

t1 (MeV fm5 ) 486.82 570.88

t2 (MeV fm5 ) −546.39 −67.70

t3 (MeV fm3+3α ) 13777.0 8000.0

x0

x1

x2

x3

0.834 −0.020

−0.344 0.0

−1.0 0.0

1.354 −0.286

W0 (MeV fm5 ) 123.0 125.0

α

1/6 1/3

Table 2. Calculated values of binding energy E, neutron and proton separation energy Sp,n , root-mean-square radii rp,n quadrupole moments Qp,n and deformation parameters β2p,n for the stable isotope 40 O as calculated with Ska forces.

E (MeV) 168.274

Sn (MeV) 0.593

Sp (MeV) 36.822

rn (fm) 4.202

Qn (e fm2 ) 0.031

rp (fm) 2.943

2

Qp (e fm2 ) 0.003

β2n

β2p

0.004

0.004

2

The obtained data for 40 O is given in table 2. One can see from table 2 that the values of proton and neutron deformation for 40 O are negligibly small. The map of proton and neutron distributions in r, z coordinates (incorporating the symmetry of the problem) for 40 O is shown in fig. 2. Figure 2 also compares the given distributions with the same maps for 20 O. One can see from these figures that although the proton “cloud” is expanding it remains coated with the neutron halo which is about 2 fm thick. We claim that the stability of 40 O with Ska forces compared to its instability with SLy4 forces stems from the difference in t2 and x2 components of the Skyrme force. Preliminary calculations of nearby isotopes showed that there are stable isotopes around 40 O among eveneven nuclei, namely 40,42,44 Ne with one-neutron separation energies are respectively Sn = 0.13, 0.43, 0.1 MeV and 44,46 Mg with one-neutron separation energies Sn = 0.8, 0.67 MeV. These stable isotopes were also found with Ska forces and except 44 Mg they lie beyond the conventional stability valley. Fig. 2. The map of proton ρp and neutron ρn distributions calculated for 40 O (panels a, b) and for 20 O (panels c, d).

emission, though the last filled level is close to zero and one can talk about “quasistability” in this case. From nucleus to nucleus the situation repeats itself, whenever the nucleus is “quasistable” with interactions Ska, then it is “quasistable” with interactions SLy4. In all investigated cases the last filled level for nuclei close to nucleon stability borderline always had a negative parity. And under “quasistable” we mean that this nucleon has a non-zero orbital momentum and the resulting centrifugal barrier prevents the neutron from emission at its low energies.

This work was partially supported by Deutsche Forschungsgemeinschaft (grant 436 RUS 113/24/0-4), Russian Foundation for Basic Research (grant 03-02-04021) and the HeisenbergLandau Program (JINR, Dubna). D.K. Gridnev appreciates the financial support from the Humboldt Foundation.

References 1. 2. 3. 4. 5.

D. Vautherin, D.M. Brink, Phys. Rev. C 5, 626 (1972). Yu.V. Gontchar et al., Yad. Fiz. 41, 590 (1985). S.A. Fayans et al., Nucl. Phys. A 676, 49 (2000). M.V. Stoitsov et al., Phys. Rev. C 61, 034311 (2000). M.V. Stoitsov et al., Phys. Rev. C 68, 054312 (2003).

6 Excited states 6.1 Shell structure

Eur. Phys. J. A 25, s01, 357–362 (2005) DOI: 10.1140/epjad/i2005-06-025-1

EPJ A direct electronic only

Shell structure from astrophysics

100

Sn to

78

Ni: Implications for nuclear

H. Grawe1,a , A. Blazhev1,2 , M. G´ orska1 , I. Mukha1,3,4 , C. Plettner1,5 , E. Roeckl1 , F. Nowacki6 , R. Grzywacz7 , and 8 M. Sawicka 1 2 3 4 5 6 7 8

GSI, Planckstr. 1, D-64291 Darmstadt, Germany University of Sofia, Sofia, Bulgaria Katholieke Universiteit Leuven, Leuven, Belgium RRC “Kurchatov Institute”, RU-123481 Moscow, Russia Yale University, New Haven, CT, USA IReS, Strasbourg, Cedex 2, France ORNL, Oak Ridge, TN, USA IEP Warsaw University, Warsaw, Poland Received: 11 November 2004 / Revised version: 18 February 2005 / c Societ` Published online: 25 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The single-particle structure and shell gap of 100 Sn is inferred from prompt in-beam and delayed γ-ray spectroscopy of seniority and spin-gap isomers. Recent results in 94,95 Ag and 98 Cd stress the importance of large-scale shell model calculations employing realistic interactions for the isomerism, np-nh excitations and E2 polarisation of the 100 Sn core. The strong monopole interaction of the Δl = 0 spin-flip partners πg9/2 -νg7/2 in N = 51 isotones below 100 Sn is echoed in the Δl = 1 πf5/2 -νg9/2 pair of nucleons, which is decisive for the persistence of the N = 50 shell gap in 78 Ni. This is corroborated by recent experimental data on 70,76 Ni, 78 Zn. The importance of monopole driven shell evolution for the appearance of new shell closures in neutron-rich nuclei and implications for r-process abundances near the N = 82 shell is discussed. PACS. 21.60.Cs Shell model – 27.30.+t 20 ≤ A ≤ 38 – 27.60.+j 90 ≤ A ≤ 149 – 26.50.+x Nuclear physics aspects of novae, supernovae, and other explosive environments

1 Introduction The evolution of shell structure towards exotic nuclei with extreme isospin has become a major topic of experimental and theoretical studies. Especially on the neutron-rich side of the Segr´e chart, where the drip line is far beyond reach for experiments, the understanding of the underlying shell driving mechanism is of key importance for astrophysics applications as, e.g., the r-process. Two scenarios with differing experimental signature have been proposed to describe the shell structure of nuclei with large N/Z ratios. The first is based on the larger radial extension due to the softer neutron potential. This reduces the spin-orbit (SO) splitting, which is proportional to the potential gradient, for nucleon orbitals probing the nuclear surface [1, 2]. It evolves smoothly with A and N/Z and only large variations of these parameters as expected towards the neutron dripline will change the shell structure substantially. The second scenario originates from the strong monopole shifts of selected shell model orbits [3, 4, 5] and will be discussed a

Conference presenter; e-mail: [email protected]

in sect. 4. Experimental evidence for monopole driven shell structure is presented in sects. 2 and 3 and generalised to light and r-path nuclei in sect. 4.

2 The

100

Sn region

The shell structure of 100 Sn and its striking similarity to 56 Ni one major shell below has been discussed abundantly [6, 7,8]. The study of seniority and spin-gap isomers provides a sensitive probe of single-particle energies, residual interaction, core excitation and shell gaps as demonstrated in recent experiments on 98 Cd [9] and 94 Ag [10]. The search for a predicted core excited spin trap [11] at the EUROBALL IV array in Strasbourg resulted in the identification of an I π = (12+ ) isomer in 98 Cd, the two-proton hole neighbour of 100 Sn [9]. The inferred level scheme as shown in fig. 1 solves a long-standing puzzle about two largely deviating results for the apparent I π = (8+ ) halflife from fusion-evaporation [12] and fragmentation [13] experiments. While the previously nonobserved (12+ ) isomer masks the measured (8+ ) halflife in

358

The European Physical Journal A

Table 1. Observed (EX) and shell model predicted (SM) spin-gap and seniority isomers below

Ex (keV)

Isotope 94

Pd Pd 96 Pd

4884 1875 2531 7040 ∼ 660 ∼ 6600 2531 4859 ∼ 5300 ∼ 2400 2428 6635 ∼ 4200

95

94

Ag

95

Ag

96

Cd Cd 98 Cd 97

100

Sn

Iπ +

14 21/2+ 8+ (15+ ) 7+ (21+ ) 23/2+ (37/2+ ) 16+ 25/2+ 8+ (12+ ) 6+

Decay

Reference

−4 −2 πg9/2 νg9/2 −4 −1 πg9/2 νg9/2 −4 πg9/2 −4 −1 πg9/2 νg9/2 d5/2 −3 −3 πg9/2 νg9/2 −3 −3 πg9/2 νg9/2 −3 −2 πg9/2 νg9/2 −3 −2 πg9/2 νg9/2 −2 −2 πg9/2 νg9/2 −2 −1 πg9/2 νg9/2 −2 πg9/2 −2 −1 πg9/2 νg9/2 d5/2 −n πνg9/2 (d5/2 , g7/2 )n

γ(E2) βγ, βpγ, γ(E4) γ(E2) γ(E2) βγ, βpγ βγ, βpγ, p, (2p) γ(E3) γ(E4) βγ, βpγ βγ, βpγ γ(E2) γ(E4) γ(E2)

EX; [12] EX; [14, 15] EX; [16] EX; [16] EX/SM; [10, 17, 18] EX/SM; [10, 17, 19] EX; [20] EX; [20] SM; [21] SM; [21] EX; [12] EX; [9] SM; [9]

12 +

T = (12 + ) 1/2

6635

Excitation energy (MeV)

eπ = 1.3 e

8+

2428 2281

4+

2

B(E2; 8+ --> 6 +) 35(11) e fm 30( 5) e fm

6+

10 + 12 + 14 +

E4

4207

5

40 ) ns 230 ( +- 30

N=Z=50 shell gap 6.46(15) MeV

6

(8 + )

147

(6 + )

198

eπ = 1.1 e

60 ) ns T1/2= 170( +- 40 T1/2< 20 ns

8+ 6+

(4 + )

2083

4+

688

2

+

(2 + )

1395

2

+

1 1395

0+

0

ESM

0

0

98 Cd50 48

Sn from N = Z to N = 50.

Configuration

10 + 14 +

7

100

0+

+

GDS

Fig. 1. 98 Cd level scheme in comparison to empirical (ESM) and large-scale shell model (GDS) results.

mer and the E2 transition rates are excellently reproduced by a large scale shell model (LSSM) calculation in the 0g, 1d, 2s model space allowing for up to 4p4h excitations of the 100 Sn core [9], yielding values of 6.46 (15) MeV for the 100 Sn shell gap and a small proton polarisation charge of δeπ ≤ 0.2e (fig. 1). A second example for the sensitivity of spin-gap isomers to details of the proton-neutron (πν) interaction is provided by the I π = (21+ ) state in 94 Ag featuring a degree of exotic properties as to spin, excitation energy and decay modes (table 1) [10,17,19], which is unprecedented in the Segr´e chart. The isomerism is not predicted in the pure πν(1p1/2 , 0g9/2 ) hole space below 100 Sn but requires inclusion of core excitations in the gds model space. Excellent agreement between LSSM calculations and experiment is observed without any modification of the shell model input. A number of isomers with similar structure have been studied recently between the N = 50 and the N = Z lines below 100 Sn, such as 95 Ag, I π = (37/2+ ) [20], 96 Ag, I π = (15+ ) [22], besides the well-known 94 Pd, I π = 14+ [23] and 95 Pd, I π = 21/2+ [14,15]. The status of observed isomers and LSSM predicted ones is summarised in table 1. Note the intriguing 100 Sn, I π = 6+ E2 isomer prediction. It is the monopole part of the πν interaction that determines the evolution of the neutron single-particle (hole) energies and the N = 50 shell gap upon filling of the π0g9/2 orbit from the experimentally known Z = 40 region towards Z = 50. This provides the key input for the shell model and is further demonstrated in fig. 2. The monopole for a specific multiplet (j, j  ) is defined by   Vjjm = (2J + 1) jj  J |V | jj  J/ (2J + 1) (1) J

the fusion-evaporation reaction, it is virtually not populated at all in fragmentation of a 106 Cd beam [13]. The decay pattern exhibits a striking analogy to 54 Fe, two proton holes from 56 Ni [6]. The level scheme, the core excited iso-

J

which gives rise to the single-particle energy evolution between two shell closures CS and CS  [6]    2j  + 1 − δjj  Vjjm . CS + = CS (2) j j j

H. Grawe et al.: Shell structure from

100

Sn to

78

Ni: Implications for nuclear astrophysics

100

90

Sn

Zr

Sr

-10

0g9/2

N=50

Ni

4

π g9/2

50

0

πf7/2 100

Sn

38

This simple formula can be used to calculate the singleparticle energies for 100 Sn from the experimentally known ones in 90 Zr or 88 Sr as shown in fig. 2 for neutrons and a given residual interaction [24]. It should be noted that eq. (2) holds only for closed j  shells, i.e. in the example of fig. 2 for the points, in between due to configuration mixing the trend may deviate from the lines drawn to guide the eye. The exact progression can be inferred from a full shell model calculation (see fig. 2 in [11] for the same model space but a modified interaction [25]). In fig. 2 the spin-flip pairs π0g9/2 -ν0g7/2 , which are spin-orbit partners (Δl = 0), and π0g9/2 -ν1d3/2 (Δl = 2) exhibit much steeper slopes, i.e. comparatively larger monopoles. This is a very general feature of the πν interaction which is especially strong when the corresponding radial wave functions have good overlap [5, 6] (see sects. 3 and 4). We also note that the evolution of neutron single-particle energies from 90 Zr (Z = 40) to 100 Sn (Z = 50) and single-hole energies from 132 Sn to 122 Zr is described by the same interaction only slightly modified due to the different core mass (see sect. 4). 78

N=50

Zr

6

78

4 νd5/2 88

νg9/2 50

4038

Ni

Sr 84 Se 34

28

Z

Z

Fig. 2. Evolution of single neutron particle (hole) energies from Z = 38, 40 to Z = 50. Measured and extrapolated values are indicated by filled and open symbols.

3 Towards

N 90

Fig. 3. Evolution of the Z = 28 (upper panel) and N = 50 (lower panel) shell gaps towards 78 Ni. For symbols see fig. 2.

π p1/2

40

Z=28

2

0 0g9/2

πf5/2 Ni πp3/2

πf5/2

2

-20

68

6

0g7/2 0h11/2 1d3/2 2s 1/2 1d5/2

N=82 0h11/2 1d3/2 2s 1/2 0g7/2 1d5/2

78

88

Δ [MeV]

ε(j) [MeV]

0

359

Ni

On the neutron-rich side of the valley of stability 78 Ni, the doubly magic N = 50 isotone of 100 Sn, has been subject of numerous experimental studies with respect of the persistence of the N = 50 shell and its relevance for the astrophysics r-path. Early β-decay results seem to indicate a substantial shell quenching [26], while in-beam experiments on N ∼ 50 Ge-Se isotopes [27] and isomer studies following fragmentation [28, 29,30, 31] give evidence for the persistence of the N = 50 shell. In β-decay of odd-mass Ni

isotopes a strong monopole shift of the π0f5/2 level in Cu isotopes upon filling of the ν0g9/2 shell beyond N = 40 was observed [5,6,32]. This is decisive for both the Z = 28 and N = 50 shell gaps in 78 Ni which are determined by the interaction of the spin-flip Δl = 1 π0f5/2 -ν0g9/2 pair of nucleons. In Ni isotopes (Z = 28) beyond N = 40 by filling of the ν0g9/2 shell the π0f5/2 orbit is bound more strongly than the adjacent π1p3/2 and π0f7/2 and eventually crosses the π1p3/2 to enter the shell gap. Along N = 50 the removal of π0f5/2 protons will release the ν0g9/2 stronger than ν1d5/2 which will reduce the gap. In fig. 3 (lower panel) the extrapolation of the shell gap along the N = 50 line from 100 Sn to 78 Ni for successive removal of the π0g9/2 , π1p1/2 , π1p3/2 and π0f5/2 protons is shown for different experimentally known starting points at Z = 50, 40, 38, 32. Monopoles inferred from a realistic 1p, 0f , 0g interaction [24] were used for ν0g9/2 , whereas the unknown monopoles involving the ν1d5/2 were taken from a 1d, 0g, 1f interaction above 132 Sn after A−1/3 mass scaling. The experimental gaps at Z = 50, 40, 38 are well reproduced, and the N = 50 gap at Z = 28 is extrapolated to be ∼ 3.5 MeV, which is reduced by ∼ 3.0 MeV from 100 Sn (see sect. 2) but still maintains a shell closure. Between the proton subshells the experimental gaps are smaller due to core excitations and configuration mixing as discussed in sect. 2. The shell gap is defined as the energy difference between the highest hole (ν0g9/2 ) and the lowest particle (ν1d5/2 ) levels. In the upper panel the evolution of the proton gap between π0f7/2 and π0f5/2 (dashed line), and π1p3/2 , respectively, is shown, and this latter is the lowestlying particle orbit at N = 40. Therefore, the effect is not as dramatic as along N = 50. From N = 40 to N = 50 the gap is reduced by ∼ 1 MeV to ∼ 5 MeV, i.e. in conclusion the 78 Ni shell closure is preserved in agreement with exper2 seniority isoimental evidence on the persistence of ν0g9/2 70 78 merism from N = 42 ( Ni) to N = 48 ( Zn, 76 Ni) [28, 29, 30,31] and the N = 50 shell strength in Ge isotopes [27].

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50 N~Z

HO --> SO N >> Z (CS)ls--> (CS’)jj

N+1

50

100Sn

g9/2

n,l+1,j=l+3/2 (1d,1f, ...) 90 Zr

CS N

π

CS’ n,l,j=l-1/2 (1p,1d,...) n,l,j=l+1/2

ν

20 48Ni 28

Z

p3/2

ν

28 56Ni f7/2

32,34, 36,40Ca

d5/2 s1/2 d3/2 36 S 34Si

p3/2

f5/2

32 Mg

8 8

16O

p1/2

6

22,24O

d s d p1/2 5/2 1/2 3/2 p3/2

14 16

p1/2

78Ni

28

g 66Fe 9/2

f7/2

64Cr 48Ca

f d3/2 7/2 s1/2

f5/2

40 68Ni

f7/2

20

p1/2

88 Sr

52,54Ca

p3/2 p1/2

28

32 34

f5/2

g9/2

40

50

20

N

d5/2

8 20

Fig. 4. Schematic chart of known and expected new shell structure in N  Z nuclei. The insert illustrates the scenario when moving from N ∼ Z closed shells (CS) along isotonic chains to neutron-rich nuclei. Standard (CS) and new closed shell (CS  ) nuclei are indicated as full and hatched squares. Open squares mark deformed shell quenched nuclei.

The inferred 78 Ni shell gaps along with the recently determined empirical T = 1 interaction and single-particle (hole) energies for the N = 50 isotones and Ni isotopes [33] provide a bench mark for tuning the monopole interaction in the 48 Ca to 78 Ni model space. The puzzling disappearance of the I π = 8+ isomers in the midshell nuclei 72,74 Ni [34], which is intimately connected to the low I π = 2+ excitation energies [6,11], is nicely reproduced by the new T = 1 empirical interaction for Z = 28 [33].

4 Shell structure towards N  Z Strong monopole drifts have been experimentally observed all over the Segr´e chart, the most prominent being the Δl = 0 spin-orbit πν pairs 0p3/2 -0p1/2 , 0d5/2 -0d3/2 , 0f7/2 0f5/2 , 0g9/2 -0g7/2 and the Δl = 1 spin-flip pairs 0p1/2 0d5/2 , 0d3/2 -0f7/2 , 0f5/2 -0g9/2 , 0g7/2 -0h11/2 . They are summarised in recent reviews [3,5,6,35] and can be traced

back to the στ and tensor parts of the NN interaction [3,4]. Recently, based on sound evidence from spectroscopic factors the π0g7/2 -ν0h11/2 drift was confirmed, and for the first time a high-spin Δl = 2 case π0g7/2 -ν0i13/2 was established [36]. This translates into the following criteria for strong monopoles: i) the interacting nucleons are spinflip partners with ii) Δl = 0, 1, 2 and iii) should have the same number of nodes in their radial wave functions to optimize the overlap. These features are also borne out in realistic interactions as derived from effective NN potentials fitted to scattering data via standard many-body techniques [24] as shown in fig. 17 of [6]. They suffer, however, from the fact that due to the neglect of three-body effects the monopole part is not determined well and has to be tuned to experimental shell evolution, which hampers their predictive power. The dramatic impact of monopole drifts and the sensitivity to subtle details of the interaction is due to the factor (2j  + 1) in eq. (2) which is large in filling (emptying) a high-spin orbital j  and translates

H. Grawe et al.: Shell structure from

100

Sn to

78

Ni: Implications for nuclear astrophysics

monopole corrections of about 100 keV into MeV. In the following the shell driving by monopole interaction will be discussed for light nuclei (sect. 4.1) and r-path nuclei below 132 Sn (sect. 4.2) in a qualitative way.

Based on the above-mentioned criteria the monopole driven shell structure scenario evolves as sketched in the insert of fig. 4. Starting from an N = Z harmonicoscillator (HO) closed shell nucleus as, e.g., 16 O or 40 Ca progression along an isotonic chain of semimagic nuclei towards N  Z results in: – Removing protons from a filled (πn, l, j< = l − 1/2) orbit, as, e.g., 0p1/2 , 0d3/2 , in a closed shell (CS) will shift the neutron (νn, l + 1, j> = l + 3/2) orbit, as, e.g., 0d5/2 , 0f7/2 , upward as its binding is weakened relative to the neighbouring orbits as a consequence of the tensor force. This is due to the Δl = 1 monopole created by the tensor force [4], which stabilises the shell as, e.g., in 14 C, 36 S, 34 Si and may rearrange the orbitals beyond the closed shell (CS) as observed, e.g., in 15 C. – On further removal of protons from the next lowerlying orbit (πn, l, j> = l + 1/2), e.g. 0p3/2 , 0d5/2 , its spin-orbit neutron partner j< (Δl = 0) will be released in a dramatic way due to the στ force to create a new shell CS  . In summary a HO shell with magic number Nm = 8, 20, 40 changes to Nm − 2 · N = 6, 16(14), 34(32) where N is the HO major quantum number. The new magic nuclei are shown as hatched squares in fig. 4. The two-fold closures for N > 1 are due to the presence of j = 1/2 orbits as 1s1/2 or 1p1/2 and the strongly binding T = 1, j 2 , J = 0 two-body matrix-element, which in this case is identical to the monopole. As a consequence according to eq. (2) after filling of the j = 1/2 orbit its binding is increased opening another gap. The effect was nicely demonstrated recently for N = 32, 34 [4, 37]. Experimentally it is well established since long for the pairs of nuclei 36 S-34 Si (1s1/2 ) and 90 Zr88 Sr (1p1/2 ). When further proceeding beyond the point of shell change the previously semi-magic nuclei will develop deformation due to ph excitation across the quenched shell gap as indicated by white squares in fig. 4. Monopole driven shell structure is characterised by the following signature, which substantially deviates from the mechanisms described in the introduction (sect. 1): – a HO (ls-closed) shell changes to a SO (jj-closed) shell; – the change is rapid with subshell occupation, and highly localized; – the scenario is symmetric in isospin projection Tz ; – upon removal of protons the apparent SO splitting between the neutron l, j< and j> SO partners (Δl = 0) due to the στ interaction is increased, as, e.g., ν0g7/2 0g9/2 upon filling of the π0g9/2 shell (see long-dashed lines in figs. 2, 5); – contrary in the adjacent HO shell N + 1 the SO splitting between the l, j> and j< is decreased due to the

0

ε(j) [MeV]

4.1 New (sub)shells at N = 6, 14/16, 32/34

361

132

122

Sn

Zr 1d3/2 0g7/2 2s 1/2 0h11/2

1f 7/2

1d5/2

N=82

-5

1d3/2 0h11/2 2s 1/2

N=50

1d5/2

-10

0g7/2

50

π g9/2

π p1/2

40

38

Z

Fig. 5. Evolution of the N = 82 shell gap below symbols see fig. 2.

132

Sn. For

tensor force interaction with the Δl = 1 partner, e.g. π0f5/2 -0f7/2 splitting increases when filling the ν0g9/2 orbit (see dashed line in the upper panel of fig. 3). Further verification is reviewed in refs. [3,5,6,37]. Predictions of this scenario comprise the N = 32, 34 closures in Ca isotopes, where first evidence has been presented [38, 39, 40], the closure at N = 14, 16 in 34,36 Ca probing isospin symmetry, and the strongly deformed 32 Ca, mirror to 32 Mg, 66 Fe [41], 67 Fe [42] and 64 Cr, the N = 40 analogues to N = 20 32 Mg. 4.2 Implication for structure at the r-path The success of the concept of monopole driven shell structure especially for the partially quenched N = 50 shell at 78 Ni, raises the question whether this could provide a possible scenario to understand the r-path abundance deficiency trough below the A  130 peak in astrophysical network calculations [43]. Quenching of the N = 82 shell due to a softening of the neutron potential as described in the introduction [2] has been invoked to explain this abundance deficiency [43] and experimental evidence for a reduced shell gap for N = 82, Z ≤ 50 has been presented [44,45]. While the nuclear structure origin of the astrophysics problem is still controversial, it might be appropriate to also look into alternative structure scenarios. In essence a reduced N = 82 shell gap causes increased excitation of neutrons into orbitals beyond N = 82 leading eventually to deformation. As a consequence the β-decay halflives at the previous waiting points become shorter due to larger Qβ values while they are increased for smaller neutron numbers due to the delayed filling of the ν0g7/2 subshell which is the key orbital for the ν0g7/2 → ν0g9/2 allowed Gamow-Teller (GT) transition.

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The relevant r-path nuclei are found below 132 Sn at Z ≤ 50 with the single neutron states playing the key role. In fig. 5 the evolution of neutron single-particle (hole) energies around the N = 82 shell gap from 132 Sn towards 122 Zr is shown, where the π0g9/2 orbit should be emptied. Starting points are the experimental values adopted for 132 Sn [8,6]. The slopes of the neutron hole states are governed by the same π0g9/2 -νj interaction [24] as for the neutron particles along N = 50 as shown in fig. 2 except for a renormalisation due to the different shell model core, which in the simplest case is an A−1/3 scaling (see sect. 2). The π0g9/2 -ν1f7/2 monopole was scaled up from the π0h11/2 -ν1g9/2 interaction at 208 Pb [46]. Apparently the shell gap remains unchanged on the way from 132 Sn to 122 Zr. According to the caveat discussed in connection with eq. (2) and the N = 50 shell gap extrapolation in fig. 3 this does not exclude a shell gap reduction due to cross shell excitations when moving away from a doubly magic nucleus along a semi-magic chain of nuclei. Note that from 100 Sn to 94 Ru this amounts to a ∼ 2 MeV reduction (fig. 3) without invoking any additional quenching. The steep upsloping of the ν0g7/2 level from the deepest in the shell at Z = 50 to the Fermi surface at Z = 40, however, provides an alternative scenario to explain the same physics as the invoked shell quenching [43]. The allowed GT transition is delayed as the ν0g7/2 starts to be filled only about 12 nucleons below N = 82 thus increasing β-decay halflives in the region A < 130. On the other hand a filled ν0g7/2 orbit at N ∼ 82 at the Fermi surface causes large effective Qβ values, which decreases the halflives in this region. As a consequence the abundance peak intensities will be shifted to lighter masses. It should be recalled with respect to the caveat expressed in sect. 2 that this is a qualitative estimate, which hinges on the applicability of eq. (2) and the persistence of a Z = 40 subshell in 122 Zr. It therefore awaits corroboration by a full shell model calculation employing a monopole tuned realistic interaction, which can be done in less remote nuclei as, e.g., 90 Zr, 100 Sn and 132 Sn in this case.

5 Summary and conclusions It has been shown that isomer decay spectroscopy close to magic nuclei provides a very sensitive probe of residual interactions and single-particle energies employed in shell model calculations. An indispensable prerequisite for sound predictions are readily available large-scale shell model codes along with realistic interactions that in their monopole part are well adjusted to experimental singleparticle energies. This does not hamper the predictive power of shell model calculations as the tuning can be done in regions accessible to detailed spectroscopy (see sects. 3 and 4.2). Monopole driven shell evolution can account for many aspects of structural changes on the pathway from proton-rich N ∼ Z nuclei (100 Sn) to the neutron-rich N  Z (78 Ni) region. The concept has been

shown to account for the new shell closures established in light nuclei and may provide an alternative access to the structure of r-path nuclei.

References 1. A. Bohr, B.R. Mottelson, Nuclear Structure (World Scientific, Singapore, 1998). 2. J. Dobaczewski et al., Phys. Rev. Lett. 72, 981 (1994). 3. T. Otsuka et al., Phys. Rev. Lett. 87, 0852502 (2002). 4. T. Otsuka et al., Acta Phys. Pol. B 36, 1213 (2005). 5. H. Grawe, Acta Phys. Pol. B 34, 2267 (2003). 6. H. Grawe, Springer Lect. Notes Phys. 651, 33 (2004). 7. H. Grawe et al., Phys. Scr. T 56, 71 (1995). 8. H. Grawe, M. Lewitowicz, Nucl. Phys. A 693, 116 (2001). 9. A. Blazhev et al., Phys. Rev. C 69, 064304 (2004). 10. C. Plettner et al., Nucl. Phys. A 733, 20 (2004). 11. H. Grawe et al., Nucl. Phys. A 704, 211c (2002). 12. M. G´ orska et al., Phys. Rev. Lett. 79, 2415 (1997). 13. R. Grzywacz, Proceedings ENAM98, AIP Conf. Proc. 455, 38 (1998). 14. E. Nolte, H. Hicks, Phys. Lett. B 97, 55 (1980). 15. J. D¨ oring et al., Scientific Report 2003, GSI 2004-1, Nuclear Structure (2004) p. 12, and to be published. 16. D. Alber et al., Z. Phys. A 332, 129 (1989). 17. I. Mukha et al., Phys. Rev. C 70, 044311 (2004). 18. K. Schmidt et al., Z. Phys. A 350, 99 (1994). 19. I. Mukha et al., these proceedings. 20. J. D¨ oring et al., Phys. Rev. C 68, 034306 (2003). 21. K. Ogawa, Phys. Rev. C 28, 958 (1983). 22. R. Grzywacz et al., Phys. Rev. C 55, 1126 (1997). 23. M. G´ orska et al., Z. Phys. A 353, 233 (1995). 24. M. Hjorth-Jensen et al., Phys. Rep. 261, 125 (1995) and private communication. 25. M. G´ orska et al., Proceedings ENPE99, AIP Conf. Proc. 495, 217 (1999). 26. K.-L. Kratz et al., Phys. Rev. C 38, 278 (1988). 27. Y.H. Zhang et al., Phys. Rev. C 70, 024301 (2004). 28. R. Grzywacz et al., Phys. Rev. Lett. 81, 766 (1998). 29. J.M. Daugas et al., Phys. Lett. B 476, 213 (2000). 30. M. Sawicka et al., Eur. Phys. J. A 20, 109 (2004). 31. R. Grzywacz, these proceedings. 32. S. Franchoo et al., Phys. Rev. C 64, 054308 (2001). 33. A. Lisetskiy et al., Phys. Rev. C 70, 044314 (2004); these proceedings. 34. M. Sawicka et al., Phys. Rev. C 68, 044304 (2003). 35. T. Otsuka et al., Eur. Phys. J. A 15, 151 (2002). 36. J.P. Schiffer et al., Phys. Rev. Lett. 92, 162501 (2004). 37. M. Honma et al., Phys. Rev. C 69, 034335 (2004); these proceedings. 38. R.V.F. Janssens et al., Phys. Lett. B 546, 55 (2002). 39. S.N. Liddick et al., Phys. Rev. Lett. 92, 072502 (2004). 40. P. Mantica, these proceedings. 41. M. Hanawald et al., Phys. Rev. Lett. 82, 1391 (1999). 42. M. Sawicka et al., Eur. Phys. J. A 16, 151 (2002). 43. B. Pfeiffer et al., Nucl. Phys. A 693, 282 (2001). 44. I. Dillmann et al., Phys. Rev. Lett. 91, 162503 (2003). 45. T. Kautzsch et al., Eur. Phys. J. A 9, 201 (2000). 46. E.K. Warburton et al., Phys. Rev. C 44, 233 (1991).

Eur. Phys. J. A 25, s01, 363–366 (2005) DOI: 10.1140/epjad/i2005-06-016-2

EPJ A direct electronic only

News on mirror nuclei in the sd and fp shells J. Ekmana , L.-L. Andersson, C. Fahlander, E.K. Johansson, R. du Rietz, and D. Rudolph Department of Physics, Lund University, S-22100 Lund, Sweden Received: 3 December 2004 / c Societ` Published online: 3 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Novel experimental results on mirror nuclei in the sd and f p shells are presented. Their respective Mirror Energy Difference (MED) diagrams are interpreted by means of large-scale shell-model calculations. A unique way of extracting effective charges from isospin symmetry studies is also discussed. PACS. 23.20.Lv γ transitions and level energies – 21.10.Sf Coulomb energies – 21.60.Cs Shell model – 29.30.Kv X- and γ-ray spectroscopy

The isospin T is a good quantum number under the fundamental assumptions of charge symmetry and charge independence of the strong force, which imply that the proton and neutron can be viewed as two different states of the same particle, the nucleon [1]. However, the electromagnetic interaction between protons obviously breaks this symmetry. These effects can be studied in mirror nuclei, which are pairs of nuclei where the number of protons and neutrons are interchanged. In this contribution we present novel results on mirror nuclei in the sd and f p shells, namely the TZ = ±1/2 A = 35 [2], A = 51 [3,4], and A = 61 [5] mirror nuclei. The interpretation of the experimentally obtained Mirror Energy Difference (MED) diagrams in these systems goes beyond the traditional picture. The A = 35 mirror nuclei were populated in an experiment at the Legnaro National Laboratory (LNL), where the heavy-ion fusion-evaporation reaction 24 Mg + 40 Ca was studied at a beam energy of 60 MeV [6]. As oxygen was present in the 40 Ca target the reaction 24 Mg + 16 O produced the A = 35 mirror nuclei 35 Ar and 35 Cl, via the evaporation of one α-particle and one neutron and one α-particle and one proton, respectively. The γ-rays were detected with the GASP array [7] in its standard configuration with 40 Ge detectors. For the detection of light, charged particles, the 4π charged-particle detector ISIS [8] was used. The NeutronRing replaced six of the 80 BGO elements at the most forward angles. As expected, the resulting level energies of the A = 35 mirror nuclei displayed in fig. 1 are very similar. However, there are two obvious differences. The first concerns the γ-ray energies of the topmost 13/2− → 11/2− transitions, which differ by as much as 300 keV. This difference a

Conference presenter. Present address: School of Technology and Society, Malm¨ o University, SE-205 06 Malm¨ o, Sweden; e-mail: [email protected]

6088 13/2 5766 13/2( 5384 11/2 382

)

680

( )

35

Ar

1025 4359 (9/2 ) 2187 1162

3197 7/2(

35

Cl

593 1446

883 1763 5/2 2603

7/2

518

2603 (7/2 ) 2646 7/2

852 5/2

3197 1751

2244

1185 1702 3163

1756

)

5407 11/2

1059 4348 9/2

1400 3163

2646 1763

1751

0 3/2

0 3/2

Fig. 1. Experimentally obtained level schemes for the A = 35 mirror nuclei. See text for details.

translates directly into a dramatic decrease of the MED at J π = 13/2− , which is shown in fig. 2. To understand the origin of the very large 13/2− MED it is useful to follow the procedure outlined in ref. [9] and expand the Coulomb part of the MED in a Coulomb monopole component (Cm) and a Coulomb multipole component (CM). The CM component represents the effect of breaking and aligning pairs of protons and is expected to play a minor role for the 13/2− states. However, the effect can be seen in the gradual decrease in the MED values between the 3/2+ and 7/2+ states and between the 7/2− and 11/2− states. In both cases this is the result when a pair of 1d3/2 protons (neutrons) aligning in 35 Ar (35 Cl). The Cm term can be expanded in several components. Here the focus is on one of them, namely the hitherto often overlooked electromagnetic spin-orbit component (Cls). Cls is a single-particle contribution and its effect is proportional to differences in the differences of neutron and proton orbital occupancies.

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the 7/2− states in the A = 35 mirror pair can also be seen when calculating the relevant transition probabilities. Using the known lifetime τ = 45.3(6) ps [11, 12] of the 7/2− state in 35 Cl, and the relative intensities of transitions [2] we obtain B(M 2; 7/2− → 3/2+ ) = 0.25 W.u. and B(E1; 7/2− → 5/2+ ) = 2 · 10−8 W.u. Assuming identical B(M 2)’s in both members of the mirror system it follows that B(E1; 7/2− → 5/2+ ) = 3 · 10−5 W.u. for 35 Ar, which is three orders of magnitude larger than in 35 Cl. This huge difference in the B(E1) values could in principle be explained by a cancellation of the E1 matrix elements due to isospin mixing. The amount of isospin mixing must then exceed five percent, which is much more than expected. However, there is no obvious reason for the assumption of identical B(M 2) values. In fact, assuming identical B(E1) values is an even stronger criterion from isospin symmetry arguments [1]. However, this leads to B(M 2) values that differ with three orders of magnitude. Future investigations will hopefully pin down the driving mechanism responsible for the very asymmetric decay patterns of the 7/2− states.

A=35

100 0 -100 -200

Exp. π = − Exp. π = +

-300

MED (keV)

3

7

5

9

11

13

A=51

100 0 -100

Exp. VCm + VCM + VBM 9

5

13

200

17

21

29

25

A=61

100 0

Exp. VCM VCM + VCls 1

3

5

7

9

11

13

2J Fig. 2. Experimental and calculated MED values for the A = 35, A = 51, and A = 61 mirror nuclei.

It can be written as [10] Cls = (gs − gl )

1

2m2nucleon c2

%

1 dVC (r) r dr

&

l · s ,

(1)

where gs and gl are the free gyromagnetic factors. For the negative-parity states in the upper sd shell the Cls term becomes significant. This is principally because the negative-parity states involve excitations from an orbital with j = l − s to one with j = l + s. Specifically, there is a gain of some 100 keV for the 1f7/2 proton orbit with respect to the neutron orbit, and the 1d3/2 orbit loses almost as much. Shell-model calculations indicate that − the 13/2 states are the only states where the dominant configurations are based on 1f7/2 to 1d3/2 singleparticle excitations. Thus the Cls term is expected to contribute with roughly half of the observed MED value of the − 13/2 states. To account for the remaining 150 keV other Coulomb monopole terms have to be considered [9, 2]. The second remarkable difference comes from the decay pattern of the 7/2− states. In 35 Ar the 1446 keV E1 branch clearly dominates the 3197 keV M 2 decay, while the corresponding 1400 keV E1 decay is essentially absent in 35 Cl. The state decays directly to the ground state through the strong 3163 keV M 2 transition. The effect is truly striking and has never been observed before in mirror studies. The dramatic difference in decay patterns of

The A = 51 results are based on two different data sets. The first set is based on two Gammasphere experiments performed at the Argonne National Laboratory (1999) and at the Lawrence Berkeley National Laboratory (2001) [4,13]. Both experiments employed the fusionevaporation reaction 32 S + 28 Si at 130 MeV beam energy. The γ-rays were detected in the Gammasphere array [14], which at the time comprised 78 Ge-detectors. For the detection of light, charged particles the 4π CsI-array Microball [15] was used. The Neutron Shell [16] replaced the five most forward rings of Gammasphere to enable the detection of evaporated neutrons. The reaction leads to the A = 51 mirror nuclei 51 Fe and 51 Mn following the evaporation of two α-particles and one neutron, and two α-particles and one proton, respectively. The second data set is based on an experiment aiming at measuring the lifetimes of the 27/2− analogue states in the A = 51 mirror nuclei by means of the recoil distance Doppler shift technique. The experiment was performed at LNL using the reaction 32 S + 24 Mg with a beam energy of 95 MeV [3]. The enriched 24 Mg target was mounted inside the Cologne plunger device [17] and data were taken at 21 targetstopper distances ranging from electric contact to 4.0 mm. From the Gammasphere data it was possible to identify some fifty core excited states in the TZ = +1/2 nucleus 51 Mn [18]. Despite the much lower experimental cross section three (one tentative) previously unknown core-excited states were also identified in the TZ = −1/2 mirror partner 51 Fe [4]. The obtained experimental level schemes (only the relevant part for 51 Mn) are shown in fig. 3 and the experimentally obtained MED diagram is shown in fig. 2 as open squares. The data up to spin J = 27/2 represent previously known experimental data [19,20], whereas the data points for J = 29/2 and J = 31/2 represent the new information arising from the yrast core excited states. As seen in fig. 2 the MED decreases rapidly from the fully aligned J = 27/2 states, which are based on a single 1f7/2 configuration (∼ 70%), to the core excited states.

J. Ekman et al.: News on mirror nuclei in the sd and f p shells

365

12791 31/2

(31/2 ) 12650

(29/2 ) (11712) (29/2 ) 11468

11510 29/2

51Fe

5381 (4443)

51Mn

5615

4199

4605

4333

(25/2 ) 25/2

7933

27/2

664 7269

23/2

777 6492

7892 717 27/2 7176 1421 704 23/2 6471

1441

884

5608

21/2

21/2

5640

831 2331

2394 1510

4098

15/2

508 3589 17/2 3275 314 636 13/2 322 2953 1437

11/2

1516

7/2

1263 893 253 253

1500

1959

19/2

1759

11781 29/2

19/2 4140 3681 459 888 430 3251 15/2 723 13/2 2957 294

17/2

1807

1469

1818

1762

1489 370 1146

0

9/2

1146 5/2

9/2

1140

5/2

11/2

1140 349

0

1251 902 7/2 237 237

Fig. 3. Experimentally obtained level schemes for the A = 51 mirror nuclei. See text for details.

To interpret the experimental MED diagram large-scale shell-model calculations were performed using the shellmodel code ANTOINE [21,22]. The calculations were performed using the KB3G with Coulomb interaction [23] in the full f p space containing the 1f7/2 orbit below and the 2p3/2 , 1f5/2 , and 2p1/2 orbits above the N = Z = 28 shell closures. The configuration space was truncated, i.e., five particle excitations from the 1f7/2 shell to the upper f p shell were allowed. This was found to provide virtually identical results compared to calculations in the f p space without truncations on yrast states in 1f7/2 nuclei [23]. To account for the Coulomb interaction the proton two-body matrix elements were constructed by adding harmonic oscillator Coulomb matrix elements to the plain two-body matrix elements of the KB3G interaction. The calculations of MED values follow a procedure suggested and discussed in detail in ref. [9]. The results are included in fig. 2 as filled squares. Although the agreement for the yrast core excited states is not perfect it was found that the inclusion of the Coulomb monopole term is crucial for explaining the observed MED values. The lifetimes of the yrast 27/2− states in the A = 51 mirror nuclei was deduced from the LNL experiment. The resulting lifetimes are τ ∼ 101 ps and τ ∼ 70 ps for 51 Mn and 51 Fe, respectively [3]. To study the consequences of the lifetime results on polarization and effective charges large-scale shell-model calculations were performed using the shell-model code ANTOINE with the same model space and truncations as described above. Three different interactions were used in the analysis: The standard KB3G interaction without any Coulomb interaction, with theoretical harmonic-oscillator Coulomb matrix elements

(Coulomb HO), and with the 1f7/2 Coulomb matrix elements replaced with the experimental values from the A = 42 mirror pair (Coulomb A42). The effective proton and neutron charges used in the calculations are expanded (0) (1) in terms of isoscalar epol and isovector epol polarization charges according to (0)

(1)

εp = 1 + epol − epol ;

(0)

(1)

εn = epol + epol ,

(2)

To obtain agreement between experimental and theoret(0) (1) ical B(E2) values epol ∼ 0.47 and epol ∼ 0.32 must be used, almost independent of the interaction. This converts into effective proton and neutron charges of ∼ 1.15 and ∼ 0.80, respectively. Interestingly, this is very close to the predicted values in ref. [24] in the case of N ∼ Z nuclei. It was also investigated how the harmonic-oscillator parameter, b0 , which determines the radii of the wave functions, influences the polarization charges. As seen in fig. 4 the isoscalar polarization charge is affected the most when changing the b0 parameter. The A = 61 experiment was conducted at the Holifield Radioactive Ion Beam Facility (HRIBF) at Oak Ridge National Laboratory as described in detail in ref. [5]. In fusion-evaporation reactions of a 40 Ca beam at 104 MeV, impinging on a 24 Mg target foil, the mirror nuclei 61 Ga and 61 Zn nuclei were produced via the evaporation of one proton and two neutrons and two protons and one neutron, respectively. The Ge detector array CLARION [25] was used to detect the γ radiation at the target position. After the particle evaporation and prompt γ-decay processes the reaction products are recoiling from the thin target into the Recoil Mass Spectrometer [25] before finally being stopped in an Ionization Chamber.

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b0 = 1.01

0.5 epol

isoscalar

0.4

Coulomb A42 Coulomb HO

no Coulomb

0.3

isovector

0.98

1.00

1.02

1.04

b0

Fig. 4. Polarization charges, necessary to reproduce the B(E2; 27/2− → 23/2− ) values in the A = 51 mirror nuclei, as a function of b0 for three different shell-model calculations.

through the 2399 keV 9/2+ state in 61 Zn has about the same intensity as the 13/2− → 9/2− → 5/2− cascade. A possible explanation for the non-observed γ-rays decaying from a 9/2+ state in 61 Ga is a 1g9/2 proton decay from that level into the ground state of 60 Zn. To summarize, experimental isospin symmetry studies have been extended to involve nuclei in the sd and upper f p shells. The importance of the hitherto overlooked electromagnetic spin-orbit effect has been shown. The strong asymmetry in the decay pattern of the 7/2− states in the A = 35 mirror nuclei indicate the presence of isospin mixing and needs to be investigated further. Studies of the A = 51 mirror nuclei have revealed two interesting and novel features: i) mirror symmetry studies of core-excited states and ii) an unique way of extracting isoscalar and isovector polarization charges simultaniously. The authors would like to thank all colleagues which partcipated in the experiments and the preparation of the manuscripts. A token of gratitude also goes to the accelerator crews at the various laboratories for their supreme effort in making the experiments succesful. This research was supported in part by the Swedish Science Council.

Fig. 5. Experimentally obtained level schemes for the A = 61 mirror nuclei. See text for details.

Four excited states in the TZ = −1/2 nucleus 61 Ga were identified and are shown in fig. 5. When comparing with the relevant part of the 61 Zn level scheme, MED values represented by open squares in fig. 2 are obtained. Predictions from large-scale shell-model calculations using the shell-model code ANTOINE are included in fig. 2. The calculations were performed in the same model space as before, but this time the configuration space was truncated to allow for three particle excitations from the 1f7/2 shell into the upper f p shell. The calculations were performed using the GXPF1 [26, 27] with Coulomb interaction. In the first calculation the standard GXPF1 single-particle energies were used for both protons and neutrons, to estimate the Coulomb multipole component. The result is shown as filled circles in fig. 2. It is seen that the correct sign of the MED values is reproduced, although the calculated MED values are typically 50 to 100 keV smaller than the experimental values. These discrepancies may be the result of Coulomb monopole effects discussed above, and especially the Cls component is expected to be important since excitations from the 2p3/2 orbit to the 1f5/2 and 2p1/2 orbits are present in the formation of the observed states. The result from a calculation where the single-particle energies have been modified according to eq. (1) is shown in fig. 2 as filled squares. It is seen that the agreement with the observed MED values has improved considerably. Last but not least it is intriguing to take a closer look at the level schemes in fig. 5. There is no apparent hint for the 9/2+ → 7/2− → 5/2− (1403–873 keV in 61 Zn) or the 9/2+ → 7/2− → 3/2− (1403–996 keV in 61 Zn) sequence in 61 Ga in the present data set, even though the branch

References 1. D.H. Wilkinson, Isospin in Nuclear Physics (NorthHolland Publishing Company, Amsterdam, 1969). 2. J. Ekman et al., Phys. Rev. Lett. 92, 132502 (2004). 3. R. du Rietz et al., Phys. Rev. Lett. 93, 222501 (2004). 4. J. Ekman et al., Phys. Rev. C 70, 057305 (2004). 5. L.-L. Andersson et al., Phys. Rev. C 71, 011303 (2005). 6. C. Andreoiu et al., Eur. Phys. J. A 15, 459 (2002). 7. C. Rossi Alvarez, Nucl. Phys. News, 3, 3 (1993). 8. E. Farnea et al., Nucl. Instrum. Methods Phys. Res. A 400, 87 (1997). 9. A.P. Zuker et al., Phys. Rev. Lett. 89, 142502 (2002). 10. R.J. Blin-Stoyle, Chapt. 4 in [1]. 11. P.M. Endt, C. Van Der Leun, Nucl. Phys. A 310, 1 (1978). 12. P.M. Endt, Nucl. Phys. A 521, 1 (1990); 633, 1 (1998). 13. J. Ekman et al., Phys. Rev. C 66, 051301(R) (2002). 14. I.-Y. Lee, Nucl. Phys. A 520, 641c (1990). 15. D.G. Sarantites et al., Nucl. Instrum. Methods A 381, 418 (1996). 16. D.G. Sarantites et al., Nucl. Instrum. Methods A 530, 473 (2004). 17. A. Dewald et al., Nucl. Phys. A 545, 822 (1992). 18. J. Ekman et al., Phys. Rev. C 70, 014306 (2004). 19. J. Ekman et al., Eur. Phys. J. A 9, 13 (2000). 20. M.A. Bentley et al., Phys. Rev. C 62, 051303(R) (2000). 21. E. Caurier, shell model code ANTOINE, IRES, Strasbourg 1989-2002. 22. E. Caurier, F. Nowacki, Acta Phys. Pol. 30, 705 (1999). 23. A. Poves et al., Nucl. Phys. A 694, 157 (2001). 24. A. Bohr, B.R. Mottelson, Nuclear Structure, Vol. 2 (Benjamin Inc., New York, 1975) Chapt. 6. 25. C.J. Gross et al., Nucl. Instrum. Methods A 450, 12 (2000). 26. M. Honma, T. Otsuka, B.A. Brown, T. Mizusaki, Phys. Rev. C 69, 034335 (2004). 27. M. Honma, T. Otsuka, B.A. Brown, T. Mizusaki, Phys. Rev. C 65, 061301 (2002).

Eur. Phys. J. A 25, s01, 367–370 (2005) DOI: 10.1140/epjad/i2005-06-048-6

EPJ A direct electronic only

Study of single-particle states in reaction

23

F using proton transfer

S. Michimasa1,a , S. Shimoura2 , H. Iwasaki3 , M. Tamaki2 , S. Ota4 , N. Aoi1 , H. Baba2 , N. Iwasa5 , S. Kanno6 , S. Kubono2 , K. Kurita6 , M. Kurokawa1 , T. Minemura1 , T. Motobayashi1 , M. Notani2,b , H.J. Ong3 , A. Saito2 , H. Sakurai3 , S. Takeuchi1 , E. Takeshita6 , Y. Yanagisawa1 , and A. Yoshida1 1 2 3 4 5 6

RIKEN (Institute of Physical and Chemical Research), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Center for Nuclear Study, University of Tokyo, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 133-0033, Japan Department of Physics, Kyoto University, Kitashirakawa, Kyoto 606-8502, Japan Department of Physics, Tohoku University, Aoba, Sendai, Miyagi 980-8578, Japan Department of Physics, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan Received: 22 November 2004 / c Societ` Published online: 9 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The proton shell structure in neutron-rich fluorine 23 F was investigated using the in-beam γ-ray spectroscopy technique via the proton transfer reaction onto the unstable nucleus 22 O, in addition to α inelastic scattering on 23 F, and the neutron-knockout reaction from 24 F. The level and γ-decay scheme in 23 F was deduced from de-excitation γ-ray–particle coincidence events. We found that a single-particle state at 4.061 MeV has a large contribution from the d shell by the analysis of population strengths and the angular distribution for the state. We reported here the present experiment and the preliminary results. PACS. 21.10.Pc Single-particle levels and strength functions – 23.20.Lv γ transitions and level energies – 25.55.Hp Transfer reactions – 27.30.+t 20 ≤ A ≤ 38

1 Introduction Nuclear shell structure is mainly interpreted by singleparticle motion in a mean-field including a spin-orbit potential. Recent findings of the disappearance of magic numbers and/or of new magic numbers in neutron-rich nuclei may indicate that the mean-field changes as a function of neutron number. In this respect, neutron-rich fluorine isotopes are interesting because they are the nuclei between the new magic number of N = 16 [1] and the island of inversion [2]. So far, nuclear structure physics in neutron-rich nuclei, including fluorine isotopes, mainly proceeds by focusing on neutron orbitals. However, protons composing a nucleus are strongly affected by neutrons through proton-neutron interactions, and vice versa. Therefore, studies of proton orbitals in neutron-rich nuclei are also essential for understanding these structures; proton orbitals may change irregularly due to shell evolution in neutron-rich regions. Thus, we studied proton nuclear structure in neutron-rich a

Conference presenter; e-mail: [email protected] Present address: Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA. b

fluorine 23 F using in-beam γ-ray spectroscopy by a oneproton transfer reaction. Proton transfer reactions are well known to be a good probe to investigate proton orbitals in a nucleus, and many one-proton stripping reactions have been used for studying single-particle nature, e.g., (d, n) and (α, t). In the present experiment, we selected the α-induced one-proton transfer reaction (α, t). In this case, a proton is transferred onto the unstable nucleus 22 O, thus it is important for a transfer reaction to match well with secondary beam conditions. With respect to beam intensity, intermediate-energy fragmentation reactions are useful in production of secondary beam. The beam energy is typically at 30–50 A MeV and somewhat higher for (d, n) reactions. However, the cross section for the (α, t) reaction has a maximum (on the order of mb) in this energy region, and it is expected to be larger than those of the (d, n) reaction. The reason is naively considered to be why a proton is picked up on the Fermi surface of an α particle which is deeply bound and has high-momentum components. As another merit, intermediate-energy fragmentation reactions enabled us to measure simultaneously some of other reactions for investigating 23 F, because the secondary beam was a cocktail of some nuclei in vicinity of 23 F. In the present configuration, we additionally observed α inelastic scattering of 23 F

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4. 06

3. 39

2. 92

2 3 Eγ [MeV]

3. 89

We simultaneously measured de-excitation γ rays from three different reactions aiming at excited states in 23 F: proton transfer reaction onto 22 O, α inelastic scattering on 23 F and neutron-knockout reaction from 24 F. The experiment was performed at the secondary beam line in RIKEN Accelerator Research Facility. The secondary beam, including 22 O, 23 F and 24 F, was produced by projectile fragmentation reactions of 63-MeV/nucleon 40 Ar beam impinging on a 9 Be target of 180-mg/cm2 thickness. Fragments were analyzed by the RIPS separator [3] using a wedge aluminum degrader of 321 mg/cm2 thickness at the first dispersive focal plane, where the momentum acceptance was set to be 4%. Secondary beam particles were identified event-by-event by energy losses in a silicon detector and time-of-flight between two plastic scintillators set 5 meters apart. The averaged intensities and mean energies of components in the cocktail beam are listed in table 1. The secondary beam bombarded a liquid-helium target [4] of 100 mg/cm2 , which was contained in an aluminum cell with two windows of 6-μm havar foils. The window size was 30 mm diameter. The helium was condensed by a cryogenic system, and kept at around 4 K through the experiment. Reaction products were detected by a ΔE-E telescope located at the end of the beam line, and were identified by the method of time-of-flight (TOF), energy loss (ΔE), and energy (E). The telescope consists of 9 silicon detectors for ΔE arranged in a 3 × 3 matrix, and 36 NaI(Tl) detectors [5] for E arranged in a 6 × 6 matrix. The angular acceptance of the telescope was in 0–6 degrees in laboratory system. TOF was measured between the secondary target and NaI(Tl) scintillators. In the present experiment, the resolutions for atomic and mass numbers in fluorine isotopes were 0.18 (σ) and 0.35 (σ), respectively. Scattering angles of the reaction products were measured by three parallel-plate avalanche counters (PPACs) [6]. The two PPACs, with effective areas of 100 × 100 mm2 , were placed before the secondary target to determine the direction and the hit point of the beam. The other PPAC, with an effective area of 150 × 150 mm2 , was placed after the target to measure the direction of the reaction products. Their position resolutions were about

0.91

3. 39

2 Experiment

(c)

2. 92

and neutron-knockout reaction from 24 F. A comparison of population strengths from all of these reactions is effective in deducing the single-particle nature of excited states.

(b)

2. 92

F 36 4% 3 × 102 6.9%

(a)

2. 28

F 41.5 4% 6 × 102 12.8% 3 days

24

1. 71

O 35 4% 2 × 103 42.0%

23

Yield [counts/30keV]

Nuclide Energy [A MeV] Momentum acceptance Intensity [particle/s] Flux percentage Measurement

22

500 400 300 200 100 0 400 300 200 100 0 500 400 300 200 100 0

0. 91

Table 1. Composition of the secondary beam.

0. 91

368

4

5

Fig. 1. Gamma-ray spectra from three different reactions: (a) proton transfer reaction 4 He(22 O,23 Fγ), (b) inelastic scattering 4 He(23 F,23 Fγ), and (c) neutron-knockout reaction 4 He(24 F,23 Fγ).

1 mm and the resolution of the scattering angles were estimated to be 0.25 degrees (σ) in laboratory flame. For de-excitation γ-ray detection from the reaction products, we used the DALI(II) [7] NaI(Tl) detector array. The array consisted of 150 NaI(Tl) scintillators and surrounded the secondary target in the angular range of 20–160 degrees with respect to the beam axis. The entire system was composed of 13 layers, and was designed for γ-ray detection from nuclei moving with high velocity. In the present experiment, the full-energy-peak efficiency was 17.6% for 1.33-MeV γ rays from 60 Co, and the energy resolution, including Doppler-shift corrections, was 8.2% (σ) for the de-excitation γ rays at 3.2 MeV from 22 O moving with β ∼ 0.27.

3 Analysis outline We obtained remarkably different γ-ray spectra in 23 F from the proton transfer 4 He(22 O,23 F), the inelastic scattering 4 He(23 F,23 F), and the neutron-knockout 4 He(24 F,23 F) reactions as shown in fig. 1. We observed de-excitation γ rays at 0.9 and 2.9 MeV in all reactions, whereas the other γ rays observed were reactiondependent. This difference was considered to be derived from populating different excited states by these reactions. In order to deduce a scheme of excited states in 23 F, we examined coincidences of multiple γ rays in the three reactions. The energies of excited states in 23 F were determined by total energies of sequential γ decays. In the present analysis, each sequential γ decay was identified by the evidence that a yield of the coincident event was

S. Michimasa et al.: Study of single-particle states in

23

F using proton transfer reaction

369

40 0.91

Yield [Counts/60keV]

4

30

He( 22O, 23Fγ2.92 γ)

Coincidence with 2.92-MeV γ-ray

20 1.25

2.01 3.44 2.64

10

0

1

2

3 E γ [MeV]

3.95

4

5

Fig. 2. Gamma-ray spectrum from the transfer reaction 4 He(22 O,23 F) in coincidence with the 2.92-MeV γ ray. The thin solid curves show response functions of the γ-ray detectors array for each of γ lines, which were calculated by MonteCarlo simulation, and the dashed curves show contaminated events from 22 F and the exponential background. The thick solid curve shows the summation of these thin solid and dashed curves. In the figure, we identified five γ lines coincident with the 2.92-MeV γ ray pointed by closed circles, whereas the γ line with an open circle was found to correspond to the sequential γ decay of the 3.39-MeV and 1.25-MeV lines.

consistent with yields of the members within the precision of the statistical error. Figure 2 shows the γ-ray spectrum obtained from the transfer reaction in coincidence with the 2.92-MeV γ ray. So far, two previous works were performed to investigate excited states in 23 F: Orr et al. [8] has reported six excited states at 2310(80), 2930(80), 4050(50), 5000(60), 6250(80), and 8180(110) keV in 23 F; Belleguic et al. [9] has reportedly observed two γ rays at 2900 keV and 910 keV from 23 F. The first one corresponded to the decay from the 2900-keV state to the ground state, whereas the second one corresponded to the decay from the 3810-keV state to the 2900-keV state. The present result was consistent with the previous results as we observed the coincidence events of the 2.92-MeV and the 0.91-MeV γ rays. We identified, moreover, the coincidental γ rays at 2.01, 2.64, 3.44 and 3.95 MeV shown with closed circles in fig. 2. These γ rays were found to correspond to the decays from higher excited states to the 2.92-MeV states. The 1.25-MeV γ ray shown with a open circle in fig. 2 was, however, found to be sequential with the 3.39-MeV γ decay by the analysis of plural γ-detection events in coincidence with the 3.39-MeV γ ray. This false peak came from 1.25-MeV photons in coincidence with the Compton events of the 3.39-MeV line. We examined possible coincidences of multiple γ rays in the three reactions as the above-mentioned case and preliminarily reconstructed the γ-decay scheme in 23 F.

Fig. 3. Tentative level and γ-decay scheme in 23 F. Level energies with underlines show newly observed excited levels in the present experiment. Shown errors with γ ray and excited energies are statistical errors obtained by fittings of γ-ray spectra with simulated response functions of DALI(II). The bars in the right side of excitation energies show relative cross sections to populate these states.

The placement of γ rays was determined by requiring that the weaker one was located on the top of the stronger one.

4 Results and discussion Figure 3 shows the proposed level scheme in 23 F deduced from the three reactions. Many of the excited states shown in the figure were commonly observed from the three reactions, and the level scheme greatly agrees with the previous results. We reconfirmed the six excited states shown with roman style, and found eight excited states at 3385(10), 3887(19), 4619(17), 4756(3), 5508(38), 5549(23), 5563(27) and 6872(36) keV for the first time, which are shown with underlined bold style. Here, numbers in parentheses show the statistical errors deduced from fitting with simulated response functions of the γ-ray detectors array. In fig. 3, the bar graph on the right side of the excitation energies shows the relative cross sections to populate the excited states. In these relative cross sections, one can see that the 4.06-MeV state was strongly populated by the proton transfer reaction, but hardly at all by the other reactions. Such differences of population strengths

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10.0

dσ/dΩcm [mb/sr]

state in 23 F, respectively. The measured angular distribution was found to agree with the  = 2 transition. The 4.061-MeV state, therefore, is preliminarily assigned to have J π = 3/2+ or 5/2+ . The previous works [8,10,11] reported the ground state in 23 F to have 5/2+ . Therefore, the state at 4.061 MeV is considered reasonably to have 3/2+ as a proton single-particle state in the d3/2 .

Ex = 4.06 MeV σint = 2.9(4) mb ΔL = 0 ΔL = 2 ΔL = 3

5.0

5 Summary 2.0

Preliminary

1.0 0

5

10 15 θcm [deg.]

20

25

Fig. 4. Angular distribution for the 4.061-MeV state from the proton transfer reaction. Curves in the figure show the predictions obtained from DWBA calculations. Dashed, solid and dotted curves correspond to transferred orbital angular momenta  = 0, 2 and 3, respectively. The optical potential parameters used are described in the text.

are naively considered to reflect the matching between the reaction channel and the property of excited states. In the present experiment, the three kinds of reactions are considered to populate different states as follows: The transfer reaction mainly populates proton single-particle states; The α inelastic scattering makes core excitations and possibly populates single-particle states through non spin-flip excitation; and the neutron-knockout reaction populates neutron-hole states. Therefore, the difference of population strengths among these reactions is significant to estimate the properties of the excited state. Concerning the 4.06-MeV state, this strongly suggests that the state has the single-particle nature and is excited from the ground state through a spin-flip process. Figure 4 shows the angular distribution of outgoing 23 F for the 4.061-MeV state together with predictions calculated by distorted-wave Born approximation (DWBA) to transfer a proton into the s, d and f orbitals. Optical potentials used in the initial and final channel were determined by angular distributions of α inelastic scattering for the first 2+ state in 22 O, and for the 2.92-MeV

We investigated the proton shell structure in neutronrich 23 F by in-beam γ-ray spectroscopy from the proton transfer reaction corresponding with inverse kinematics of (α, t). Moreover we studied the excited states in 23 F through the α inelastic scattering on 23 F and the neutronknockout reaction from 24 F. The level and γ-decay scheme in 23 F was deduced from de-excitation γ rays and these coincidence data obtained from the three reactions. From this study, we reconfirmed the previous results and found eight excited states. Furthermore the 4.061-MeV state was found to have single-particle nature and reasonably considered to have J π = 3/2+ . The authors thank the RIKEN Ring Cyclotron staff for cooperation during the experiment. One of the authors (S.M.) is grateful for the financial assistance from the Special Postdoctoral Researcher Program of RIKEN.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

A. Ozawa et al., Phys. Rev. Lett. 84, 5493 (2000). E.K. Warburton et al., Phys. Rev. C 41, 1147 (1990). T. Kubo et al., Nucl. Instrum. Methods B 70, 322 (1992). H. Akiyoshi et al., RIKEN Accel. Prog. Rep. 34, 193 (2001). M. Tamaki et al., CNS-REP-59, 76 (2003). S. Kumagai et al., Nucl. Instrum. Methods A 470, 562 (2001). S. Takeuchi et al., RIKEN Accel. Prog. Rep. 36, 148 (2003). N.A. Orr et al., Nucl. Phys. A 491, 457 (1989). M. Belleguic et al., Nucl. Phys. A 682, 136c (2001). D.R. Goosman et al., Phys. Rev. C 10, 756 (1974). E. Sauvan et al., Phys. Rev. C 69, 044603 (2004).

Eur. Phys. J. A 25, s01, 371–374 (2005) DOI: 10.1140/epjad/i2005-06-127-8

EPJ A direct electronic only

Single-neutron excitations in neutron-rich N = 51 nuclei J.S. Thomas1,a , D.W. Bardayan2 , J.C. Blackmon2 , J.A. Cizewski1 , R.P. Fitzgerald3 , U. Greife4 , C.J. Gross2 , M.S. Johnson5 , K.L. Jones1 , R.L. Kozub6 , J.F. Liang2 , R.J. Livesay4 , Z. Ma7 , B.H. Moazen7 , C.D. Nesaraja2,7 , D. Shapira2 , M.S. Smith2 , and D.W. Visser3 1 2 3 4 5 6 7

Department of Physics and Astronomy, Rutgers University, New Brunswick, NJ 08903, USA Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599, USA Physics Department, Colorado School of Mines, Golden, CO 80401, USA Oak Ridge Associated Universities, Oak Ridge, TN 37831, USA Department of Physics, Tennessee Technological University, Cookeville, TN 38505, USA Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA Received: 14 January 2005 / c Societ` Published online: 10 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Single-neutron transfer reactions have been measured on two N = 50 isotones at the Holifield Radioactive Ion Beam Facility (HRIBF). The single-particle-like states of 83 Ge and 85 Se have been populated using radioactive ion beams of 82 Ge and 84 Se and the (d, p) reaction in inverse kinematics. The properties of the lowest-lying states —including excitation energies, orbital angular momenta, and spectroscopic factors— have been determined for these N = 51 nuclei. PACS. 25.60.Je Transfer reactions – 21.10.Dr Binding energies and masses – 21.10.Pc Single-particle levels and strength functions – 26.50.+x Nuclear physics aspects of novae, supernovae, and other explosive environments

1 Introduction The single-particle properties of nuclei near closed shells are important probes of nuclear structure. With the growing availability of beams of radioactive ions, these properties can be investigated in exotic, neutron-rich nuclei. Very few experimental data exist for the thousands of neutronrich nuclei for which nuclear shell structure is expected to change. It has been suggested that the shift of singleparticle orbitals, leading to non-traditional “magic numbers”, is the result of the spin-isospin part of the monopole proton-neutron interaction [1, 2]. This argument has been used to explain the emergence of a new sub-shell closure at N = 32 near neutron-rich56 Cr [3, 4]. Alternatively, extremely neutron-rich nuclei are predicted to exhibit more uniformly spaced single-particle spectra, similar to a harmonic oscillator with a spin-orbit interaction as a result of pairing interactions [5]. For both of these scenarios the single-particle structure of neutron-rich nuclei determines the extent to which the shell structure has changed. a

Conference presenter; e-mail: [email protected]

The same low-lying structure near the closed shells may also affect the synthesis of elements in the rapid neutron capture (r-) process. In some r-process scenarios the final abundance pattern may be modified by neutron capture reactions on near-closed-shell nuclei after the fall out from nuclear statistical equilibrium [6]. But in weakly bound nuclei with small neutron separation energies, the level density of the final compound nucleus near the neutron threshold is low and neutron capture is more likely to proceed through the direct radiative capture mechanism. Without measurements of these reactions, the neutron capture rates and their influence on the final abundance must be estimated. For the direct capture component, these rates depend on specific nuclear structure data including energy levels, spins, parities, electromagnetic transition probabilities, and single-particle spectroscopic factors [7]. All of these quantities, with the exception of electromagnetic transition probabilities, can be determined from measurements of (d, p) reactions on neutron-rich nuclei. Two (d, p) transfer measurements on N = 50 isotones were performed at the Holifield Radioactive Ion Beam Facility (HRIBF) to investigate the single-particle structure of the neutron-rich, N = 51 nuclei 83 Ge and 85 Se.

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(b)

Se

ΔE (channels)

ΔE (channels)

(a)

As Ge E (channels)

E (channels)

Fig. 1. Energy loss vs. total energy as measured by the ionization chamber for incoming beams of a) A = 82 and b) A = 84 isobars.

2 The measurements Radioactive ion beams at the HRIBF at Oak Ridge National Laboratory are produced using the isotope separation on-line (ISOL) technique [8]. Proton bombardment of a UC target induces fission of the uranium. The resultant neutron-rich fission fragments are then transported to an ion source. It has been shown that for some group 4A elements of the periodic table (e.g. Sn, Ge) transport of the isotope of interest as a sulfide molecule through the ion source enhances the relative isobaric purity of the beam [8]. After mass analysis, the ions are injected into the 25 MV tandem accelerator. 2.1 2 H(82 Ge, p)83 Ge An isobaric A = 82 beam, accelerated to 4 MeV/nucleon, bombarded a 430 μg/cm2 deuterated polyethylene (CD2 ) target for 4 days at an average intensity of 7×104 pps. The beam was highly contaminated, even with the sulfur technique to enhance the relative fraction of 82 Ge: 85% was stable 82 Se, 15% was 82 Ge, and < 1% 82 As. The beam and beam-like recoils exited the target in a narrow cone with an opening angle < 1◦ , and were stopped, counted, and identified in a segmented, gas-filled ionization chamber downstream of the target. An elemental resolution of ΔZ = 1 was achieved with energy loss measurements from the anodes of the ionization chamber (fig. 1a). Protons from the reaction were detected in a large area silicon detector array (SIDAR) [9] covering the laboratory angular range of θlab = 105◦ –150◦ (θcm = 36◦ –11◦ ) in 16 strips. Coincidences between these protons and recoils in the ionization chamber indicate the states populated in the A = 83 nuclei.

The concurrent measurement of the 2 H(82 Se, p)83 Se reaction was a source of internal calibration as this reaction has been studied previously in normal kinematics [10]. The 83 Se data provided an upper limit of the excitation energy resolution that was achievable (ΔEx ≈ 300 keV). Further details of the analysis of this measurement are presented in [11]. The Q-value for the 2 H(82 Ge, p)83 Ge reaction is Q = 1.47 ± 0.02 stat. ± 0.07 sys. MeV; the first-excited state is populated at an excitation energy Ex = 280±20 keV. Proton angular distributions are consistent with  = 2 transfer to the ground state and  = 0 transfer to the first-excited state (fig. 2). Spin-parity assignments of J π = 5/2+ and J π = 1/2+ were made for the ground and first-excited states, respectively, based on the  transfer and energy level systematics of other even-Z, N = 51 isotones. Spectroscopic factors were also deduced for these two states from a DWBA analysis using global optical model parameters (see [11]). The values S = 0.48 ± 0.14 for the ground state and S = 0.50 ± 0.15 for the first-excited state have been reported [11], with the quoted uncertainties reflecting both statistical and systematic effects. The largest of the latter are a result of the ambiguities of the DWBA parameters used to describe the bound state of 83 Ge, a contribution to the uncertainty 25% of the value of S. 2.2 2 H(84 Se, p)85 Se The measurement of 85 Se was performed with a similar arrangement of beam conditions and detector positions as the 83 Ge measurement. One of the largest contributions to the overall energy resolution of final states is the energy lost by the beam as it passes through the target [11]. For

J.S. Thomas et al.: Single-neutron excitations in neutron-rich N = 51 nuclei 12

82

and a trace of other elements, as determined from energy loss measurements in the ionization chamber (fig. 1b). Protons were detected in SIDAR at backward laboratory angles (θlab = 105◦ –150◦ or θcm = 38◦ –12◦ ) and in an additional annular silicon detector covering θlab = 160◦ –170◦ (θcm = 8◦ –4◦ ). Coincidences between the protons and recoils in the ionization chamber, once again, determined the states populated in 85 Se. Figure 3 is a preliminary Q-value spectrum for the 2 H(84 Se, p)85 Se reaction showing at least 4 populated groups (ΔEx ≈ 220 keV) in 85 Se, including the ground and first-excited states.

83

Ge(d,p) Ge

10

8

dσ/dΩ (mb/sr)

373

6

4

l=2 l=0

2

0

5

10

15

20 25 θc.m. (deg.)

30

3 Discussion

35

40

Fig. 2. Proton angular distributions for the 2 H(82 Ge, p)83 Ge reaction. Filled squares represent the ground state (populated with  = 2), open triangles represent the first-excited state (populated with  = 0). The curves are DWBA calculations fit to the data yielding the spectroscopic factors (see text).

Vek 02/stnuoc

The measurement of 83 Ge is the first study of the lowlying level structure of this nucleus. Previously, the halflife (t1/2 = 1.85 s) was the only measured property [12]. The Q-value for the (d, p) reaction, when corrected for the binding energy of the deuteron, yields the neutron separation energy Sn (83 Ge) = 3.69 ± 0.07 MeV. The separation energy is also the Q-value for the (n, γ) reaction involving the same initial and final nuclei. The small Q-value for neutron capture on 82 Ge is actually lower than for any stable nucleus heavier than 15 N, suggesting direct neutron capture is a significant component to the 82 Ge(n, γ)83 Ge reaction rate. Since the mass of 82 Ge has been measured, the Q-value for the (d, p) reaction corresponds to an indirect measurement of the mass of 83 Ge, quoted first in [11] as a mass excess Δ(83 Ge) = −61.25 MeV ± 0.26 MeV. The large uncertainty in the measured 82 Ge mass (244 keV) leads to the large uncertainty of the derived mass. The energy levels of 85 Se have been identified in a previous study of gamma transitions following β decay of 85 As [13]. Tentative level assignments were made in that study based on log f t values and energy level systematics. Preliminary proton angular distributions from the present study support the J π = 5/2+ and J π = 1/2+ assignments to the ground and first-excited states, respectively [14]. The distributions also yield preliminary spectroscopic factors of S = 0.30 for the ground state and S = 0.35

Q-value (chan)

Fig. 3. The H( Se, p) Se reaction Q-value spectrum. 2

84

85

the 85 Se measurement, a higher beam energy and thinner target were used to reduce this effect. A 380 MeV (4.5 MeV/nucleon), isobaric A = 84 beam bombarded a 200 μg/cm2 CD2 target with an average intensity of 105 pps. Sulfur was not introduced in the beam production because Se is one of the elements that is reduced with the technique. The beam was composed of 92% Br, 8% Se,

Fig. 4. Energy level systematics for even Z, N = 51 isotones. The length of the shaded bars represents the fraction of the single-particle strength observed in a (d, p) reaction. (Dark gray: present work; light gray: from [15].)

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for the first-excited state with estimated uncertainties of 30% for each. Figure 4 is a summary of the single-particle properties of the first two states of the N = 51 isotones measured in this work, compared with other even Z, N = 51 isotones [15]. The striking decrease of the first 1/2+ state with respect to the 5/2+ state as protons are removed from the Z = 40 nucleus 91 Zr could be evidence of a significant monopole drift: as protons are removed from the 2f5/2 orbital beginning at 89 Sr, any attractive monopole residual interaction between the spin-flip, Δ = 1 pair of πf5/2 and νd5/2 orbitals would weaken, raising the νd5/2 relative to the νs1/2 . However, as fig. 4 shows, only about half of the single-particle strength was observed in the first two states for the most neutron-rich of these isotones. It is not clear that the effective single-particle energies (see, e.g., [2]) follow the same trend as the observed energy levels. In summary, these first (d, p) transfer measurements on two neutron-rich N = 50 nuclei inform the singleparticle structure “northeast” of doubly-magic 78 Ni. The ground and first-excited states of 83 Ge were observed for the first time, and level assignments were made based on proton angular distributions and energy level systematics. The mass of 83 Ge was measured indirectly through the reaction Q-value. The related neutron separation energy is low enough to suggest a strong direct capture component to the overall neutron capture reaction rate. The preliminary analysis of the populated states of 85 Se lends support to the tentative level assignments made in [13]. Together, the two measurements show a continued trend of a

decreasing 1/2+ state relative to the ground state in nuclei with increasing neutron-richness; however, additional theoretical work is needed to interpret this result.

References 1. T. Otsuka et al., Phys. Rev. Lett. 87, 082502 (2001). 2. N.A. Smirnova, A. De Maesschalck, A. Van Dyck, K. Heyde, Phys. Rev. C 69, 044306 (2004). 3. J.I. Prisciandaro et al., Phys. Lett. B 510, 17 (2001). 4. D.E. Appelbe et al., Phys. Rev. C 67, 034309 (2003). 5. J. Dobaczewski et al., Phys. Rev. C 53, 2809 (1996). 6. R. Surman, J. Engel, Phys. Rev. C 64, 035801 (2001). 7. T. Rauscher et al., Phys. Rev. C 57, 2031 (1998). 8. D.W. Stracener, Nucl. Instrum. Methods Phys. Res. B 204, 42 (2003). 9. D.W. Bardayan et al., Phys. Rev. C 63, 065802 (2001). 10. L.A. Montestruque et al., Nucl. Phys. A 305, 29 (1978). 11. J.S. Thomas et al., Phys. Rev. C 71, 021302 (2005). 12. J.A. Winger et al., Phys. Rev. C 38, 285 (1988). 13. J.P. Omtvedt, B. Fogelberg, P. Hoff, Z. Phys. A 339, 349 (1991). 14. J.S. Thomas et al., in Proceedings of the Eighth International Symposium on Nuclei in the Cosmos, edited by L. Buchmann, M. Comyn, J. Thompson, Nucl. Phys. A 758, 663 (2005). 15. M. Bhat, Evaluated Nuclear Structure Data File (SpringerVerlag, Berlin, Germany, 1992); data extracted using the NNDC ON-Line Data Service from the ENSDF database, file revised as of October 13, 2004.

Eur. Phys. J. A 25, s01, 375–376 (2005) DOI: 10.1140/epjad/i2005-06-054-8

EPJ A direct electronic only

High-spin shape isomers and the nuclear Jahn-Teller effect A. Odahara1,a , Y. Wakabayashi2,3 , T. Fukuchi3 , Y. Gono4 , and H. Sagawa5 1 2 3 4 5

Nishinippon Institute of Technology, Kanda, Fukuoka 800-0394, Japan Department of Physics, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan Center for Nuclear Study (CNS), University of Tokyo, Wako-shi, Saitama 351-0198, Japan RIKEN, Wako-shi, Saitama 351-0198, Japan University of Aizu, Aizu-Wakamatsu, Fukushima 965-8580, Japan Received: 14 November 2004 / Revised version: 26 January 2005 / c Societ` Published online: 6 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. High-spin isomers were systematically studied in N = 83 isotones. These isomers are of stretch coupled configurations and have oblate shapes. High-spin isomers can be categorized to be high-spin shape isomer, as they are caused by the sudden shape change from near spherical to an oblate shape. These isomers are considered to be a good example of the nuclear Jahn-Teller effect. By the systematic study of high-spin isomers, several results were obtained, such as (1) change of Z = 64 sub-shell gap energy and (2) experimental pairing gap energy at high-spin states. The Z = 64 sub-shell gap energy was found to decrease from 2.4 to 1.9 MeV as the proton number decreases from 64 to 60. Paring gap energies of high-spin states were experimentally extracted by the three-point expression using binding energies and excitation energies of high-spin isomers. These pairing gap energies at high-spin states are as large as those of the ground states, even though isomers have oblate shapes(β ∼ −0.19). PACS. 21.10.-k Properties of nuclei; nuclear energy levels – 27.60.+j 90 ≤ A ≤ 149

1 Introduction High-spin isomers in N = 83 isotones have been systematically studied [1]. Figure 1 shows the systematics of highspin isomers. Their spin-parities are 49/2+ and 27+ for odd and odd-odd nuclei, respectively. Life times of these isomers range between ∼ 10 ns and ∼ μs. High-spin isomers were theoretically studied using a deformed independent particle model(DIPM) [2]. Configurations of high-spin isomers are deduced experimentally and theoretically to be for odd nuclei and [ν (f7/2 h9/2 i13/2 ) π h211/2 ]+ 49/2 + 2 [ν (f7/2 h9/2 i13/2 ) π (d5/2 h11/2 )]27 for odd-odd nuclei. These isomers are of stretch coupled configurations and have oblate shapes.

(67/2,71/2) 10.286+x 420ns

49/2+ (49/2+) 8.989 + +) + (27 + ) (27 + ) 8.786 (27 ) 8.649 49/2 8.588 35ns 8.620 ( 49/28.523 8.597 0.96 μ s 10ns 1.310μ s >2 μ s 510ns 28ns

27ns 27/2- 3.582 4.4ns 21/2+2.760

5.750ns 13/2+1.228

2 High-spin shape isomers The deformation parameter β values of yrast states obtained by using the DIPM calculation are shown in fig. 2 as a function of spin. Filled squares and open circles indicate the β values for 145 Sm and 147 Gd, respectively. The experimental deformation parameters of the 13/2+ , 27/2− and 29/2+ isomers in 147 Gd were deduced from the quadrupole a

Conference presenter; e-mail: [email protected]

8.033+y 751ns

11-

84ns 0.5s ( 27/2- ) 2.661 (17 +) 2.625+y 27/2- 0.6s 2.586

4.5ns 1.769

18ns + 10ns 12.5ns 22ns + 22ns 11- 1.096 13/2+ 1.073 (11- ) 1.096+y13/2 1.140 235 μ s13/2 0.997 + 7 + 4.5ns 0.328 9 0.666 4- 80ns 0.110 + 9+ 23.3s y stable - 23.5s 363d - 4.23m (2,3) - 340d - 4.59d 7/2- 38.1h 9- 2m 0.090 7/20 50 72s x 7/2 0 0 0 2 0 60m 7/2 0 4 0 7/2 149 150 151 143 144 145 146 147 148 66 Dy 67 Ho 68 Er 60 Nd 61 Pm 62 Sm 63 Eu 64 Gd 65 Tb 14ns 0.71 μ s 13/2+1.105 9 + 0.841

Fig. 1. Systematics of high-spin isomers in N = 83 isotones [1].

moments [3]. Experimental values are shown by cross points. They were well reproduced by the DIPM calculation. The β values of the DIPM calculation are nearly

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Fig. 2. Deformation parameters β of yrast states as a function of spin.

Fig. 4. Paring gap energies at high-spin isomeric and ground states.

isotones with 60 ≤ Z ≤ 66, as shown in fig. 1. However, theoretical ones calculated by DIPM increase as the proton number decreases. In order to reproduce the experimental values, calculations were made by changing the Z = 64 proton sub-shell gap energies between 2d5/2 and 1h11/2 orbits. As a result, these gap energies decreases from 2.4 to 1.9 MeV as the proton number decreases from 64 to 60. This shows the softness of the Z = 64 sub-shell closure. Fig. 3. Deformation dependence of total energy for culated by DIPM.

147

Gd cal-

−0.05 below the spin of 49/2. However, these values above this spin are larger than −0.16. This indicates that highspin isomer may be caused by the sudden shape change from near spherical to oblate shape. Therefore, these isomers could be categorized to be high-spin shape isomers. It is considered that high-spin isomers maybe a good example of nuclear Jahn-Teller effect. Figure 3 shows the deformation dependence of total energy for 147 Gd calculated by DIPM. The mixing amplitude of two wave functions with different shapes was experimentally deduced to be ∼ 10−2 from the reduced transition probability of the transition directly deexciting the high-spin isomer. As this value is so small, their coupling is weak. The DIPM calculation reproduces well this weak coupling.

3 Systematic study of high-spin isomers Systematic study of high-spin isomers in N = 83 isotones gave several results, such as a change of Z = 64 sub-shell gap energy and experimental paring gap energies for highspin states. 3.1 Z = 64 sub-shell gap The experimental excitation energies of high-spin isomers are almost constant between 8.5 and 9.0 MeV for N = 83

3.2 Paring gap energy for high-spin isomeric states Pairing gap energies at high-spin isomeric states were experimentally deduced from the binding energies as well as excitation energies of high-spin isomers based on the three-point expression [4]. Figure 4 shows the extracted pairing gap energies at high-spin states (filled squares) and ground states (open circles). It was found that the pairing energies at high-spin states are as large as those of the ground states, although the high-spin isomers have oblate shapes of β ∼ −0.19.

4 Summary Systematic studies for high-spin isomers were carried out experimentally and theoretically. Paring gap energy at high-spin states deduced experimentally are as large as those of ground states.

References 1. Y. Gono et al., Eur. Phys. J. A 13, 5 (2002) and references therein. 2. T. Døssing et al., Phys. Scr. 24, 258 (1981). 3. O. H¨ ausser et al., Nucl. Phys. A 379, 287 (1982); E. Dafni et al., Nucl. Phys, A 443, 135 (1985). 4. W. Satula et al., Phys. Rev. Lett. 81, 3599 (1998).

Eur. Phys. J. A 25, s01, 377–379 (2005) DOI: 10.1140/epjad/i2005-06-047-7

EPJ A direct electronic only

Identification of mixed-symmetry states in odd-A

93

Nb

C.J. McKay1 , J.N. Orce1,a , S.R. Lesher1 , D. Bandyopadhyay1 , M.T. McEllistrem1 , C. Fransen2 , J. Jolie2 , A. Linnemann2 , N. Pietralla2,3 , V. Werner2 , and S.W. Yates1,4 1 2 3 4

Department of Physics & Astronomy, University of Kentucky, Lexington, KY 40506-0055, USA Institut f¨ ur Kernphysik, Universit¨ at zu K¨ oln, 50937 K¨ oln, Germany Nuclear Structure Laboratory, Department of Physics & Astronomy, SUNY, Stony Brook, NY 11794-3800, USA Department of Chemistry, University of Kentucky, Lexington, KY 40506-0055, USA

Erratum article: Eur. Phys. J. A 25, s01, 773 (2005) DOI: 10.1140/epjad/i2005-06-211-1 Received: 18 October 2004 / c Societ` Published online: 3 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The low-spin structure of 93 Nb has been studied using the (n, n γ) reaction at neutron energies ranging from 1.5 to 2.6 MeV and the 94 Zr(p, 2nγ)93 Nb reaction at bombarding energies from 11.5 to 19 MeV. Excitation functions, lifetimes, and branching ratios were measured, and multipolarities and spin assignments were determined. The J π = 3/2− and 5/2− states at 1840 and 2013 keV, respectively, are identified as mixed-symmetry states associated with the (2+ 1,ms ) ⊗ 2p1/2 particle-core coupling. These assignments are in agreement with energy systematics, spins and parities, and the observed strong M 1 transitions to the 2p1/2 one-phonon structure. PACS. 21.10.Re Collective levels – 21.10.Tg Lifetimes – 25.20.Dc Photon absorption and scattering – 27.60.+j 90 ≤ A ≤ 149

Mixed-symmetry (MS) states can be viewed as lowenergy collective modes in which protons and neutrons move uncoupled relative to each other. These collective excitations were first identified at about 3 MeV in the rotational nucleus, 156 Gd [1], where the large B(M 1; 1+ → + scissor mode excitation 0+ gs ) was associated with the 1 predicted by Lo Iudice and Palumbo [2] and soon after discovered in a wider range of deformed nuclei [3]. In the vibrational U (5) limit of the IBM-2, the lowest + MS state has J π = 2+ 1,ms , and is coupled to the first 21 phonon structure by an M 1 isovector transition (unlike isoscalar transitions between fully symmetric states). MS states have been identified at a rather constant energy of about 2 MeV in the so-called vibrational A ∼ 110 region [4,5]. Recently, new species of two-phonon MS states have been discovered [6, 7] in the nearly spherical even N = 52 isotones, indicating that the one-phonon 2+ 1,ms state acts as a building block of vibrational nuclear struc+ ture. In particular, in 92 40 Zr, the MS state (21,ms ) has been + identified as the 22 state at 1.847 MeV, with a strong + 2 B(M 1; 2+ 1,ms → 21 ) = 0.46(15) μN and a weakly col+ + lective B(E2; 21,ms → 01 ) = 3.7(8) W.u. [8]. In 94 42 Mo, + MS state has been identified as the 2 state at the 2+ 1,ms 3 a

Conference presenter; e-mail: [email protected]

2.067 MeV. It also displays a strong M 1 transition with + 2 B(M 1; 2+ 1,ms → 21 ) = 0.56(5) μN and a weakly collec+ tive E2 transition with B(E2; 21,ms → 0+ 1 ) = 2.2 W.u. [9]. From systematics, MS states in the odd-Z N = 52 isotone, 93 41 Nb, are expected at similar excitation energies as their even-Z, N = 52 isotone neighbors with feeding of the symmetric one-phonon structures coupled to the low-lying 1g9/2 and 2p1/2 single-particle states. We have identified, for the first time in a nearly spherical odd-A nucleus, MS states from M 1 strengths, energy systematics, and spin and parity assignments. The nucleus 93 Nb was studied using the (n, n γ) reaction at the University of Kentucky and the 94 Zr(p, 2nγ)93 Nb reaction at the University of Cologne. Figure 1 shows the partial level scheme of interest for 93 Nb. One of the proposed MS states in 93 Nb, the 1840 keV level, has been identified from excitation function and coincidence data in the current work and assigned as a J π = 3/2− state by the analysis of the angular correlation between the 1153 and 656 keV transitions depopulating states at 1840 and 687 keV, respectively (3/2− → 3/2− → 1/2− ). As shown at the bottom of fig. 2, a mean life of 26(4) fs has been measured for the 1840 keV state through the Doppler-shift attenuation method following the (n, n γ) reaction [10]. Here, the shifted γ-ray energy is given by Eγ (θγ ) = Eγ0 [1 + vc0 F (τ ) cos θγ ], with Eγ0 being the

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mixed-symmetry states

5/2 ms 3/2 ms

1840

+0.59

0.79-0.41

0.94(2)

1326

5/2 3/2

124

1153

0.62(14) 1030

811 687

1-phonon 780

656 31

1/2

2p 1/2 Fig. 1. 93 Nb partial level scheme showing the 2p1/2 singleparticle, 1-phonon, and mixed-symmetry structures. M 1 strengths in μ2N are given for decays depopulating MS states. 1327

2013 keV state 1326.5

E(n) = 2.6 MeV

Energy (keV)

1326 +29

τ= 30-12 fs

1325.5 1325 1154

1840 keV state 1153.5

E(n) = 2.1 MeV

1153

τ = 26(4) fs 1152.5 1152

-1

-0.5

0

0.5

1

cos θ

Fig. 2. Lifetime of the 1840 (bottom) and 2013 keV (top) levels from the Doppler-shift attenuation method at different neutron energies [10]. The fits to the experimental data give lifetimes of 30+29 −12 fs and 26(4) fs, respectively, for these levels.

unshifted γ-ray energy, v0 the initial recoil velocity in the center of mass frame, θ the angle of observation and F (τ ) the attenuation factor, which is related to the nuclear stopping process described by Blaugrund [11]. The 1030 and 1153 keV transitions depopulating this state to the 2p1/2 one-phonon structure present branching ratios of 49(4) and 100(4), respectively, and mixing ratios, δ, of −0.23(7) and −0.13(6), respectively. Hence, the 1030 keV transition has a B(M 1) value of 0.62(14) μ2N and a B(E2) strength of 18(4) W.u., while the 1153 keV transition presents similar properties with an even stronger B(M 1) value of 0.94(2) μ2N and B(E2) = 6.9(2) W.u. The other proposed MS state at 2013 keV is also identified from excitation function and coincidence data in the current work. The angular correlation of the 1326 and 656 keV transitions (5/2− → 3/2− → 1/2− ) confirms its assignment as J π = 5/2− . From the angular correlation, the mixing ratio of the 1326 keV transition is determined as δ = −0.14(5). A mean life of 30+29 −12 fs has been mea-

sured for this state (as shown at the upper panel of fig. 2), +2.5 2 giving B(M 1) = 0.79+0.59 −0.41 μN and B(E2) = 4.9−3.5 W.u. This enhanced M1 strength supports its assignment as the 5/2− ms MS state in spite of the large uncertainty of the lifetime. In fact, the B(M 1) values from the MS states are greater than from any other negative-parity states feeding the one-phonon structure, with the exception of a 1289 keV transition depopulating the 7/2− state at 2099 keV, which has a B(M 1) value of 0.62(17) μ2N and a weak B(E2) of 1.2(3) W.u. However, the assignment of this state as a J π = 7/2− prevents it from being part of the (2+ 1,ms )⊗2p1/2 particle-core coupling. This observation, together with the fact that transitions from other levels in the region are predominantly E2, support the assignment of the 1840 and 2013 keV states as MS states. Indeed, these other negative-parity states with E2 character might be part of the 2-phonon symmetric quadrupole structure. According to the IBM-2, even-even nuclei in the vibrational U (5) limit present an M 1 transition strength from the one-phonon 2+ MS state (2+ 1,ms ) to the one-phonon + + fully symmetric 21 state given by, B(M 1; 2+ 1,ms → 21 ) = 3 2 Nν Nπ 2 4π (gν − gπ ) 6 N 2 μN [12]; where N = Nπ + Nν and the standard boson g-factors, gπ and gν , are gπ = 1 for protons and gν = 0 for neutrons. Considering the lowest MS state in 94 Mo and 88 38 Sr50 as the inert core [13], the proton and neutron boson numbers are Nπ = 2 and Nν = 1, − 2 giving B(M 1; 2+ ms → 21 ) = 0.32 μN . In the weak coupling limit, the IBFM predicts that the − strength of B(M 1; 2+ ms → 21 ) in the IBM-2 should equal 93 the strength  of the sum of B(M 1)’s for MS states in Nb, that is, J B(M 1; 1 − phononMS , J → 1 − phonon, J  ); − ) = 0.62(14) μ2N giving  B(M 1; MS → 1 − phonon, 5/2 − and B(M 1; MS → 1 − phonon, 3/2 ) = 1.73(59) μ2N , respectively, both exceeding the schematic U (5) estimate from above. However, the M 1 strength from the 5/2− ms + state equals within the errors the 2+ 1,ms → 21 M 1 strength found in the even isotone 94 Mo [9]. The M 1 strength from 94 Mo the 3/2− ms state is still larger than the value found in (although with large uncertainties). This might be due to the spin contribution of the unpaired proton to the M 1 strength which is absent in the IBM-2 for even-even nuclei. Shell model calculations are being carried out in order to quantify the spin contribution to the M 1 transitions in 93 Nb and for understanding the large B(M 1) values found for the 3/2− ms state, or that one of the anomalous 1289 keV transition. Finally, the quintuplet of MS states associated with the (2+ 1,ms ) ⊗ 1g9/2 particle-core coupling has not yet been identified.

References 1. D. Bohle et al., Phys. Lett. B 137, 27 (1984). 2. N. Lo Iudice, F. Palumbo, Phys. Rev. Lett. 41, 1532 (1978). 3. S.A.A. Eid et al., Phys. Lett. B 166, 267 (1986). 4. P.E. Garrett et al., Phys. Rev. C 54, 2259 (1996). 5. D. Bandyopadhyay et al., Phys. Rev. C 67, 034319 (2003). 6. N. Pietralla et al., Phys. Rev. Lett. 83, 1303 (1999).

C.J. McKay et al.: Identification of mixed-symmetry states in odd-A 7. 8. 9. 10.

C. V. C. T.

Fransen et al., Phys. Lett. B 508, 219 (2001). Werner et al., Phys. Lett. B 550, 140 (2002). Fransen et al., Phys. Rev. C 67, 024307 (2003). Belgya et al., Nucl. Phys. A 607, 43 (1996).

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Nb

379

11. A.E. Blaugrund, Nucl. Phys. 88, 501 (1966). 12. P. Van Isacker et al., Ann. Phys. (N.Y.) 171, 253 (1986). 13. A.F. Lisetskiy et al., Nucl. Phys. A 677, 100 (2000).

6 Excited states 6.2 Coulomb excitation of radioactive ion beams

Eur. Phys. J. A 25, s01, 383–387 (2005) DOI: 10.1140/epjad/i2005-06-205-y

EPJ A direct electronic only

Coulomb excitation and transfer reactions with neutron-rich radioactive beams D.C. Radford1,a , C. Baktash1 , C.J. Barton2,b , J. Batchelder3 , J.R. Beene1 , C.R. Bingham1,4 , M.A. Caprio2 , M. Danchev4 , B. Fuentes1,5 , A. Galindo-Uribarri1 , J. Gomez del Campo1 , C.J. Gross1 , M.L. Halbert1 , D.J. Hartley4,c , P. Hausladen1 , J.K. Hwang6 , W. Krolas4,6 , Y. Larochelle1,4 , J.F. Liang1 , P.E. Mueller1 , E. Padilla1,7 , J. Pavan1 , A. Piechaczek8 , D. Shapira1 , D.W. Stracener1 , R.L. Varner1 , A. Woehr3 , C.-H. Yu1 , and N.V. Zamfir2,d 1 2 3 4 5 6 7 8

Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA A.W. Wright Nuclear Structure Laboratory, Yale University, New Haven, CT 06520, USA UNIRIB, Oak Ridge Associated Universities, Oak Ridge, TN 37831, USA Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA Facultad de Ciencias, UNAM, 04510, D.F., Mexico Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, USA Instituto de Ciencias Nucleares, UNAM, 04510, D.F., Mexico Louisiana State University, Baton Rouge, LA 70803, USA Received: 1 February 2005 / Revised version: 31 March 2005 / c Societ` Published online: 12 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Neutron-rich radioactive ion beams available from the HRIBF allow a variety of measurements around the 132 Sn region, including Coulomb excitation and single-nucleon transfer. The B(E2; 0 + → 2+ ) values for first 2+ excited states of even-even neutron-rich 132–136 Te and 126–130 Sn have been measured by Coulomb excitation in inverse kinematics. Neutron transfer onto a 134 Te beam from 9 Be and 13 C targets, to populate single-particle states in 135 Te, has also been studied. Gamma rays from the 13 C(134 Te, 12 C) reaction were used to identify the νi13/2 state in 135 Te, at an energy of 2109 keV. These and other results, and plans for future experiments with these neutron-rich beams, are presented. PACS. 21.10.Ky Electromagnetic moments – 21.10.Pc Single-particle levels and strength functions – 25.70.De Coulomb excitation – 25.70.Hi Transfer reactions

1 Introduction At the Holifield Radioactive Ion Beam Facility (HRIBF), located at Oak Ridge National Laboratory (ORNL), heavy neutron-rich fragments from proton-induced fission in a uranium carbide target are extracted, ionized and charge-exchanged, and then injected into a 25 MV tandem electrostatic accelerator. This provides post-accelerated beams of over 100 radioactive species with at least 1000 ions per second on target; intensities for some beams are as high as 108 ions per second. In general, the beams are isobarically contaminated, i.e., contain significant numbers of other nuclear species with the same mass. However, chemical techniques [1] can produce isobarically pure beams of a few selected elements, including Sn and Ge. a

Conference presenter; e-mail: [email protected] Present address: Department of Physics, University of York, York YO12 5DD, UK. c Present address: United States Naval Academy, Annapolis, MD 21402, USA. d Present address: National Institute for Physics and Nuclear Engineering, Bucharest, Romania. b

These neutron-rich radioactive ion beams (RIBs) open exciting possibilities for a wide range of new spectroscopic studies around doubly-magic 132 Sn, including B(E2) measurements through Coulomb excitation in inverse kinematics, γ-ray spectroscopy following fusion-evaporation reactions, and neutron- and proton transfer reactions to investigate single-particle states. Experiments using these beams also provide an excellent training ground for developing techniques to be used at the future high-intensity Rare Isotope Accelerator facility, RIA. These novel experiments, however, involve significant technical and experimental challenges. Even a small fraction of stopped or scattered radioactive beam close to the target can generate large backgrounds of γ and β radiation in γ-ray and chargedparticle detectors. Good beam quality, such as provided by the HRIBF tandem accelerator, is therefore crucial. The low beam currents of these radioactive species implies that γ and γ-γ coincidence rates from induced reactions are small compared to background. A selective trigger for the events of interest is thus of vital importance. The heavy beam, coupled with the light targets required for most

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Pure 130Sn beam

130

+

Sn 2 1221 keV

12 8 4

2 2 Table 1. B(E2; 0+ → 2+ 1 ) values (e b ) measured in the present work, compared with shell-model [2, 7] (SM) and Quasiparticle Random Phase Approximation [8] (QRPA) calculations. The results for the Sn isotopes are preliminary.

Counts

0 60

Nuclide Pure 128Sn beam

128

+

Sn 2 1169 keV

40

126

Sn Sn 130 Sn

0 1600

132

Te Te 136 Te

128

Te 2

1200

+ 128

800

Sn 2+

QRPA [8]

0.069 0.034 0.007

0.172(17) 0.096(12) 0.103(15)

134

Mixed A = 128 beam

SM [2, 7]

0.10(3) 0.073(6) 0.023(5)

128

20

This work

0.15 0.08 0.16

0.131 0.072 0.091

400 0 600

1000

1400

Xe

(keV)

Fig. 1. Spectra of γ-rays from Coulomb excitation of 128,130 Sn + beams using CLARION. 2+ transitions are labeled. 1 → 0

experiments, yields excited nuclei with high recoil velocities, typically ∼ 0.07c. This, in turn, generates significant Doppler broadening for γ-rays. A related problem is the extreme kinematic broadening of light-ion energies from inverse-kinematics transfer reactions close to the Coulomb barrier.

2 Coulomb excitation measurements with CLARION We have developed a novel method [2] for measuring Coulomb excitation of RIBs, in which scattered target nuclei are detected at forward angles, and used both as a clean trigger for selecting γ-rays from the Coulombexcited beam and to normalize to the integrated beam current through Rutherford scattering. This technique was first applied to measure the B(E2; 0+ → 2+ 1 ) values for the first-excited 2+ states of neutron-rich 132,134,136 Te and 126,128 Sn. Energetic carbon nuclei, from collisions of the beam in a natural carbon target, were detected in the HyBall array [3] of 95 CsI crystals. Gamma rays, detected by the segmented clover Ge detectors of the CLARION array [4], were recorded along with the HyBall data whenever they were in coincidence. The high 2+ energies and low B(E2) values yield low cross-sections for excitation, which together with the weak beam makes these experiments challenging. The Te results have been reported in ref. [2]. A measurement for the 132,134 Te beams also been performed at the HRIBF by Barton et al. [5] using a different method. More recently, B(E2; 0+ → 2+ 1 ) measurements were made for 128,130 Sn beams [6], using the new isotopically purified beams formed from molecular SnS+ [1]. Beam intensities were about 3 × 106 s−1 and 5 × 105 s−1 , respectively. The Sn ions were primarily in their 0+ ground states, but 8.5% and 11% were in the metastable 7− state for 128 Sn and 130 Sn, respectively. Isobars of

2+) (e2b2)

E

B(E2; 0+

200

Ba

0.5

Ce

Te

0.3

Sn

0.1

70

74

78

82

86

Neutron Number Fig. 2. Values of B(E2; 0+ → 2+ 1 ) for even-even Sn, Te, Xe, Ba and Ce isotopes around neutron number N = 82. Open symbols are adopted values from ref. [9] while filled symbols are from the present work (132–136 Te, 126–130 Sn) or from Varner et al. [10] (132,134 Sn). The thick shaded dotted lines show the results of QRPA calculations by Terasaki et al. [8].

other elements made up less than 1% of these two beams. Since the uncertainties in the measurements made using cocktail beams are dominated by the uncertainty in the beam composition, use of these purified beams results in a significantly higher precision. Spectra of γ-rays from 128,130 Sn, gated by prompt coincidence with carbon recoils and Doppler-shift corrected, are shown in fig. 1. Also shown for comparison is a corresponding spectrum from an earlier experiment on the isobar “cocktail” A = 128 beam, ∼ 14% of which was 128 Sn. Absolute γ-ray efficiencies were measured using 60 Co and 152 Eu sources, and corrected for Doppler shifts and for the modified solid angle of the Ge detectors in the frame of the γ-emitting recoils. Using these efficiencies and the ratios of coincidence to singles yields, we can extract a ratio of Coulomb-excitation to Rutherfordscattering cross-sections. These same cross-section ratios

D.C. Radford et al.: Coulomb excitation and transfer reactions with neutron-rich radioactive beams

385

i13/2 Sn f5/2 p1/2 h9/2

f5/2 p1/2 11/2 = f7/2 2 h9/2

p3/2

p3/2

i13/2

f7/2

f7/2 133

135 137 139 141 145 Sn Te Xe Ba Ce 143Nd Sm Fig. 3. Systematics of single-neutron level energies in N = 83 nuclei.

were then calculated using the Winther-DeBoer code to extract the B(E2) values. Final values for the B(E2) of Te isotopes, and preliminary values for Sn isotopes, are listed in table 1. They are also displayed together with the B(E2) systematics for this mass region in fig. 2. Also shown in fig. 2 are the results from Varner et al. [10] for the Coulomb excitation of 132 Sn and 134 Sn, using the ORNLMSU-TAMU BaF2 array at the HRIBF. It was expected from shell-model calculations [7] and systematics that the B(E2) value for 136 Te would conform to the symmetry about neutron number N = 82 exhibited by Ba, Ce and other heavier nuclei, and be similar to the value for 132 Te. Instead, the 136 Te value is significantly smaller, close to that of 134 Te. We also point out the different excitation energies of 2+ 1 states in Sn and Te isotopes across N = 82. There is a significant drop in the 2+ 1 energy for both 134 Sn (725 keV) and 136 Te (606 keV) as compared to their N = 80 isotopes (1221 and 974 keV, respectively.) Recently, a series of Quasiparticle Random Phase Approximation (QRPA) calculations have been performed by J. Terasaki et al. [8]. The excitation energy asymmetry in Sn and Te and the B(E2) asymmetry in Te are both well reproduced in these calculations, as is the B(E2) symmetry in heavier elements. The reduced N = 84 Sn and Te 2+ energies arise in the calculation primarily as a result of the small neutron monopole pairing gap extracted from observed odd-even mass differences. This reduces the energy required to break the neutron pair to form a 2+ state, relative to that required for the proton pair. Thus, the mixed 2+ 1 state is calculated to be of predominately 2ν character, with a low B(E2) value. Results from these calculations are shown as the thick shaded dotted lines in fig. 2.

3 Single-neutron transfer reactions Energies of single-particle states in odd-mass, near-magic nuclei are vital quantities for nuclear models, either as tests of large-scale shell model calculations or as input to more empirical models. This is especially true close to doubly magic nuclei, such as 132 Sn.

Until recently, the i13/2 level in the N = 83 isotones was known only for 139 Ba and heavier; it had not been identified in 137 Xe or 135 Te, and is believed to lie above the neutron-separation threshold in 133 Sn [11]. All these nuclei have f7/2 ground states, and all have levels previously assigned as p3/2 , p1/2 , h9/2 and f5/2 single-neutron excited states. The systematics of these levels are shown in fig. 3. We have investigated the inverse-kinematics neutron transfer reactions 9 Be(134 Te,8 Be) and 13 C(134 Te,12 C) leading to 135 Te, using a 134 Te beam on nat Be and 13 C targets, at energies just above the Coulomb barrier. The Be-target data are strikingly clean; the immediate disintegration of the unstable 8 Be produces correlated α-particle pairs, which are detected in single elements of the HyBall array. This in turn provides a very clean trigger for coincident γ-rays. The C spectrum is significantly less clean than that from the Be target, due to the lack of isotopic sensitivity in the particle detectors. Inelastic excitation to the 2+ and neutron stripping to 133 Te are the dominant contaminants. Spectra from a preliminary investigation of these reactions have been reported in ref. [6]. More recently, we have performed a second, higherstatistics experiment at the HRIBF, with these same two reactions, in an attempt to identify the νi13/2 level in 135 Te. The 134 Te beam had an intensity of about 2 × 106 ions per second, and an energy of 4.3 MeV per nucleon. Light charged ions from the reaction were detected in the new ORNL “Bare HyBall” array of CsI detectors, and coincident gamma rays were detected in the CLARION array. From systematics, the νi13/2 level was expected at a little above 2 MeV in excitation. It was also expected to γ-decay to the known 11/2− state at 1180 keV; we therefore searched for γ-γ coincidences between the 1180 keV transition and a new transition at around 800–1000 keV. The resulting γ-ray spectra are shown in fig. 4; the lowest part shows the spectrum from the Be target, gated by pairs of α-particles, and the upper parts show data gated by carbon ions from the 13 C target. Transitions from previously assigned states [12] are clearly visible, and are labeled by γ-ray energy and level assignment. Also visible in the 13 C spectrum is a new transition at 929 keV. The top two spectra in fig. 4 show γ-γ coincidence spectra from

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The European Physical Journal A 7 5 3 1 7 5 3 1 1100

Gate 929

1180 11/2-

929 i13/2 11/2-

308 Te 1/2+

900

Gate 1180

657 p3/2

133

13

700 500

424 p1/2 p3/2

300

929 i13/2 11/2-

C(134Te, C)

1279 134 Te 2+ 1180 11/2-

100 250

657 p3/2

424 p1/2 p3/2

9

150

Be(134Te, 8Be)

1127 f5/2

50 200

600

1000

E

1400

(keV)

Fig. 4. Gamma-ray spectra from the neutron transfer experiment with 134 Te on nat Be and 13 C targets. The spectra are gated by coincidence with α-particle pairs (Be target, lowest part) or carbon ions (13 C target, upper parts) detected in the “Bare HyBall” array. The two top panels show the gated γ-γ coincidence spectra from the carbon target that were used to determine the feeding of the 11/2− state (1180 keV) by the new 929 keV transition.

the 13 C target, gated on this new transition, and on the 1180 keV transition depopulating the 11/2− state. Clearly these two lines are in coincidence, leading us to assign a new level at 2109 keV in 135 Te. Gamma-carbon angularcorrelation measurements confirm that the 929 keV transition is of stretched dipole or unstretched quadrupole character, and is emitted from a state with angular momentum strongly aligned perpendicular to the reaction plane. The alignment of the i13/2 should indeed be large, due to the large transferred angular momentum (L = 7) required to populate it from the p1/2 initial state in 13 C. The new level, at an excitation energy of 2109 keV, is therefore assigned as the νi13/2 state in 135 Te, and is included as the heavy line in fig. 3. There is no simple way to extract absolute cross-sections for the the population of observed levels in this experiment. It is however possible to determine the relative cross-sections for the various excited states, from an analysis of the γ-ray intensities. The results of such an analysis, normalized to the cross-section for the p3/2 level at 659 keV, are presented in table 2. Feeding of low-lying levels by transitions from higher-lying levels, when known, was subtracted; such feeding was also searched for using the γ-γ coincidence data. The errors quoted in table 2 allow for estimates of the systematic uncertainty in this procedure. Also shown in table 2 are the ratios of calculated cross-sections, obtained using the finite-range DWBA code PTOLEMY [13]. With the exception of the 1180 keV 11 − level, the calculations show good agreement with ex2 periment, both in terms of the overall trends and in the

Table 2. Relative cross-sections observed and calculated for the 13 C(134 Te,12 C) and 9 Be(134 Te,8 Be) single-neutron transfer reactions leading to levels in 135 Te. See text for details.

Energy

Level

(keV)

13

C(134 Te,12 C)

9

Be(134 Te,8 Be)

Expt

DWBA

Expt

DWBA

p3/2

659

≡1.00(8)

≡1.00

≡1.00(7)

≡1.00

p1/2

1083

0.22(2)

0.193

0.92(4)

0.452

f5/2

1126

0.17(3)

0.181

0.59(4)

0.603

11 − 2

1180

0.13(5)

[0.536]

0.22(2)

[0.089]

(h9/2 )

1246

0.042(12)

0.023

0.054(13)

0.086

i13/2

2109

0.22(2)

0.335

0.04(3)

0.056 −

level is relative strengths for the two reactions. The 11 2 known to arise from a fully aligned coupling of the 2+ − quadrupole phonon with the 72 ground state. Since such a configuration cannot easily be accomodated in the DWBA − level was done assuming an code, calculation for the 11 2 h11/2 configuration instead. This is not expected to produce realistic results, but the calculated ratios are listed in table 2 for the sake of completeness.

4 Plans for future measurements The variety and high intensity of these neutron-rich beams holds the potential for a large variety of new experiments. Some of the approved experiments planned for the near

D.C. Radford et al.: Coulomb excitation and transfer reactions with neutron-rich radioactive beams

future include a measurement of the static quadrupole moment of the first 2+ state in 126 Sn through the Coulombexcitation reorientation effect. In single-particle transfer reaction studies, we plan to investigate sub-Coulomb transfer of single neutrons on a doubly magic 132 Sn beam, and attempt to extract quantitative spectroscopic information from asymptotic normalization coefficients. Targets of nat Be and 13 C would again be used for these studies. In addition, using the possible (7 Li,8 Be) proton-pickup reaction, and/or other similar reactions, we hope to search for the unobserved πs1/2 state in 133 Sb and πp3/2 , πf5/2 hole states in 131 In. We will also identify the νi13/2 single-neutron level in 137 Xe, using the 13 C(136 Xe,12 C)137 Xe reaction at the Argonne National Laboratory’s ATLAS facility, with Gammasphere and the Microball as detector systems. A longer-term goal is the measurement of spectroscopic factors in light-ion transfer reactions such as (d, p) and (3 He, d), but again measured in inverse kinematics. The major difficulty for these studies is the low beam energy available at the HRIBF for beams close to 132 Sn, in practice limited to less than 5 MeV per nucleon. The low energy results in rather featureless angular distributions. Furthermore, drastic kinematic broadening results in a poor Q-value resolution that makes it difficult or impossible to identify the populated state based on the detected light-ion energy alone. We are exploring possible avenues to alleviate these difficulties, including use of the Spin Spectrometer to identify final states using particlegamma coincidences and gamma calorimetry.

5 Conclusion B(E2; 0+ → 2+ ) values for neutron-rich 132,134,136 Te and 126,128,130 Sn isotopes have been measured by Coulomb excitation of radioactive ion beams in inverse kinematics. The results for 132 Te and 134 Te (N = 80, 82) show excellent agreement with systematics of lighter Te isotopes, but the B(E2) value for 136 Te (N = 84) is unexpectedly small. QRPA calculations [8] suggest that this anomaly is linked to weak neutron pairing in 136 Te. The value for 130 Sn is very small, around 1.4 single-particle units. We have also been able to observe neutron transfer to single-particle levels in 135 Te through the detection of γ-ray transitions in coincidence with target-like residues.

387

The 13 C(134 Te, 12 C) reaction was used to identify the νi13/2 state in 135 Te, at an energy of 2109 keV, by utilizing γ-γ-particle coincidences and particle-γ angular correlations. In addition, observed cross-section ratios agree well with DWBA calculations. This technique appears to be a promising tool in the search for more new levels, and possibly also for determining quantitative spectroscopic information. We gratefully acknowledge very helpful discussions with W. Nazarewicz, A. Stuchbery, I. Hamamoto, A. Covello, K. Heyde and J. Blomqvist. The outstanding efforts of the HRIBF operations staff in developing and providing the radioactive ion beams used for this work are greatly appreciated. Oak Ridge National Laboratory is managed by UTBattelle, LLC, for the U.S. D.O.E. under contract DE-AC0500OR22725. This work is also supported by the U.S. D.O.E. under contracts DE-AC05-76OR00033, DE-FG02-91ER-40609 and DE-FG02-88ER-40417.

References 1. D.W. Stracener, Nucl. Instrum. Methods Phys. Res. B 204, 42 (2003). 2. D.C. Radford et al., Phys. Rev. Lett. 88, 222501 (2002). 3. A. Galindo-Uribarri et al., to be published in Nucl. Instrum. Methods Phys. Res. 4. C.J. Gross et al., Nucl. Instrum. Methods Phys. Res. A 450, 12 (2000). 5. C.J. Barton et al., Phys. Lett. B 551, 269 (2003). 6. D.C. Radford et al., Nucl. Phys. A 746, 83c (2004). 7. A. Covello, private communication; see also A. Covello et al., in Challenges of Nuclear Structure, in Proceedings of the 7th International Spring Seminar on Nuclear Physics, edited by A. Covello (World Scientific, Singapore, 2002) p. 139. 8. J. Terasaki, J. Engel, W. Nazarewicz, M. Stoitsov, Phys. Rev. C 66, 054313 (2002). 9. S. Raman, C.W. Nestor jr., P. Tikkanen, At. Data Nucl. Data Tables 78, 1 (2001). 10. R.L. Varner et al., these proceedings. 11. See, for example, W. Urban et al., Eur. Phys. J. A 5, 239 (1999). 12. P. Hoff et al., Z. Phys. A 322, 407 (1989). 13. M. Rhoades-Brown, S.C. Pieper, M.H. McFarlane, PTOLEMY, unpublished; M.H. McFarlane, S.C. Pieper, ANL-76-11.

Eur. Phys. J. A 25, s01, 389–390 (2005) DOI: 10.1140/epjad/i2005-06-168-y

EPJ A direct electronic only

132

Te and single-particle density-dependent pairing

N.V. Zamfir1 , R.O. Hughes1,2 , R.F. Casten1,a , D.C. Radford3 , C.J. Barton4 , C. Baktash3 , M.A. Caprio1,5 , A. Galindo-Uribarri3 , C.J. Gross3 , P.A. Hausladen3 , E.A. McCutchan1 , J.J. Ressler1 , D. Shapira3 , D.W. Stracener3 , and C.-H. Yu3 1 2 3 4 5

Wright Nuclear Structure Laboratory, Yale University, New Haven, CT 06520, USA Department of Physics, University of Surrey, Guildford GU2 7XH, UK Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA University of York, Heslington, YO10 5DD UK Sloane Physics Laboratory, Yale University, New Haven, CT 06520, USA Received: 5 November 2004 / c Societ` Published online: 7 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. 132 Te has been studied through β − decay of 132 Sb radioactive beam at HRIBF leading to a significantly revised level scheme. A number of newly identified, likely 2 + states allows for a test of recent quasiparticle random phase approximation calculations with a density-dependent pairing force. In addition, the removal of a previously proposed 3− state allows for a simple shell model interpretation of the low-lying negative-parity states.

a

Conference presenter; e-mail: [email protected]

0

JS

1665

974

2

1665

+2 /

691

+3,4/

2764 2602 2488

823

+4,5/

937

Access to neutron-rich nuclei in the region around doubly magic 132 Sn at the Holifield Radioactive Ion Beam Facility (HRIBF) has revealed very interesting aspects of nuclear structure in this region. Coulomb excitation measurements [1, 2,3] have discovered anomalies in the structure of Te isotopes with N > 82. These were subsequently explained by Terasaki et al. [4] with new microscopic calculations involving a density-dependent pairing force. The nucleus 132 Te was populated in β − decay using a 396 MeV radioactive beam of 132 Sb with an intensity of ∼ 107 particles/s, embedded in a thick target. Gamma-ray coincidence spectroscopy was performed with the CLARION array [5] at the Holifield Radioactive Ion Beam Facility (HRIBF). The new data has led to a significantly revised γ-decay scheme. Partial results were published in ref. [6]. Many new transitions were observed and new levels proposed. A number of previous placements were found to be inconsistent with the new high quality coincidence data and several previously proposed levels were shown not to exist. Some of these changes also appear in the unpublished work of ref. [7]. New coincidence data allowed for the identification of a number of new states below 2500 keV. Four of these new levels, at 1665 keV, 1788 keV, 2249 keV, and 2364 keV, show a similar decay pattern. For example, the level at 1665 keV was identified on the basis of two depopulating and three populating transitions, illustrated in the partial

1098

PACS. 21.10.-k Properties of nuclei; nuclear energy levels – 21.60.Cs Shell model – 27.60.+j 90 ≤ A ≤ 149

974

0

Ex+keV/

Fig. 1. Partial level scheme for 132 Te highlighting those transitions involved in the identification of a new level at 1665 keV.

level scheme of fig. 1. A strong decay by a 691 keV transition to the 2+ 1 level and a weak 1665 keV transition to the 0+ 1 were observed. These decays were observed in coincidence with three strong populating transitions of 823 keV, 937 keV and 1098 keV. Coincidence spectra gated on the 823 keV feeding transition showing the depopulating transitions are given in fig. 2. The decay of the 1788 keV, 2249 keV and 2364 keV levels is similar, with each level

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Gate on 823 keV

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Counts

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2 2

+2 / 

100

+2 / 600

700

800

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E+keV/

0

2

+2 / +2 /

300

1000

Energy (keV) 15

Gate on 823 keV

2 2

1000

2

0

0

Counts

10

1665 5

132 0 1550

1600

1650

1700

1750

Energy (keV) Fig. 2. Spectra gated on the 823 keV feeding transition illustrating coincidences with 691 keV (top) and 1665 keV (bottom) transitions, providing evidence for a new level at 1665 keV. + observed to decay only to the 2+ 1 and 01 states. Assuming E1, M 1, or E2 de-excitation transitions, the decay properties restrict the spin assignment of these levels to 1± , 2+ . Since all available configurations place the 1± states quite high in energy [6], all 4 states are given a tentative spin assignment of 2+ . These results allow a test of very recent quasiparticle random phase approximation calculations [4] with a density-dependent pairing force that accounts for the anomalous violation of the Grodzins rule below and above N = 82 in the Te isotopes and provides an important new approach to shell model calculations in both stable and exotic nuclei. These calculations take account of the differing density of neutron single-particle levels below and above N = 82. However, this interpretation was developed to explain a previously known anomalous behavior. The newly identified 2+ energies provide an independent test of these calculations. In fig. 3, a comparison of the energies of the 2+ states with those predicted in the calculations of ref. [4] is presented. Overall, the agreement is very good: The correct number of low-lying 2+ levels is predicted and at approximately the observed energies. Another important result is the removal of a previously reported [8] 3− state at 2281 keV. The previous placement was based on three depopulating transitions from this + + level at 2281 keV to the 4+ 1 , 21 and 01 states. The new coincidence data show that all three γ-rays have the reported

0

Te

Th.

Fig. 3. Comparison of the low-lying 2+ states in the theoretical calculation of ref. [4].

132

Te with

intensities but, in fact, have different placements within the level scheme of 132 Te. (The lowest candidate for a 3− state is identified at 2488 keV.) A simple shell model analysis [6] leads to a simple interpretation of the structure − of the negative-parity states. The 7− 1 and 51 states are based on two-neutron configurations [8,9] and the 3− state could be the lowest member of the (1h11/2 , 2d5/2 ) twoproton multiplet. This work was supported by the U.S. Department of Energy under grants Nos. DE-FG02-91ER-40609, DE-FG02-91ER40608 and contract DE-AC05-00OR22725.

References 1. 2. 3. 4.

5. 6. 7. 8. 9.

D.C. Radford et al., Eur. Phys. J. A 15, 171 (2002). D.C. Radford et al., Phys. Rev. Lett. 88, 222501 (2002). C.J. Barton et al., Phys. Lett. B 551, 269 (2003). J. Terasaki, J. Engel, W. Nazarewicz, M. Stoitsov, Phys. Rev. C 66, 054313 (2002); J. Terasaki et al., private communication. C.J. Gross et al., Nucl. Instrum. Methods Phys. Res. A 450, 12 (2000). R.O. Hughes et al., Phys. Rev. C 69, 051303(R) (2004). R.A. Meyer, E.A. Henry, unpublished, private communication. A. Kerek, P. Carle, S. Borg, Nucl. Phys. A 224, 367 (1974). J. Sau, K. Heyde, R. Chery, Phys. Rev. C 21, 405 (1980).

Eur. Phys. J. A 25, s01, 391–394 (2005) DOI: 10.1140/epjad/i2005-06-128-7

EPJ A direct electronic only

Coulomb excitation measurements of transition strengths in the isotopes 132,134Sn R.L. Varner1,a , J.R. Beene1 , C. Baktash1 , A. Galindo-Uribarri1 , C.J. Gross1 , J. Gomez del Campo1 , M.L. Halbert2,b , P.A. Hausladen2 , Y. Larochelle3,c , J.F. Liang2 , J. Mas1 , P.E. Mueller1 , E. Padilla-Rodal2,4 , D.C. Radford1 , D. Shapira1 , D.W. Stracener1 , J.-P. Urrego-Blanco3 , and C.-H. Yu1 1 2 3 4

Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Joint Institute for Heavy Ion Research, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA Instituto de Ciencias Nucleares, UNAM, 04510, D.F., Mexico Received: 17 January 2005 / Revised version: 1 April 2005 / c Societ` Published online: 10 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We describe an experiment optimized to determine the transition probabilities for excitation of the first excited 2+ state in 132 Sn. The large excitation energy (4.04 MeV) and consequent small excitation cross-section, together with the modest beam intensity available makes this a challenging experiment. The preliminary result is B(E2; 0+ → 2+ ) = 0.11 ± 0.03e2 b2 . The high efficiency and generalized nature of the setup enabled us to also measure the first 2+ state in the two-neutron nucleus 134 Sn. We have determined a value of B(E2; 0+ → 2+ ) = 0.029 ± 0.005e2 b2 which shows no sign of the asymmetry with respect to the N = 82 shell closure exhibited by the Te isotopes. PACS. 21.10.Re Collective levels – 25.70.De Coulomb excitation – 27.60.+j 90 ≤ A ≤ 149

1 Background One of the first stops in the terra incognita of exotic, neutron-rich nuclei is the region around the shell closures at Z = 50 and N = 82. In particular, around the double closed shell nucleus 132 Sn, we will examine the structure of nuclei to look for new features and to compare with nuclei near the next heavier double-closed-shell nucleus, 208 Pb. There have been extensive studies of nuclei around 132 Sn using β-decay and spontaneous fission [1]. With the advent of neutron-rich radioactive beams at the Holifield Radioactive Ion Beam Facility (HRIBF) at ORNL, there have for the first time been measurements of the B(E2; 0+ → 2+ ) for a number of nuclei in the vicinity of the N = 50 and N = 82 [2,3] shell closures. The results of the N = 82 measurements, especially for Te isotopes, provide significant a

Conference presenter; e-mail: [email protected]; research supported by the U.S. Department of Energy under contract DE-AC05-00OR22725 with UT-Battelle, LLC. b The Joint Institute for Heavy Ion Research has as member institutions the University of Tennessee, Vanderbilt University, and the Oak Ridge National Laboratory; it is supported by the members and by the Department of Energy through contract number DE-FG05-87ER40361 with the University of Tennessee. c Supported by the U.S. Department of Energy, under contract DE-FG02-96ER40983.

new data on low-lying collective strength in these regions to test theoretical models. They also provided a puzzle, especially the results for 136 Te. Across the table of nuclides, the excitation energy of the first 2+ states are, broadly speaking, inversely related to the strength of the transition or B(E2; 0+ → 2+ ) [4]. In Te isotopes, across the N = 82 shell closure, this relationship does not appear to hold. Both the energy of the first 2+ and the B(E2; 0+ → 2+ ) decrease by about 40%. This puzzle was addressed by Terasaki, et al. [5] who found that reducing the neutron pairing gap above N = 82 could explain this behavior within their QRPA calculations. In addition, the theory made predictions for the adjacent isotopes 132,134 Sn. The recent availability of isotopically-enriched, neutron-rich Sn [6] beams at HRIBF presented us with the opportunity to make the first measurement of excitation matrix elements in the exotic double-closed shell nucleus 132 Sn, as well as the two-valence-neutron nucleus 134 Sn. The 132 Sn measurements can provide an instructive comparison with the unusual properties of low-lying collective states of the next more massive doubly closed shell nucleus 208 Pb.

2 Measurement with

132

Sn

The high-energy (4.04 MeV) of the 2+ state in the 132 Sn nucleus presented severe challenges for a low-energy

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Coulomb excitation experiment, including small excitation probabilities and the necessity of detecting a 4-MeV photon. The anticipated beam intensity of 104 per second compounded the challenges. We developed a setup which was optimized to deal with these issues. The 132 Sn experiment was performed using 470 MeV and 495 MeV 132 Sn ions incident on a 1.3 mg/cm2 48 Ti target. Using a Ti target gave us the largest cross-section for this excitation, eight times more than C and ten times more than Pb. Scattered 132 Sn ions and target recoils were detected in a 7 cm diameter annular (CD-style) doublesided Si-strip detector mounted 8 cm downstream of the target. The detector has 48 radial strips and 16 azimuthal sectors, and covered the full range of center-of-mass angles relevant to the Coulex angular distribution (30◦ to 166◦ ) with a total efficiency of almost 80%. Gamma rays were detected in an array of 150 BaF2 crystals arranged in six blocks mounted in close proximity to the target. A total trigger efficiency of 55% and a full-energy efficiency of 30% was achieved for 4-MeV gamma-rays. In addition, a carbon-foil-MCP beam counter was employed 57 cm downstream of the target and a Bragg counter was mounted at the beam dump 2 m downstream of the target to monitor beam composition. Beam intensities in excess of 105 132 Sn ions per second were achieved, with a purity of 96% [6]. The bombarding energies employed, 3.75 and 3.6 MeV/u, are higher than would be considered safe for Coulomb excitation. A commonly accepted definition of this is a minimum nuclear surface approach of 5 fm [7,8] for 180◦ scattering. For 132 Sn + 48 Ti this energy is 2.8 MeV/u at which the excitation cross-section of the 4.04-MeV 2+ would have been negligibly small, about 30 μb, compared with the 2.5 mb yield at 3.75 MeV/u. At these higher energies, we limit the distance of closest approach by limiting the range of center-of-mass scattering angles included in the analysis (maximum angle is 85◦ at 3.75 MeV/u and 90◦ at 3.6 MeV/u). These angles actually correspond to a surface approach of 4 fm at 3.75 MeV/u and 4.4 fm at 3.6 MeV/u. The effect of using these angles is negligible on the value of the B(E2; 0+ → 2+ ), and only slightly increases the uncertainty of the value. Another feature of the setup resulted from the inverse-kinematics of the reaction. The events in which we are interested are detected as forward scattered projectiles in the Si-strip array. Backward scattering of the projectiles to angles larger than our cut-off also strike the Si array, at the same laboratory angles as good scattering. Fortunately, these overlapping events can be identified by observing the coincidence with knock-on target nuclei (Ti). We can therefore determine the shape of the γ-ray spectrum (background) corresponding to these “unsafe” events very well. This is clear from fig. 1, which shows the reaction kinematics. Backscattered Sn nuclei between 132◦ and 164◦ in the center of mass are in coincidence with recoiling Ti nuclei in our particle detector. In fig. 2, we show the separation which allows us to distinguish the part of the angular distribution most interesting to us and exclude the background from forward-scattered target ions. The spectrum on the bot-

Fig. 1. Kinematics of the 132 Sn + 48 Ti reaction. “Front” and “Back” refer to the sides of the target. The angles shown in the figure are center-of-mass angles for the scattering.

tom shows the effects of non-Coulomb scattering in the large concentration of yield around 118◦ . The yield from this part of the spectrum contributes a surprisingly large background of photon events near 4 MeV. A spectrum of photon yield subject to our “safe” center-of-mass angles, θ ≤ 90◦ , energy greater than that corresponding to about channel 175 on the vertical axis of fig. 2, and the one-particle requirement is shown in fig. 3. From this result we extract our total yield. Using the yield shown in fig. 3, we have determined the B(E2; 0+ → 2+ ) = 0.11(3) e2 b2 , which amounts to almost 13% of the isoscalar quadrupole energy weighted sum rule. Our measured B(E2; 0+ → 2+ ) is shown in fig. 5, along with results for other Sn isotopes. This is similar to the fraction of the quadrupole sum rule strength exhausted by the 208 Pb 2+ state, which is 14%. This preliminary analysis does not yet include a complete experimental calibration of the photon detector efficiency. This analysis has been done with detailed simulations of the response of the BaF2 .

3 Measurement with

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The large increase in the intensity of neutron-rich Sn beams available at HRIBF presented us with the opportunity to apply our highly-optimized setup to a measurement on the two-neutron nucleus 134 Sn. The beam intensity of the purified [6] A = 134 isotopes was 9000 ions per second, which was determined to be 61.6(3)% Te, 25.6(2)% Sn, 12.2(2)% Sb and 0.56(4)% Ba. Without purification the beam is 98.7(7)% Te, 1.1% Sb. In this case, a 90 Zr target with a thickness of 1.0 mg/cm2 was employed along

R.L. Varner et al.: Coulomb excitation measurements of transition strengths in the isotopes

132,134

Fig. 3. Yield of photons around 4 MeV in citation.

Fig. 2. Measured yield of the 132 Sn + 48 Ti reaction, sorted by particle multiplicity. The horizontal axis is proportional to the laboratory scattering angle; channel 34 corresponds to 85◦ in the center of mass. The vertical axis is proportional to the pulse height in the detector. The acceptable data correspond to energy greater than channel 175.

with a beam energy of 400 MeV, which is safe by any measure. The Si detector was moved to 4 cm from the target to accommodate the change in kinematics, but otherwise the setup was identical. In order to better understand the spectra, measurements were made with a pure beam of 134 Ba and an unpurified beam of A = 134. The resulting spectra can be seen in fig. 4.

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Fig. 4. Results of the 134 Sn measurement. The black curve is the sum of the background and individual peak curves shown. The region where the background exceeds the data indicates the detection threshold of the array.

In panel (a), the short dashed curves are fits to the known peaks in Te and Ba and the thick solid-line Gaussian is the fit to the Sn 2+ , fixed to the known γ-energy of 725 keV. The thin solid-line Gaussians are unexplained peaks, one at 539 keV and the other at 961 keV; these contribute only trivially to the uncertainty of the 134 Sn yield. The thick solid curve is the sum of the continuum response and the fitted peaks. There is no arbitrary background included in these fits. The continuum underlying the peaks, both shape and intensity, is obtained from

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seen from fig. 5, is very close to the value for the two-hole nucleus 130 Sn. The behavior of the B(E2; 0+ → 2+ ) in the Sn isotopes as a function of neutron pairing has been investigated by Terasaki et al. [5,10]. They find that the 134 Sn B(E2; 0+ → 2+ ) is insensitive to the pairing gap, as one would expect. The energy of the 134 Sn 2+ state is much more sensitive; the low experimental value (725 keV) is better reproduced with weaker pairing. However it is worthy of note that shell model calculations of Brown et al. [11, 12] agree very well with both the energy of the 2+ state in 134 Sn and the B(E2; 0+ → 2+ ), as do relativistic RPA calculations of the Munich group [13].

References

Fig. 5. Dependence of B(E2; 0+ → 2+ ) on A for Sn isotopes. The dark curve is the calculation of Terasaki [5], discussed in the text. The light curve is from Colo [9].

simulations of the detector response, normalized to the peak areas. Panel (b) is the spectrum for the 98% 134 Te beam. Panel (c) is the result for a stable beam of 134 Ba. The yields in spectrum (a) for Te and Ba are consistent with the measurements shown in panels (b) and (c), accounting for the Bragg detector measurements of the mixed beam composition. In all panels, the long-dashed curve is the self-consistent Monte Carlo simulation of the detector response discussed above. The γ-threshold is ∼ 300 keV. The preliminary experimental result obtained was B(E2; 0+ → 2+ ) = 0.029(5) e2 b2 , which, as can be

1. H. Mach, Acta Phys. Pol. B 32, 887 (2001). 2. D.C. Radford et al., Phys. Rev. Lett. 88, 222501 (2002). 3. E. Padilla-Rodal, Ph.D. Thesis, UNAM, Mexico (2004); Phys. Rev. Lett. 94, 122501 (2005). 4. S. Raman, C.W. Nestor jr., P. Tikkanen, At. Data Nucl. Data Tables 78, 1 (2001). 5. J. Terasaki, J. Engel, W. Nazarewicz, M. Stoitsov, Phys. Rev. C 66, 054313 (2002). 6. D.W. Stracener, G.D. Alton, R.L. Auble, J.R. Beene, P.E. Mueller, J.C. Bilheux, Nucl. Inst. Meth. A 521, 126 (2004). 7. D. Cline, H.S. Gertzman, H.E. Gove, P.M.S. Lesser, J.J. Schwartz, Nucl. Phys. A 133, 445 (1969). 8. O. Hausser, D. Pelte, T.K. Alexander, H.C. Evans, Nucl. Phys. A 150, 417 (1970). 9. G. Colo, P.F. Bortignon, D. Sarchi, D.T. Khoa, E. Khan, N. Van Giai, Nucl. Phys. A 722, 111c (2003). 10. W. Nazarewicz, private communication. 11. B.A. Brown, private communication. 12. J. Shergur et al., Phys. Rev. C 65, 034313 (2002). 13. A. Ansari, P. Ring, private communication.

Eur. Phys. J. A 25, s01, 395–396 (2005) DOI: 10.1140/epjad/i2005-06-144-7

EPJ A direct electronic only

Coulomb excitation of odd-A neutron-rich radioactive beams C.-H. Yu1,a , C. Baktash1 , J.C. Batchelder2 , J.R. Beene1 , C. Bingham3 , M. Danchev3 , A. Galindo-Uribarri1 , C.J. Gross1 , P.A. Hausladen1 , W. Krolas4 , J.F. Liang1 , E. Padilla4 , J. Pavan1 , and D.C. Radford1 1

Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Oak Ridge Associated Universities, Oak Ridge, TN 37831, USA University of Tennessee, Knoxville, TN 37966, USA The Joint Institute For Heavy Ion Research, Oak Ridge, TN 37831, USA

2 3 4

Received: 14 January 2005 / c Societ` Published online: 11 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A test experiment was carried out at the Holifield Radioactive Beam Facility to extend Coulomb excitation studies of heavy neutron-rich radioactive isotopes from even-even to odd-A nuclei. The experiment identified 10 and 4 gamma rays in 129 Te and 129 Sb, respectively. The B(E2) value of one transition in 129 Sb was tentatively established. More B(E2) values in 129 Te and 129 Sb will be extracted upon completion of the data analysis. PACS. 21.10.Ky Electromagnetic moments – 25.70.De Coulomb excitation – 27.60.+j 90 ≤ A ≤ 149

n

1 Introduction Pr

Te

Counts

35000

ΔE

oj

ec

tio

Sb Coulomb excitation of heavy even-even neutron-rich nuclei near 132 Sn has been a tremendous success [1] at the Holifield Radioactive Ion Beam Facility (HRIBF). Because of the weak intensity and isobaric contamination of the beams, as well as the low B(E2) values in this region and the much more complicated level structure in an odd-A or odd-odd nucleus, extending such studies to odd-mass nuclei is in general difficult. However, studies of odd-A and odd-odd nuclei are important, since they often provide additional information on nuclear structure that cannot be obtained from even-even nuclei. This paper reports some preliminary results from the first experiment at the HRIBF aimed at studying heavy odd-A neutron-rich nuclei via Coulomb excitation.

E 15000

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2 Experiment For this proof-of-principle experiment, self-supporting Ti targets (with thicknesses of 1 and 1.5 mg/cm2 ) were bombarded by a 400 MeV, A = 129 radioactive beam provided by the HRIBF. The A = 129 radioactive beam was selected because of its relatively intense 129 Sb and 129 Te components. The goal of the experiment was to extract B(E2) values of low-lying excitations in these two nuclei, which were not known prior to the present experiment. Ti was chosen as the target because of its relatively high Z, which enhances the Coulomb-excitation 50

a

Conference presenter; e-mail: [email protected]

Fig. 1. Projection (solid curve) of the beam-particle ΔEversus-E spectrum recorded by the Bragg detector positioned behind the target. Dashed curves are Gaussian fits of the various peaks representing the four measurable A = 129 isobars in the beam. The relative intensities of these isobars were used in the extraction of B(E2) values. The original 2D spectrum is shown as inset at the upper-right corner, with the projection window and projection axis indicated.

cross-section. Targets heavier than Ti were not used in order to avoid multi-step Coulomb excitations, which would significantly complicate data analysis. The HRIBF CLARION array, which consisted of 10 segmented clover Ge detectors at the time of this

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experiment, was used to detect the gamma rays. The Hyball CsI detector array [3] (absorbers removed) was used to detect scattered-beam and recoiling-target ions. A Bragg detector [4] downstream from the target position was used to monitor the beam composition. The Bragg-detector spectrum and its projection are shown in fig. 1. From this spectrum, relative intensities of the A = 129 isobars in the beam were determined and then used for extracting B(E2) values. The average total-beam intensity during the run was about 5 × 107 ions/second, and about 45 million gamma-particle coincidence events were recorded during the 72-hour experiment. Hyball-singles events were also recorded for normalization with Rutherford cross-sections. By gating on the 50 Ti particles detected in Hyball, which determines the energies and angles of detected ions, the kinematics of each scattering event could be reconstructed. Using the reconstructed kinematics information, the Doppler effect of the corresponding scattered-beam particles could be corrected event by event. The gammaray spectrum obtained after such Doppler corrections was then obtained and shown in fig. 2. Almost all peaks in this spectrum can be identified as decays of excited states in 129 Te or 129 Sb, which are the main components of the beam (see also fig. 1). Using the available information [2] on 129 Te and 129 Sb, these Coulex gamma rays are placed in the two partial level schemes shown as inset in the upperright corner of fig. 2.

3 Preliminary result and discussion A comprehensive analysis of the B(E2) values of all transitions shown in fig. 2 has not yet been completed. However, the B(E2, 7/2+ → 11/2+ ) in 129 Sb can be quickly extracted because of its simple feeding pattern

Te

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Fig. 2. Spectrum of gamma rays in coincidence with recoiling 50 Ti target ions that were bombarded by a 400 MeV, A = 129 neutron-rich radioactive beam. The gamma rays are corrected for Doppler effect event by event according to the scattered A = 129 beam velocity. The partial level schemes shown are based on ref. [2] and represent those gamma rays observed in the present work.

124

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Fig. 3. Preliminary result of B(E2, 7/2+ → 11/2+ ) in 129 Sb (solid circle) extracted from this work and that in 123 Sb compared with the B(E2, 0+ → 2+ )’s of their neighboring eveneven isotones. Data for 123 Sb is taken from ref. [5], for 128 Sn from ref. [1], and for other Sn and Te nuclei from adopted values given in ref. [6].

and stretched-E2 multipolarity. Preliminary data analysis yielded the B(E2, 7/2+ → 11/2+ ) in 129 Sb to be 0.015 e2 b2 , which is about 5 times the corresponding single-particle estimate. Figure 3 shows a comparison of the newly measured B(E2, 7/2+ → 11/2+ ) in 129 Sb with the B(E2, 0+ → 2+ ) values in its even-even neighbors (normalized by corresponding (2Ii +1) factors). The trend is very similar to that of the N = 72 isotones (diamonds in fig. 3). The data indicate that the nomalized B(E2) strengths for the (7/2+ → 11/2+ ) transitions in both 129 Sb and 123 Sb are smaller than the average of the B(E2, 0+ → 2+ ) values in their corresponding neighboring even-even isotones. To summarize, a test experiment was successfully carried out at the HRIBF to study heavy odd-A neutron-rich radioactive beams via Coulomb excitation. Results of this and future experiments aimed at odd-A and odd-odd nuclei will provide important nuclear-structure information in the region of 132 Sn. This work was supported by the U.S. DOE under contract No. DE-AC05-00OR22725.

References 1. D.C. Radford et al., Phys. Rev. Lett. 88, 222501. (2002) 2. R.B. Firestone et al., Table of Isotopes, Vol. I, 8th edition (Wiley-Interscience, 1996) pp. 1107-1110. 3. A. Galindo-Uribarri et al., to be published in Nucl. Instrum. Methods Phys. Res. A. 4. P.A. Hausladen et al., to be published in Nucl. Instrum. Methods Phys. Res. A. 5. K.C. Jain et al., Phys. Rev. C 40, 2400 (1989). 6. S. Raman, C.W. Nester jr., P. Tikkanen, At. Data Nucl. Data Tables 78, 1 (2001).

Eur. Phys. J. A 25, s01, 397–402 (2005) DOI: 10.1140/epjad/i2005-06-165-2

EPJ A direct electronic only

Coulomb excitation of neutron-rich beams at REX-ISOLDE H. Scheit1,a , O. Niedermaier1 , V. Bildstein1 , H. Boie1 , J. Fitting1 , R. von Hahn1 , F. K¨ock1 , M. Lauer1 , U.K. Pal1 , H. Podlech1 , R. Repnow1 , D. Schwalm1 , C. Alvarez2 , F. Ames2 , G. Bollen2 , S. Emhofer2 , D. Habs2 , O. Kester2 , R. Lutter2 , K. Rudolph2 , M. Pasini2 , P.G. Thirolf2 , B.H. Wolf2 , J. Eberth3 , G. Gersch3 , H. Hess3 , P. Reiter3 , O. Thelen3 , N. Warr3 , D. Weisshaar3 , F. Aksouh4 , P. Van den Bergh4 , P. Van Duppen4 , M. Huyse4 , O. Ivanov4 , ¨ o5 , P.A. Butler5 , J. Cederk¨all5 , P. Delahaye5 , H.O.U. Fynbo5 , L.M. Fraile5 , P. Mayet4 , J. Van de Walle4 , J. Ayst¨ oster5 , T. Nilsson5,7 , M. Oinonen5 , T. Sieber5 , F. Wenander5 , M. Pantea7 , O. Forstner5 , S. Franchoo5,6 , U. K¨ 7 7 auser8 , T. Kr¨oll8 , R. Kr¨ ucken8 , M. M¨ unch8 , A. Richter , G. Schrieder , H. Simon7 , T. Behrens8 , R. Gernh¨ 9 10 6 11 12 13 14 15 T. Davinson , J. Gerl , G. Huber , A. Hurst , J. Iwanicki , B. Jonson , P. Lieb , L. Liljeby , A. Schempp16 , A. Scherillo3,17 , P. Schmidt6 , and G. Walter18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Max-Planck-Insitut f¨ ur Kernphysik, Heidelberg, Germany Ludwig-Maximilians-Universit¨ at, M¨ unchen, Germany Institut f¨ ur Kernphysik, Universit¨ at K¨ oln, K¨ oln, Germany Instituut voor Kern- en Stralingsfysica, University of Leuven, Leuven, Belgium CERN, Geneva, Switzerland Johannes Gutenberg-Universit¨ at, Mainz, Germany Institut f¨ ur Kernphysik, Technische Universit¨ at Darmstadt, Darmstadt, Germany Technische Universit¨ at M¨ unchen, Garching, Germany University of Edinburgh, Edinburgh, UK Gesellschaft f¨ ur Schwerionenforschung, Darmstadt, Germany Oliver Lodge Laboratory, University of Liverpool, UK Heavy Ion Laboratory, Warsaw University, Warsaw, Poland Chalmers Tekniska H¨ ogskola, G¨ oteborg, Sweden Georg-August-Universit¨ at, G¨ ottingen, Germany Manne Siegbahn Laboratory, Stockholm, Sweden Johann Wolfgang Goethe-Universit¨ at, Frankfurt, Germany Institut Laue-Langevin, Grenoble, France Institut de Recherches Subatomiques, Strasbourg, France Received: 10 January 2005 / c Societ` Published online: 18 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. After the successful commissioning of the radioactive beam experiment at ISOLDE (REXISOLDE) —an accelerator for exotic nuclei produced by ISOLDE— in 2002 and the promotion to a CERN user facility in 2003, first physics experiments using these beams were performed. Initial experiments focused on the region of deformation in the vicinity of the neutron-rich Na and Mg isotopes. Preliminary results on the neutron-rich Na and Mg isotopes show the high potential and physics opportunities offered by the exotic isotope accelerator REX in conjunction with the modern Germanium γ spectrometer MINIBALL. PACS. 25.70.De Coulomb excitation – 27.30.+t 20 ≤ A ≤ 38 – 21.10.Re Collective levels

1 REX-ISOLDE The Radioactive beam EXperiment (REX) [1,2, 3] is a pilot experiment to demonstrate the feasibility of an efficient and cost-effective way to accumulate, bunch, charge breed, and accelerate radioactive exotic ions. In addition, beams of these nuclei should be produced for physics experiments, e.g. investigating the structure of nuclei far from a

Conference presenter; e-mail: [email protected]

stability. The REX accelerator is situated at the ISOLDE facility at CERN, which routinely provides a multitude of exotic nuclei for its users [4]. The main components of the REX accelerator are a trap (REX-TRAP), an ion source (REX-EBIS), a mass separator and the actual accelerator consisting of a radio frequency quadrupole, a re-buncher, an IHstructure, three 7-gap resonators and since 2004 a 9-gap IH-structure. REX-TRAP is a buffer-gas filled penning

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trap that continuously traps the ions (with a charge state 1+) coming from the ISOLDE beam line. The accumulated ions are cooled and form bunches which are periodically (typically every 20 ms) transferred to the electron beam ion source REX-EBIS. Here charge breeding takes place and when a charge state to mass number ratio of q/A > 1/4.5 is reached the ions are extracted, mass separated (mainly to remove copious residual gas ions) and accelerated to energies around 0.8–3.1 MeV/u. It should be noted that in an EBIS the average charge state depends mainly on the breeding time and always a large fraction (about 15% for A ∼ 20) of the ions is in one charge state. Still, as only one charge state of the ions can be accelerated, the largest reduction in transmission occurs after the EBIS. The total transmission from the ISOLDE target to the REX target is on the order of about 5%. The first radioactive nuclear beam was accelerated in October 2001 to an energy of 2 MeV/u and in 2002 already several radioactive beams were produced with an energy of 2.2 MeV/u and used for commissioning experiments. First physics experiments using the accelerated exotic nuclei with a maximum beam energy of 2.2 MeV/u and 3.1 MeV/u were performed in 2003 and 2004, respectively. An upgrade to a beam energy of 4.3 MeV/u is planned in the near future, which will significantly extend the accessible region of nuclides toward heavier isotopes, especially for Coulomb excitation experiments. By the end of 2003 REX became a dedicated CERN user facility. A picture of the setup in early 2002 is shown in fig. 1 with the MINIBALL array on the 65◦ beamline in the foreground.

Fig. 1. The REX-ISOLDE experimental hall in 2002. In the background the REX accelerator can be seen. After the bending magnet at the 65◦ the MINIBALL array is installed.

The main experimental device currently used with REX is the MINIBALL HPGe array [5,6]. The array consists of 24 6-fold segmented, individually encapsulated, HPGe detectors arranged in 8 triple cryostats. The crystal geometry is shown in fig. 2. The detectors are mounted on an adjustable frame which allows for an easy adaptation of the geometry to the specific experimental requirements. The central core and six segment electrodes of each detector are equipped with a preamplifier with a cold stage and a warm main board. The charge integrated signals are subsequently digitized (12 bit, 40 MHz) and analyzed online and onboard the DGF-4C CAMAC card from XIA [7]. Besides energy and timing information the (user) algorithms implemented on the card [6,7,8, 9,10] determine the interaction point of each γ-ray in the detector via pulse shape analysis (PSA), resulting in an about 100-fold increase in granularity in comparison to a non-segmented detector (the position resolution is about 7-8 mm FWHM, depending on the energy of the γ-ray). All digitizers run independently (receiving the same clock signal) and each single event is time stamped by a 40 MHz clock for offline event reconstruction. In addition to the MINIBALL array an annular charged particle detector telescope (of CD type, see [11]) is employed consisting of a ∼ 500 μm thick ΔE followed by

80 mm

2 Experimental setup r

φ

70 mm Fig. 2. MINIBALL HPGe crystal. The electrical segmentation is indicated.

a ∼ 500 μm thick E detector. The ΔE detector is highly segmented (24×4 annular and 16×4 radial strips) to allow for a kinematic reconstruction of the events and covers an angular range from 15◦ to 50◦ . A parallel plate avalanche counter [12] was used to monitor the beam at zero degrees without stopping it, so that the (radioactive) beam particles are not deposited in the target area and reach the beam dump to reduce the radioactive decay background.

3 First experiments The primary aim of REX and MINIBALL is the investigation of the development of the structure of nuclei far from

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Utsuno et al. (1999,2002), MCSM Dean et al. (1999), SMMC

200

Rodriguez-Guzman et al. (2000,2002), AMPGCM

100

Caurier et al. (2001), SM (normal, intruder) Stevenson et al. (2002), GCM Kimura et al. (2002), AMD Peru et al. (2002), cHFB Yamagami et al. (2004), HFB+QRPA

0

12

14

REX-ISOLDE/MINIBALL (preliminary)

20

18 16 Neutron number

22

+ Fig. 3. B(E2; 0+ gs → 21 ) values for the neutron-rich even-even magnesium isotopes. The values for

stability. The reactions of choice to study the single particle and collective properties of nuclei with low-energy reaccelerated ISOL beams (Ebeam ∼ Coulomb barrier) are single-nucleon transfer reactions and Coulomb excitation, respectively. Especially favorable for neutron-rich nuclei are (d, p) reactions (in inverse kinematics) on deuterated polyethylene targets, since here the cross sections are relatively high [14] and the neutron-pickup product is more neutron-rich by one neutron. By determining the differential cross sections to certain states as well as the angular distribution of the de-excitation γ-rays their spins and parities can be determined. From the absolute cross section, spectroscopic factors can be extracted. An interesting region in the chart of nuclides is around the N = 20 nucleus 32 Mg. This region is well known as the island of deformation for almost 30 years [15, 16], yet still, the knowledge on the nuclei in this region is very limited. Even today the extent of intruder ground state configurations in this region of the nuclear chart is not + known. B(E2; 0+ gs → 21 ) values for the even-even nuclei up to N = 22 (34 Mg) have been measured [17, 18, 19,20] rather recently, mainly by intermediate-energy Coulomb excitation at projectile fragmentation facilities. However, the data are very imprecise and measurements of different laboratories disagree by as much as a factor of two indicating that the systematic errors are not completely understood. The main contribution to the systematic error in these experiments is probably due to Coulomb-nuclear interference effects, which are always present at such high beam energies, even if the scattering angle of the projectiles is restricted to small values. Furthermore, the population of higher-lying states and subsequent feeding of the first 2+ state also needs to be accounted for. In contrast, the Coulomb excitation studies at REX-ISOLDE are performed with beam energies well below the Coulomb barrier, yielding model independent results. In fig. 3 the the-

π

26,28

Mg were taken from [13].

ν Ζ=16

Vστ Ζ=8...16

8

0d3/2 1s1/2

Ν ∼ 20

0d5/2

Fig. 4. Illustration of the Vστ interaction between neutron and proton orbitals with the same orbital angular momentum l and different total angular momentum j. This interaction was found to be very attractive for stable nuclei and rather weak for exotic neutron-rich nuclei, where the corresponding proton orbitals are often not filled, contributing to the appearance of new magic numbers [21].

+ oretical and experimentally determined B(E2; 0+ gs → 21 ) values for the neutron-rich Mg isotopes as a function of neutron number N are shown. It should be noted that all the theoretical results [21,22,23,24,25,26,27,28,29] are rather recent but give (nevertheless) very different values. Based on the data shown, a discrimination between the theoretical models is not possible. Most information on the odd and odd-A nuclei stems from β decay experiments (see e.g. [30] and references therein) and in the future it will be attempted to measure ground state nuclear moments by the β NMR technique after polarization with a LASER beam [31,32]. In a recent publication Otsuka et al. [21] pointed out the importance of the Vστ (residual) interaction between orbits of the same orbital angular momentum, but with different total angular momentum between neutron and proton orbitals (see illustration in fig. 4 for the sd-shell). It is due to this interaction that the effective single particle

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E Beam=2.2 MeV/u

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preliminary

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gate on 171 keV

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60 +

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Mg

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+

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+

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Ni

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100

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20

30

Ebeam = 2.25 MeV/u

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200

0

35 30 25 20 15 10 5 0 25

15

222

171 keV

0

Counts / 4 keV

30

250

300

350

400

450

E γ [keV]

Fig. 5. γ spectrum coincident with any signal in the particle detector. Please note the almost negligible background and the extremely low-energy threshold of only 40–50 keV. The inset shows a γ energy spectrum in coincidence with the 171 keV line. As expected only the 50.5 keV transition is seen with still good statistics, demonstrating the high efficiency of the MINIBALL array.

energy (ESPE) of the νd 32 orbital is much lower in energy for stable nuclei, where the πd 52 orbital is nearly filled (resulting in a strong attraction of the orbitals) in comparison to very neutron-rich nuclei, where the πd 52 is nearly empty. 24 O (πd 52 completely empty), e.g., shows features of a double magic nucleus due to the rise of the ESPE of the νd 32 orbital [21]. To further test the role of Vστ in the structure of these neutron-rich nuclei more precise experimental data are urgently needed. At REX-ISOLDE with MINIBALL there is the possibility to study nuclei far from stability with standard nuclear physics tools (in inverse kinematics), which are not only well proven, but which also allow a direct comparison of the experimental results to ones obtained with stable beams. Therefore a program was started to systematically study the neutron-rich nuclei in this region via neutronpickup reactions and Coulomb excitation.

4 Preliminary results Preliminary γ energy spectra are shown in figs. 5 and 6 to demonstrate the quality of the spectra measured with a radioactive beam. Figure 5 shows a spectrum taken in about 66 hours with a 30 Mg beam (4 neutrons away from stability with a halflife of only 335 ms) with an intensity of about 2 · 104 s−1 (Ebeam = 2.2 MeV/u) on a 10 μm thick deuterated polyethylene foil. Several known transitions in 31 Mg can be seen, namely at 50.5 keV, 171 keV, and 222 keV. In addition a strong line at 54.6 keV is evident. This transition is coincident with tritons in the particle detector and corresponds therefore to the transition of the first excited state in 29 Mg (populated via the d(30 Mg, 29 Mg)t reaction)

1250

1300

1350

1400 1450 Eγ (keV)

1500

1550

1600

Fig. 6. Doppler corrected γ-ray spectra containing only events where 30 Mg projectiles were scattered in the CD detector. The upper panel shows the spectrum with Doppler correction for magnesium, while the lower panel the spectrum Doppler corrected for recoiling nickel.

to the ground state. The inset shows a spectrum gated on the 171 keV line. As expected only the 50.5 keV transitions can be seen in this spectrum. The statistics is still rather good demonstrating the high efficiency of the MINIBALL array. Please note the very low background seen in these spectra, even though the beam particles are radioactive, and the extremely low-energy threshold of only 40–50 keV, which should be compared to a threshold of typically several 100 keV in experiments with fast beams. For the Coulomb excitation study the 30 Mg beam provided by REX was incident on a natural nickel foil with a thickness of 1.0 mg/cm2 located at the center of the scattering chamber. The measured γ-ray energy spectra obtained after 76 hours of data taking are shown in fig. 6, where peaks due to projectile and target excitation can be seen. The upper panel shows the γ spectrum obtained when the proper Doppler correction for 30 Mg is performed. The prominent peak at 1482 keV corresponds to the transition from the first 2+ state to the ground state. When performing the Doppler correction for the recoiling nickel nuclei (bottom panel) the well known γ transitions at 1454 keV and 1333 keV, from the excitation and decay of the first excited 2+ states in 58 Ni and 60 Ni, respectively, are evident. In the top/bottom spectrum the contribution of the peaks in the bottom/top spectrum is suppressed, i.e. the magnesium spectrum (top) does not include counts attributed to transitions in the nickel isotopes, since these counts correspond to wrongly Doppler corrected nickel γrays, and vice versa. Please note that the small change in peak area due to this procedure was taken into account in the extraction of the B(E2) ↑ value (see below). The two spectra contain only events where A = 30 nuclei were scattered into the CD detector. The recoiling nickel nuclei were separated from those by their lower kinetic energies at the same laboratory scattering angle. For the extraction of the B(E2)↑ value of 30 Mg only the events observed in coincidence with forward scattered 30 Mg were analyzed, ensuring safe surface distances Ds between projectile and target ranging from 6 fm to 23 fm [33].

H. Scheit et al.: Coulomb excitation of neutron-rich beams at REX-ISOLDE

Due to the occurrence of both projectile and target excitation the Coulomb excitation cross section σCE of the first excited 2+ state in 30 Mg can be deduced relative to that of 58,60 Ni from the measured γ-ray yields Nγ alone σCE

30



Mg =

58,60

30

γ ( Ni) Nγ ( Mg) · σCE · γ (30 Mg) Nγ (58,60 Ni)

58,60



– A LASER-on/off measurement was performed, where the RILIS LASER beam to the ISOLDE target was blocked periodically. During the LASER-off periods only surface ionized contaminants are extracted, while during the LASER-on periods, in addition, the (wanted) magnesium ions are extracted. – The time dependence of the incident beam intensity with respect to the proton pulse impact on the ISOLDE target (T1) was analyzed. While a possible aluminum contamination is almost constantly present The recently published B(E2)↑ values for 58,60 Ni in [37] do not agree with this measurement and were not used (see [38]). 2 Only aluminum can be present as it is easily surface ionized. Other isobars have a negligible yield (refractory of too short lived). 1

Table 1. Experimental B(E2)↑ values in e2 fm4 .

Isotope

RIKEN [17] [20]

MSU [18]

GANIL REX-ISOLDE [19] (preliminary)

30

Mg

–

–

295(26) 435(58)

241(31)

32

Mg

454(78)

449(53)

333(70) 622(90) 440(55)

–

34

Mg

–

631(126)

Ni ,

where γ is the full energy peak efficiency (including the angular correlation of the emitted γ-rays) at the corresponding γ energy. The cross sections for the excitation of the nickel nuclei was calculated using the known spectroscopy [34,35,36] (B(E2)↑ and quadrupole moments). For magnesium the B(E2) ↑ value was varied until the cross section was reproduced. The procedure was performed separately for the two nickel isotopes and the weighted average of the results was taken as the final value. For all measurements the γ yield of the two nickel isotopes was consistent with the natural abundance and the calculated Coulomb excitation cross section of the two isotopes. Even though the analysis presented above is straight forward a measurement with stable 22 Ne beam was performed for which the deduced B(E2)↑ of 242(26) e2 fm4 is in very good agreement with the adopted value [13] of 230(10) e2 fm4 1 . With the method proven the only difference to the measurement with a radioactive beam is a possible isobaric contamination. A contamination with a different mass is excluded due to the A/Q selection of the REX accelerator and the measurement of the total energy, which is proportional to the mass of the projectile, by the CD detector. There can be two sources of isobaric contamination, though: decay of 30 Mg during trapping and charge breeding and isobaric contamination directly released from and ionized at the primary ISOLDE target. The first contribution can be calculated from the known trapping and breeding time, which ranges from 12 ms to 32.4 ms, depending on the time, when a certain 30 Mg ion entered the trap. From the known lifetime of 483(25) ms an 30 Al contamination of 4.5% is calculated. The total 30 Al beam contamination and the contamination directly from the ISOLDE target2 was investigated by the following methods:

401

< 670

–

–

due to the long decay time of the release curve [39] the 30 Mg ions show a high intensity only for a short time after proton impact due to their fast release and short lifetime. – The time dependence of the γ yield in the 30 Mg and 58,60 Ni peaks with respect to T1 was investigated to check what fraction of counts in the nickel peaks occurs during times, when there can be no 30 Mg in the beam. – The Coulomb excitation of the first excited state in 30 Al at 244 keV was investigated. – The γ yields due to β decay of 30 Mg and 30 Al were analyzed. This analysis yields a value for the total beam contamination by 30 Al of 6.5% resulting in a correction of 5% of the nickel count rates. See [38] for details. In addition the time structure of the EBIS pulse was investigated and no peculiarities were found. Including the determined beam impurities, a + 30 Mg of 241(31) e2 fm4 B(E2; 0+ gs → 21 ) value of was determined. The error is dominated by the statistical uncertainty, but also contains contributions due to the uncertainties of the B(E2)↑ values of 58,60 Ni, the uncertainty in diagonal matrix elements for 30 Mg, a remaining uncertainty in the beam composition, the uncertainty due to angular distribution and possible reorientation of the emitted γ-rays [38]. Figure 3 shows the present value together with previously measured B(E2)↑ values for the neutron-rich magnesium isotopes (see also table 1). While the initial goal was to confirm one or the other measurement for 30 Mg, it stands out that the B(E2)↑ values of 30 Mg measured at MSU and GANIL are larger than the present value by about 20% and 80%, respectively (see also table 1). While the source of this discrepancy is unknown it should be noted that in the intermediate-energy measurements with beam energies around 30–50 MeV/u several effects can influence the deduced B(E2) ↑ values such as feeding from higher-lying states and Coulomb-nuclear interference which have to be corrected. While the adiabatic cutoff limits the single-step excitation energy to values below 1–2 MeV in sub-barrier experiments, as presented here, in experiments with intermediate or relativistic beams, states up to several (5–10) MeV excitation energy can readily be populated [40]. Therefore, in these experiments any 2+ (or even 1− ) state below 5–10 MeV can be excited and feeding of the first 2+ state, unless it is corrected for, will result in an increased B(E2)↑ rendering this type of measurement strongly model-dependent.

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It is interesting to note that this feeding correction is performed differently by the different groups, ranging from no correction to corrections of more than 25%, sometimes based on experimental evidence of feeding [18], sometimes based on model calculations [17,19,20]. In conclusion, REX and MINIBALL are fully operational and first physics experiments focusing on the nuclear structure of the neutron-rich Na and Mg isotopes were performed. A preliminary analysis shows the high quality of the data that can be obtained with MINIBALL at REX-ISOLDE with a radioactive, low-energy and lowintensity beam. The analysis of the Coulomb excitation of + a 30 Mg beam on a nat Ni target yields a B(E2; 0+ gs → 21 ) which is lower by about 20% and 80% that the MSU and GANIL results, respectively. Support by the German BMBF (06 OK 958, 06 K 167, 06 BA 115), the Belgian FWO-Vlaanderen and IAP, the UK EPSRC, and the European Commission (TMR ERBFMRX CT97-0123, HPRI-CT-1999-00018, HRPI-CT-2001-50033) is acknowledged as well as the support by the ISOLDE Collaboration.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

D. Habs et al., Hyperfine Interact. 129, 43 (2000). O. Kester et al., Nucl. Instrum. Methods B 204, 20 (2003). J. Cederk¨ all et al., Nucl. Phys. A 746, 17 (2004). E. Kugler, Hyperfine Interact. 129, 23 (2000). J. Eberth et al., Prog. Part. Nucl. Phys. 46, 389 (2001). D. Weisshaar, PhD Thesis, University of Cologne (2002). http://www.xia.com/. C. Gund, PhD Thesis, University Heidelberg (2000). M. Lauer, Master’s thesis, University Heidelberg (2001). M. Lauer, PhD Thesis, University Heidelberg (2004). A. Ostrowski et al., Nucl. Instrum. Methods A 480, 448 (2002). 12. J. Cub et al., Nucl. Instrum. Methods A 453, 522 (2000).

13. S. Raman, C.W. Nestor jr., P. Tikkanen, At. Data Nucl. Data Tables 78, 1 (2001). 14. H. Lenske, G. Schrieder, Eur. Phys. J. A 2, 41 (1998). 15. R. Klapisch et al., Phys. Rev. Lett. 23, 652 (1969). 16. C. Thibault et al., Phys. Rev. C 12, 644 (1975). 17. T. Motobayashi et al., Phys. Lett. B 346, 9 (1995). 18. B. Pritychenko et al., Phys. Lett. B 461, 322 (1999). 19. V. Chist´e et al., Phys. Lett. B 514, 233 (2001). 20. H. Iwasaki et al., Phys. Lett. B 522, 227 (2001). 21. T. Otsuka et al., Eur. Phys. J. A 15, 151 (2002). 22. Y. Utsuno et al., Phys. Rev. C 60, 054315 (1999). 23. D.J. Dean et al., Phys. Rev. C 59, 2472 (1999). 24. R. Rodr´ıguez-Guzm´ an, J. Egido, L. Robledo, Phys. Lett. B 474, 15 (2000). 25. E. Caurier, F. Nowacki, A. Poves, Nucl. Phys. A 693, 374 (2001). 26. S. P´eru, M. Girod, J. Berger, Eur. Phys. J. A 9, 35 (2000). 27. P. Stevenson, J. Rikovska Stone, M.R. Strayer, Phys. Lett. B 545, 291 (2002). 28. M. Kimura, H. Horiuchi, Prog. Theor. Phys. 107, 33 (2002). 29. M. Yamagami, N.V. Giai, Phys. Rev. C 69, 034301 (2004). 30. S. Nummela et al., Phys. Rev. C 64, 054313 (2001). 31. M. Keim et al., Eur. Phys. J. A 8, 31 (2000). 32. M. Kowalska, these proceedings. 33. D. Schwalm, in International School of Heavy Ion Physics: 3rd Course: Probing the Nuclear Paradigm with Heavy Ion Reactions, edited by R. Broglia, P. Kienle, P.F. Bortignon (World Scientific, 1994) p. 1. 34. M. Bhat, Nucl. Data Sheets 80, 789 (1997). 35. M. King, Nucl. Data Sheets 69, 1 (1993). 36. P. Raghavan, At. Data Nucl. Data Tables 42, 189 (1989). 37. O. Kenn et al., Phys. Rev. C 63, 064306 (2001). 38. O. Niedermaier et al., Phys. Rev. Lett. 94, 172501 (2005). 39. U. K¨ oster et al., Nucl. Instrum. Methods B 204, 347 (2003). 40. K. Alder, A. Winther, Electromagnetic Excitation: Theory of Coulomb Excitation with Heavy Ions (North-Holland, 1975).

Eur. Phys. J. A 25, s01, 403–408 (2005) DOI: 10.1140/epjad/i2005-06-188-7

EPJ A direct electronic only

Spectroscopy on neutron-rich nuclei at RIKEN Hiroyoshi Sakuraia Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Received: 14 December 2004 / c Societ` Published online: 11 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Recent studies on nuclear structure by using radioactive isotope beams available at the RIKEN projectile-fragment separator (RIPS) are introduced. Special emphasis is given to experiments selected from recent programs that highlight studies; the particle stability of very neutron-rich nuclei, 34 Ne, 37 Na and 43 Si, the nuclear structure of 27 F, 30 Ne and 34 Si at N ∼ 20, and the anomalous quadrupole transition in 16 C. PACS. 21.10.Dr Binding energies and masses – 23.20.-g Electromagnetic transitions – 23.20.Lv γ transitions and level energies – 25.60.-t Reaction induced by unstable nuclei – 29.30.Kv X- and γ-ray spectroscopy

1 Introduction Radioactive isotope (RI) beams, bringing out a high isospin degree of freedom, have given a great opportunity to investigate nuclei far from stability and to reveal out new phenomena under extreme conditions of isospin asymmetry. Experimental programs at the RIKEN projectile fragment separator (RIPS) [1] have demonstrated such potentials of RI beams. Intensities of fast RI beams available at the RIPS are at the world-highest level in the light mass region. This situation has been realized by combination of the RIPS and the high energy and intense primary beams. The RIPS has large momentum and angular acceptances as well as a sizable maximum magnetic rigidity, hence has a high collecting power of projectile fragments. The intense RI beams have made it possible to use secondary nuclear reactions for studies of the nuclear structure, and unique spectroscopic methods and techniques are being developed to obtain exotic properties of unstable nuclei. In this report, we introduce recent highlights of experimental programs at RIKEN for last three years. Recently the RIKEN Accelerator Research Facility (RARF) has been upgraded in concert with a new project, RI Beam Factory (RIBF) [2], as introduced in sect. 2. A new injection scheme has been developed according to additional accelerator equipments installed at the RARF, and being used to deliver more intense primary beams than before. One of highlights in experimental programs based on the new acceleration scheme is presented in sect. 3. To overcome experimental difficulties stemming from low yield rates, we developed a liquid hydrogen/deuterium target. a

Conference presenter; e-mail: [email protected]

This target is useful to access nuclei very far from the stability line, and has been intensively used for studies of the nuclear structure via the in-beam γ spectroscopy. Some of highlights for N ∼ 20 nuclei are shown in sect. 4. To study nuclear collectivity in the light mass region, new experimental techniques in terms of the in-beam γ spectroscopy have been developed and applied for the 16 C nucleus. In sect. 5, results of three experimental programs are shown and discussed.

2 Recent upgrades of RIKEN facility Combination of the accelerator facility existing and a new facility being constructed will deliver intense heavyion beams for RI productions at the RIBF, as shown in fig. 1 [2]. The accelerator complex in the present facility consists of the RIKEN Ring Cyclotron (RRC) and two injectors; the AVF cyclotron and RIKEN heavy-ion linear accelerator (RILAC). The RILAC and RRC will be used as injectors for two post-accelerators in the new facility; the Intermediate stage Ring Cyclotron (IRC) and the Super-conducting Ring Cyclotron (SRC). To provide powerful primary beams for the post-accelerators, additional accelerator devices were installed at the RILAC; an 18GHz ECR ion source, an RFQ and a booster system called the Charge-state multiplier (CSM). Based on the upgraded RILAC, a new acceleration scheme for the RRC has been developed to obtain intense primary beams at the RIPS. An alternative injection scheme, which is often employed to have higher-energy beams, is by use of the AVF cyclotron. The new acceleration scheme with the RILAC can provide much more intense primary beams than the AVF injection. For instance,

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The European Physical Journal A RILAC

CSM

RRC

20

Stripper

FCRFQ

Accel.

IRC, SRC

Decel.

Under construction

18GHz ECRIS

10GHz ECRIS

RIPS

AVF pol. d IS

RARF

Fig. 1. A schematic layout of the present RIKEN Accelerator Research Facility (RARF).

a typical beam intensity of 48 Ca is 4 pnA by the AVF injection, and 150 pnA by the RILAC injection. Differences of beam energy at the RRC between the two schemes are small for neutron-rich stable isotopes; 70A MeV for 48 Ca via the AVF injection and 63A MeV via the RILAC injection. Thus, the RILAC injection has given 30 times higher production rates of RI beams than the AVF injection. The RILAC scheme also delivers a 64A MeV 86 Kr beams with an intensity of 100 pnA at maximum. Combination of the RIPS and the powerful primary beams accelerated via the new injection scheme has provided further opportunities to proceed towards the neutron-drip line. Several experimental programs by use of the powerful primary beams have been already performed; to search for new neutron-rich isotopes [3] and to study the nuclear structure via the in-beam γ spectroscopy [4,5,6].

3 Particle stability at N = 20–28 The experiment searching for new isotopes by using the Ca beam [3] is introduced as one of experimental programs using the powerful beams realized by the new acceleration scheme, as described in the previous section. The neutron-rich stable isotope 48 Ca is a major source to produce extremely neutron-rich nuclei up to Z ∼ 20 and N ∼ 28 via the projectile fragmentation reaction. The 48 Ca beam reacted with a 181 Ta target and the reaction fragments were collected and analyzed with the RIPS. Two different settings of the magnetic rigidity (Bρ) were employed to search for new isotopes; one optimized for 40 Mg and the other for 43 Si. Particle identification was performed event by event by a standard method on the basis of TOF-ΔE-E-Bρ measurements. Further details of the experimental setup are found in ref. [3]. We observed for the first time three new isotopes, 34 Ne, 37 Na and 43 Si. The 33 Ne, 36 Na and 39,40 Mg isotopes were not observed in this experiment. According to the systematic behaviors of the production cross sections for the observed isotopes, the expected cross sections for the 33 Ne, 36 Na and 39 Mg isotopes were obtained to be about 10, 3, and 1 pb, respectively. The 1 pb cross section corresponds to about 30 events for 39 Mg at the 40 Mg Bρ setting. Thus, the absence of events of 33 Ne, 36 Na and 39 Mg clearly deviates from the expectation and provides a proof for the 48

Si Al Mg Na Ne F 8 O N C

28 43Si

39Mg 37Na 36Na 34Ne 33Ne

stability jump

neutron drip line

particle bound particle unbound

Fig. 2. New neutron-rich isotopes found at RIKEN. 34 Ne, 37 Na and 43 Si are found particle stable, while evidence on particle instability of 33 Ne, 36 Na and 39 Mg is obtained.

particle unbound character of 33 Ne, 36 Na and 39 Mg. The expected cross section for 40 Mg is an order of 0.01 pb. One event observation of 40 Mg at the 40 Mg Bρ setting corresponds to about 0.03 pb, which gives the detection limit of the experiment. Therefore, the question whether 40 Mg is particle bound or not is left for a future attempt requiring a higher luminosity. In this work, the heaviest isotopes of Ne, Na and Si have been extended to 34 Ne, 37 Na and 43 Si, and particle instability of 33 Ne, 36 Na and 39 Mg has been found, as illustrated in fig. 2. These findings are rather in good agreement with the recent mass formula [7]. Concerning the stability of 43 Si, two mass formulas, FRDM [7] and ETFSI [8], disagree each other. The FRDM predicts instability with Sn = −1.68 MeV, while the ETFSI does stability. A major difference between the two formulas lies in the degree of deformation. The ETFSI predicts a larger deformation than the FRDM for the silicon isotopes at N ∼ 28. Recent shell models and mean field calculations, cited in ref. [3], have also predicted a possible deformation of a nearby nucleus 42 Si. Thus, the particle stability found for 43 Si may be attributed to a deformation effect. A recent half-life measurement for 42 Si has also suggested the possible deformation at N = 28 [9].

4 Neutron-rich nuclei at N ∼ 20 Since 1970s, a spot of the nuclear chart at Z ∼ 11 and N ∼ 20, the so-called “island-of-inversion” region, has been investigated with respect to the magicity loss at N = 20. According to recent developments of RI production methods at both ISOL and in-flight facilities, RI production rates in this region have been drastically increased, and secondary reactions have been applied to study the nuclear structure. One of spectroscopic methods based on reactions is the in-beam γ spectroscopy. Since the intermediate-energy Coulomb excitation was applied for 32 Mg to obtain a B(E2) value [10], several reactions and experimental techniques dedicated for fast RI beams have been developed and applied to nuclei in the island-of-inversion region. “Cocktail” beams containing a bunch of nuclei of interest have led to efficient production of data on B(E2) for

Hiroyoshi Sakurai: Spectroscopy on neutron-rich nuclei at RIKEN

4.1

30

Ne

To determine energies of first excited states (E(2+ 1 )) for even-even isotopes is essential for understanding the nuclear structure and collectivity. The experimental finding 30 Ne was performed by using the liquid hyof E(2+ 1 ) for drogen target [17]. The neutron-rich isotope 30 Ne was produced via a primary 40 Ar beam of 95 A MeV with a typical intensity of 60 pnA, which bombarded a 181 Ta target. The beam was accelerated via the AVF injection scheme (sect. 2). Particle identification was made by measuring event by event the energy loss, time of flight, and magnetic rigidity. Horizontal positions of the fragments at the momentum dispersive focal plane of RIPS (F1) were measured to determine the Bρ values using a parallel plate avalanche counter (PPAC) [21]. The Bρ measurement is essential to have the maximum intensity of 30 Ne at the RIPS. To identify A = 30 fragments without the Bρ measurement, the momentum acceptance should be limited to 1/A, namely, less than 3%, while the Bρ measurement allows us to set the momentum acceptance of RIPS at maximum (6%).

data

Energy [keV]

neutron-rich nuclei at N = 20–28 [11]. The projectile fragmentation reaction with primary beams has been possible to obtain information on higher spin and excited states, compared with the Coulomb excitation [12]. The fragmentation reaction with fast RI beams instead of primary beams, the so-called two step fragmentation, has given a larger access to nuclei far from the stability line [13]. The two-nucleon knock-out reaction has been recently developed and applied for 32 Mg [14]. Further efforts at RIKEN have been made to obtain new information by developing new techniques in the inbeam γ spectroscopy. For the Mg isotopes beyond N = 20, two experimental works for 34 Mg were performed; the two step fragmentation [13] and the Coulomb excitation [15]. The two experiments showed that 34 Mg has a larger deformation than 32 Mg. To find whether and how deformation evolves in the isotopes with a lower Z along N = 20, increase of luminosity by enhancement of number of target nuclei should be desirable, since the beam intensity of 30 Ne is one order of magnitude lower than that of 34 Mg. To overcome the low beam intensity, we developed a liquid hydrogen/deuterium target at RIKEN [16]. In this section, we present results of three experiments with the liquid hydrogen/deuterium target [16]. Two of them using the proton inelastic scattering have found excited states of 30 Ne and 27 F [17, 18]. The other experiment with the deuterium target is to study for 34 Si [19], where multitudes of excited states were populated and γ-γ coincidence technique was employed. One of the experiments [18] utilized a new NaI setup for γ detection, called DALI2 [20], while the other experiments used an old NaI setup (DALI) [10]. Compared with the DALI, the DALI2 was designed to have higher detection efficiency by larger angular coverage and higher angular resolution due to higher segmentation.

405

0p-0h 0hw 0p-0h calc. Siiskonen et al. Courier et al.

2hw 2p-2h

2p-2h calc. Kimura et al. Utsuno et al. Fukunishi et al. Siiskonen et al.

885

791

32Mg

30Ne

Courier et al.

36S

34Si

Fig. 3. Energies of the first 2+ states in even-even N = 20 isotones (circles) together with theoretical predictions (from ref. [17]). The theoretical works cited are found in ref. [17].

The PPAC used at F1 is a delay-line readout type for position determination, hence giving a large tolerance under high rate circumstance and a wide dynamic range for Z of fragments. The mean intensity of the 30 Ne beam was about 0.2 particles per second, and the purity was 6.7%. The liquid hydrogen target was placed at the final focus of RIPS to excite the projectile. The thickness of the hydrogen target cell was 186 mg/cm2 on average. The average energy of 30 Ne at the center of the target was estimated to be 48 A MeV. Identification of Z for ejectiles was made by the TOF-ΔE method, by using a PPAC and a silicon telescope. Other details of the experimental setup are found in ref. [17]. Doppler-corrected energy spectrum of γ-rays for the 30 Ne beam was found to have a significant γ-line at 791(26) keV. The corresponding cross section of the 791 keV transition was evaluated to be 30±18 mb. By use of a coupled channel calculation and a phenomenological optical potential, the deformation parameter of βpp was obtained to be ∼ 0.58. Under the assumption that electromagnetic deformation is the same as for (p, p ) scattering, the reduced E2 transition probability B(E2; 0+ → 2+ ) was estimated to be ∼ 460 e2 fm4 . Details of analysis procedures are found in ref. [17]. This result for 30 Ne is compared to E(2+ 1 ) values measured for neighboring N = 20 isotones together with theoretical predictions, as cited in fig. 3. The measured E(2+ 1) values for 30 Ne and 32 Mg are considerably smaller than for other N = 20 isotones. The energy of 791 keV obtained for 30 Ne is even smaller than that of 32 Mg (885 keV), suggesting a larger deformation for 30 Ne. Theoretical predictions as cited in fig. 3 [17] are categorized into two groups as 0p-0h and 2p-2h models across N = 20. Obviously shown

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30 in this figure, the experimental value of E(2+ Ne fa1 ) for 30 vors 2p-2h models, and suggesting that the Ne nucleus belongs to the island-of-inversion region.

4.2

27

F

One interesting question related to the island-of-inversion region is the extra-enhancement of binding energies for heavy fluorine isotopes. The heaviest fluorine isotope observed so far is 31 F while that for oxygen is 24 O [21]. It is remarkable that at least six additional neutrons can be bound by moving from oxygen to fluorine. Based on mass information for nuclei in the island-of-inversion region [22], extra-enhancement of their binding energies has been observed as one of exotic features. This enhancement may be due to deformation effects manifested in this region. To understand mechanism of the bound nature of 31 F, a key issue is magnitude of deformation for the heavy fluorine isotopes. As presented in the previous subsection, 30 Ne is suggested to have a larger deformation than 32 Mg. One may ask further whether the fluorine isotopes at N ∼ 20 have a larger deformation than 30 Ne or not. To answer this question, the bound states of 27 F have been searched for [18]. Their existence or energies would provide useful information on the magnitude of deformation. γ-lines were searched for p(27 F, 25,26,27 F) channels. Doppler corrected energy spectrum of γ-rays for each channel showed two γ-lines originated from each ejectile. The 27 F spectrum was found to have the γ-lines at 504(15) and 777(19) keV of which statistical confidences are 2.4 and 3.0 σ, respectively. The experimental cross sections for the γ-ray transitions are σ(504 keV) = 11.0±5.0 mb and σ(777 keV) = 18.0±6.0 mb. The other γ-lines found for 25 F (26 F) are at 727(22) and 1753(53) keV (468(17) and 665(12) keV). All the above bound states have been observed for the first time. The existence of the bound excited states in 27 F suggests a significant deformation for 27 F. An sd-shell model predicts that the first excited state of 1/2+ is located at about 2 MeV [23], which is beyond the particle threshold of 27 F(Sn = 1.4 MeV). This prediction is obviously contradictory on the experimental findings. On the other hand, an spdf -shell model calculation [24] leads to the melting of N = 20 shell gap and hence predicting the 1/2+ energy of about 1 MeV. According to this shell model work, when one moves to a lower Z along N = 20, collectivity becomes larger due to a larger fraction of 4p-4h configuration. It is interesting to note that the energy observed for the excited state (777 keV) is even lower than that predicted (1 MeV), suggesting that 27 F may have a larger deformation than predicted. More elaborated theoretical works are necessary to understand mechanism for the low-lying excited state in 27 F.

with the 2p-2h intruder configuration has been searched for. Recently, an experimental work via 34 Al β-γ spectroscopy found several γ lines [25]. Three of them at 1.193, 1.715 and 2.696 MeV were not placed in 34 Si. In addition, it was suggested that the 1193 keV γ line observed is the + candidate of 2+ 1 → 02 transition. To clarify the nature of these unplaced γ lines and to examine the suggestion 34 Si was of the 0+ 2 state, deuteron inelastic scattering of studied [19]. High statistics given by the liquid deuterium target enabled us to perform γ-γ coincidence. Doppler-corrected γ energy spectrum was obtained in coincidence with the + 3.326 MeV γ-rays corresponding to the 2+ 1 → 01 transition. In this spectrum, four γ lines at 0.930, 1.193, 1.715 and 2.696 were found to be associated with the 3.326 MeV γ-rays. In addition, all the transitions corresponding to the γ lines were found to feed finally the 2+ 1 state with almost 100% probability. According to the experimental facts, a level scheme of 34 Si was constructed [19]. It was also indicated that the possible existence of the 0+ 2 state at 2.133 MeV is unlikely. Further experimental efforts have to be made to search for the 0+ 2 state for future.

5 Anomalous quadrupole collectivity in

16

C

One of the important E2 transitions in an even-even nucleus is that from the first 2+ state to the ground state. The reduced transition probability B(E2) for the transition has long been a basic observable in the extraction of the magnitude of nuclear collectivity or in probing anomalies in the nuclear structure. With the recent advance of the intermediate energy Coulomb excitation, the magicity has been examined over the nuclear chart through measurements of E2 strengths [10]. In the light mass region of Z < 8, however, the Coulomb excitation may suffer from contamination of nuclear excitation. Thus, new experimental techniques were desired to deduce B(E2) values for the light mass region. To obtain the B(E2) information, we have developed a new technique applied for the 16 C isotope, where lifetime of an excited state is measured with fast RI beams. This experiment has shown an anomalously hindered B(E2) [26]. Alternatively, the Coulomb-nuclear interference method has given a large difference of proton and neutron transition matrix elements [27]. In addition to the proton collectivity deduced from B(E2), magnitude of neutron collectivity has been studied via the proton inelastic scattering [28], which is the most neutron sensitive reaction. Results of the three experiments based on the in-beam γ spectroscopy are presented and possible mechanism of the anomaly would be discussed. 5.1 Recoil shadow method

4.3

34

Si

The nuclear structure of 34 Si is interesting in terms of a shape coexistence proposed, hence a deformed 0+ 2 state

+ 16 C The electric quadrupole transition from 2+ 1 to 0g.s. in was studied through measurement of the lifetime for the 2+ 1 state by a recoil shadow method [26]. In this method, an emission point of the de-excitation γ-ray is located and

Hiroyoshi Sakurai: Spectroscopy on neutron-rich nuclei at RIKEN

the γ-ray intensity is recorded as a function of the flight distance of the de-exciting nucleus. As the flight velocity of the de-exciting nucleus is close to half the velocity of light, the flight distance over 100 ps corresponds to a macroscopic length of about 1.7 cm. Experimental observables reflecting lifetime were γ-ray yields recorded at two NaI rings located around a target, of which acceptances were geometrically determined with respect of a lead slab around the target and the emission point. Thus, yield ratios between the two rings had lifetime dependence. Details of the experimental setup and analysis procedures are found in ref. [26]. The adopted value for the lifetime is 77 ± 14(stat) ± 19(syst) ps. The central value corresponds to the B(E2; 2+ → 0+ ) value of 0.63 e2 fm4 or 0.26 in Weisskopf units (W.u.). The systematic error was deduced by taking into account two major sources; geometrical uncertainty, optical potential dependences of the angular distribution of γ-ray emission. It should be noted that the γ-ray yield measurement was conducted at two target positions to examine validity of this method. The B(E2) value obtained for 16 C was compared with all the other B(E2) values known for the even-even nuclei with A ≤ 50 [26]. Nuclei with open shells tend to have B(E2) values greater than 10 W.u., whereas nuclei with shell closure of neutrons or protons tend to have distinctly smaller B(E2) values. Typical examples of the latter category are doubly magic nuclei, 16 O and 48 Ca, of which B(E2) values are 3.17 and 1.58 W.u., respectively. The value of B(E2) for 16 C is even smaller than these extreme cases by as much as an order of magnitude. Comparison of the B(E2) value with an empirical formula based on a quantum liquid-drop model [29] illustrates the anomalously strong hindrance of the transition. The experimental B(E2) value for 16 C relative to that predicted by the formula is 0.036, which is exceptionally small, far smaller than for any other nuclei, including closed-shell nuclei. 5.2 Coulomb-nuclear interference method The neutron and proton quadrupole excitations in 16 C were investigated by use of the Coulomb-nuclear interference method applied to the 208 Pb + 16 C scattering. To observe the interference pattern in angular distribution of the 16 C nuclei for the inelastic channel, a high angular resolution of 0.28◦ (r.m.s.) was achieved in this experiment. A thin Pb target with a thickness of 50 mg/cm2 was used to minimize the multiple-scattering effect, and four PPACs with a position resolution of 0.2 mm (r.m.s.) were employed for the scattering angle measurement [27]. The obtained differential cross section was analyzed with the standard coupled channel code and two sets of optical potentials [27]. Parameters of the Coulomb deformation length δC and the matter deformation length δM were obtained from the best fit of the data. There were two χ2 -minima for δM /δC . The ratio giving a better χ2 was 3.1. Combination of the ratio with Bernstein’s prescription [30] leads to a ratio of the neutron and proton

407

matrix elements, Mn /Mp of 7.6 ± 1.7. The Mn /Mp ratio is larger than N /Z =1.67 that would be expected for a purely isoscalar transition. By normalizing the absolute cross section, the absolute values for δC and δM were deduced to be 0.42 ± 0.05 and 1.3±0.15 fm, respectively. The corresponding B(E2) value was 0.28 ± 0.06 W.u., consistent with the lifetime measurement [26]. 5.3 Proton inelastic scattering The B(E2) value obtained through the lifetime measure16 C was found to be remarkment of the 2+ 1 state in ably small. This finding raises an intriguing question as to whether or not the neutron contribution is similarly small for the relevant quadrupole transition. To answer this question, a study using a proton probe sensitive to neutrons, namely via the inelastic proton scattering, was performed. In this experiment, the in-beam γ spectroscopy was used in inverse kinematics [31]. Ingredients of this experiment are use of the liquid hydrogen target [16] and the new NaI setup DALI2 [20]. These equipments enhanced the feasibility of this method. More information on the experimental setup is found in ref. [28]. The deformation parameter βpp was obtained to be 0.50(8) from the measured angular-integrated cross section of 24.1 mb. This deformation parameter was found to be significantly larger than that of the lifetime measurement (0.14). Combination of the result of the lifetime measurement [26] with Bernstein’s prescription gives us a ratio of the neutron and proton quadrupole matrix elements (Mn /Mp )/(N /Z) of 4.0 ± 0.9 [28], which is in good agreement with the result obtained by the Coulombnuclear interference [27]. 5.4 Discussion The three experiments for the quadrupole transition in 16 C have provided the results consistent with each other, and strengthening the fact of the anomaly of B(E2) in 16 C. To find a possible mechanism for understanding the anomaly, two experimental facts observed in the neighboring nuclei are emphasized. The first one is proton and neutron shell gaps in the light mass region, which can be deduced from the mass information. The proton (neutron) shell gaps Gp (Gn ) are calculated through the following empirical formulas; Gp = S2p (Z, N ) − S2p (Z + 2, N ) and Gn = S2n (Z, N )−S2n (Z, N +2). The values of S2p and S2n are taken from ref. [22]. The values of the shell gaps are shown in fig. 4. A region of 6 ≤ Z ≤ 8 and 10 ≤ N ≤ 13 has a small value of Gn , less than about 1 MeV, and showing a “degeneracy” of sd-shell for neutron orbitals. On the other hand, the Gp values in this region are about 10 MeV. As for 16 C, the value of Gn is as small as 0.6 MeV, while that of Gp is as large as 12 MeV. This remarkable contrast of shell gaps between protons and neutrons may depict a hard proton matter and a soft neutron matter of

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proton number

MeV

(a) Z=6

N=10

16C

proton number

neutron number

MeV

(b) Z=6

N=10

16C

neutron number

Fig. 4. Shell gaps calculated for protons (a) and for neutrons (b), by using the nuclear mass compilation [22].

nuclei in this region. The second fact to be noted is magnitude of the effective charges for neutrons. Measurement of electric quadrupole moments for 15,17 B [32] suggests that the E2 effective charges can be remarkably reduced for the neutron-rich nuclei. According to the two observation, the hard proton core and the valence neutrons degenerating with the small effective charges give qualitatively a small B(E2) value. Quantitative predictions based on microscopic models are found and cited in refs. [26, 27]. These discussions raise a next question: how the anomalous B(E2) region is extended toward a larger N and what underlying mechanism causing the asymmetric dynamics between protons and neutrons is. To answer these questions, further experimental studies on neighboring nuclei as well as theoretical attempts would be necessary.

6 Summary It has been demonstrated that the new spectroscopic information has been obtained by means of the new spectroscopic techniques developed for fast RI beams, which illustrate the activities at the RIKEN-RIPS and potentials of fast RI beams. Before the new facility RIBF constructed, the present accelerator facility has been upgraded and several experiment programs have been performed by use of intense primary beams, such as 40 Ar, 48 Ca and 86 Kr. The methods and techniques developed at the RIKEN-RIPS will be naturally extended to experimental programs at the RIBF to investigate heavier or more neutron-rich nuclei

than available at the present facility. The two accelerators IRC and SRC and a new RI beam separator Big-RIPS are being constructed. In 2007, RI beams will be delivered for experimental programs at the RIBF. This work described here represents the efforts of many people, whom I have tried to adequately reference. In particular, most of the experiments presented here were performed in collaboration with University of Tokyo, Rikkyo University and RIKEN. The experiment for particle stability [3] was undertaken with University of Tokyo, JINR and RIKEN collaboration. A few experiments [18, 27, 28] were under the ATOMKI-RIKEN collaboration.

References 1. T. Kubo et al., Nucl. Instrum. Methods B 70, 309 (1992). 2. http://www.rarf.riken.go.jp/RIBF/overview-e.htm. 3. M. Notani et al., Phys. Lett. B 542, 49 (2002) and references therein. 4. S. Michimasa et al., these proceedings, p. 367. 5. H. Iwasaki et al., these proceedings, p. 415. 6. E. Ideguchi et al., these proceedings, p. 429. 7. P. M¨ oller et al., At. Data Nucl. Data Tables 39, 185 (1995). 8. Y. Aboussir et al., At. Data Nucl. Data Tables 61, 127 (1995). 9. S. Gr´evy et al., Phys. Lett. B 594, 252 (2004). 10. T. Motobayashi et al., Phys. Lett. B 346, 9 (1995). 11. T. Glasmacher et al., Phys. Lett. B 395, 163 (1997). 12. F. Azaiez et al., Eur. Phys. J. A 15, 93 (2002). 13. K. Yoneda et al., Phys. Lett. B 499, 233 (2001). 14. D. Bazin et al., Phys. Rev. Lett. 91, 012501 (2003). 15. H. Iwasaki et al., Phys. Lett. B 522, 227 (2001). 16. H. Akiyoshi et al., RIKEN Accel. Prog. Rep. 32, 167 (1999). 17. Y. Yanagisawa et al., Phys. Lett. B 566, 84 (2003) and references therein. 18. Z. Elekes et al., Phys. Lett. B 599, 17 (2004). 19. N. Iwasa et al., Phys. Rev. C 67, 064315 (2003). 20. S. Takeuchi et al., RIKEN Accel. Prog. Rep. 32, 148 (2003). 21. H. Sakurai et al., Phys. Lett. B 448, 180 (1999). 22. G. Audi, A.H. Wapstra, C. Thibault, Nucl. Phys. A 729, 337 (2003). 23. B.A. Brown, http://www.nscl.msu.edu/sde.htm. 24. Y. Utsuno et al., Phys. Rev. C 64, 011301(R) (2001). 25. S. Nummela et al., Phys. Rev. C 63, 044316 (2001). 26. N. Imai et al., Phys. Rev. Lett. 92, 062501 (2004). 27. Z. Elekes et al., Phys. Lett. B 586, 34 (2004). 28. H.J. Ong et al., these proceedings, p. 347. 29. S. Raman et al., Phys. Rev. C 37, 805 (1988). 30. A.M. Bernstein et al., Commun. Nucl. Phys. 11, 203 (1983). 31. H. Iwasaki et al., Phys. Lett. B 481, 7 (2000). 32. H. Izumi et al., Phys. Lett. B 366, 51 (1996); H. Ogawa et al., Phys. Rev. C 67, 064308 (2003).

Eur. Phys. J. A 25, s01, 409–413 (2005) DOI: 10.1140/epjad/i2005-06-094-0

EPJ A direct electronic only

Reduced transition probabilities for the first 2+ excited state in 46 Cr, 50Fe, and 54Ni K. Yamada1,a , T. Motobayashi1 , N. Aoi1 , H. Baba2 , K. Demichi3 , Z. Elekes4 , J. Gibelin5 , T. Gomi1 , H. Hasegawa3 , N. Imai1 , H. Iwasaki6 , S. Kanno3 , T. Kubo1 , K. Kurita3 , Y.U. Matsuyama3 , S. Michimasa1 , T. Minemura7 , M. Notani8 , T. Onishi K.6 , H.J. Ong6 , S. Ota9 , A. Ozawa10 , A. Saito2 , H. Sakurai6 , S. Shimoura2 , E. Takeshita3 , S. Takeuchi1 , M. Tamaki2 , Y. Togano3 , Y. Yanagisawa1 , K. Yoneda11 , and I. Tanihata8 1 2 3 4 5 6 7 8 9 10 11

RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Center for Nuclear Study (CNS), University of Tokyo, RIKEN Campus, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Department of Physics, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan Institute of Nuclear Research of the Hungarian Academy of Sciences, P.O. Box 51, Debrecen H-4001, Hungary Institut de Physique Nucl´eare, F-91406 Orsay Cedex, France Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439, USA Department of Physics, Kyoto University, Kita-Shirakawa-Oiwake, Sakyo, Kyoto 606-8502, Japan Department of Physics, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba, Ibaraki 305-8577, Japan National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824-1321, USA Received: 22 December 2004 / c Societ` Published online: 27 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 + 46 Cr, 50 Fe, and 54 Ni nuclides by Abstract. We measured B(E2; 0+ g.s. → 21 ) values for the proton-rich intermediate-energy Coulomb excitation in order to study the systematic behavior of collectivity in the Z = 20–28 region. The present study completes the B(E2) values for the T z = ±1 even-even pair nuclei up to Z = 28. The double ratios of proton and neutron matrix elements, (|Mn |/|Mp |)/(N/Z), have been extracted from the B(E2) values combining with the ones of their mirror nuclei, and compared with theoretical predictions.

PACS. 25.70.De Coulomb excitation – 23.20.Lv γ transitions and level energies

1 Introduction Systematic behaviors of the reduced transition probability B(E2) and energy E(2+ ) for the first excited state in even-even nuclei provide useful information for investigating the evolution of the nuclear collectivity. These properties were extensively studied for the isotopes on and near the stability line, and expanded mainly into the neutronrich region. However, the experimental studies for excited states have not so often been performed in the protonrich region because of the relatively poor quality for available RI beams. Thus, the systematics of B(E2) for isospin Tz = ±1 even-even pairs had only been completed up to A = 42 mass system. The aim of the present study is to extend the systematics of B(E2) and E(2+ ) up to 56 Ni along the N = Z line in order to clarify the collective aspects in the beginning of pf shell up to N = Z = 28 double shell closure. a

Conference presenter; e-mail: [email protected]

To complete the systematics in that region, one should measure the B(E2) values for 46 Cr, 50 Fe, and 54 Ni, and the E(2+ ) value for 54 Ni. The E(2+ ) values for the 46 Cr and 50 Fe were deduced to be 892 keV [1] and 765 keV [2], respectively, by using HPGe detectors. Recently, the B(E2 ↑) and E(2+ ) values for the 54 Ni have been reported by Yurkewicz et al. [3] to be 626(169) e2 fm4 and 1396(9) keV. Their mirror nuclei, 46 Ti, 50 Cr, and 54 Fe, are all stable, and their B(E2) and E(2+ ) values are well known. In the present work, we performed in-beam γ-ray spectroscopy of 46 Cr, 50 Fe, and 54 Ni with intermediate-energy Coulomb excitation using inverse kinematics. The fraction of these proton-rich nuclei in secondary beams produced by the projectile fragmentation is too low for direct experimental measurement. To increase the fraction, we constructed a Radio Frequency (RF) deflector system [4] for purification of the secondary beams. The B(E2) values were extracted from the Coulomb excitation cross-sections by Distorted-Wave Born Approximation (DWBA) analysis. In order to study general trends of collectivity, the

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proton and neutron matrix elements, Mp and Mn , were separately extracted from the B(E2) values by using Bernstein’s mirror nucleus method [5], which is based on the equality between the Mp and Mn in the mirror pair under the assumption of isospin symmetry.

2 Experimental procedure The experiment was carried out at the RIKEN Accelerator Research Facility. Secondary beams of 46 Cr, 50 Fe, and 54 Ni were produced by the projectile fragmentation of a 58 Ni primary beam accelerated up to 95 MeV/nucleon by the RIKEN Ring Cyclotron. The primary beam irradiated a nickel target of 303 mg/cm2 thickness with a typical beam intensity of 4.0 pnA. Each fragment was separated by the RIKEN Projectile-Fragment Separator (RIPS) [6] with a wedge-shape aluminum degrader of 116 mg/cm2 thickness. The fraction of 46 Cr, 50 Fe, and 54 Ni in the secondary beam were only 0.1%, 0.05%, and 0.02%, respectively. These secondary beams were purified by the RF deflector system located around the second focal plane (F2) of RIPS. The RF deflector system consists of an electrode part and a variable separation slit (Y-SLIT). After the selection by the magnetic rigidity, each nuclide in the secondary beam has a different velocity. Thus, we can use the difference of flight time between the production target and F2. A vertically arranged parallel-electrode is set along the beam line, and high alternating voltage with sinusoidal form is applied to the electrode in the direction perpendicular to the beam axis. Since the arrival time of particles at F2 depends on the species, a particle passing through the electrode is deflected by an amount depending on the species. When the oscillation phase is adjusted so as to permit the nucleus of interest to pass through the electrodes without deflection, other contaminants coming in the electrodes are deflected by the electric field and stopped on the Y-SLIT placed downstream of the electrodes. The RF deflector was operated at a voltage of 100 kV with a frequency of 14.05 MHz, synchronized with the RF signal of the injector cyclotron. The momentum spread of each secondary beam was set to ±0.7%, and the Y-SLIT was set to limit the total beam intensity to 1×104 counts per second. Fractions of 46 Cr, 50 Fe, and 54 Ni beams were about ten times improved to 1.0%, 0.5%, and 0.2% by the RF deflector, respectively. These secondary beams had typical intensities of 40 counts per second, 60 counts per second, and 10 counts per second on the reaction target, respectively. A lead target was used to study Coulomb excitation. The thickness was 224 mg/cm2 for the measurement of 46 Cr and 50 Fe, and the one for 54 Ni was 189 mg/cm2 thick. The beam energies were 44 MeV/nucleon, 41 MeV/nucleon, and 42 MeV/nucleon in the middle of the lead target, respectively. Particle identification of the incident beam was performed on an event-by-event basis by measuring the timeof-flight (TOF) information using a 0.1 mm plastic scintillator placed at the final focal plane (F3) of RIPS and

cyclotron RF signals. The plastic scintillator had an active area of 80×80 mm2 , and the scintillation light was detected by two photomultiplier tubes from both ends of the scintillator. The fluxes of the incident beams were also counted by this scintillator. We placed a 325-μm-thick silicon detector with an active area of 50×50 mm2 at F3 to make separate runs for measuring the fraction of the nucleus of interest in the beam. The incident angle of the beam was measured by a set of two delay-line ParallelPlate Avalanche Counters (PPACs) [7] with a sensitive area of 100×100 mm2 installed at F3. The two PPACs were placed 30 cm apart along the beam line. The typical position resolution of the PPACs was about 1.0 mm in FWHM. Another PPAC of the same type was placed behind the Y-SLIT in order to monitor the beam deflection in the vertical direction. Outgoing particles were detected by a delay-line PPAC with 150×150 mm active area (PI-PPAC) and nine sets of PIN silicon-detector telescope in order to select inelasticscattering events. The PI-PPAC was located 57 cm downstream of the reaction target, and its position information was used to determine the scattering angle, combined with the one from the two PPACs in beam line. The silicon-detector telescope was placed 62 cm downstream of the reaction target, which was arranged as a 3×3 matrix with three layers consisting respectively of 325 μm thick-, 500 μm thick-, and 500 μm thick-detectors. All silicon detectors had the same active area of 50×50 mm2 with single electrode and were mounted on 56×56 mm2 frames. The telescope covered the angles up to 7.2 degrees with respect to the beam axis, which sufficiently accepted most of inelastically scattered particles. The particles were identified from energy deposits in the first and second layers of the silicon detectors by the ΔE-E method. The third layer was used as veto to reject light particles passing through the second layer. To estimate the acceptance of the silicon telescope, we performed a Monte Carlo simulation, which took into account the detector geometry including frames between the silicon detectors, the finite size and angular spread of the incident beam, the multiple scattering in the reaction target, and the theoretical angular distribution of Coulomb excitation calculated by the coupled-channel code ECIS97 [8]. In order to check the accuracy of the simulation, we compared the simulated acceptance with the one deduced from interpolating the spatial distribution of scattered particles at the silicon telescope obtained from the image at the PI-PPAC. They agreed with 3% accuracy. De-excitation γ-rays were measured by using a subset of DALI21 [9] consisting of 116 NaI(Tl) scintillators with eleven layers. The array surrounded the target from 44 to 156 degrees with respect to the beam axis. Each scintillator crystal had a size of 8×4.5×16 cm3 coupled to a 3.8 cm  photomultiplier tube. Lead blocks with 50 mm thickness were placed just downstream of the NaI(Tl) array to reduce the background γ-rays from the silicon telescope. The high granularity of the setup allowed us to measure the angle of γ-ray emission with approximately 10-degree accuracy. The angle information was used to 1

Detector Array for Low Intensity radiation 2.

+ K. Yamada et al.: Systematic study of B(E2; 0+ g.s. → 21 ) for

46

Cr,

50

Fe, and

54

Ni

411

Table 1. E(2+ ) and B(E2 ↑) values deduced from the present experiment together with their previous ones.

E(2+ ) (keV)

Nucleus

Present

46

900(10) 892 767(7) 765 1370(30) 1396(9)

Cr Fe 54 Ni 50

Fig. 1. Doppler-corrected γ-ray spectra obtained for the Coulomb excitation of 46 Cr (a), 50 Fe (b), and 54 Ni (c). The solid curves are fits to the data, which contain the simulated line shapes for γ-rays (dashed curves) and exponential background contributions (dotted curves).

correct for the large Doppler shift of γ-rays emitted from the particles in flight with β = v/c ≈ 0.3. The intrinsic energy resolution of each detector and the total photopeak efficiency of DALI2 were typically 9.2% FWHM and 18.1% for 662 keV photons from a 137 Cs standard source. The absolute efficiencies were also obtained by a Monte Carlo simulation using the GEANT3 code [10], which were compared with the ones for source data in order to confirm the accuracy of the simulation. The results were consistent with the source data within 5% errors. The detection efficiency of DALI2 for the γ-rays emitted from moving nuclei are simulated and used to extract the Coulomb excitation cross-sections.

3 Result and discussion Figure 1 shows the Doppler-corrected γ-ray spectra measured in coincidence with the scattered particles of 46 Cr, 50 Fe, and 54 Ni. A single distinct peak is observed in each spectrum, and their energies have been determined to be 900(10) keV, 767(7) keV, and 1370(30) keV, respectively. The present results agree with their previously reported values, 892 keV, 765 keV, and 1396(9) keV, respectively. The angle-integrated cross-sections were determined from the γ-ray yields after correcting for the detection

Previous

B(E2 ↑) (e2 fm4 )

Present

Previous

930(200) – 1400(300) – 590(170) 626(169)

Fig. 2. Differential cross-sections for Pb induced inelastic excitation of 46 Cr (a), 50 Fe (b), and 54 Ni (c). The solid (dashed) curves represent calculated ones using the optical-potential set A (B).

efficiencies. The yields were evaluated by an analysis with a function y = af (Eγ ) + b · exp(−cEγ ), where f (Eγ ) is the spectral shape obtained by the GEANT simulation, and a, b, and c are free parameters. Results of the fits are shown by the solid curves in fig. 1 together with their individual components. The data are well reproduced by the sum of the two components. The cross-sections for 46 Cr, 50 Fe, and 54 Ni were deduced to be 460(90) mb, 690(120) mb, and 300(80) mb, respectively. The DWBA analysis was performed using the ECIS97 code assuming the collective deformation model. For the calculation, we used two different optical-potential parameter sets A and B, respectively obtained from the elastic scattering of 40 Ar on 208 Pb at 44 MeV/u [11] and 58 Ni on 208 Pb at 17 MeV/u [12]. The B(E2) values were extracted by taking the average of the calculations obtained with the two potential sets, and their differences were included + in the error. The resultant B(E2; 0+ g.s. → 21 ) values are 2 4 2 4 930 ± 200 e fm , 1400 ± 300 e fm , and 590 ± 170 e2 fm4 for 46 Cr, 50 Fe, and 54 Ni, respectively. The complete systematics of B(E2) for the Tz = ±1 even-even pairs up to Z = 28 has been established by the present study. The results of E(2+ ) and B(E2 ↑) are listed in table 1 together with their previous values. The validity of the DWBA calculation was examined by comparing with the angular distribution of differential

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cross-sections. The results are shown in fig. 2. The experimental data exhibit typical angular dependence for the E2 Coulomb excitation. Theoretical angular distributions calculated by the ECIS97 code assuming Coulomb excitation are shown for the potential A (B) by the solid (dashed) curves. The components of nuclear excitation are also shown by solid or dashed curves in each figure. These calculated cross-sections are smeared by angular resolution of the measurement, 1.2 degrees. As shown in the figure, the calculation reproduces well the experimental data, and hence, indicates the applicability of the DWBA calculation. In addition, the results indicates a negligibly small contribution from the nuclear excitation and E2 dominance in the present cases. The angular distribution of γ-ray emission was analyzed to check a possible influence to the cross-section evaluation. The experimental distribution was compared with the one obtained from a statistical tensor calculated by the ECIS97 assuming the 2+ → 0+ transition. From the comparison, the anisotropy of the angular distribution was found to affect only 5% of the evaluation assuming an isotropic emission, indicating a good coverage of detection angle in the present experiment. The double ratio (|Mn |/|Mp |)/(N/Z) is a measure for the collectivity of the 2+ 1 states. In even-even nuclei in which both proton and neutron shells are open, the ratio is generally close to unity, while nuclei with closed shells systematically deviate from unity. To evaluate the ratios, the |Mp | values for 46 Cr, 50 Fe, and 54 Ni were extracted from the B(E2) values by taking their square root as 4.4 ± 0.5, 5.1 ± 0.5, and 3.1 ± 0.4, respectively, in single-particle units Bsp (E2 ↑) = 0.297A4/3 e2 fm4 . The |Mn | values were obtained from the square root of B(E2) values for their mirror nuclei [13] to be 4.4 ± 0.1, 4.4 ± 0.1, and 3.2 ± 0.1 in the single-particle units for 46 Cr, 50 Fe, and 54 Ni, respectively. Figure 3 shows the results of (|Mn |/|Mp |)/(N/Z) for Tz = −1 even-even nuclides in the Z = 10–28 region. In the figure, the ratios fairly deviate from unity near the closed shells and follow the trend expected for nuclei close to the shell closure. The results obtained for both 46 Cr and 50 Fe are close to unity and are consistent with the pictures of collective nuclei without neutron and proton shell closures. The ratio for 54 Ni, which is close to unity, indicates the weakness of the Z = 28 shell closure. In fig. 3, the ratios are compared with theoretical predictions. The dashed lines indicate the results by the shellmodel calculations. The results using the USD interaction by Brown and Wildenthal [14] are shown in the sd-shell region, while the results calculated by Honma et al. [15] using GXPF1 interaction with ep = 1.5 and en = 0.5 are plotted in the pf -shell region. The dot-dashed line indicates the ratios extracted from the intrinsic electric quadrupole moment predicted by Sagawa et al. [16] using the deformed Hartree-Fock + BCS calculation with SIII interaction. The tendency of the systematic behavior for (|Mn |/|Mp |)/(N/Z) values is reproduced by these predictions. However, the experimental results exhibit smaller extents of single-particle natures compared with the shellmodel predictions in the vicinity of the shell closure 20 and

Fig. 3. The double ratio (|Mn |/|Mp |)/(N/Z) for Tz = −1 even-even nuclides in the Z = 10–28 region. The open circles indicate the ratios extracted from the present results. The closed circles are obtained from the B(E2) values in ref. [13].

28, suggesting the importance of collective aspects which should be taken into account. Better agreements are obtained by the deformed HF + BCS prediction. However, it considerably underestimates the amplitude of the matrix elements: for example, the predicted |Mp | values are smaller by a factor of about 20 for 38 Ca and 42 Ti.

4 Summary We have measured the B(E2) values for 46 Cr, 50 Fe, and Ni by intermediate-energy Coulomb excitation. The RF deflector system enables efficient measurements for these proton-rich nuclei. The present study completes the systematics of experimental B(E2) values for the isospin Tz = ±1 even-even pair nuclei up to Z = 28. Using the data of their mirror nuclei, the double ratios of matrix elements (|Mn |/|Mp |)/(N/Z) have been extracted up to A = 54 system. The present result suggests the necessity of more elaborate treatment of the nuclear collectivity in this mass region. 54

The authors are grateful to the researchers and staffs in the RIKEN Accelerator Research Facility for their valuable advice and collaboration.

References 1. 2. 3. 4. 5. 6.

P.E. Garrett et al., Phys. Rev. Lett. 87, 132502 (2001). S.M. Lenzi et al., Phys. Rev. Lett. 87, 122501 (2001). K.L. Yurkewicz et al., Phys. Rev. C 70, 054319 (2004). K. Yamada et al., Nucl. Phys. A 746, 156c (2004). A.M. Bernstein et al., Phys. Rev. Lett. 42, 425 (1979). T. Kubo et al., Nucl. Instrum. Methods Phys. Res. B 70, 309 (1992).

+ K. Yamada et al.: Systematic study of B(E2; 0+ g.s. → 21 ) for

7. H. Kumagai et al., Nucl. Instrum. Methods Phys. Res. A 470, 562 (2001). 8. J. Raynal, Coupled channel code ECIS97, unpublished. 9. S. Takeuchi et al., RIKEN Accel. Prog. Rep. 36, 148 (2003). 10. GEANT3: Detector Description and Simulation Tool (CERN, Geneva, 1993).

11. 12. 13. 14. 15. 16.

46

Cr,

50

Fe, and

54

Ni

413

N. Alamanos et al., Phys. Lett. B 137, 37 (1984). M. Beckerman et al., Phys. Rev. C 36, 657 (1987). S. Raman et al., At. Data Nucl. Data Tables 78, 1 (2001). B.A. Brown et al., Phys. Rev. C 26, 2247 (1982). M. Honma et al., Phys. Rev. C 69, 034335 (2004). H. Sagawa et al., submitted to Phys. Rev. C.

Eur. Phys. J. A 25, s01, 415–417 (2005) DOI: 10.1140/epjad/i2005-06-154-5

EPJ A direct electronic only

Intermediate-energy Coulomb excitation of the neutron-rich Ge isotopes around N = 50 H. N. T. Y. 1 2 3 4 5 6 7

Iwasaki1,a , N. Aoi2 , S. Takeuchi2 , S. Ota3 , H. Sakurai1 , M. Tamaki4 , T.K. Onishi1 , E. Takeshita5 , H.J. Ong1 , Iwasa6 , H. Baba5 , Z. Elekes2 , T. Fukuchi4 , Y. Ichikawa1 , M. Ishihara2 , S. Kanno5 , R. Kanungo2 , S. Kawai5 , Kubo2 , K. Kurita5 , S. Michimasa4 , M. Niikura4 , A. Saito5 , Y. Satou7 , S. Shimoura4 , H. Suzuki1 , M.K. Suzuki1 , Togano5 , Y. Yanagisawa2 , and T. Motobayashi2

Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Department of Physics, Kyoto University, Kitashirakawa, Kyoto 606-8502, Japan Center for Nuclear Study (CNS), University of Tokyo, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Department of Physics, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan Department of Physics, Tohoku University, Aoba, Sendai, Miyagi 980-8578, Japan Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo 152-8551, Japan Received: 1 October 2004 / Revised version: 20 April 2005 / c Societ` Published online: 4 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Structure of the neutron-rich Ge isotopes at and around N = 50 has been investigated via intermediate-energy Coulomb excitation using secondary beams of 78–82 Ge incident on a Pb target. The B(E2) values for the low-lying 2+ states have been extracted and compared with the data for neighboring isotopes around N = 50. In addition, a new method of intermediate-energy two-step Coulomb excitation has been proposed as a spectroscopic tool to study the 4+ states in neutron-rich even-even nuclei. The first application of the method and its results are presented. PACS. 23.20.Js Multipole matrix elements – 25.70.De Coulomb excitation – 27.50.+e 59≤ A ≤89

1 Introduction

2 Experiment

Neutron-rich nuclei in the vicinity of the doubly magic nucleus 78 Ni afford one of the best opportunities to investigate the evolution of nuclear structure toward the drip lines. We have recently performed in-beam γ studies of the neutron-rich isotopes 78–82 Ge around N = 50 by means of intermediate-energy Coulomb excitation. Among the various reactions employed in γ-spectroscopic studies with intermediate-energy radioactive-ion (RI) beams [1, 2, 3,4, 5], Coulomb excitation provides a unique means to determine both energies and transition probabilities B(E2) for the low-lying 2+ states. The aim of the present work is to investigate such E2 properties of the neutron-rich Ge isotopes, which enables us to depict systematic trends of the collective behavior toward the neutron magic number N = 50. In addition, a new method of intermediate-energy two-step Coulomb excitation has been applied for the first time to examine a possible access to higher excited states.

The experiment was performed at the RIPS facility in RIKEN. The secondary beams of the Ge isotopes were produced by fragmentation of a 63 AMeV 86 Kr beam on a 66.2-mg/cm2 -thick 9 Be target. A maximum intensity of around 100 pnA was achieved for the primary 86 Kr beam, owing to the recently developed acceleration scheme of the RIKEN Ring Cyclotron with the RFQ+RILAC+CSM injection system [6]. The event-by-event measurement of magnetic rigidity (Bρ), time-of-flight, and energy loss (ΔE) information allowed a clear isotopic identification of the incident beams. The secondary-beam intensities were around 6 kcps for 76 Ge, 2 kcps for 78 Ge, 1 kcps for 80 Ge, and 100 cps for 82 Ge in the separate Bρ settings optimized for each isotope. The secondary beams were transported to the experimental area, where a Pb target was set to excite the projectiles. Scattered particles were detected and identified by an array of a Si telescope and a NaI(Tl) calorimeter [7], which provided energy-loss (ΔE) and E information, respectively. The Si telescope consisted of 16 silicon detectors, while the NaI(Tl) calorimeter comprised 132 NaI(Tl) crystals.

a

Conference presenter; e-mail: [email protected]

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Fig. 1. Doppler-shift corrected γ-ray energy spectra following the 78,80,82 Ge + Pb reactions.

De-excitation γ-rays were measured in coincidence with the scattered particles by the DALI2 array [8], which is composed of 158 NaI(Tl) scintillators. Typical γ-ray energy spectra measured in coincidence with the even-even Ge isotopes are shown in fig. 1.

3 Intermediate-energy Coulomb excitation of Ge

78–82

Fig. 2. Doppler-shift corrected γ-ray energy spectra obtained in the 76 Ge + Pb scattering. The inset shows the spectrum gated on the 563 keV transition in 76 Ge.

excitation. So far, no significant transition associated with two-step excitation has been observed in Coulomb excitation studies with intermediate-energy RI beams of Z  10–20 nuclei [1, 4,5]. However, for heavier nuclei with Z ≥ 30, one may expect a large two-step excitation cross-section even at intermediate incident energies, since Coulomb excitation cross-section sharply rises with increasing Z. Figure 2 shows the experimental results of the twostep excitation applied for the secondary beam of 76 Ge at 37 AMeV. A γ-ray peak associated with the 2+ → 0+ transition (563 keV) in 76 Ge is evident. In the γ-γ coincidence spectrum gated on the 563 keV transition, the γ-ray peak corresponding to the 4+ → 2+ transition is also observed at around 850 keV. The B(E2) values for the observed transitions were obtained from the γ-ray peaks, and found to be in fairly good agreement with the previously known values. These observations thus demonstrate the usefulness of the present method for a simultaneous determination of the excitation energies of the 2+ and 4+ states as well as the B(E2) values for the 0+ → 2+ and 2+ → 4+ transitions in neutron-rich even-even nuclei.

As shown in fig. 1, the γ-ray peaks corresponding to the 2+ → 0+ transitions are clearly seen for 78,80,82 Ge (620 keV for 78 Ge, 660 keV for 80 Ge, and 1350 keV for 82 Ge). From the yields of the peaks, one can extract the Coulomb excitation cross-sections and hence the reduced transition probabilities B(E2). Preliminary analysis suggests the B(E2) values of around 0.2 e2 b2 for 78 Ge and 0.1 e2 b2 for 80,82 Ge. The systematic trends of B(E2) for the Ge isotopes with N = 46–50 are very similar to the Kr isotopes with N = 46–50 [9] (0.223(10) e2 b2 for 82 Kr, 0.125(6) e2 b2 for 84 Kr, and 0.122(10) e2 b2 for 86 Kr), suggesting a picture that N = 50 is still magic in the neutronrich Ge isotopes. The reliability of our measurements of B(E2) has been checked by comparing the present results on stable nuclei with adopted values determined from several measurements of low-energy Coulomb excitation [9]. Good agreement between the present B(E2) results of 0.25(3) e2 b2 for 80 Se and 0.17(3) e2 b2 for 82 Se and the adopted values of 0.253(6) e2 b2 for 80 Se and 0.184(5) e2 b2 for 82 Se supports the validity of the method of the intermediateenergy Coulomb excitation.

We have studied intermediate-energy Coulomb excitation of the neutron-rich Ge isotopes around N = 50. The present measurement completes the systematic data of B(E2) for the Ge isotopes up to N = 50. We have also showed that intermediate-energy Coulomb excitation provides a useful spectroscopic tool to investigate the lowlying 2+ and 4+ states of neutron-rich nuclei.

4 Intermediate-energy two-step Coulomb excitation

References

To develop a new method for the investigation of higher excited states in neutron-rich nuclei, we have performed a measurement of intermediate-energy two-step Coulomb

1. T. Motobayashi et al., Phys. Lett. B 346, 9 (1995). 2. H. Iwasaki et al., Phys. Lett. B 481, 7 (2000), 3. H. Iwasaki et al., Phys. Lett. B 522, 227 (2001).

5 Summary

H. Iwasaki et al.: Intermediate-energy Coulomb excitation of the neutron-rich Ge isotopes around N = 50 4. T. Glasmacher et al., Nucl. Phys. A 693, 90 (2001). 5. F. Azaiez: Nucl. Phys. A 704, 37c (2002). 6. M. Kase et al., RIKEN Accel. Prog. Rep. 34, 188 (2001).

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7. M. Tamaki et al., CNS-REP-59, 76 (2003). 8. S. Takeuchi et al., RIKEN Accel. Prog. Rep. 36, 148 (2003). 9. S. Raman et al., At. Data Nucl. Data Tables 36, 1 (1987).

6 Excited states 6.3 Deep inelastic collisions

Eur. Phys. J. A 25, s01, 421–426 (2005) DOI: 10.1140/epjad/i2005-06-107-0

EPJ A direct electronic only

First results of the CLARA-PRISMA setup installed at LNL A. Gadeaa Laboratori Nazionali di Legnaro, I-35020 Legnaro (Padova), Italy Received: 15 January 2005 / Revised version: 22 March 2005 / c Societ` Published online: 10 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Spring 2004 has seen the first experiments performed with the CLARA-PRISMA setup installed at LNL (Legnaro). The setup consists of CLARA, an array of 25 Clover (EUROBALL type) Ge detectors, placed at the target position of the large acceptance PRISMA magnetic spectrometer. The setup is an excellent tool to investigate the structure of neutron-rich nuclei, populated in multinucleon transfer reactions and deep inelastic collisions with stable beams. PRISMA allows the identification of the reaction products opening the possibility to go further away from stability in comparison with previous experimental activities using the aforementioned reactions. The setup has been commissioned in the first three months of the year and since March is fully operational. Five experiments had been performed, with beams delivered by the LNL tandem and the ALPI linac. In this contribution the main features of the setup as well as the preliminary outcome of the first experiments will be described. PACS. 29.40.Wk Solid-state detectors – 29.30.-h Spectrometers and spectroscopic techniques – 29.30.Kv X- and gamma-ray spectroscopy – 23.20.Lv Gamma transitions and level energies

1 Introduction Multinucleon transfer reactions and deep inelastic collisions have been used successfully in the last two decades to study the structure of nuclei far from stability in the neutron-rich side of the nuclear chart. Already in the ’80s, Guidry and collaborators [1] suggested the possibility to populate high spin states in transfer reactions induced by heavy projectiles. Since then the use of these reactions in nuclear spectroscopy studies has increased, following the evolution of the gamma multidetector arrays, in some cases competing successfully with results from first generation radioactive beam facilities. A good example are the neutron-rich nuclei around 68 Ni, the structure of this nucleus has revealed the quasi-doubly-magic character of N = 40, Z = 28 [2]. Nuclei in this region has been investigated both with fragmentation and deep inelastic collision techniques [2, 3, 4]. Ancillary devices capable of identifying the reaction products or at least one of them, were already used in early works: PPAC counters in kinematic coincidences [5, 6, 7] or Si telescopes to identify the light fragment [8]. Increasing the gamma-ray efficiency in Comptonsuppressed arrays allowed selection techniques purely based on the detection of gamma-gamma coincidences between unknown transitions from the neutron-rich nucleus and known ones from the reaction partner. The method a

Conference presenter; e-mail: [email protected]

was first used by Broda and coworkers [9] and since then it has been successfully applied up to the present day. The increasing interest for going further away from the stability for neutron-rich medium mass or heavy nuclei, has created the necessity of new techniques to identify the gamma transitions belonging to the product of interest. Recently, a collaboration working at ANL and MSU, have used the information obtained from beta-decay to select γ-rays from deep inelastic collisions detected by the Gammasphere array [10]. This technique is limited to nuclei where some states are populated both in the parent β-decay and in in-beam experiments with deep inelastic collisions. The assignment of any other transition to the nucleus is done exclusively on the basis of γ-coincidences. The Clover array (CLARA) coupled to the PRISMA magnetic spectrometer is a step forward in the use of the multinucleon transfer and deep inelastic collisions in gamma spectroscopy. The setup aims to measure in-beam prompt coincidences of γ-rays detected with CLARA and the reaction product seen by the PRISMA detectors. The setup allows in most cases to assign unequivocally the transitions to the emitting nucleus by identifying the mass and Z of the product going into PRISMA. It will therefore lower the sensitivity limit in the measurements and consequently allow to study excited states of nuclei away from stability produced with low cross-section. Recently, it has been proved the persistency of a sizable deep inelastic cross-section, populating neutron-rich nuclei, in peripheral reactions at Fermi energies [11,12].

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Fig. 1. Photographic view of the CLARA-PRISMA setup. At the left of the picture is the CLARA array of Clover detectors followed by the quadrupole and dipole magnets of the PRISMA magnetic spectrometer. The picture ends at the right with the flight and focal plane detector chambers of the spectrometer.

This finding will open the perspective of using such mechanism, in appropriate facilities, with the advantage of the product forward focusing, for the overall efficiency of the magnetic spectrometers.

2 The CLARA-PRISMA setup PRISMA is a large acceptance magnetic spectrometer for heavy ions, installed at LNL. It has been designed for the heavy-ion beams of the XTU Tandem-ALPI-PIAVE accelerator complex [13]. The most interesting features of the spectrometer are its large angular acceptance (80 msr), momentum acceptance ±10%; measured mass (via TOF) and Z resolutions ΔM/M ≈ 1/190 and ΔZ/Z ≈ 1/60 respectively; and energy resolution up to 1/1000 and rotation around the target in a large angular range (−20◦ ≤ θ ≤ 130◦ ). The mass resolution performance is achieved by software reconstruction of the ion trajectory, using the position, time and energy signals from the entrance position sensitive Micro-Channel-Plate (MCP) and the Multi-Wire Parallel Plate Avalanche (MWPPAC) focal-plane detectors [14]. The Z identification is provided by the Ionization Chamber (IC) installed after the MWPPAC. The project of coupling an array of Compton suppressed γ-ray detectors to the PRISMA spectrometer has been developed in the framework of a series of campaigns using EUROBALL detectors for specific research programs in few European facilities.

The array CLARA, working in conjunction with PRISMA aims at using binary reactions (quasi-elastic, multinucleon transfer or deep inelastic scattering) in order to populate excited states in the reaction products. In many cases it is compulsory to use stable heavy n-rich targets. The use of binary reactions implies in most cases large velocities for the products of interest. Therefore the design of the γ-ray detector array has been done to optimize the sensitivity, taking under consideration the kinematics of the aforementioned reactions and the mechanical constrains imposed by the spectrometer. PRISMA prevents the use of more than 1π of the forward solid angle, and to keep the resolution at a sensible level (1% at v/c ≈ 0.1) at large product velocity, high granularity and a large Ge-crystal to target distances are fundamental. The adopted solution uses 25 EUROBALL Clover detectors [15], taking advantage of the reduced dimensions of each of the four crystals composing the detector, being the granularity guaranteed by the large number of detectors (hundred crystals) building up the array. This solution, with a target-crystal distance of about 29.5 cm, leads to an array efficiency above 3% for 1.3 MeV γ-rays. The MCP entrance detector covers a small fraction (below 1%) of the total solid angle, but taking into account the kinematics and the angular distribution of the cross-section, efficiencies of the order of 3 to 5% are expected, at the grazing angle, for a typical reaction. A picture of the experimental setup is shown in fig. 1. The CLARA array rotates with PRISMA and therefore, the angle between the Clover detectors and the trajectory of

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the outcoming products are kept within the PRISMA acceptance. The characteristics of the setup allowed not only the assignment of gamma transitions to moderately exotic nuclear species, but also the investigation of the character and multipolarity of the radiation through angular distributions and linear polarization measurements [16]. It is possible as well to measure lifetime of excited states by using the techniques described in ref. [16]. The setup is presently fully functional and the experimental program is in progress. In the following section some preliminary results from the first experiments will be described.

3 Experimental activity The experimental program of the CLARA-PRISMA setup, started in March 2004, is focused mainly on the nuclear structure in neutron-rich nuclei and on the investigation of “non-yrast” states populated by quasi-elastic reactions. A consistent fraction of the experimental activity is connected to the study of the magic numbers in neutronrich nuclei. Concerning this subject nuclei in the vicinity of N = 50 have been studied and some preliminary results will be described. The appearance of unexpected magic numbers and the onset of the collectivity in nuclei beyond this new magicity, in particular in n-rich nuclei with A ≈ 60 and N ≈ 34 have also concentrated experimental efforts and some preliminary results obtained with CLARA-PRISMA in this region will be also shown. 3.1 The N = 50 shell closure in neutron-rich nuclei Nuclei in the neighborhood of the neutron-rich doubly magic nucleus 78 Ni has concentrated experimental efforts on stable and radioactive beam facilities in the last few years. Several reasons justify the interest in this area of the nuclear chart. Firstly the large N/Z ratio, much larger than any other known n-rich heavy doubly magic nucleus. This large ratio qualifies the region for searching for shell effects connected with nuclei with large neutron excess. In recent works it has been extensively discussed the effect of the difference between the proton and neutron root mean square radius in neutron-rich nuclei [17, 18,19, 20], in particular on the nuclear potential. The reduction of the spin-orbit term of the potential at the neutron drip-line, reduces the energy splitting between the spin-orbit partners, and thus the energy gap. The vicinity to the drip-line is not the only effect that can modify the shell structure in neutron-rich nuclei. It has been suggested recently that the attractive tensor interaction between spin-flip orbitals (repulsive between non– spin-flip) may contribute to the weakening of the shell gaps in neutron-rich nuclei [21]. The spectroscopic information provided by experiments in this region can be compared with shell model calculations, and from the comparison it is expected to infer

Fig. 2. ΔE-E matrix from the ionization chamber of the PRISMA focal plane. The matrix belongs to the 82 Se 505 MeV + 238 U experiment.

possible changes in the N = 50 shell gap. It is of particular interest to check if the modification of the gap starts as early on Z as in 82 Ge as predicted by Nayak and collaborators [22] or on the contrary, if it does not appear at all before 78 Ni as deduced from the relativistic mean field calculations performed by Geng and collaborators [23]. The experimental activity in this region [24] has been performed with a 82 Se beam at 505 MeV, delivered by the Tandem-ALPI complex, bombarding a 238 UO2 400 μgr/cm2 target. The spectrometer was placed at the grazing angle (θG = 64◦ ), in order to select mainly the quasi-elastic projectile-like reaction products from the multi-nucleon transfer process. Spectra from more than 50 nuclear species, from Kr to Cr isotopes, were obtained in 4 days of experiment with a beam intensity of 5 to 6 pnA. The ΔE-E matrix coming from the focal plane ionization chamber had enough resolution to have a good Z identification (see fig. 2). The mass distributions for the nuclides ranging from Kr to Ni are shown in fig. 3. For this experiment only 22 Clover detectors were used and the efficiency of CLARA in this case was ≈ 2.6%. The described experimental conditions prevented the measurement of γ − γ−PRISMA coincidences for many of the measured nuclei and therefore, to build the level scheme it was necessary to resort to a previous GASP experiment [25] performed again with 82 Se beam at an energy of 460 MeV bombarding a thick 192 Os target. An example of the quality of the data is shown in fig. 4, the spectrum and level scheme correspond to the odd-odd 80 As nucleus (one-proton and one-neutron stripping reaction channel). The transitions placed in the preliminary level scheme are marked also in the spectrum, and several other transitions are still under investigation [24]. The ground-state transition of 237 keV is hardly present in the CLARA spectrum shown in the figure, this suggests a relatively large lifetime (in the order of ns) for the state de-excited by this transition in 80 As. The transition was identified and placed in the level scheme with the help of the already mentioned GASP data set.

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Kr

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Mass Number Fig. 3. Mass distribution for the Kr to Ni isotopes populated in the 82 Se 505 MeV + 238 U experiment. It has been observed population up to Cr isotopes.

For the more exotic N = 50 isotones, due to the low population cross-section and the limited duration of the experiment, it was only possible to identify a candidate for the 4+ state in 82 Ge [24]. In fig. 5 the confirmed 4+ in 84 Se and the candidate for the 4+ in 82 Ge are shown together with the systematics and shell model calculation performed by Lisetskiy and collaborators [26]. This calculation is done with a new effective interaction based in a G-matrix Bonn-C Hamiltonian fitted to the experimental data available in the region, and takes into account the changes in the effective single particle energies due to evolution of the monopole interactions, between 56 Ni and 78 Ni (Z = 28 isotopes) and between 78 Ni and 100 Sn (N = 50 isotones), for the proton and neutron orbitals, respectively. The above-mentioned picture reflects how important is to have information on the excited states for nuclei in the vicinity of 78 Ni. 3.2 The onset of deformation in neutron-rich A = 60 nuclei Recently, a new shell closure at N = 32 has been identified for Ca isotopes [27]. The presence of this shell gap has been explained by Otsuka and collaborators as coming from

Fig. 4. Spectrum (upper panel) and level scheme (lower panel) for the odd-odd nucleus 80 As corresponding to the 1-proton stripping – 1-neutron stripping channel in the 82 Se beam experiment.

1 

0H9

0.0

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Ni

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$ Fig. 5. Calculated [26] (circles) and experimental (squares) 2+ and 4+ excitation energies for the even-even N = 50 isotones from 98 Cd to 82 Ge. The excitation energy of the 4+ in 84 Se has been confirmed and a preliminary value for 82 Ge is also reported.

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Mass (a.m.u)

Fig. 6. Mass distribution for the Cr isotopes measured with the PRISMA spectrometer following the 64 Ni 400 MeV + 238 U reaction. The 58 Cr peak has been marked.

the strong spin-flip proton-neutron monopole interaction between the πf7/2 and the νf5/2 orbitals [28]. This shell closure gets progressively weaker, in Ti and Cr isotopes, as Z increases. β-decay studies of even-even Cr isotopes produced by fragmentation reactions have allowed the identification of the first 2+ states [29]. The excitation energy of these states is decreasing very fast when going from the N = 32 to the N = 40 Cr isotope, the 2+ states in 58 Cr, 60 Cr and 62 Cr are placed at 880, 646 and 446 keV, respectively, suggesting the possible onset of deformation towards N = 40. Shell model calculations are able to reproduce this behavior only when the model space includes the intruder g9/2 and d5/2 orbitals [30]. An experiment, aiming to study the structure of Cr and Fe isotopes in this region [31], has been performed at CLARA-PRISMA setup with a 64 Ni beam impinging in a 238 UO2 400 μgr/cm2 target. The PRISMA spectrometer was placed at the grazing angle for this reaction (θG = 64). With this PRISMA detection angle and beam energy (≈ 17% above the Coulomb barrier), it is expected to detect mainly products of the multi-nucleon transfer channels. The preliminary mass spectrum obtained in a partial analysis of the data set obtained in the experiment is shown in fig. 6. A CLARA γ-ray spectrum is obtained for this nucleus setting a condition on the 58 Cr in the PRISMA data. The spectrum is shown in fig. 7 [31], even with a partial analysis of the data, several peaks are easily seen in it. Only the 2+ level at 880 keV, was previously known from β-decay data [27]. Our assignment for the transition de-exciting the (4+ ) has the same energy as a temptatively assigned 0+ → 2+ transition in ref. [27]. If, as expected, the two transitions are the same, the direct population of the (4+ ) state in β-decay would suggests a 3+ assignment for the spin and parity of the 58 V ground state. The tentative location of the (4+ ) state at 1937 keV excitation energy, ratio E(4+ )/E(2+ ) = 2.2, characterizes the 58 Cr as a transitional nucleus. The excitation energy









(QHUJ\NH9 Fig. 7. CLARA γ-ray spectrum obtained with the 58 Cr condition in the PRISMA spectrometer in the 64 Ni beam experiment. Spin parity assignment are preliminary above the already known 2+ .

of the (6+ ) state is preliminary assigned to 3217 keV and therefore, the ratio between the excitation energy of the 6+ and 2+ states is equal to 3.65. The two aforementioned ratios are very closed to the expected values for a nucleus described by the E(5) critical point symmetry [32], i.e. a nucleus at the U (5)-O(6) shape phase transition.

4 Conclusions This contribution describes the preliminary results of two experiments of the seven already performed at the CLARA-PRISMA setup installed at LNL. The setup is now fully operational and the results obtained show the high potential of the multinucleon transfer and deep inelastic reactions with stable beams in populating neutronrich nuclei. The upgrades realized for the LNL accelerators (low beta cavities for the ALPI linac and the new PIAVE injector) open new perspectives concerning the variety of nuclear species that will be available for the users in the next years. The author thanks the members of the CLARA and PRISMA2 collaborations as well as the technical groups, involved in the construction and running of the CLARA-PRISMA setup, for the excellent work done. Special thanks for their support on preparing this contribution are due to Nicu Marginean, Enrico Farnea, Giacomo de Angelis, Silvia Lenzi, Calin Ur, Daniel Napoli, Alberto Stefanini, Lorenzo Corradi and Giovanna Montagnoli.

References 1. M.W. Guidry et al., Phys. Lett. B 163, 79 (1985). 2. R. Broda et al., Phys. Rev. Lett. 74, 868 (1995).

426 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

14. 15. 16. 17.

The European Physical Journal A R. Grzywacz et al., Phys. Rev. Lett. 81, 766 (1998). T. Ishii et al., Phys. Rev. Lett. 81, 4100 (1998). A.O. Machiavelli et al., Nucl. Phys. A 432, 436 (1985). C.Y. Wu et al., Phys. Lett. B 188, 25 (1987). S. Juutinen et al., Phys. Lett. B 192, 307 (1987). H. Takai et al., Phys. Rev. C 38, 1247 (1988). R. Broda et al., Phys. Lett. B 251, 245 (1990). R.V.F. Janssens et al., Phys. Lett. B 546, 55 (2002). G.A. Souliotis et al., Phys. Lett. B 543, 163 (2002). G.A. Souliotis et al., Phys. Rev. Lett. 91, 022701 (2003). A. Lombardi et al., Proceedings of the Particle Accelerator Conference, Vancouver, Canada, 1997 (IEEE, Piscataway, NJ, 1998). A.M. Stefanini et al., LNL Annual Report 2002, in press. G. Duchˆene et al., Nucl. Instrum. Methods A 432, 90 (1999). A. Gadea et al., Eur. Phys. J. A 20, 193 (2004). G.A. Lalazissis et al., Phys. Rev. C 57, 2294 (1998).

18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.

D. Vretenar et al., Phys. Rev. C 57, 3071 (1998). J. Meng et al., Nucl. Phys. A 650, 176 (1999). M. Del Estal et al., Phys. Rev. C 63, 044321 (2001). T. Otsuka et al., in Proceedings of the XXXIX Zakopane School of Physics, Acta Phys. Pol. B 36, 1216 (2005). R.C. Nayak et al., Phys. Rev. C 60, 064305 (1999). L.S. Geng et al., nucl-th/0402083. G. de Angelis, G. Duchˆene, N. Marginean et al., private communication. Y.H. Zhang et al., Phys. Rev. C 70, 024301 (2004). A.F. Lisetskiy et al., Phys. Rev. C 70, 044314 (2004). J.I. Prisciandaro et al., Phys. Lett. B 510, 17 (2001). T. Otsuka et al., Phys. Rev. Lett. 87, 082502 (2001). O. Sorlin et al., Eur. Phys. J. A 16, 55 (2003). E. Caurier et al., Eur. Phys. J. A 15, 145 (2002). S.M. Lenzi, S.J. Freeman, N. Marginean et al., private communication. F. Iachello, Phys. Rev. Lett. 85, 3580 (2000).

Eur. Phys. J. A 25, s01, 427–428 (2005) DOI: 10.1140/epjad/i2005-06-201-3

EPJ A direct electronic only

Multinucleon transfer reactions studied with the heavy-ion magnetic spectrometer PRISMA L. Corradi1,a , A.M. Stefanini1 , S. Szilner1,6 , S. Beghini2 , B.R. Behera1 , E. Farnea2 , A. Gadea1 , E. Fioretto1 , F. Haas3 , A. Latina1 , N. Marginean1 , G. Montagnoli2 , G. Pollarolo4 , F. Scarlassara2 , M. Trotta5 , C. Ur2 , and the PRISMA-CLARA Collaboration 1 2 3 4 5 6

INFN - Laboratori Nazionali di Legnaro, I-35020 Legnaro (Padova), Italy Dipartimento di Fisica, Universit` a di Padova and INFN, Sezione di Padova, I-35131 Padova, Italy Institut de Recherches Subatomiques, IN2P3-CNRS-Universit´e Louis Pasteur, F-67037 Strasbourg, France Dipartimento di Fisica Teorica, Universit` a di Torino and INFN, Sezione di Torino, I-10125 Torino, Italy INFN - Sezione di Napoli and Dipartimento di Fisica, Universit` a di Napoli, Napoli, Italy Ruder Boˇskovi´c Institute, HR-10 002 Zagreb, Croatia

Received: 1 October 2004 / c Societ` Published online: 15 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Recent inclusive measurements on multinucleon transfer reactions reveal important information on the interplay between single-particle and nucleon pair degrees of freedom. More detailed studies are being performed with the new magnetic spectrometer PRISMA, coupled to the CLARA γ-array.

In inclusive measurements performed with time-of-flight and magnetic spectrometers multineutron and multiproton transfer channels have been studied for different systems (see [1] and references therein). The complete identification in nuclear charge, mass and Q-values of the binary reaction products allows to make a significant comparison with coupled channels calculations [2]. In this way, one can investigate the role played by the different degrees of freedom acting in the transfer process, for instance single particle or pair transfer modes. The understanding of these processes is important in view of future research to be done with radioactive beams [3]. Two examples are given below of recently measured systems with closed shell structure.

2 The

40

Ca +

208

Pb system

The interplay between single particle and pair transfer modes has been investigated [1] with the time-of-flight spectrometer PISOLO [4] at LNL by measuring differential and total cross sections and total kinetic energy loss (TKEL) distributions for multinucleon transfer channels. a

Conference presenter; e-mail: [email protected]

+

0

E lab =225 MeV

gs

2

1 Introduction

d σ / dE d Ω (a.u.)

PACS. 25.70.Hi Transfer reactions – 24.10.-i Nuclear reaction models and methods – 23.20.Lv γ transitions and level energies – 29.30.Aj Charged-particle spectrometers: electric and magnetic

TKEL (MeV)

Fig. 1. Experimental (histogram) and theoretical CWKB (curve) total kinetic energy loss distribution of the two neutron pick-up channel. The arrows correspond to the energies of 0+ states in 42 Ca with an excitation energy lower than 7 MeV, gs marks the ground to ground state Q-value.

In the 40 Ca + 208 Pb system measurements have been recently performed [5] at 3 bombarding energies close to the Coulomb barrier. Figure 1 shows the TKEL distribution at Elab = 225 MeV for the two neutron pick-up (+2n) channel together with calculations performed within the semiclassical Complex WKB (CWKB) theory [1,6]. One sees that this channel has a well defined maximum, which, within the energy resolution of the experiment, is consistent with a dominant population, not of the ground state of 42 Ca, but of the excitation region close to 6 MeV. In this region 0+ states were observed to be strongly populated

The European Physical Journal A

3 The

90

Zr +

208

Pb system

More detailed experiments able to distinguish between excited states of the transfer reaction products must exploit the full capability of magnetic spectrometers with solid angles much larger than conventional ones and resolutions sufficient to deal with very heavy mass ions. This is possible now with the PRISMA [8] spectrometer that has recently been installed at LNL and is designed for the A = 100–200, E = 5–10 MeV/u heavy-ion beams of the accelerator complex of LNL. The main features of the spectrometer are its large solid angle 80 msr, wide momentum acceptance ±10%, mass resolution 1/300 via time-offlight and energy resolution up to 1/1000. PRISMA has also been coupled to the CLARA γ-array [9] consisting of 25 Clover detectors from the Euroball Collaboration. First experiments on grazing collisions between heavy ions have been already performed with different beams. The main goals of these measurements were to investigate the population of neutron-rich nuclei in the A = 40–90 mass region by means of multinucleon transfer reactions [10], and to study the dynamics of such transfer processes. Figure 2 shows an example of spectra very recently obtained in the 90 Zr + 208 Pb reaction [11] at Elab = 560 MeV, with a 90 Zr beam accelerated with the ALPI + Tandem complex of LNL at intensities of  3 particle-nA. This exploratory experiment with PRISMA + CLARA was performed with the main aim of investigating the production of Zr and Sr isotopes for specific Q-values that are close to those where the excitation of pair vibrational modes is expected. As the Zr isotopes span a range from spherical to highly deformed shapes, it will be interesting to investigate into detail the change of the population and decay pattern of specific levels populated via multinucleon transfer reactions. The upper part of fig. 2 shows the mass distributions of Zr isotopes after gating on the nuclear charge Z = 40. One observes events corresponding to the pick-up as well as stripping of neutrons. One observes different relative yields in mass spectra for the Zr isotopes, due to the different γ multiplicities for the various multinucleon transfer channels populated in the reaction. The ratio of events in the two

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in light-ion reactions and were interpreted as multi (additional and removal) pair-phonon states [7]. Nuclear structure and reaction dynamics studies attribute this behavior to the influence of the p3/2 orbital that gives a much larger contribution to the two-nucleon transfer cross section than the f7/2 orbital which dominates the ground state wave function. At all bombarding energies one has a very similar behavior [5] and the features of the spectra are well reproduced by theory indicating that the used single particle levels cover the full TKEL spanned by the reaction. The results show that, at least in suitable cases, one can selectively populate specific energy ranges even in transfer reactions with heavy ions, opening the possibility to study multi pair-phonon excitations.

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spectra for specific masses is consistent with an overall efficiency of a few % of CLARA for γ transitions in the range  2 MeV. The single coincident γ spectrum for 90 Zr has been obtained after Doppler correction for the projectile-like nuclei selected by the spectrometer, taking into account the two-dimentional position determination at the entrance of PRISMA, the ion time of flight and the geometry of the Clover detectors. The determination of the reaction yields for levels populated in the Zr and Sr isotopes will be important for both nuclear structure and reaction mechanism. In particular, detailed comparison with coupled channel calculations can be performed.

References 1. L. Corradi et al., Phys. Rev. C 66, 024606 (2002). 2. A. Winther, Nucl. Phys. A 572, 191 (1994); 594, 203 (1995). 3. The EURISOL Report, Key experiment task group, J. Cornell (Editor), GANIL, December 2003; http://www. ganil.fr/eurisol. 4. G. Montagnoli et al., Nucl. Instrum. Methods Phys. Res. A 454, 306 (2000). 5. S. Szilner et al., Eur. Phys. J. A 21, 87 (2004). 6. E. Vigezzi, A. Winther, Ann. Phys. (N.Y.) 192, 432 (1989). 7. R.A. Broglia, O. Hansen, C. Riedel, in Advances in Nuclear Physics, edited by M. Baranger, E. Vogt, Vol. 6 (Plenum, New York, 1973) p. 287. 8. A.M. Stefanini et al., LNL-INFN (Rep) - 120/97 (1997); Nucl. Phys. A 701, 217c (2002). 9. A. Gadea et al., Eur. Phys. J. A 20, 193 (2004). 10. A. Gadea, these proceedings. 11. L. Corradi et al., LNL PAC proposal, July 2003.

Eur. Phys. J. A 25, s01, 429–430 (2005) DOI: 10.1140/epjad/i2005-06-153-6

EPJ A direct electronic only

Study of high-spin states in the fusion reactions

48

Ca region by using secondary

E. Ideguchi1,a , M. Niikura1 , C. Ishida2 , T. Fukuchi1 , H. Baba1 , N. Hokoiwa3 , H. Iwasaki4 , T. Koike5,b , T. Komatsubara6 , T. Kubo7 , M. Kurokawa7 , S. Michimasa7 , K. Miyakawa6 , K. Morimoto7 , T. Ohnishi7 , S. Ota8 , A. Ozawa6 , S. Shimoura1 , T. Suda7 , M. Tamaki1 , I. Tanihata9 , Y. Wakabayashi3 , K. Yoshida7 , and B. Cederwall2 1 2 3 4 5 6 7 8 9

Center for Nuclear Study, University of Tokyo, Wako Branch at RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Department of Physics, Royal Institute of Technology, Roslagstullsbacken 21, S-106 91 Stockholm, Sweden Department of Physics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 133-0033, Japan Department of Physics and Astronomy, SUNY at Stony Brook, Stony Brook, NY 11794-3800, USA Institute of Physics, University of Tsukuba, Ibaraki 305-8577, Japan The Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Department of Physics, Kyoto University, Kitashirakawa, Kyoto 606-8502, Japan Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA Received: 4 January 2005 / c Societ` Published online: 4 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. An in-beam gamma-ray spectroscopy study, following a fusion reaction induced by a neutronrich secondary beam, 46 Ar + 9 Be, is presented. A low-energy secondary beam of 46 Ar at ∼ 5 MeV/A was developed in order to induce fusion reactions. Gamma-gamma coincidence and excitation function analysis was performed to study high-spin states in the vicinity of 48 Ca, 49–52 Ti . PACS. 25.60.Pj Fusion reactions – 29.30.Kv X- and γ-ray spectroscopy – 23.20.Lv γ transitions and level energies – 27.40.+z 39 ≤ A ≤ 58

1 Introduction

2 Experimental results

In-beam gamma-ray spectroscopy using fusionevaporation reactions has been one of the most efficient methods for the study of nuclear structure at high spin since large angular momentum can be brought into the system. However, nuclei produced by fusion-evaporation reactions using stable isotopes are limited in many cases to the proton rich side of the β-stability line. Therefore, in order to study high-spin states of neutron rich nuclei by means of heavy ion induced fusion reactions, it is necessary to use neutron-rich secondary beams. In 48 Ca and 50 Ti, the presence of deformed shell gaps at Z = 20, 22 and N = 28 is expected to result in deformed collective states at high spin similar to the observed superdeformed band in 40 Ca [1]. In this article experimental results for the high-spin study of 49–52 Ti via a secondary fusion reaction, 46 Ar + 9 Be, are presented.

High-spin states in 49–52 Ti have been populated following a fusion-evaporation reaction induced by a low-energy 46 Ar beam of ∼ 5 MeV/A, which was produced at the RIPS Facility [2] in RIKEN via fragmentation reactions. A primary 48 Ca beam with an energy of 63 MeV/A, provided by the RIKEN Ring Cyclotron, with a maximum intensity of 100 pnA bombarded a 9 Be target of 1.0 mm thickness. An aluminum wedge energy degrader with a mean thickness of 221 mg/cm2 placed at the momentumdispersive focal plane (F1) was used to achieve a clear isotope separation and to lower the energy of the fragments to ∼ 30 MeV/A. By operating RIPS at the maximum values of momentum acceptance and solid angle, a typical beam intensity of 7.3×105 particles per second was obtained at the achromatic focal plane (F2). Particle identification of the secondary beam was performed by the time-of-flight (TOF)-ΔE method. The purity of the 46 Ar beam was measured to be 90%. The energy of the 46 Ar beam was further lowered by using an aluminum rotatable degrader of 0.5 mm thickness at F2 and measured to be 4.1 ± 0.9 MeV/A. The 46 Ar beam was transported to the final focal plane (F3)

a Conference presenter; e-mail: [email protected] b Present address: Physics Department, Tohoku University, Aramaki, Aoba-ku, Sendai 980-8578, Japan.

430

The European Physical Journal A

Fig. 1. Gamma-ray spectrum obtained in the reaction, Ar + 9 Be.

46

and irradiated on the secondary 9 Be target of 10 μm thickness in order to induce the secondary fusion reaction. The beam spot size on the secondary target was measured to be 39 mm and 19 mm (FWHM) in the horizontal and vertical directions, respectively. The intensity of the 46 Ar beam at F3 was about 3.2 × 105 particles per second. Gamma rays emitted in the fusion-evaporation reaction were detected using the GRAPE system [3] consisting of 17 Ge detectors in this experiment. Each detector contains two cylindrical-shaped planar Ge crystals and each crystal is electrically segmented in nine pieces. These detectors were placed around the secondary target to cover the angles between 60◦ and 120◦ relative to the beam axis. Two PPAC counters [4] placed at the up stream of the target as well as the TOF between the plastic scintillator signal at F2 and the PPACs provided beam profile information containing the position, incident angle, and energy of the beam. These were used for Doppler correction as shown in fig. 1. Gamma rays emitted from excited states in 49,50,51 Ti [5, 6, 7] are clearly observed. The energy of the 46 Ar beam is distributed between 2 and 7 MeV/A due to the energy straggling after passing through the degraders and beam counters. By utilizing this broad energy range of the beam, an excitation function measurement was performed by gating on the different regions of the beam-energy spectrum. Under the assumption that all gamma-ray cascades decay through the first yrast state of each nucleus, the relative gammaray intensity of these transitions in the Ti products, normalized by the beam intensity, is plotted as a measure of the excitation function in fig. 2(a). Figure 2(b) shows a calculated cross-section for 49–52 Ti production in the 46 Ar + 9 Be reaction as a function of the incident beam energy. The statistical model code, CASCADE [8] was used for the calculations. The peak position of the measured excitation function curve for 50 Ti is about 0.6 MeV/A lower than the CASCADE prediction. The angular momenta brought into the compound nucleus were estimated, by the Bass model calculations [9], to be ∼ 21 and ∼ 25

Fig. 2. (a) Normalized gamma-ray yields gated by different energy intervals of 46 Ar beam. (b) Cross-section for 49–52 Ti production as a function of incident beam energy in the 46 Ar + 9 Be reaction calculated by the statistical model code, CASCADE.

at the 46 Ar beam energy of 3.0 MeV/A and 5.0 MeV/A, respectively. By taking this and the observed gamma-ray yield into account, an optimum beam energy to produce high-spin states ≥ 16 in 50 Ti will be ∼ 4.0 MeV/A.

3 Summary A method to study high-spin states in the 48 Ca region by using a fusion-evaporation reaction with a neutronrich secondary beam was presented for the first time. A low-energy 46 Ar beam was developed in order to induce the fusion reactions. Gamma rays following the secondary fusion reaction, 46 Ar + 9 Be, were successfully observed and high-spin levels up to 11 were identified in 50 Ti. An excitation function measurement was performed simultaneously utilizing the energy spread of the secondary beam. This method will open new regions for the study of highspin states in neutron rich isotopes presently not accessible with conventional fusion-evaporation reactions with stable isotopes.

References 1. 2. 3. 4. 5. 6. 7. 8. 9.

E. Ideguchi et al., Phys. Rev. Lett. 87, 222501 (2001). T. Kubo et al., Nucl. Instrum. Methods B 461, 309 (1992). S. Shimoura, Nucl. Instrum. Methods A 525, 188 (2004). H. Kumagai et al., Nucl. Instrum. Methods A 470, 562 (2001). M. Behar et al., Nucl. Phys. A 366, 61 (1981). J. Styczen et al., Nucl. Phys. A 327, 295 (1979). S.E. Arnell et al., Phys. Scr. 6, 222 (1972). F. P¨ uhlhofer, Nucl. Phys. A 280, 267 (1977). R. Bass, Nucl. Phys. A 231, 45 (1974).

Eur. Phys. J. A 25, s01, 431–432 (2005) DOI: 10.1140/epjad/i2005-06-155-4

EPJ A direct electronic only

Spectroscopy of Ne and Na isotopes: Preliminary results from a EUROBALL + Binary Reaction Spectrometer experiment K.L. Keyes1,a , A. Papenberg1,b , R. Chapman1 , J. Ollier1 , X. Liang1 , M.J. Burns1 , M. Labiche1 , K.-M. Spohr1 , N. Amzal1 , C. Beck2 , P. Bednarczyk2 , F. Haas2 , G. Duchˆene2 , P. Papka2 , B. Gebauer3 , T. Kokalova3 , S. Thummerer3 , W. von Oertzen3 , and C. Wheldon3 1 2 3

The Institute of Physical Research, University of Paisley, Paisley, PA1 2BE, UK IReS, 23 Rue du Loess, 67037, Strasbourg, France Hahn-Meitner-Institut, Glienicker Str. 100, 14109 Berlin-Wannsee, Germany Received: 23 December 2004 / Revised version: 20 April 2005 / c Societ` Published online: 4 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The gamma-decay of fragments from deep-inelastic and multi-nucleon transfer processes which occur when a beam of 26 Mg at 160MeV is incident on a thin 150 Nd target was studied using the EUROBALL IV array of escape suppressed Ge detectors at Strasbourg. The good resolving power of EUROBALL IV was further increased by combining it with the Binary Reaction Spectrometer (BRS), used for the detection of projectile-like fragments. The BRS allows full kinematic reconstruction of the binary reaction allowing crucial Doppler corrections of gamma-ray spectra to be performed. Some preliminary results are presented. PACS. 23.20.Lv γ transitions and level energies – 25.70.Lm Strongly damped collisions – 27.30.+t 20 ≤ A ≤ 38

A beam of 26 Mg at 160MeV incident on a target of Nd of thickness 0.4mg/cm2 was used to initiate deepinelastic and multi-nucleon transfer reactions in order to populate nuclei in the vicinity of the projectile and target. These are good methods of populating yrast and non-yrast states of projectile-like and target-like nuclei. Very little is known of the higher spin states of nuclei in the projectile-like region. Their study was a primary objective of the experiment. Measurements using the BRS also allow kinematic reconstruction of the binary reaction channels to be made thus allowing the γ-decay of both projectile-like and target-like species to be investigated. The Vivitron accelerator at IReS, Strasbourg, France, was used to accelerate a beam of 26 Mg ions to an energy of 160MeV. The highly efficient γ-ray spectrometer EUROBALL IV was used in conjunction with the BRS. The array consisted of 26 Ge clover detectors, 15 Ge cluster detectors and an inner BGO array. A previous set-up had included tapered detectors at forward angles but these had been removed prior to the run to allow for the installation of the BRS. The BRS comprises two large-area heavy-ion detection telescopes either side of the beam axis covering 21% of the 150

a

Conference presenter; e-mail: [email protected] b e-mail: [email protected]

full solid angle Θ = 12◦ –46◦ [1]. The BRS was used to measure the energy and (Θ, Φ) coordinates of the projectilelike reaction fragments in coincidence with γ-rays detected by EUROBALL. Z-identification was based on data in the form of a 2-dimensional plot of Bragg peak versus ion energy. Mass identification by time of flight was not possible for this experiment. This was the first experiment which had employed the BRS with an array such as EUROBALL to study the γ-decay of deep-inelastic fragments. The trigger conditions for an event corresponded to two or more Compton-suppressed Ge signals and particle detection in the BRS. The data were sorted into Z-gated two dimensional γ-γ matrices using the highly sophisticated Data8m [2] and Datajo [3] sorting programs. The matrices thus generated were compatible with the RADWARE analysis package [4] which is currently being used to analyse the data. Two dimensional γ-γ matrices were generated for each projectile-fragment Z value from Z = 3 to Z = 15. Our attention so far has been focused on matrices corresponding to Mg, Na and Ne. Figure 1 shows an example of γ-ray spectra for Ne. The top spectrum corresponds to a gate at 2.97 MeV, the first 6+ to 4+ transition of 22 Ne. The transitions up to the 6+ to 4+ are known and can be clearly identified. Various experiments have identified the 8+ state (possibly yrast) located at an energy of 11.03 MeV [5,6, 7], in agreement with shell model calculations of Preedom

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and Wildenthal [8]. This is confirmed by the results of the present experiment which indicate the presence of a photopeak at 4.72 MeV which decays to the yrast 6+ . Figure 2 shows the partial level scheme for 22 Ne from the present work. An experiment performed by Szanto et al. in 1979 [9] observed the 10+ yrast state at an energy of 15.46 MeV. This was used to confirm a backbend in 22 Ne at around spin 8. However this state has not been referred to in subsequent papers and no evidence for it has been seen in this work. Figure 3 shows γ-ray spectra with a gate on Z = 11. 23 Na is known up to the 11/2+ state. A possible 13/2+ state has been observed [10] at an energy of 6.23 MeV. The same publication, in agreement with other works [11, 12], presents evidence for an additional state at 15/2+ [9.038 MeV]. Gomez del Campo et al. also tentatively suggests states at 17/2+ [13.82 MeV], 19/2+ [14.24 MeV] and 21/2+ [14.70 MeV], however these states have not been referred to in subsequent compilations. The present

Fig. 3. Spectra obtained with a gate on Z = 11.

experiment confirms the existence of the 13/2+ state. The top spectrum of fig. 3 is gated on the 9/2+ to 5/2+ transition of 2.26 MeV. The peak at 3.53 MeV is associated with the 13/2+ to 9/2+ transition and is consistent with shell model predictions and previous work. The bottom spectrum is gated on this transition and the the decay sequence down to the ground state can clearly be seen. Preliminary results have been presented from an experiment to study the spectroscopy of fragments from multinucleon transfer/deep-inelastic collisions initiated by a beam of 160 MeV 26 Mg incident on a thin target of 150 Nd. The use of the Binary Reaction Spectrometer leads to the Z-identification of projectile-like species and allows Doppler corrections to be made to the γ-ray energies. So far, only those nuclei close to the projectile have been partially studied. M.J. Burns, K.L. Keyes, A. Papenberg acknowledge support from the EPSRC during the course of this work.

References 1. S. Thummerer, PhD Thesis, Freie Universit¨ at Berlin, unpublished (1999). 2. http://www.hmi.de/people/beschorner/data8m/html/ data8m.html. 3. J. Ollier, private communication. 4. D.C. Radford, Nucl. Instrum. Methods Phys. Res. A 361, 306 (1995). 5. C. Broude et al., Phys. Rev. Lett. 25, 14 (1970). 6. C. Broude et al., Phys. Rev. C 13, 3 (1976). 7. H.P. Trautvetter et al., Nucl. Phys. A 297, 489 (1978). 8. B.M. Preedom, B.H. Wildenthal Phys. Rev. C 6, 5 (1972). 9. E.M. Szanto et al., Phys. Rev. Lett. 42, 10 (1979). 10. G.J. KeKelis et al., Phys. Rev. C 15, 2 (1977). 11. J. Gomez del Campo et al., Phys. Rev. C 12, 4 (1975). 12. D.E. Gustafson et al., Phys. Rev. C 13, 2 (1976).

6 Excited states 6.4 Collective excitations and shape coexistence

Eur. Phys. J. A 25, s01, 435–436 (2005) DOI: 10.1140/epjad/i2005-06-046-8

EPJ A direct electronic only

Ground-state properties and phase/shape transitions in the IBA E.A. McCutchan1,a , N.V. Zamfir1 and R.F. Casten1,b Wright Nuclear Structure Laboratory, Yale University, New Haven, CT 06520, USA Received: 5 November 2004 / c Societ` Published online: 3 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Detailed fits to energies and electromagnetic transition rates for isotopic chains in the rare-earth region were performed using a simple IBA-1 Hamiltonian. The resulting parameters were then used to calculate two-neutron separation energies, isomer and isotope shifts. Comparison of the isotope shift behavior with other observables in this mass region suggests that the isotope shift could provide an indication for a first-order phase transition. PACS. 21.10.Re Collective levels – 21.60.Fw Models based on group theory – 27.70.+q 150 ≤ A ≤ 189

The nature of phase/shape transitions as nuclei evolve from spherical to deformed shapes is a fundamental issue and recently has been the focus of many theoretical and experimental investigations. The study of phase transitional behavior in nuclei can easily be accomplished using the Interacting Boson Model (IBA) [1], where a study of the total energy surface of the IBA Hamiltonian has shown [2] that first- and second-order phase transitions occur as a function of the IBA parameters. Signatures of phase transitions can be observed in the evolution of observables related to the masses and radii of nuclei. Intuitively, one would expect these quantities to provide the most obvious evidence for phase/shape transitional behavior since they are closely connected to the shape of the nucleus. Observables such as two-neutron separation energies [2] and isomer shifts [3] have provided experimental evidence of phase transitions. In order to understand the evolution of these quantities within the framework of the IBA and their connection to actual nuclei, we have performed detailed fits [4] to collective even-even nuclei with Z = 64 to 72 and N = 86 to 104 using the IBA-1 model. Calculations were performed using the extended consistent Q formalism (ECQF) [5] with the Hamiltonian [6,7]

ζ ˆχ ˆχ (1) Q ·Q . H(ζ) = c (1 − ζ)ˆ nd − 4NB

The above Hamiltonian contains two parameters, ζ and χ (c is a scaling factor), while NB is given by half the number of valence protons and neutrons, each taken separately relative to the nearest closed shell. Parameters for each nucleus were extracted by considering basic properties of the ground, 0+ 2 , and quasi-2γ a b

e-mail: [email protected] Conference presenter; e-mail: [email protected]

bands, where the 2+ γ state is a member of the two-phonon– like multiplet in vibrational nuclei or else the bandhead of the quasi-γ band in rotational nuclei. Emphasis was + placed on fitting the energy ratios R4/2 ≡ E(4+ 1 )/E(21 ), + + + E(02 )/E(21 ), and E(2+ γ )/E(21 ) as well as the electromagnetic decay of these states. In most cases, a small range of parameter values is able to reproduce the above energy ratios to within 5%. Electromagnetic transition strengths were also reasonably reproduced. The quality of the fits to experimental energies in the Gd and Yb isotopic chains is demonstrated in fig. 1. The parameters obtained in the fits to the above spectroscopic information were then used to calculate two-neutron separation energies, isomer and isotopic shifts. The isomer shift, δ r 2 , provides a measure of the change in the nuclear radius between the 2+ 1 state and the ground state, given by [1]   ! ! ! (2) δ r2 = r2 2+ − r2 0+ = β nd 2+ − nd 0+ , 1

1

1

1

where the additional parameter β acts only as a scaling factor to connect the results of the calculations to the experimental data. The isotope shift, Δ r 2 , provides a measure of the differences in ground-state radii of nuclei differing by one neutron pair, given by [1] Δ r2

!(N )

= r2

!(N +2) 0+ 1



− r2

!(N )

(N +2)

= γ + β nd 0+ 1

0+ 1

 (N ) − nd 0+ ,

(3)

1

where β is the same quantity as in the isomer shift expression and γ is the contribution from the core which is independent of the structure of the nucleus and the same for the entire region.

436

The European Physical Journal A

+

Gd

2

+

1.2

2γ

+

0.8

(a)

Gd β = 0.03

30 20

2

41

-3

+

1.6

02

10

0.4 0

0.0

Yb

β = 0.15, γ = 0.0

β = 0.03, γ = 0.15

2

1.6

2

1.2 0.8

0.2

0.0

0.4 0.0

Gd

(b) 0.4

Δ < r > (fm )

Energy (MeV)

40

21

δ < r > (10 fm )

2.0

86

88

90

92

94

96

N 86 90 94 98 102

N Fig. 1. Comparison of experimental level energies (symbols) + and IBA calculations (solid lines) for the 2+ 1 , 41 members of + the ground-state band and the heads of the 2+ γ and 02 bands for the Gd and Yb isotopes.

The results of the calculation for the isomer shift, δ r2 , for the Gd isotopic chain along with the available experimental data are given in fig. 2(a). The dramatic change in the isomer shift between N = 88–90 is reproduced well by the calculations, taking β = 0.03 fm2 . The behavior of Gd resembles that of the Sm isotopic chain [8], which has been suggested [3] as an indication of a firstorder phase transition. In fig. 2(b), the results of the calculations for the isotope shift, Δ r 2 , for Gd are compared to the available experimental data. Again, a sharp change in the isotope shift is observed around N = 88–90. Using β = 0.03 fm2 from the isomer shift calculation and γ = 0.15 fm2 gives results which do not reproduce the sharp spike observed at N = 88. In order to reproduce the data, a large β value (= 0.15 fm2 ) and no γ term are necessary. This creates an obvious problem since the IBA parameter β in the isomer and isotope shift is expected to be the same. This is perhaps not surprising since the isomer shift relates to the data in a single nucleus while the isotope shift relates two nuclei differing in neutron number. This suggests that for the isotope shift, IBA-2 calculations might be required. In fact, IBA-2 fits (see for example [9]) to isotope and isomer shifts require different values for the proton and neutron components of β.

Fig. 2. Experimental values (symbols) and calculations (lines) of (a) isomer and (b) isotope shifts for the Gd isotopes.

The sharp change in the isotope shift at N = 88–90 is evocative of the behavior of both two-neutron separation energies and isomer shifts which also undergo a large change around N = 88–90. Since both two-neutron separation energies [2] and isomer shifts [3] can provide an indication of a first-order phase transition in this mass region, their similarities with the isotope shift behavior is consistent with the concept of a first-order phase transition at N ∼ 90. This work was supported by the U.S. Department of Energy under grant DE-FD02-91ER-40609.

References 1. F. Iachello, A. Arima, The Interacting Boson Model (Cambridge University Press, Cambridge, England, 1987). 2. A.E.L. Dieperink, O. Scholten, F. Iachello, Phys. Rev. Lett. 44, 1747 (1980). 3. F. Iachello, N.V. Zamfir, Phys. Rev. Lett. 92, 212501 (2004). 4. E.A. McCutchan, N.V. Zamfir, R.F. Casten, Phys. Rev. C 69, 064306 (2004). 5. P.O. Lipas, P. Toivonen, D.D. Warner, Phys. Lett. B 155, 295 (1985). 6. N.V. Zamfir, P. von Brentano, R.F. Casten, J. Jolie, Phys. Rev. C 66, 021304(R) (2002). 7. V. Werner, P. von Brentano, R.F. Casten, J. Jolie, Phys. Lett. B 527, 55 (2002). 8. O. Scholten, F. Iachello, A. Arima, Ann. Phys. (N.Y.) 115, 325 (1978). 9. R. Bijker, A.E.L. Dieperink, O. Scholten, Nucl. Phys. A 344, 207 (1980).

Eur. Phys. J. A 25, s01, 437–438 (2005) DOI: 10.1140/epjad/i2005-06-175-0

EPJ A direct electronic only

Chiral symmetry in odd-odd neutron-deficient Pr nuclei M.S. Feteaa , V. Nikolova, and B. Crider Department of Physics, University of Richmond, Richmond, VA 23173, USA Received: 2 January 2005 / Revised version: 22 April 2005 / c Societ` Published online: 21 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We investigate the features of the electromagnetic transitions in the chiral 132 Pr and 134 Pr within the framework of particle rotor model, to understand why the measured B(M 1)/B(E2) ratios for the yrare band are almost an order of magnitude larger than the corresponding ratios for the yrast band at low spins. PACS. 21.60.Ev Collective models – 27.60.+j Properties of specific nuclei listed by mass ranges

A system is chiral if it is not symmetric with respect to a mirror reflection in any plane. Nuclear chirality [1] results from an orthogonal coupling of the angular momentum vectors in triaxial nuclei. The spontaneous symmetry breaking of the chiral symmetry manifests itself in a pair of degenerate bands [2]. The energy degeneracy between chiral doublets built on the same band structure, a nearly independent of spin S(I) = [E(I) − E(I − 1)]/2I for the chiral region, and the characteristic electromagnetic properties [3, 4] are the experimental chiral fingerprints. Following the first example of a chiral nucleus, 134 Pr, twelve chiral candidates have been found in odd-odd nuclei in the mass 130 region: 126–132 Cs, 130–134 La, 132–134 Pr, 136 Pm, 138–140 Eu. Possible chiral pairs have been also reported in the even-odd 135 Nd [5] and in the even-even 136 Nd [6]. Recently, experimental work around the mass 100 region 102–106 Rh [7] gives promising results. The best known example of a chiral doublet is provided by 104 Rh [8]. The appearance of chiral bands is considered a strong evidence for the existence of triaxial deformations, since the chiral geometry cannot occur in an axially symmetric nucleus. In the mass 130 region, the chiral geometry is realized when the proton and neutron-hole occupy the lowest and the highest substates, respectively. The interplay of these tendencies towards elongated and disk-like shapes, may yield to a stable triaxiality [9]. Existing 134 Pr calculations reproduce the staggering pattern for the B(M 1)/B(E2) ratio for both the yrast and yrare bands and the B(M 1)in /B(M 1)out for the yrare band, but could not explain why for spins below 16+ , the measured B(M 1)/B(E2) ratios for the yrare band are almost an order of magnitude larger than corresponding ratios for the yrast band [10]. The calculated ratios for both the yrast and yrare bands are almost identical [10,11,12]. The aim of this work is to calculate the electromagnetic transitions in the chiral 132 Pr and 134 Pr using the Particle a

Conference presenter; e-mail: [email protected]

Rotor Model (PRM). Although it lacks self-consistency, ignores the change in shape induced by rotation, and does not take into account the nucleus’ polarization by the valence particles, the PRM uses wavefunctions having a good angular momentum and describes the system in the laboratory frame. Therefore the PRM directly yields the splitting between bands and the transition probabilities. Even having lifetime measurements available, because the nuclei of interest are triaxial, the values of ε2 and γ cannot be extracted from the experimental data. The irrotational flow formula produces the largest moment of inertia with respect to the medium axes for γ = 30◦ , which favors the aplanar orientation of the angular momentum. The value of γ practically does not influence the alignments of the valence particle and hole on the short and long axis, but these alignments are well defined only for sufficiently large values of deformation ε2 [13,14]. Calculations for 132 Pr and 134 Pr were performed for γ = 30◦ and various values of ε2 . The values for the other parameters used in the calculations were: u0 = −0.90 MeV, and u1 = −0.10 MeV for the Vnp interaction, gn0 = 18.3 and gn1 = 7.0 for the pairing strength, and ξ = 0.70 and η = 1.0 for the Coriolis attenuation. The PRM calculations reproduce well the experimental [15,16,17] trend in excitation energies and the staggering pattern in energy splitting S(I), in B(M 1)/B(E2) for both chiral partners, and in B(M 1)in /B(M 1)out ratios. For the choice of parameters mentioned above, larger values of the ε2 (0.333) reproduce the ∼ 300 keV measured separation energy between the chiral bands. Smaller values of the ε2 (0.275) give closer values to the experimental B(M 1)/B(E2) and B(M 1)in /B(M 1)out ratios in 134 Pr. The calculated inband B(M 1) for the yrast and yrare bands are shown in figs. 1 and 2, while the B(E2) are presented in figs. 3 and 4. As the spin increases, the B(E2) values within the two chiral partners become equal and slowly increase. The B(M 1) show the characteristic

The European Physical Journal A 132

Pr - yrast

∂2=0.275

Pr - yrare

132

∂2=0.275 2

BE2 Heb L

2.5 1.5 0.5

132

Pr - yrast

∂2=0.333

Pr - yrare

132

∂2=0.333

0.15

Pr - yrast

∂2=0.275

134

Pr - yrare

∂2 =0.275

134

Pr - yrast

∂2=0.333

134

Pr - yrare

∂2 =0.333

1. 0.5

2.

10.

15. Spin, I HÑL

20. 10.

15. Spin, I HÑL

134

Pr - yrast

∂2=0.275

134

Pr - yrare

∂2 =0.275

134

Pr - yrast

∂2=0.333

134

Pr - yrare

∂2 =0.333

1.5 0.5

BM1 Hnm2L

0.25 0.15 0.05

10.

15. Spin, I HÑL

20. 10.

15. Spin, I HÑL

20.

Fig. 2. The calculated yrast (left panels) and yrare (right panels) B(M 1) vs. spin for 134 Pr. The ε2 deformation parameters used were 0.275 (top panels) and 0.333 (bottom panels).

2

BE2 Heb L

132

1.5

Pr - yrast

∂2=0.275

132

Pr - yrare

15. Spin, I HÑL

20. 10.

15. Spin, I HÑL

20.

Fig. 4. The calculated yrast (left panels) and yrare (right panels) B(E2) vs. spin for 134 Pr. The ε2 deformation parameters used were 0.275 (top panels) and 0.333 (bottom panels).

at low spins. Also, the values of ε2 that reproduce the ∼ 300 keV measured separation energy between the chiral bands and the energy splitting S(I) are large compared to the predicted values for the mass 130 region [18], and to the measured deformations in the neighboring nuclei. Smaller measured deformations than the sufficiently large theoretical values of ε2 needed to build a chiral geometry [13,14] may be the reason why the Pr nuclei are not the best known examples of chiral nuclei. Especially for weak pairing, the moments of inertia may deviate from the irrotational-flow values. More work is currently undertaken to find the influence other PRM-related parameters have on improving the theoretical understanding of the B(M 1) and B(E2) for the chiral doublets in 132 Pr and 134 Pr.

∂2 =0.275

This work was supported by the NSF Grant No. PHY 0204811 and Research Corporation Grant No. CC5494.

1. 0.5 132

2.

Pr - yrast

∂2=0.333

132

Pr - yrare

∂2 =0.333

2

BE2 Heb L

1.

10.

20.

Fig. 1. The calculated yrast (left panels) and yrare (right panels) B(M 1) vs. spin for 132 Pr. The ε2 deformation parameters used were 0.275 (top panels) and 0.333 (bottom panels). 2.5

1.5 0.5

0.05

BM1 Hnm2 L

134

1.5

2

BM1 Hnm2L

0.25

BE2 Heb L

BM1 Hnm2 L

438

References

1.5 1. 0.5 10.

15. Spin, I HÑL

20. 10.

15. Spin, I HÑL

20.

Fig. 3. The calculated yrast (left panels) and yrare (right panels) B(E2) vs. spin for 132 Pr. The ε2 deformation parameters used were 0.275 (top panels) and 0.333 (bottom panels).

odd-even staggering, more pronounced at higher spins. This calculation indicates that for 132 Pr the ratios for the yrare band are a factor of 2.0 and 2.5 smaller than for the yrast band with the ε2 values 0.333 and 0.275, respectively, and almost identical in 134 Pr, for both ε2 values 0.333 and 0.275. Further, the calculation underestimates the experimental staggering in the B(M 1)in /B(M 1)out for 134 Pr by a factor of 2. The PRM calculations described above could not explain why in 134 Pr, the measured B(M 1)/B(E2) ratios for the yrare band are almost an order of magnitude larger than the corresponding ratios for the yrast band

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

11. 12. 13. 14. 15. 16. 17. 18.

S. Frauendorf, Rev. Mod. Phys. 73, 463 (2001). S. Frauendorf, J. Meng, Nucl. Phys. A 617, 131 (1997). S. Frauendorf, J. Meng, Nucl. Phys. A 557, 259c (1993). J. Peng et al., Phys. Rev. C 68, 044324 (2003). S. Zhu et al., Phys. Rev. Lett. 91, 132501 (2003). E. Mergel et al., Eur. Phys. J. A 15, 417 (2002). P. Joshi et al., Phys. Lett. B 595, 135 (2004). C. Vaman et al., Phys. Rev. Lett. 92, 032501 (2004). L.L. Riedinger et al., Acta Phys. Pol. B 32, 2613 (2001). K. Starosta et al., in Proceedings of the International Nuclear Physics Conference: Nuclear Physics in the 21st Century: INPC 2001, Berkeley, USA, 30 July-3 August 2001, edited by E. Norman, L. Schroder, G. Wozniak, AIP Conf. Proc. 610, 815 (2002). S. Brant et al., Phys. Rev. C 69, 017304 (2004). G. Rainowski et al., Phys. Rev. C 68, 024318 (2003). K. Starosta et al., Nucl. Phys. A 682, 375c (2001). K. Starosta et al., Phys. Rev. C 65, 044328 (2002). C.M. Petrache et al., Nucl. Phys. A 597, 106 (1996). S.P. Roberts et al., Phys. Rev. C 67, 057301 (2003). T. Koike et al., Phys. Rev. C 63, 051301 (2001). P. M¨ oller et al., At. Data Nucl. Data Tables 66, 131 (1997).

Eur. Phys. J. A 25, s01, 439–440 (2005) DOI: 10.1140/epjad/i2005-06-018-0

EPJ A direct electronic only

Soft triaxial rotor in the vicinity of γ = π/6 and its extensions L. Fortunatoa , S. De Baerdemacker, and K. Heyde Vakgroep Subatomaire en Stralingfysica, University of Gent (Belgium), Proeftuinstraat, 86 B-9000, Gent, Belgium Received: 5 October 2004 / c Societ` Published online: 18 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The collective Bohr Hamiltonian is solved for the soft triaxial rotor around γ 0 = π/6 with a displaced harmonic oscillator potential in γ and a Kratzer-like potential in β. The properties of the spectrum are outlined and a generalization for the more general triaxial case with 0 < γ < π/6 is proposed. PACS. 21.60.Ev Collective models – 21.10.Re Collective levels

Analytic or approximated solutions of the Bohr collective model may be given for a variety of different model potentials. The functional dependence of this potential on the deformation (β) and asymmetry (γ) variables determines the properties of the spectrum and eigenfunctions. These solutions are not limited to rigid cases (where either one or two of the variables are constrained to take a fixed value), but may be found in the case of soft potentials too (here the potential function is represented by a well and it is associated with extended wave functions). A soft solution represents a more physical case than a rigid one and a mathematical benchmark for our understanding of collective states in nuclear spectroscopy. Recently, Iachello introduced new solutions based on the infinite square well potential, named E(5), X(5) and Y (5), to describe the critical point of shape phase transitions [1]. These solutions have initiated on one side intense and successful efforts aimed at the identification of the predicted patterns (nuclear spectra and electromagnetic properties) in experimentally observed spectroscopic data. On the other side a number of theoretical studies have explored new analytic solutions in various cases, from γ-unstable to axial rotor [2]. A solution of the stationary Schr¨odinger equation HB Ψ (β, γ, θi ) = EΨ (β, γ, θi ),

(1)

for the Bohr collective Hamiltonian, HB = Tβ +Tγ +Trot + V (β, γ) may be achieved for the β-soft, γ-soft triaxial rotor making use of a harmonic potential in γ and Coulomb-like and Kratzer-like potentials in β (see fig. 1): V (β, γ) = V1 (β) + a

V2 (γ) , β2

Conference presenter; e-mail: [email protected]

(2)

γ

β

Fig. 1. Polar plot of the potential V (β, γ) discussed in the text with minimum in γ0 = π/6 and β = 0.2.

with V1 (β) = −

B A + 2, β β

V2 (γ) = C(γ − γ0 )2 .

(3)

Unimportant multiplicative factors have been omitted here for simplicity. The Schr¨ odinger equation above, (1), with the choice (2), is separable and can be solved in the vicinity of γ0 = π/6, thus providing a paradigm for the spectrum of soft triaxial rotors. It has been shown in [3] that the γ-angular part in the present case gives rise to a straightforward extension of the rigid triaxial rotor energy, also called Meyer-terVehn formula [4], in which now an additive harmonic term appears, namely ωL,R,nγ =

√

3 C(2nγ + 1) + L(L + 1) − R2 , 4

(4)

The European Physical Journal A

8

440

4

0

3.5

+ β

3.5

3

3

reduced energy

3

+

2.5

2.5

4

+

2

2

2

+

1.5

1.5

1

2

1

+

0.5

0

10

20

30

40

8

0.5 0

4

0

B

Fig. 2. Reduced energies of the lowest state of the β-band (dashed line) and of a few lowest states of the ground-state band (solid lines) as a function of B. The limits for the energy levels when B → ∞, that correspond to the rigid triaxial rotor energies, are reported on the right side. Here we fixed C = 1. From [3].

where R is the quantum number associated with the projection of the angular momentum on the intrinsic 1-axis (that is a good quantum number for the γ = π/6 rotor [4]). The solution of the equation in β depends on the particular choice of the β-potential and may results instead in a non-trivial expression for the energy spectrum. Using the Kratzer-like potential we obtain: A2 /4 . (5) (nγ , nβ , L, R) =  ( 9/4+B + ωL,R,nγ +1/2 + nβ )2

The negative anharmonicities of the energy levels with respect to a simple rigid model are in qualitative agreement with general trends as observed in experimental data. This model is more general than the Davydov (rigid) model [5]: in fact the rigid model is recovered when the potential well becomes very narrow (that is when B → ∞) as can be seen on the right side of fig. 2. Here we present the expression of the spectrum in another well-known solvable case: the Davidson potential, AD β 2 + BD /β 2 , discussed in [6, 7] and references therein. The spectrum may again be found in an analytical way. We obtain    (6) D (nγ , nβ , L, R) = AD 2nβ + τL,R,nγ + 5/2 ,

where τ is found from (τ + 1)(τ + 2) = BD − ωL,K,nγ . Recently it has become possible to extend these results to soft triaxial rotors with a harmonic potential (as in eq. (3) on the right) centered around any asymmetry in the sector 0 < γ0 < π/3 by means of a group theoretical approach based on the su(1, 1) algebra [7]. Here the labeling is more difficult since neither K nor R (quantum numbers associated with the projections of the third component of the angular momentum on the 3rd and 1st

intrinsic axis, respectively) are good quantum numbers, but a classification of the states is still possible on the basis of the remaining quantum numbers. Retaining the same procedure used in the γ0 = π/6 case for the separation of variables we are faced with the problem of solving the equation in γ that contains a rather complicated rotational kinetic term (Here a simplification like the one used in [1] (2nd paper) or [3] may not be adopted). The components of the moment of inertia that occur in that term are simplified here, neglecting fluctuations in the γ-variable, in the following way 1 1 . (7) −→ Aκ = 2 2 4 sin (γ0 − 2πκ/3) 4 sin (γ − 2πκ/3)

The equation in γ is then transformed in a set of coupled differential equations by expanding the (general triaxial) wave functions in a basis of rotational (axial) wave functions. Introducing also some standard trigonometric approximations it is possible to define a realization of the algebra su(1, 1) in terms of differential operators with which, for each L, we can reduce the secular problem to an algebraic equation. When the algebraic equation has a low order it can be solved analytically, while for higher orders one can always get a numerical (accurate) solution. The results have the same structure of eq. (4): the “rotational part”, that coincides in every detail with the well-known solution of the rigid model, is accompanied by an additive harmonic term, that takes into account the γ quanta. Once ω is obtained, it must be used in the differential equation in β, that may be solved in standard ways, depending again on the β-potential. This extension automatically generates the particular results obtained above when γ0 = π/6. This model contains in total 3 parameters (2 from the β and γ potentials, B and C, and one from the moments of inertia, A3 , or alternatively γ0 ) and may provide a simple model for the interpretation of collective spectra of a large number of nuclei that do not posses axial symmetry. The dependence of the reduced spectrum on the three parameters is however non-linear and at present we have only applied the model to spectroscopic data in a preliminary way. A more complete description of the problem, of the methodology used and applications will soon be presented [7]. We acknowledge financial support from “FWO-Vlaanderen” and “Universiteit Gent” (Belgium).

References 1. F. Iachello, Phys. Rev. Lett. 85, 3580 (2000); 87, 052502 (2001); 91, 132502 (2003). 2. L. Fortunato, A. Vitturi, J. Phys. G 29, 1341 (2003); 30, 627 (2004). 3. L. Fortunato, Phys. Rev. C 70, 011302(R) (2004). 4. J. Meyer-ter-Vehn, Nucl. Phys. A 249, 111 (1975). 5. A.S. Davydov, A.A. Chaban, Nucl. Phys. 20, 499 (1960). 6. D.J. Rowe, C. Bahri, J. Phys. A 31, 4947 (1998). 7. L. Fortunato, S. De Baerdemacker, K. Heyde, Solution of the Bohr Hamiltonian for triaxial nuclei, preprint.

Eur. Phys. J. A 25, s01, 441–442 (2005) DOI: 10.1140/epjad/i2005-06-024-2

EPJ A direct electronic only

RDDS lifetime measurement with JUROGAM + RITU T. Grahn1,a , A. Dewald2 , O. M¨ oller2 , C.W. Beausang3 , S. Eeckhaudt1 , P.T. Greenlees1 , J. Jolie2 , P. Jones1 , R. Julin1 , 1 1 oll4 , R. Kr¨ ucken4 , M. Leino1 , A.-P. Lepp¨ anen1 , P. Maierbeck4 , D.A. Meyer3 , S. Juutinen , H. Kettunen , T. Kr¨ 1 1 1 5 1 2 P. Nieminen , M. Nyman , J. Pakarinen , P. Petkov , P. Rahkila , B. Saha , C. Scholey1 , and J. Uusitalo1 1 2 3 4 5

Department of Physics, University of Jyv¨ askyl¨ a, PL35, FIN-40014 Jyv¨ askyl¨ a, Finland Institut f¨ ur Kernphysik, Universit¨ at zu K¨ oln, Z¨ ulpicher Str. 77, 50937 K¨ oln, Germany Wright Nuclear Structure Laboratory, Yale University, New Haven, CT 06520, USA Physik-Department E12, TU M¨ unchen, 85748 Garching, Germany Institut for Nuclear Research and Nuclear Energy, Sofia, Bulgaria Received: 13 December 2004 / c Societ` Published online: 18 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 oln plunger in combination with the RITU sepaAbstract. Lifetimes in 188 Pb were measured using the K¨ rator and JUROGAM. Four lifetimes were measured, from which the deformation of the prolate band was experimentally determined for the first time. The squared prolate mixing amplitude of the 2 + 1 state was deduced from the measured B(E2) values. PACS. 21.10.Tg Lifetimes – 27.70.+q 150 ≤ A ≤ 189 – 23.20.Lv γ transitions and level energies

In recent years considerable theoretical and experimental effort has been devoted to the very exciting region of neutron-deficient lead nuclei where triple shape coexistence can be investigated at low excitation energies [1]. After the experimental establishment of spherical shapes in coexistence with oblate and prolate deformations many different theoretical approaches were made to explain this interesting phenomenon as well as related features like the interplay between the different nuclear structures. Aside from 186 Pb, where the lowest states have been attributed to the three different structures, a lot of experimental work has been focused on the even neighbour 188 Pb. A considerable amount of experimental information concerning the energy spectra was collected by many groups. Recently, G.D. Dracoulis et al. [2] published a rather detailed level scheme including well-developed bands built on the oblate and prolate band heads. These well-established bands, which were observed up to spin 14, reveal the stability of the coexisting deformed structures. Although our knowledge on the energy spectra is quite developed, the experimental data on absolute transition probabilities is very limited. Only one lifetime measurement has been per+ formed so far, where the lifetimes of the 2+ 1 and the 41 states were measured [3]. We performed a plunger measurement using the K¨oln coincidence plunger device in combination with the RITU separator and the JUROGAM spectrometer at Jyv¨askyl¨a [4]. This was the first time that a gas-filled separator was combined with a plunger. The set-up is shown a

Conference presenter; e-mail: [email protected]

Fig. 1. RITU-JUROGAM-Plunger set-up.

in fig. 1. The reaction 108 Pd(83 Kr, 3n)188 Pb was used at a beam energy of 340 MeV in the middle of the target. The beam intensity on the target was 3 pnA. The current was limited by the single count rate (≤ 10 kHz) of the Ge detectors. The standard stopper foil was replaced by a 2.5 mg/cm2 gold degrader foil allowing the recoiling fusion products to enter into the RITU separator and to be identified with the focal-plane detectors [5]. In this way the weak reaction channel of interest was separated from a dominant fission background. Examples of recoil gated spectra are shown in fig. 2 measured at three different target-degrader separations. The thickness of the degrader foil was chosen such that the fully shifted component was separated from the degraded component, which originates

442

The European Physical Journal A Detector−Ring2; + + 4 −> 2

+ + 8 −> 6

+ + 6 −> 4

133°

+ + 10 −> 8

300

+ + 2 −> 0 200

20 μm

200

100

100 10 200

counts

50 μm

300 200

100

100 10 200

200 μm

300

200

100

100 20

320

340

360

380

400

420

440

460

480

500

// 660

680

700

720

740

760

energy (keV)

Fig. 2. Recoil gated γ spectra measured at different targetdegrader separations.

Fig. 4. Partial level-scheme of 188 Pb [2] and preliminary Qt and B(E2) values between yrast states. + mation of the prolate band from the B(E2; 8+ 1 → 61 ) and + + B(E2; 61 → 41 ) values in a model-independent way for the first time. Using the relations

5 2 Q I020|I − 202 , 16π 0 3 Q0 = √ ZR02 β(1 + 0.16β), 5π

B(E2; I → I − 2) = Fig. 3. Experimental decay curves of transitions in the yrast band. Id,f denotes the intensities of the degraded and the fully shifted component, respectively.

from a γ emission after the recoiling nucleus has passed the degrader foil. Only 15 detectors of the JUROGAM spectrometer positioned at 157.6◦ (5 detectors) and 133.6◦ (10 detectors) with respect to the beam axis were used to separate the two components in the off-line data analysis. In total it was possible to measure four lifetimes. The corresponding decay curves are shown in fig. 3. No lifetime could be extracted from recoil gated γγ-coincidence data because of insufficient statistics. Therefore, the results obtained depend on the assumptions made for the unobserved feeding. We assumed feeding times similar to those of the corresponding observed discrete feeding times. It has been shown in many cases (e.g. [6]), that this assumption is realistic whenever no special structure effects dominate the feeding pattern of the state of interest. This is valid for the feeding of the considered states except that of the 2+ 1 state. This strongly mixed state is populated up to 80% from the prolate 4+ 1 state, which is very slow (≈ 18 ps) due to the low transition energy (340 keV) and the difference in the underlying nuclear structure. Therefore, we varied the feeding times for the unobserved feeding between 0.1 ps and 18 ps. The resulting value for the 2+ 1 lifetime varies between 5 ps and 12 ps including also the effect of the nuclear deorientation which has to be considered for low spin states. In fig. 4 a partial level scheme of 188 Pb [2] is given together with preliminary B(E2) values obtained from this + + work. Since the 8+ 1 , 61 , and 41 states are considered to be rather pure prolate deformed states and less mixed than the 2+ 1 state, it is possible to determine the nuclear defor-

we obtain β = 0.286(14), which is in good agreement with the theoretical predictions [7,8, 9,10]. The reduced transi+ tion strength observed for the 4+ 1 → 21 decay indicates + the strong mixture of the 21 state. From the B(E2; 4+ 1 → ) value a squared prolate mixing amplitude can directly 2+ 1 be determined using Q0 = 8.8(5) eb, determined from the + + + averaged B(E2; 8+ 1 → 61 ) and B(E2; 61 → 41 ) values. We find a value a2pro = 0.42(10) which is somewhat smaller than the values given in [2, 3], where different assumptions were made to extract the mixing amplitude. This work was supported in part by the U.S.D.O.E. under grant No. DE-FG02-91ER-40609, the Academy of Finland (the Finnish Centre of Excellence Programme, project 44875), the EU-FP5 projects EXOTAG (HPRI-1999-CT-50017) and Access to Research Infrastructure (HPRI-CT-1999-00044), and the BMBF (Germany) under Contract No. 06K167.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

A.N. Andreyev et al., Nature 405, 430 (2000). G.D. Dracoulis et al., Phys. Rev. C 69, 054318 (2004). A. Dewald et al., Phys. Rev. C 68, 034314 (2003). M. Leino et al., Nucl. Instrum. Methods B 99, 653 (1995). R.D. Page et al., Nucl. Instrum. Methods B 204, 634 (2003). P. Petkov et al., Nucl. Phys. A 543, 589 (1992). J.L. Egido et al., Phys. Rev. Lett. 93, 082502 (2004). M. Bender et al., Phys. Rev. C 69, 064303 (2004). T. Nik˘si´c et al., Phys. Rev. C 65, 054320 (2002). W. Nazarewicz, Phys. Lett. B 305, 195 (1993).

Eur. Phys. J. A 25, s01, 443–445 (2005) DOI: 10.1140/epjad/i2005-06-042-0

EPJ A direct electronic only

Lifetime measurements and low-lying structure in

112

Sn

A. Kumar1,a , J.N. Orce1 , S.R. Lesher1 , C.J. McKay1 , M.T. McEllistrem1 , and S.W. Yates1,2 1 2

Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506-0055, USA Department of Chemistry, University of Kentucky, Lexington, KY 40506-0055, USA Received: 22 October 2004 / c Societ` Published online: 9 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The low-lying structure of 112 Sn has been studied. γ-ray excitation functions, ranging from 2.5 to 4.0 MeV, and angular distributions at 2.9 and 3.8 MeV have been measured following the (n, n  γ) reaction to characterize the decays of the excited levels. Level lifetimes have been measured with the Dopplershift attenuation method. Low-lying 1− , (2− ), 3− and, 5− states have been identified as members of the heterogeneous quadrupole-octupole quintuplet. Decay properties and excitation energies are consistent − with the structure formed by the coupling of the lowest quadrupole, 2+ 1 , and octupole, 31 , excitations. PACS. 21.10.Re Collective levels – 21.10.Tg Lifetimes – 23.20.En Angular distribution and correlation measurements – 25.40.Fq Inelastic neutron scattering

The low-lying structure of nearly spherical nuclei is characterized by collective quadrupole and octupole vibrational modes. The homogeneous and heterogeneous interactions between these modes give rise to mutiphonon quadrupole-quadrupole, octupole-octupole and quadrupole-octupole excitations. In these couplings, the protons and neutrons oscillate in phase. Another kind of excitation can arise as a result of the relative motion of protons and neutrons with respect to each other. These so-called mixed-symmetry states are known in the nearly spherical Mo and Cd nuclei [1, 2,3]. Similarly, the lowlying structure in the tin isotopes is expected to show both multi-phonon and mixed-symmetric excitations. In fact, two and three quadrupole phonon states have been identified in 124 Sn from (n, n γ) experiments [4]. However, there is little information on vibrational excitations in the remainder of the tin isotopes. On the neutron-deficient side of the tin isotopes, 112 Sn has been studied from the radioactive decay of 112 Sb, inelastic scattering reactions, Coulomb excitation and transfer reactions. The results obtained from these studies are summarized in the NDS compilation [5], where lifetimes of a few states are available and, for a number of states, spins and parities are only tentatively assigned. While the 2+ (2150.9 keV), 0+ (2190.8 keV) and 4+ (2247.4 keV) states in 112 Sn have the typical energy pattern of a two-quadrupole-phonon structure, the lack of information on decay properties prevents a precise verification of these assignments. The lifetimes of low-lying states and decay transition rates are crucial for recognizing the different modes of excitation. a

Conference presenter; e-mail: [email protected]

It is well known that the nonselectivity of level excitation provided by the (n, n γ) reaction at low neutron energies provides a sensitive method for studying low-lying states regardless of their structure [6]. Moreover, since the neutron energy can be kept close to the threshold for a particular excitation, this reaction eliminates the side-feeding effects from the population of higher-lying levels, which otherwise may affect the lifetime determination of the level of interest. Therefore, we have used the 112 Sn(n, n γ) reaction in order to investigate the lowlying structure of 112 Sn. The experiments were carried out at the 7 MV accelerator at the University of Kentucky. A 4 g cylindrical metallic sample with 99.5% enrichment was bombarded with nearly monoenergetic neutrons (ΔE ≈ 60 keV), which were produced by the 3 H(p, n)3 He reaction. The protons were pulsed at 1.875 MHz with pulse widths of ≈ 1 ns. In the angular distribution and excitation function experiments, γ-rays were collected using a BGO Compton-suppressed HPGe detector with a relative efficiency of about 55% and an energy resolution of 2.1 keV (FWHM) at 1332 keV. Excitation functions were performed at incident neutron energies ranging from 2.5 to 4.0 MeV in steps of 0.1 MeV. Angular distributions were carried out at incident neutron energies of 2.9 and 3.8 MeV, at various angles between 40◦ and 150◦ , to measure the lifetimes with the Doppler-shift attenuation method (DSAM), as well as to remove ambiguities in spins and parities of previous work. Time-of-flight techniques were used for prompt γ-ray gating in order to suppress time uncorrelated background radiation [6]. In order to confirm the placement of γ-rays in these measurements,

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Table 1. Measured meanlives in the present experiment.

Ex ( keV)

Jπ

Present

Literaure

1256.68(1)

−

534.0+28 −29

−

2000+700 −700

2966.58(5)

2+ 1 2+ 2 0+ 2 4+ 1 3− 1 2+ 4 4+ 3 2+ 5

2969.28(6)

(1,3)

3092.69(7)

2+ 6

3133.52(3)

5− 1

3148.09(5)

820+1400 −330

3397.01(12)

4+ 6 4+ 7 2+ 8 3− 2 −

(2 )

3433.34(12)

1− 1

2.7+1.6 −1.5

3500.10(10)

(4,5)

64+63 −30

3553.70(12)

(3)

240+160 −80

3610.94(6)

(2 , 3 )

2150.85(2) 2190.80(3) 2247.37(3) 2354.06(5) 2720.90(3) 2783.89(6)

3272.76(7) 3286.05(9) 3383.98(10)

+

> 650 −

4800+900 −900

510+210 −120 1100+1500 −400 440+140 −90 660+1200 −280 430+300 −140 360+110 −70 > 1500 430+320 −140 320+220 −100 260+120 −70

+

320+140 −90

111+60 −34

we also performed a γ-γ coincidence experiment using four HPGe detectors. Twenty-three new levels have been excited and fortyfour new γ-ray observations have occurred. The computer code CINDY, based on the statistical compound nucleus theory of Hasuer-Feshbach-Moldauer [7] was used to calculate the theoretical cross-sections of the excited states. The DSAM requires the energy determination of γ-rays emitted at various angles. The energy of the observed γ-rays, Eγ , at an angle θ with respect to the incident flux direction is given by   vcm cos θ , (1) Eγ (θ) = E0 1 + F (τ ) c

where E0 is the unshifted γ-ray energy, vcm , the maximum recoil velocity of the nucleus in the center-of-mass system, and F (τ ), the Doppler-shift attenuation factor. In this work, we have precisely determined the meanlives of 15 states (see table 1). The reduced transition probabilities of a number of transitions have been ex+ tracted. The B(E2) value for the 2+ 1 → 01 transition is known from previous work [5] to be about 15 W.u., which indicates that there is less collectivity in this nucleus than in the neighbouring Te and Cd nuclei. The 2+ 2 + (2190.8 keV) and 4 (2247.4 keV) states, (2150.9 keV), 0+ 1 2 decaying to the 2+ 1 state, have nearly twice the excitation energy of the 2+ 1 (1256.7 keV) state and, therefore, are expected to be of two-phonon character. Nevertheless, the

Fig. 1. Partial level scheme of octupole coupling.

112

Sn showing the quadrupole-

+ + + measured B(E2) values from 2+ 2 , 02 and 41 to the 21 state seem not to support this characterization. The heterogeneous coupling between the lowest quadrupole and − octupole states (2+ 1 ⊗ 31 ) gives rise to a quintuplet of − states ranging from 1 to 5− . These states should lie at an energy roughly equal to the sum of the single-phonon − energies, E(2+ 1 ) + E(31 ). Their two-phonon character can be confirmed by the observation of decays either to the 3− 1 state, involving the destruction of the quadrupole phonon, or to the 2+ 1 state, involving the destruction of the octupole phonon. These negative-parity states have been observed in Cd, Ba, Ce, Nd and Sm isotopes. The 1− states in the Sn isotopes ranging from A = 116–124 have been characterized by J. Bryssinck et al. [8] as members of the two phonon quadrupole-octupole coupling. Excitation energies and reduced transition probabilities, B(E1), were found to be nearly constant in all these nuclei.

In the present work, we have identified 1− , (2− ), 3− and, 5− states which exhibit excitation energies in the range of 88% to 98% of the energy sum of the 2+ 1 (1256.7 keV) and 3− 1 (2354.1 keV) states. Figure 1 shows a partial level scheme of 112 Sn displaying the quadrupoleoctupole states. The (2− ) and 5− states decay to the one-phonon octupole 3− 1 state along with other branchings, whereas the 1− state decays to the ground state only. The 3− state of this quintuplet decays to the onequadrupole phonon 2+ 1 state. Although the observation of two quadrupole phonon excitations are not strongly confirmed, the 2+ ⊗ 3− coupling is evident from the strength of quadrupole phonon decays, which are of the same or+ der as for B(E2; 2+ 1 → 01 ). Hence, the decay properties and excitation energies agree with those expected for the coupling of the quadrupole and octupole phonons.

A. Kumar et al.: Lifetime measurements and low-lying structure in

References 1. P.E. Garrett, H. Lehman, J. Jolie, C.A. McGrath, M. Yeh, S.W. Yates, Phys. Rev. C 59, 2455 (1999). 2. C. Fransen et al., Phys. Rev. C 67, 024307 (2003). 3. D. Bandyopadhyay et al., Phys. Rev. C 66, 014324 (2003). 4. D. Bandyopadhyay et al., Nucl. Phys. A 747, 206 (2005).

112

Sn

445

5. S. Raman et al., At. Data Nucl. Data Tables 36, 1 (1987). 6. P.E. Garrett, N. Warr, S.W. Yates, J. Res. Natl. Inst. Stand. Technol. 105, 141 (2000). 7. E. Sheldon, V.C. Rogers, Comput. Phys. Commun. 6, 99 (1973). 8. J. Bryssinck et al., Phys. Rev. C 59, 1930 (1999).

Eur. Phys. J. A 25, s01, 447–448 (2005) DOI: 10.1140/epjad/i2005-06-083-3

EPJ A direct electronic only

Check for chirality in real nuclei D. Tonev1,a , G. de Angelis1,b , P. Petkov2 , A. Dewald3 , A. Gadea1 , P. Pejovic3 , D.L. Balabanski2,4 , P. Bednarczyk5 , oller3 , N. Marginean1 , A. Paleni6 , C. Petrache4 , K.O. Zell3 , and Y.H. Zhang7 F. Camera6 , A. Fitzler3 , O. M¨ 1 2 3 4 5 6 7

INFN, Laboratori Nazionali di Legnaro, Viale dell’Universit` a 2, I-35020 Legnaro (PD), Italy Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria Institut f¨ ur Kernphysik der Universit¨ at zu K¨ oln, Z¨ ulpicherstr 77, D-50937 K¨ oln, Germany Dipartimento di Fisica, Universit` a di Camerino, I-62032 Camerino, Italy Institut de Recherches Subatomiques, 23 rue du Loess, BP 28, F-67037, Strasbourg, France Dipartimento di Fisica, Universit` a di Milano, I-20133 Milano, Italy Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 73000, PRC Received: 15 November 2004 / Revised version: 28 January 2005 / c Societ` Published online: 12 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Exited states in 134 Pr were populated in the fusion-evaporation reaction 119 Sn(19 F, 4n)134 Pr. Recoil distance Doppler-shift and Doppler-shift attenuation measurements using the Euroball spectrometer, in conjunction with the inner BGO ball and the Cologne plunger were performed at beam energies of 87 MeV and 83 MeV, respectively. The measured B(E2) values within the two chiral candidates bands are not identical while the corresponding B(M 1) values have a similar behaviour within the experimental uncertainties. PACS. 21.10.Tg Lifetimes – 23.20.-g Electromagnetic transitions – 27.60.+j 90 ≤ A ≤ 149 – 11.30.Rd Chiral symmetries

1 Introduction Chirality is an interesting phenomenon which appears in chemistry, biology and particle physics. In ref. [1], it is pointed out that the rotation of triaxial nuclei may result in chiral doublet bands. Suggested candidates that exhibit chiral behaviour are nuclei in which the angular momenta of the valence proton, the valence neutron, and the core rotation are mutually perpendicular. This case can be realized in the mass A ∼ 130 region where the proton Fermi surface is positioned low, and the neutron surface high in the high-j h11/2 subshell. The most notable consequence of chirality is demonstrated as degenerate doublet ΔI = 1 bands of the same parity. In the case of γ = 30◦ and pure particle-hole configuration, the absolute B(E2) and B(M 1) strengths of transitions depopulating the respective levels in these bands should be identical. The first pair of nearly degenerate bands based on the πh11/2 νh11/2 configuration was reported for 134 Pr in ref. [2]. The splitting between levels of the same spin and parity is decreasing with increasing spin and the bands cross above I > 15 ¯h. This pair of bands has been interpreted as one of the best examples of chiral rotation [3]. They have been a

e-mail: [email protected] Conference presenter; e-mail: [email protected] b

described within the framework of the particle-core coupling model [4] and the tilted-axis cranking model [1,5]. Recently, chiral candidate bands has been reported also in the mass region A ∼ 100, e.g. in 104 Rh and 105 Rh [6,7,8]. It turns out that a classification based only on the excitation energies and branching ratios is not sufficient for a definite assignment. Critical experimental observables for the understanding of nuclear structure and for checking the reliability of the theoretical models are the electromagnetic transition probabilities. The goal of the present work is to investigate the nucleus 134 Pr, which is expected to be one of the very promising candidates to express chiral symmetry.

2 Experimental details and data analysis Excited states in 134 Pr were populated using the reaction 119 Sn(19 F, 4n)134 Pr. For the Recoil distance Dopplershift (RDDS) measurement, the beam, with an energy of 87 MeV, was delivered by the Vivitron accelerator of the IReS in Strasbourg. The target consisted of 0.5 mg/cm2 Sn (enriched to 89.8% in 119 Sn) evaporated on a 1.8 mg/cm2 181 Ta backing. The recoils, leaving the target with a velocity of 0.98(2)% of the velocity of light, c, were stopped in a 6.0 mg/cm2 gold foil.

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The γ-rays were detected using the EUROBALL IV spectrometer. Events were collected when at least three γ-rays in the Ge cluster or clover segments and three segments of the inner ball fired in coincidence. Data were taken at 20 target-to-stopper distances ranging from electrical contact to 2500 μm. For the Doppler-shift attenuation measurement (DSAM), a beam of 19 F with an energy of 83 MeV provided by the Vivitron tandem was used. The target consisted of 0.7 mg/cm2 Sn (enriched to 89.8% in 119 Sn) evaporated on a 9.5 mg/cm2 181 Ta backing used to stop the recoils. The cluster and clover detectors of EUROBALL were grouped into 10 rings corresponding to approximately the same polar angle with respect to the beam axis. Some of the investigated transitions have low energies, and since v/c is 0.98(2)%, the resulting Doppler-shift is relatively small. In the analysis, only detectors with good resolution were selected in order to obtain better line-shapes. The good statistics for the low lying states of 134 Pr allowed to construct γ-γ coincidence matrices in which the angular information is conserved on both axes. For the higher lying states of 134 Pr, because of the weaker statistics, only matrices were constructed where one of the axes was associated with a specific detection angle while on the other axis every detector (ring) firing in coincidence was allowed. For the analysis of the RDDS data, the standard version of the Differential decay-curve (DDCM) [9] method has been employed, with gates set on both shifted (S) and unshifted (U) peaks of a transition depopulating levels below the level of interest. A lifetime value is calculated at each distance and the final result for τ is determined as an average of such values within the sensitivity region of the data. More details about the DDCM applied to RDDS measurements can be found in refs. [9,10]. For the analysis of the DSAM data, we performed a Monte Carlo (MC) simulation of the slowing-down histories of the recoils using a modified [11,12] version of the program DESASTOP [13]. Complementary details on our procedure for Monte Carlo simulation as well as on the determination of stopping powers could be found in ref. [14]. The analysis of the line-shapes was carried out according to the DDCM procedure for treating DSAM data [10,11].

3 Results and discussion The lifetimes of the levels with I π = 10+ to 18+ in Band 1 and with I π = 12+ to 17+ in Band 2 have been derived. Mixing ratios and relative intensities for the calculation of the B(M 1) and B(E2) values were taken from ref. [2]. Within the experimental uncertainties, the B(M 1) values in both partner bands behave similarly, varying in an interval indicating relatively strong transition strengths. They smoothly decrease from about 1.8 μ2N at the 10+ 1 level approaching 0.2 μ2N for the 16+ 1 level and then again increase to about 0.4 μ2N for the 18+ 1 level. The B(M 1) values for the corresponding levels of the second band are slightly higher then these in the first band, showing the same behaviour. In contrast, the intraband B(E2)

strengths within the two bands differ. In the investigated spin range, for Band 1 they initially decrease from about + 2 2 0.3 e2 b2 for the 11+ 1 level to 0.1 e b for the 141 level. In + + the spin region 141 to 171 , the B(E2) values are almost constant and an increase is observed at the 18+ 1 level. The B(E2) values for the 15+ levels in both bands are similar. For Band 2 we observe a decrease of the B(E2) values for levels with spins below and above 15+ 2 . However, above the 16+ level, the B(E2) strengths in Band 1 are increasing. It is interesting to note that this effect occurs when Band 2 becomes yrast instead of Band 1, i.e. after the region where the two bands cross each other. We mention that the B(M 1)/B(E2) ratios reported in the ref. [2] also behave differently in the two bands. Those in Band 2 are higher compared to the corresponding values in Band 1. Currently, there are no reasonable theoretical predictions in the literature which could reproduce the measured transition probabilities.

4 Conclusions Fifteen lifetimes of excited states belonging to the candidate bands for a chiral doublet in 134 Pr have been determined. The intraband B(M 1) values are similar within the experimental uncertainties in both bands, while the corresponding B(E2) transition strengths considerably differ, indicating that they are not completely identical structures. A precise description of the data is obviously a challenge for the nuclear models and in particular, for those which aim at the description of chirality of nuclear rotation. D.T. expresses his gratitude to Ivanka Necheva for her outstanding support. This research has been supported by a Marie Curie Fellowship of the European Community programme IHP under contract No. HPMF-CT-2002-02018 and by the European Commission through contract No. HPRI-CT-1999-00078 E.U. Access to Research Infrastructures programme.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

S. Frauendorf, J. Meng, Nucl. Phys. A 617, 131 (1997). C.M. Petrache et al., Nucl. Phys. A 597, 106 (1996). K. Starosta et al., Phys. Rev. Lett. 86, 971 (2001). K. Starosta et al., Nucl. Phys. A 682, 375c (2001). V.I. Dimitrov et al., Phys. Rev. Lett. 84, 5732 (2000). C. Vaman et al., Phys. Rev. Lett. 92, 032501 (2004). P. Joshi et al., Phys. Lett. B 595, 135 (2004). J. Tim´ ar et al., Phys. Lett. B 598, 178 (2004). A. Dewald et al., Z. Phys. A 334, 163 (1989). G. B¨ ohm, A. Dewald, P. Petkov, P. von Brentano, Nucl. Instrum. Methods Phys. Res. A 329, 248 (1993). P. Petkov et al., Nucl. Phys. A 640, 293 (1998). P. Petkov et al., Nucl. Instrum. Methods Phys. Res. A 431, 208 (1999). G. Winter, Nucl. Instrum. Methods 214, 537 (1983). D. Tonev et al., in Nuclei at the Limits, edited by T.L. Khoo, D. Seweryniak, AIP Conf. Proc. 764, 93 (2005).

Eur. Phys. J. A 25, s01, 449–450 (2005) DOI: 10.1140/epjad/i2005-06-058-4

EPJ A direct electronic only

Probing the three shapes in spectroscopy

186

Pb using in-beam γ-ray

J. Pakarinen1,a , I. Darby1,2 , S. Eeckhaudt1 , T. Enqvist1 , T. Grahn1 , P. Greenlees1 , F. Johnston-Theasby3 , P. Jones1 , anen1 , P. Nieminen1 , M. Nyman1 , R. Page2 , P. Raddon3 , R. Julin1 , S. Juutinen1 , H. Kettunen1 , M. Leino1 , A.-P. Lepp¨ P. Rahkila1 , C. Scholey1 , J. Uusitalo1 , and R. Wadsworth3 1 2 3

Department of Physics, University of Jyv¨ askyl¨ a, P.O. Box 35, FI-40014, Jyv¨ askyl¨ a, Finland Oliver Lodge Laboratory, Department of Physics, University of Liverpool, Liverpool L69 7ZE, UK Department of Physics, University of York, Heslington, York Y01 5DD, UK Received: 2 December 2004 / c Societ` Published online: 3 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. This measurement represents the first observation of a non-yrast band in the 186 Pb nucleus by employing the Recoil-Decay Tagging (RDT) technique. Previously known yrast levels have been confirmed and the band is extended up to level I π = (16+ ). PACS. 27.70.+q 150 ≤ A ≤ 189 – 21.10.Re Collective levels – 23.20.Lv γ transitions and level energies – 25.70.Gh Compound nucleus

1 Introduction Triple shape coexistence in the light Pb region has been an intriguing topic for more than a decade. At the neutron midshell prolate and oblate minima are driven down in energy providing a unique laboratory for nuclear structure studies [1]. In 2000 Andreyev et al. [2] carried out an α-decay fine-structure measurement associating the three lowest states (I π = 0+ ) in 186 Pb with three different nuclear shapes. The ground state of 190 Po has a mixed character of 2p and 4p-2h configuration (spherical and oblate, respectively). Based on the reduced α-decay widths and on in-beam γ-ray spectroscopy [3, 4] the second minimum is associated with prolate shape. To confirm the structure of the third minimum, associated with oblate shape, it would be important to observe the band built above this state. In-beam spectroscopy of 186 Pb has been hindered by 1) γ-ray background from fission and from various open fusion evaporation-reaction channels 2) low cross-section and 3) a relatively long half-life of 4.83(3) s [5] for tagging techniques. So far the examination of this nucleus has been based on recoil-γ n (n ≥ 2) coincidence measurements [3, 4, 6]. Recent improvements in tagging techniques at the Accelerator Laboratory of the University of Jyv¨askyl¨a (JYFL) have made it possible to explore nuclei under these extreme conditions using the RDT technique. a

Conference presenter; e-mail: [email protected]

2 Experimental aspects Excited states of 186 Pb were populated in the 106 Pd(83 Kr, 3n)186 Pb reaction at a beam energy of 355 MeV. The target was a 1 mg/cm2 thick metallic foil enriched in 106 Pd. Prompt γ rays were detected at the target position by the JUROGAM γ-ray spectrometer consisting of 33 EUROGAM Phase1 [7] and 9 GASP-type [8] Compton suppressed Ge detector modules. Fusion-evaporation residues were separated from the primary beam and transported to the focal plane using the gas filled recoil separator RITU [9]. Recoils were implanted into the Double-Sided Silicon Strip Detectors (DSSSD), which are part of the GREAT [10] focal plane detector set-up. GREAT consists of two DSSSDs to detect the recoils and their decay products, a MultiWire Proportional Counter (MWPC) for energy loss and time-of-flight measurement of the recoils, a box of PIN-diodes to detect escaping α-particles and conversion electrons and a doublesided germanium strip detector for low-energy γ rays. Data were collected using the Total Data Readout (TDR) system providing minimal dead time [11]. In this method, each channel is run independently and associated in software for event reconstruction. This is made possible by time-stamping each event with a global 100 MHz clock. Data were sorted and γγ-matrices constructed using the analysis package GRAIN [12], whereas the analysis was completed with the software package RADWARE [13]. Prompt γ rays associated with the observation of a recoil together with a subsequent α decay at the same position

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The European Physical Journal A 4

1.5×10

+

4

6

α-tagged singles γ-rays

+

50 8

1.0×10

+

4

10

+ +

2

(12 )

+

40

+

(14 )

3

186

J [h /MeV]

+

8.0×10

6.0×10

4.0×10

(6 ) (4 ) + (8 ) +

1

α-tagged γγ-coincidences gates: 392+401+945 keV

+

(10 )

+

(12 )

1

*

+

(14 )

187

Tl contaminants

Pb (prolate)

186

30

Pb (new)

188

(1) _ 2

Counts

5.0×10

196

Pb (oblate)

Pb (oblate)

20

1 +

(2 )

2.0×10

*

1

200

*

*

300

10

*

400

500

700 600 Energy [keV]

800

900

1000

Fig. 1. γ-ray energy spectra measured with JUROGAM. Top: singles γ-ray energy spectrum gated with fusion-evaporation residues and tagged with 186 Pb α decays. Bottom: recoil-gated, α-tagged γγ-coincidence spectrum with a sum of gates on the three lowest non-yrast transitions. (16 )

3967.7

(14 )

3684.0

652.2 (14 )

551.3

3315.5

(12 )

3132.8

605.6 507.6 (12 )

2710.0

(10 )

549.6

462.7

478.8

414.8 1259.9

337.1 922.8

4

(650) (532)

2

(6 )

1674.7

6

260.6

2162.4

424.1

487.4

485.8 8

0 0

(8 )

2160.5

10

2625.2

414.5 674.5

1738.4

401.3 (4 )

1337.0

391.5 (2 )

945.2

0 50

100

150

200

250 hω[keV]

_

300

350

400

450

Fig. 3. Kinematic moment of inertia as a function of rotational frequency for a nuclei in the vicinity of 186 Pb. Data for other nuclei is taken from refs. [14, 15].

The recoil-gated α-tagged γ-ray singles spectrum in the upper part presents the previously known yrast band and its extension up to I π = (16+ ). In the lower part a recoilgated α-tagged γγ-coincidence condition is employed with a sum of gates on the three lowest non-yrast transitions. The γγ-coincidence data, transition energy sums and relative intensity arguments have allowed the level scheme shown in fig. 2 to be constructed. All spin and parity assignments are tentative at the present stage of the analysis. The kinematic moment of inertia for the new band in 186 Pb is plotted in fig. 3 together with those for the prolate band in 186 Pb and proposed oblate bands in 188 Pb and 196 Pb. The behavior of the new band is somewhat similar to that of the oblate band in 188 Pb, but its origin is still open to debate.

662.2

References

945.2 662.2 0.0

0 186

Fig. 2. Partial level scheme of Pb deduced from the present data. (The two 0+ states on the left side are taken from ref. [2].)

in the focal plane DSSSD within 15 s were selected in the data analysis. Escaping α particles within the same time window were collected using a PIN-diode box enhancing the γγ-coincidence data by ∼ 6%. During 151 hours of effective beam time ∼ 1.06 × 106 α’s were recorded. The cross section for the production of 186 Pb was estimated to be 185 μb.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

3 Results The power of JUROGAM + RITU + GREAT combined with the TDR system is substantiated in fig. 1, which shows two γ-ray spectra with different gating conditions.

14. 15.

R. Julin et al., J. Phys. G. 27, R109 (2001). A.N. Andreyev et al., Nature 405, 430 (2000). J. Heese et al., Phys. Lett. B 302, 390 (1993). A.M. Baxter et al., Phys. Rev. C 48, R2140 (1993). J. Wauters et al., Phys. Rev. C 50, 2768 (1994). W. Reviol et al., Phys. Rev. C 68, 054317 (2003). C.W. Beausang et al., Nucl. Instrum. Methods A 313, 37 (1992). C. Rossi Alvarez, Nucl. Phys. News 3, 3 (1993). M. Leino et al., Nucl. Instrum. Methods B 99, 653 (1995). R.D. Page et al., Nucl. Instrum. Methods B 204, 634 (2003). I.H. Lazarus et al., IEEE Trans. Nucl. Sci. 48, 567 (2001). P. Rahkila, to be published in Nucl. Instrum. Methods A. D. Radford, http://radware.phy.ornl.gov/main.html (2000). G.D. Dracoulis et al., Phys. Rev. C 67, 051301 (2003). J. Penninga et al., Nucl. Phys. A 471, 535 (1987).

Eur. Phys. J. A 25, s01, 451–452 (2005) DOI: 10.1140/epjad/i2005-06-140-y

EPJ A direct electronic only

Systematics in the structure of low-lying, non-yrast band-head configurations of strongly deformed nuclei G. Popa1,a , A. Aprahamian1 , A. Georgieva2 , and J.P. Draayer3 1 2 3

Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA Bulgarian Academy of Science, Sofia, Bulgaria Department of Physics, Louisiana State University, Baton Rouge, LA 70803, USA Received: 6 December 2004 / Revised version: 16 February 2005 / c Societ` Published online: 30 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A systematic application of the pseudo-SU (3) model for a sequence of rare earth nuclei demonstrates that an overarching symmetry can be used to predict the onset of deformation as manifested through low-lying collective bands. The results also show that it is possible to obtain a unified description of mem+ π bers of the yrast band and the K π = 2+ 1 and K = 02 excited bands by using a classification scheme based on particle occupation numbers in the valence shells. The scheme utilizes an overarching Sp(4, R) symplectic framework. The nuclei that are considered belong to the F0 = 0 and F0 = 1 symplectic multiplets of the (50,82–82,126) shell. PACS. 21.60.Fw Models based on group theory – 21.10.Re Collective levels – 27.70.+q 150 ≤ A ≤ 189

1 Introduction π The behavior of first excited K π = 0+ = 2+ 2 , and K bands in deformed even-even nuclei is investigated empirically in the rare-earth region, where the nuclei are ordered in F -spin multiplets of a Sp(4, R) classification scheme [1]. The energy levels of the ground state (g.s.) J = 2+ 1 , first + + π π excited J = 0K π =0+ , J = 2K π =2+ states of nuclei that 2

1

belong to the F0 = 0 = 1/2(N π − N ν ) multiplet (where N π and N ν are the number of valence proton and neutron pairs) are plotted in fig. 1. The energies of the same set of levels for nuclei belonging to the F0 = 1 multiplet are plotted in fig. 2. Nuclei with F0 = 0 have equal numbers of valence proton and neutron pairs. The others with F0 = 1 vary by two pairs of protons. We want to reproduce and interpret microscopically this complex and varying behavior by an application of the algebraic shell model with pseudo-SU (3) symmetry.

The Hamiltonian that is appropriate for the description of nuclei being considered includes spherical singleσ ; proton particle terms for both protons and neutrons, Hsp σ and neutron pairing terms, HP ; an isoscalar quadrupolequadrupole interaction, Q·Q; and four smaller “rotor-like” terms that preserve the pseudo-SU (3) symmetry: π ν H = Hsp + Hsp − Gπ HPπ − Gν HPν −

+ a J 2 + b KJ2 + a3 C3 + as C2 ,

1 χ Q·Q 2

(1)

where C2 and C3 are the second and third order invariants of SU (3), which are related to the axial and triaxial deformation of the nucleus. The single-particle energies are calculated in the standard form with standard values for coefficients Dπ[ν] and Cπ[ν] from [4]:   σ Cσ liσ · siσ + Dσ li2σ , (2) Hsp = iσ

2 Model space and interactions The building blocks of the model are the pseudo-SU (3) proton and neutron states having pseudo spin zero, which describe the even-even nucleus. The many-particle states are built as pseudo-SU (3) coupled states with a well-defined particle number and total angular momentum [2, 3]. a

Conference presenter; e-mail: [email protected]

where σ stands for protons (π) or neutrons (ν). The calculations assumed fixed values [5] for pairing (Gπ = 21/A, Gν = 17/A), as well as for the quadrupolequadrupole interaction strength (χ = 35A−5/3 ). The other interaction strengths were varied to give a best fit to the band heads of the first excited K π = 0+ , K π = 2+ and K π = 1+ bands, as well as the moment of inertia of the g.s. band [6]. Explicitly, the term proportional to KJ2 breaks the SU (3) degeneracy of the different K bands, the J 2 term represents a small correction to fine tune the moment

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The European Physical Journal A π Table 1. Energy values for the J π = 2+ = 1 , first excited J + + π 0 π + and J = 2 π + states for seven nuclei in the F0 = 0 K =02

K =21

multiplet. The experimental values [7] are given in parenthesis. The numbers of valence proton and neutron pairs are given in the second and third columns.

Nucleus N π N ν E(21 )

152

Nd Sm 160 Gd 164 Dy 168 Er 172 Yb 176 Hf 156

Fig. 1. The experimental energy values [7] of the J π = 2+ 1 , J π = 0+ π + , and J π = 2+ + states in a sequence of nuclei K =02

K=21

for which the numbers of valence protons and neutrons are the same (F0 = 0).

5 6 7 8 9 10 11

5 6 7 8 9 10 11

E(0+

K=0+ 2

) E(2+ π

K =2+ 1

)

Th. (Exp.) [MeV]

Th. (Exp.) Th. (Exp.) [MeV] [MeV]

0.082 0.078 0.085 0.073 0.089 0.081 0.178

1.14 1.07 1.33 1.67 1.21 1.04 1.15

(0.073) (0.076) (0.075) (0.073) (0.080) (0.078) (0.088)

(1.14) (1.07) (1.33) (1.66) (1.22) (1.04) (1.15)

1.31 1.45 0.99 0.76 0.81 1.49 1.26

(1.38) (1.47) (0.82) (0.76) (0.82) (1.47)

Table 2. Same as in table 1 for five nuclei with F0 = 1.

Nucleus N π N ν E(21 )

156

Gd Dy 164 Er 168 Yb 172 Hf 160

Fig. 2. The experimental energy values [7] of the J π = 2+ 1 , J π = 0+ π + , and J π = 2+ + states in a sequence of nuclei K =02

K=21

for which the difference in the numbers of valence proton and neutron pairs is two (F0 = 1).

of inertia, and the last term, C2 , is introduced to distinguish between SU (3) irreps with λ and μ both even from the others with one or both odd, hence fine tuning the energy of the first excited K π = 1+ state. Within this framework, the splitting and mixing of the pseudo-SU (3) irreps are generated by the proton and neutron single-particle π/ν terms (Hsp ) and the pairing interactions. This mixing plays an important role in the reproduction of the behavior of the low-lying collective states in deformed nuclei [6].

3 Results and conclusions The experimental and calculated energies of the J π = 2+ g.s. , + + π π J = 0K π =0+ , and J = 2K π =2+ states in the deformed 2

1

nuclei from the ones shown in figs. 1 and 2 are compared in tables 1 and 2. We calculated also all the states with J ≤ 8 within these three bands. The calculated results are in very good agreement with experiment [6, 7]. The main reason for obtaining the position of each collective band with respect to each other, as well as of each level within the band is the specific content of the obtained SU (3) irreps into the collective states, which is related to their deformations. For nuclei from ta-

7 8 9 10 11

5 6 7 8 9

E(0+

K=0+ 2

) E(2+ π

K =2+ 1

)

Th. (Exp.) [MeV]

Th. (Exp.) Th. (Exp.) [MeV] [MeV]

0.094 0.092 0.091 0.088 0.119

1.06 1.30 1.25 1.16 0.87

(0.089) (0.087) (0.091) (0.088) (0.095)

(1.05) (1.28) (1.25) (1.15) (0.87)

1.14 0.99 0.94 0.98 1.08

(1.15) (0.97) (0.86) (0.98) (1.07)

ble 1, in the middle of the shell, the ground and the γ band belong to the same (λ, μ) with λ > μ. At the limits of the deformed region the ground band states have oblate + π deformation (λ < μ) and the K π = 0+ 2 and the K = 21 bands are mixed in the same SU (3) irrep [6]. The analysis for nuclei from table 2 is under investigation. The correct description of collective properties of first π + excited K π = 0+ 2 , and K = 2 states is a result of representation mixing and state deformation induced by the model Hamiltonian. This study shows that pseudo-spin zero neutron and proton configurations with relatively few pseudo-SU (3) irreps with largest C2 values suffices to yield good agreement with known experimental energies.

References 1. S. Drenska, A. Georgieva, V. Gueorguiev, R. Roussev, P. Raychev, Phys. Rev. C 52, 1853 (1995). 2. R.D. Ratna Raju, J.P. Draayer, K.T. Hecht, Nucl. Phys. A 202, 433 (1973). 3. T. Beuschel, J.G. Hirsch, J.P. Draayer, Phys. Rev. C 61, 54307 (2000). 4. P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer, Berlin, 1979). 5. G. Popa, J.G. Hirsch, J.P. Draayer, Phys. Rev. C 62, 064313 (2000). 6. G. Popa, A. Georgieva, J.P. Draayer, Phys. Rev. C 69, 064307 (2004). 7. R.B. Firestone, V.S. Shirley, Table of Isotopes, Vol. I, 8th edition and Vol. II (Wiley, New York, 1996).

Eur. Phys. J. A 25, s01, 453–454 (2005) DOI: 10.1140/epjad/i2005-06-129-6

EPJ A direct electronic only

A measure for triaxiality from K (shape) invariants V. Werner1,2,a , C. Scholl2 , and P. von Brentano2 1 2

Wright Nuclear Structure Laboratory, Yale University, 272 Whitney Ave., New Haven, CT 06520-8124, USA Institut f¨ ur Kernphysik, Universit¨ at zu K¨ oln, Z¨ ulpicher Str. 77, D-50937 K¨ oln, Germany Received: 29 November 2004 / Revised version: 22 February 2005 / c Societ` Published online: 13 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We show that the cubic shape invariant K3 , which provides a measure for triaxiality for β-rigid nuclei, can be obtained from a small number of observables. This affords approximations which have been tested to hold within a few percent in the rigid triaxial rotor model and the interacting boson model. PACS. 21.10.Ky Electromagnetic moments – 21.60.Ev Collective models – 21.60.Fw Models based on group theory

1 Introduction The deformation parameters β and γ from the geometrical model are not easy to define in all cases, e.g., in vibrational nuclei. They are of course model dependent and usually do not take fluctuations into account. An alternative approach to nuclear deformation is given by quadrupole shape invariants [1, 2]. These shape invariants can be considered as the “real” shape parameters, as they are observables, and hence do not involve any model input. However, exact values can in general only be obtained from large (complete) sets of E2 matrix elements, which are rarely available, for a small set of stable nuclei. The aim of the current work is to show that the shape parameter K3 , which is related to triaxiality, can be obtained with good accuracy from only a few experimental observables. While triaxiality is discussed also for excited states and bands, e.g., in terms of chirality [3] or wobbling [4], the following discussion is restricted to triaxiality in the ground state of even-even nuclei. Quadrupole shape invariants are defined by [5]  n/2  (1) Kn = qn / q2 , with higher-order moments of the quadrupole operator in a given state, in our case the ground state, of the type

(2) qn = αn 0+ . . . Q ](0) |0+ 1 , 1 |[ Q ' () * n with geometrical factors αn and using tensor coupling for the quadrupole operators Q. In analogy to the geometrical model, where β and γ correspond to a (rigid) minimum in the potential, effective deformation parameters can be a

Conference presenter; e-mail: [email protected]

defined as averages in the ground state, 2 2   3ZeR2 3ZeR2 2 βeff 2 ,

β  ≡ q2 = 4π 4π

and K3 = −

β 3 cos 3γ ≡ − cos(3γeff ),

β 2 3/2

(3)

(4)

with nuclear radius R, proton number Z and charge e. K4 and K6 give measures for fluctuations in β and γ in the non-rigid case. While, for the rigid rotor, γeff is equal to the geometrical γ-value, it provides a measure for effective triaxiality also for vibrational or γ-soft nuclei. However, we note that the K-parameters are in general not equivalent to the geometrical deformation parameters. This is due to fluctuations in β and γ which are incorporated in the averages in the ground state (compare eqs. (2)–(4)). Due to averaging over β 3 cos 3γ, eq. (4) gives an effective γdeformation related to the geometrical model only if β is rigid. This is the case for nuclei transitional between the well-deformed and the triaxial (γ-soft) rotor. On the other hand, if γ is rigid, K3 reflects the softness in β, which can be expected for nuclei transitional between the well-deformed rotor and the vibrator for γ = 0◦ .

2 Results In general, K3 involves a large number of E2 matrix elements. Applying the Q-phonon scheme [6] and its ΔQ = 1 selection rule for E2 transitions, the number of needed matrix elements reduces drastically and K3 can be written in terms of the quadrupole moment Q(2+ 1 ) only. However, from calculations in the interacting boson model (IBM-1) and the rigid triaxial rotor model (RTRM) it is seen that this approach leads to large deviations from the exact value of K3 in transitional regions.

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The European Physical Journal A

SU(3)

1.08

1.08

1.04

1.06

1.00 −1.2

1.04

−0.8

U(5)

1 0.8 0.6

−0.4

1.02

O(6)

0.4 0

0.2

1

K3 Fig. 1. RIBM , calculated over the IBM-1 symmetry space.

In a second approximation, introducing B(E2; 2+ 1 → + 2 ) [7], and allowing one matrix ele21 ) = 35/(32π) · Q(2+ 1 ment with ΔQ = 2, we derive an approximation [8] + $ +   +  B(E2; 2+ 7 appr 1 → 21 ) sign Q 21 = K3 + 10 B(E2; 21 → 0+ 1) , ⎞ + + + B(E2; 2+ 2 → 01 ) · B(E2; 22 → 21 ) ⎠ , (5) −2 + B(E2; 2+ 1 → 01 )

involving four B(E2) values. The derivation of eq. (5) incorporates a sign relation between the four involved matrix elements [9], namely   + sign 2+ 1 ||Q||21  =   + + + + + (6) − sign 0+ 1 ||Q||22  22 ||Q||21  21 ||Q||01  . Equation (5) gives a well defined way for deriving an approximate K3 from data. In order to get an estimate on the error resulting from the truncation, the validity of the approximation needs to be tested within models, which has been done within the IBM-1 and the RTRM. Deviations of the value of K3appr given by eq. (5) from the exact K3 are small as shown in fig. 1. Herein, the ratio K3 RIBM =

1 + |K3appr | 1 + |K3 |

(7)

5

10

15

20

25

30

K3 Fig. 2. Rgeo , calculated within the RTRM for γ ∈ [0, 30].

Table 1. The approximative shape invariant K3appr for transitional Os isotopes. Effective γ- and β-deformation parameters are given in the last two columns.

K3appr

γeff

βeff

Os

−0.63(5)

17(3)

0.185

190

Os

−0.35(9)

23(3)

0.177

192

Os

−0.3(1)

25(2)

0.167

188

Exemplarily, table 1 gives K3appr and γeff , derived from eqs. (5) and (4), respectively, for Os isotopes transitional between the rigid axially symmetric rotor and the γ-soft rotor. Data has been taken from the nuclear data sheets and stems mostly from D. Cline and co-workers, who made large sets of E2 matrix elements available. Included in table 1 are the calculated values of βeff from eq. (3) where, using the same truncation as for K3appr , q2 can be approximated by   + (10) q2appr = B E2; 0+ 1 → 21 . It is seen that β-deformation decreases while the value of γ rises towards 30◦ , which is the limit of maximum (soft) triaxiality. This work was supported by the DFG under contract No. Br 799/12-1 and the USDOE under grant No. DE-FG02-91ER40609.

has been calculated over the whole parameter space of the two-parameter IBM-1 Hamiltonian HIBM = (1 − ζ) nd −

ζ Qχ · Qχ 4N

(8)

by variation of ζ and χ, including the vibrator (U (5)), the well-deformed rotor (SU (3)), and the γ-soft rotor (O(6)) limits. Calculations within the RTRM show the same qualK3 ity of our approximation as depicted in fig. 2, where Rgeo is defined in analogy to eq. (7). Note that the absolute value of the quadrupole moment can be calculated from the 3-B(E2)-relation   + B E2; 2+ 1 → 21 =     + + + (9) B E2; 4+ 1 → 21 − B E2; 22 → 21 , which was derived in a similar way in [7].

References 1. 2. 3. 4. 5. 6. 7. 8. 9.

K. Kumar, Phys. Rev. Lett. 28, 249 (1972). D. Cline, Annu. Rev. Nucl. Part. Sci. 36, 683 (1986). V.I. Dimitrov et al., Phys. Rev. Lett. 84, 5732 (2000). I. Hamamoto, Phys. Lett. B 193, 399 (1987). V. Werner, N. Pietralla, P. von Brentano, R.F. Casten, R.V. Jolos, Phys. Rev. C 61, 021301 (2000). T. Otsuka, K.-H. Kim, Phys. Rev. C 50, 1768 (1994). V. Werner, P. von Brentano, R.V. Jolos, Phys. Lett. B 521, 146 (2001). V. Werner, C. Scholl, P. von Brentano, Phys. Rev. C 71, 054314 (2005). R.V. Jolos, P. von Brentano, Phys. Lett. B 381, 7 (1996).

Eur. Phys. J. A 25, s01, 455–456 (2005) DOI: 10.1140/epjad/i2005-06-092-2

EPJ A direct electronic only

Alternative interpretation of E0 strengths in transitional regions V. Werner1,2,a , P. von Brentano1 , R.F. Casten2 , C. Scholl1 , E.A. McCutchan2 , R. Kr¨ ucken3 , and J. Jolie1 1 2 3

Institut f¨ ur Kernphysik, Universit¨ at zu K¨ oln, Z¨ ulpicher Str. 77, D-50937 K¨ oln, Germany Wright Nuclear Structure Laboratory, Yale University, 272 Whitney Ave., New Haven, CT 06520-8124, USA Physik Department E12, Technische Universit¨ at M¨ unchen, James-Franck-Str., 85748 Garching, Germany Received: 5 October 2004 / c Societ` Published online: 13 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A strong rise of E0 transition strengths between the first excited 0 + state and the ground state is predicted in shape transitional regions within the Interacting Boson Model (IBM). This rise matches well existing data and is not connected to a large mixing amplitude between both states. Moreover, a coherence of amplitudes in the wave functions causes the strong transition, without a requirement of explicit mixing of normal and intruder configurations. PACS. 21.60.Ev Collective models – 21.10.Ky Electromagnetic moments – 21.60.Fw Models based on group theory

1 Introduction The investigation of shape/phase transitions in nuclei has so far been focused on E2 properties. There has only been little study of E0 matrix elements, despite that the E0 operator ρ(E0) is directly connected to changes in nuclear shapes and radii. We will use the interacting boson model (IBM-1) [1] for a survey of E0 properties among 0+ states. Commonly, large E0 transition strengths between the 0+ 1 and 0+ 2 states are modeled by an explicit mixing of coexisting spherical and deformed intruder configurations [2]. However, our calculations show that large E0 strengths do not require such explicit mixing, they are rather inherent to the model [3].

2 IBM-1 calculations We used the simple Ising-type two-parameter Hamiltonian [4]

ζ Q·Q , (1) H = a (1 − ζ)nd − 4N †/

†

† / (2)

with the quadrupole operator Q = s d + d s + χ(d d) and boson number N . For √ ζ = 0 one obtains the U (5) limit while ζ = 1 and χ = − 7/2 gives SU (3), and ζ = 1 and χ = 0 gives O(6). Therefore, using the E0 operator

/ (0) , ρ(E0) = αN + β  (d† d) a

Conference presenter; e-mail: [email protected]

(2)

E0 strengths between 0+ states can be calculated over a wide range of symmetries, including those parameter regions (around ζ = 0.5) that are known to show phase transitional behavior. The top part of fig. 1 shows + ρ2 (E0; 0+ 2 → 01 ) for N = 16 bosons, which shows a sharp rise just in the parameter region of the vibrator-rotor shape/phase transition. E0 strength even remains large in the rotational limit. The drop at O(6) is due to an ex+ change of the 0+ 2 and 03 states —if both matrix elements are added (fig. 1 bottom part for N = 10 bosons) it is seen that the E0 strength remains large on the deformed side, as well for axially symmetric deformation as for γ-soft triaxial deformation. From a more detailed analysis it is seen that while large E0 strengths in the IBM-1 are connected to components with large nd values in the wave functions, the appearance of such large nd values alone is not sufficient. There are subtle cancellation effects of positive and negative parts in the matrix elements, ending up in a large E0 strength to the ground state only for one excited 0+ state.

3 Comparison with data The robust prediction of large E0 strengths in the few-parameter IBM-1 needs experimental testing. + ρ2 (E0; 0+ 2 → 01 ) values are known [2] in the A = 100 and 150 transition regions. Figure 2 compares these data with a schematic IBM √calculation, where with fixed parameters N = 10, χ = − 7/2, and β  = 6 × 10−3/2 /eR02 (note the incorrect equation in ref. [3]). Only the parameter ζ was + allowed to vary and was fitted to the R4/2 = E(4+ 1 )/E(21 )

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The European Physical Journal A

102

−3

[10 ] 100

NB= 16

5

SU(3)

Sr 100

Mo

154

Sm

3.5

Gd

60

152

Zr

2

100

20

0.5

96

−1.2

0

0.2

152 98

3

150

0.5

2 0

0.5

0.8

1

1

−0.6

U(5) 0

1

0.5

Fig. 2. Data compared to a schematic IBM-1 calculation. The insert gives the R4/2 ratio to which ζ was fitted.

O(6) SU(3)

3

1.5

O(6) −1.2

NB= 10

−0.6

U(5) 0

0.5

1

Fig. 1. Top: ρ2 (E0; 0+ → 0+ 2 1 ) calculated for N = 16 bosons throughout the IBM parameter space. Bottom: the sum + + + 2 ρ2 (E0; 0+ 2 → 01 ) + ρ (E0; 03 → 01 ) for N = 10 bosons.

energy ratio. The predicted rise in E0 strength between vibrator and rotor matches well the data. Nuclei for which R4/2 < 2 have not been considered as they are outside the model space.

4 Discussion Earlier calculations [5] modeled large E0 strengths by using the Duval-Barrett formalism [6], mixing two model spaces. This seems to be conflicting with our approach using one model space only. However, ref. [5] used a very small mixing for the two model spaces, e.g., in 96,102,104 Mo, that means in a spherical (A = 96) and the first two deformed Mo isotopes. Therefore, these calculations effectively go over into the single space IBM results before and after the transition region. Only for 98,100 Mo, for which the experimental values of the ra+ + + + tios B(E2; 0+ 2 → 21 )/B(E2; 21 → 01 ) and B(E2; 22 → + + 2+ 1 )/B(E2; 21 → 01 ) exceed any predictions of standard models, there is substantial mixing, and the Duval-Barrett formalism is required. + This shows that large ρ2 (E0; 0+ 2 → 01 ) values in transitional nuclei can arise either from mixing of coexisting

spherical and intruder configurations, or from the simpler IBM-1 itself. The key point is that large E0 values do not require a two-space mixing, but, in the first deformed nuclei in the mass 100 (98 Sr, 100 Zr, 102 Mo) and 150 (152 Sm, 154 Gd) regions, such large values are accounted for within the simple IBM-1 itself. Microscopically, E0 transitions are forbidden in a single harmonic oscillator shell. However, realistic shell model descriptions effectively entail mixing of several oscillator shells, which should effectively be incorporated in the IBM, e.g., by the use of effective charges. Thus, the E0 strengths in the IBM may reflect the fact that realistic major shells in the independent particle model include an intruder orbit from the next higher shell, and that additional intruder orbits appear in the Nilsson scheme with increasing deformation, that is, as the shape/phase transition proceeds. A detailed microscopic analysis would be needed to relate the IBM to such a picture. However, the appearance of intruder orbits may be reflected in the effective parameter β  in the E0 operator given in eq. (2), a simple one-body operator with constant parameters which, remarkably, is sufficient for reproducing the data in transition regions. The prediction that E0 strengths remain large in well-deformed rotors needs experimental confirmation. This work was supported by the DFG under contract No. Br799/11-1, the BMBF by grant No. 06MT190, and by the USDOE under grant No. DE-FG02-91ER-40609.

References 1. F. Iachello, A. Arima, The Interacting Boson Model (Cambridge University Press, Cambridge, 1987). 2. J.L. Wood, E.F. Zganjar, C. De Coster, K. Heyde, Nucl. Phys. A 651, 323 (1999). 3. P. von Brentano et al., Phys. Rev. Lett. 93, 152502 (2004). 4. V. Werner, P. von Brentano, R.F. Casten, J. Jolie, Phys. Lett. B 527, 55 (2002). 5. M. Sambataro, G. Molnar, Nucl. Phys. A 376, 201 (1982). 6. P.D. Duval, B.R. Barrett, Phys. Lett. B 100, 223 (1981).

6 Excited states 6.5 Structure of fission products

Eur. Phys. J. A 25, s01, 459–462 (2005) DOI: 10.1140/epjad/i2005-06-204-0

EPJ A direct electronic only

Soft chiral vibrations in

106

Mo

S.J. Zhu1,2,3,a , J.H. Hamilton1,b , A.V. Ramayya1 , P.M. Gore1 , J.O. Rasmussen4 , V. Dimitrov5,6 , S. Frauendorf 5,6 , R.Q. Xu2 , J.K. Hwang1,c , D. Fong1 , L.M. Yang2 , K. Li1 , Y.J. Chen2 , X.Q. Zhang1 , E.F. Jones1 , Y.X. Luo1,4 , I.Y. Lee4 , W.C. Ma7 , J.D. Cole8 , M.W. Drigert8 , M. Stoyer9 , G.M. Ter-Akopian10 , and A.V. Daniel10 1 2 3 4 5 6 7 8 9 10

Physics Department, Vanderbilt University, Nashville, TN 37235, USA Department of Physics, Tsinghua University, Beijing 100084, PRC Joint Institute for Heavy Ion Research, Oak Ridge, TN 37835, USA Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA IKH, FZ-Rossendorf, Postfach 510119, D-01314 Dresden, Germany Department of Physics, Mississippi State University, MS 39762, USA Idaho National Laboratory, Idaho Falls, ID 83415, USA Lawrence Livermore National Laboratory, Livermore, CA 94550, USA Flerov Laboratory for Nuclear Reactions, Joint Institute for Nuclear Research, Dubna 141980, Russia Received: 12 September 2004 / c Societ` Published online: 15 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. High-spin states in neutron-rich 106 Mo were investigated by detecting the prompt γ-rays in the spontaneous fission of 252 Cf with Gammasphere. Several new bands are observed. Two sets of ΔI = 1 bands in 106 Mo are found to have all the characteristics of a new class of chiral vibrational doublets. Tilted axis cranking calculations support the chiral assignment and indicate that the chirality is generated by neutron h11/2 particle and mixed d5/2 , g7/2 hole coupled to the short and long axis, repectively. PACS. 21.10.Re Collective levels – 23.20.Lv γ transitions and level energies – 27.60.+j 90 ≤ A ≤ 149 – 25.85.Ca Spontaneous fission

Evidence for triaxial shapes is found in neutron-rich nuclei in the A = 100–114 range [1,2, 3,4]. Low-lying oneand two-phonon states of the gamma vibration indicate the softness of 106 Mo with respect to triaxial deformations [5]. In such a soft nucleus the excitation of quasiparticles will strongly modify the shape and may induce a stable triaxial shape [6,7]. A pair of chiral doublet rotational bands, which consist of two sets of ΔI = 1 sequences of states with the same parity and very close energies can occur in triaxial nuclei. Chiral doubling emerges when the angular momentum has substantial components along all three principal axes of the triaxial density distribution. Then there are two energetically equivalent orientations of the angular momentum vector. In one case the short, intermediate and long axes form a right-handed system with respect to the angular momentum, in the other case a left-handed system [6]. Such chiral pairs of bands have been found in odd-odd nuclei around Z = 59 and N = 75 [8] where the angular momentum is composed of a component from the odd a b c

e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]

h11/2 proton along the short axis, a component from the h11/2 neutron hole along the long axis and a collective component along the intermediate axis. Chiral bands predicted for odd-odd nuclei around Z = 43 and N = 65, where the odd h11/2 neutron generates the angular momentum along the short and the g9/2 proton hole along the long axis [7] were recently observed in 104 Rh [9]. To establish the general nature of chirality, it is important to find examples of chiral bands with a different quasiparticle composition. Here we report the first evidence of a pair of chiral vibrational bands in 106 Mo where the chiral structure is due to the neutrons with h11/2 particle coupled to the short axis and mixed d5/2 , g7/2 hole coupled to the long axis. The levels of 106 Mo were investigated by measuring the prompt γ-rays emitted in the spontaneous fission (SF) of 252 Cf. A 62 μCi 252 Cf source was sandwiched between two 10 mg/cm2 Fe foils and mounted in a 7.62 cm diameter plastic (CH) ball and placed at the center of Gammasphere with 102 Compton-suppressed Ge detectors at Lawrence Berkeley National Laboratory. A total of 5.7 × 1011 triple- and higher-fold coincidence events were collected, factors of 10–100 higher than earlier

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γ

(5)

(2) 4757.9

4753.2

(14-)

γγ

4372.7

(13-)

(3)

(12-) 103 3946.4 (11-)

(12-)

(14+)

(4) 4292.4

(13+)

ΔΕ

4049.4 3812.0

3370.8

2951.0

(12+)

3707.7

(11+)

3349.8

10+

3041.7

115 3592.8 (10-) 110 3239.5 (9-) 119 2922.3 (8-) 117 2630.1 (7-) 130 2369.5 (6-)

2746.6

2559.4

2194.5

8+

1868.4

7+

1563.4

522.6

4+

171.8

2+

0

0+

9+

2499.0 2276.5 2090.6 1937.0

(5-)134 2142.9 (4-) 138 1952.4

6+

1307.0

5+

1068.0 885.4

4+ 3+

710.5

2+

4132.7

(12 +)

(11-)

3682.2

(11 +)

(10-)

3264.1

10+

2877.5

9+

2521.1

8+

2199.8

7+

1910.5

6+

(9-) (8-) (7-) (6-) (5-)

1657.9

5+

1434.9

4+

106

ground band

42

Mo64

Fig. 1. Decay patterns of chiral bands into γ and γγ bands in 106 Mo. The energy differences in keV of the same spin states in bands (4) and (5) are given between the bands. Transitions depopulating the γ-band (2) are omitted.

measurements. Coincidence data were analyzed with the RADWARE software package. In addition to previous work [5], 78 new transitions and 34 new levels in 106 Mo are identified. The partial level scheme in fig. 1 shows 45 of the new transitions and 20 of the new levels including bands (4) and (5) in 106 Mo which are proposed to be chiral doublets along with the one- and two-phonon γ vibrational bands and ground-band members to show their decay patterns. To illustrate the data, fig. 2 shows the spectrum double gated on the 1051.6 keV transition that depopulates band (4) and the 171.8 keV, 2-0 transition where the transitions in band (4) are shown along with the 205.9 keV transition from band (5) to (4) and the 117 keV transition in 143 Ba, the strong 3n partner. The β2 value of the 106 Mo ground band is 0.34 [10]. The spins and parities of the γ vibrational band (2) and γγ band (3) have been assigned previously [5]. In 106 Mo, bands (4) and (5) are consistent only with 4− and 5− or 5+ and 6+ assignments, respectively, for the band heads. These assignments are based on the decay patterns out of each level including both the transitions seen and the absence of higher energy transitions to other band members. The decay patterns are only consistent with band (5) having one unit of spin higher than band (4). We could not measure the parity of the pair of bands directly. The two-quasiproton states lie at higher energy than the two-quasineutron states, because of the larger pairing gap and the smaller level density. For this reason we interpret the bands as two-quasineutron excitations. The lowest neutron particle-hole excitations have negative par-

ity. This is expected, because the single particle levels with opposite parity cross each other with increasing deformation, whereas the distance between levels with the same parity increases [11]. For this reason we adopt the negative parity. There are two configurations which correspond to the excitation of a neutron from the highest h11/2 level to two close-lying mixed d5/2 , g7/2 positive-parity levels. The lower configuration h11/2 , (d5/2 , g7/2 )−1 would correspond to [541]3/2[[413]5/2]−1 in the case of an axial shape. However, it is found to have a triaxial deformation of β2 = 0.31 and γ = 31◦ in our TAC calculation. Our recently measured lifetimes of less than 8 ns for the decay out of the band heads support the triaxial shape. If the observed pair of bands was axial, one would expect a substantial retardation of the decay into the K = 0 ground band, because ΔK > 3 corresponds to a large retardation, which is not observed. For interpretation, we carried out 3D Titled Axis Cranking calculations using the method of ref. [12]. The proton pairing gap was chosen to be equal to the evenodd mass difference. The neutron pair gap was set equal to zero, because blocking two states will substantially reduce the neutron pair correlations [13]. The TAC calculations showed that the angular momentum of the d5/2 , g7/2 neutron hole is strongly aligned with the long axis. The angular momentum of the h11/2 neutron lies in the short-intermediate plane. It prefers the direction of the short axis, but not very strongly. The total angular momentum moves from the long-short plane through the aplanar region to the short-intermediate

350.8 ( 106Mo)

S.J. Zhu et al.: Soft chiral vibrations in

150

461

713.6 ( 106Mo)

106Mo

450

550

693.1 ( 142Ba, 4n)

666.0 ( 106Mo, band 4)

631.2 ( 142Ba, 4n)

588.6 ( 141Ba, 5n) 603.2 ( 106Mo, band 4)

511

487.2 ( 106Mo, band 5) 493.1 ( 143Ba, 3n)

456.7 ( 143Ba, 3n) 470.1 ( 106Mo, band 4)

408.4 ( 106Mo, band 4)

350

431.3 ( 144Ba, 2n)

474.9 ( 142Ba, 4n)

359.3 ( 142Ba, 4n)

339.5 ( 106Mo, band 4) 343.3 ( 143Ba, 3n)

250

Mo

Double gate on 171.8 and 1051.6 keV

330.8 ( 144Ba, 2n)

222.5 ( 106Mo, band 4)

500

185.9 ( 106Mo, band 4)

153.6 ( 106Mo, band 4)

1500

205.9 ( 106Mo, between bands 4 and 5)

2500 117.8 ( 143Ba, 3n)

Counts per Channel

3500

106

650

E (keV) Fig. 2. Coincidence spectrum obtained by double gates on the 171.8 keV 2 → 0 transition and the 1051.6 keV one depopulating band (4) in 106 Mo.

plane. The motion of the total angular momentum vector cannot be completely explained in terms of a particle angular momentum aligned with the short axis, hole angular momentum aligned with the short axis and collective angular momentum aligned with the intermediate axis. The microscopic structure of the core favors a path through the aplanar region. This mechanism is quite different from the known chiral examples, where the high-j particle(s) generates angular momentum along the short axis, the high-j hole along the long axis, and the remaining nucleons generate collective angular momentum along the intermediate axis. The microscopic TAC results cannot be reduced to the simple picture of a particle aligned with the short axis, a hole aligned with the long axis and collective angular momentum along the intermediate axis. It comes about as the interplay of the neutrons in the open shell. Although we could not come up with a simple picture as in the case of chiral bands based on the intruder orbitals, the TAC calculations do give angular momentum projections on all three axes when the rotational axis moves from the long-short to the intermediate-short plane. The TAC calculations give constant J 1 . In the case of axial prolate symmetry, the orbitals with high K have a large component of angular momentum aligned with the long axis. This component remains large at finite rotational frequency, which introduces some K-mixing. Triaxiality introduces more mixing, but there are still normal parity orbitals that retain a certain amount of angular momentum aligned with the long axis. TAC that has all these ingredients finds chiral examples, like the one we present here.

The following facts speak in favor of associating the observed bands as a chiral pair: a) Triaxiality is known for this nucleus and the lifetimes for the decays out of the bands give it further support. b) The ΔE values between like spin levels decrease with increasing angular momentum. c) Both bands have regular ΔI = 1 sequences with M 1 transitions between their even and odd spin members. The signature splitting is very small, as indicated by the very small staggering of the kinematic moment of inertia commonly denoted as J 1 = I/((E(I) − E(I − 1)) shown in fig. 3. (very small compared to even the “best ”chiral bands in 104 Rh [9] in fig. 3). d) The moments of inertia in fig. 3 are equal as expected for a chiral pair. They remain almost constant with increasing spin. The kinematic moment of inertia remains constant if the angular momentum gain is caused by adding angular momentum along the axis perpendicular to the plane in which the particle and hole angular momentum lie. This is analogous to high-K bands, where the particle-hole angular momentum is parallel to the symmetry axis and the collective angular momentum perpendicular to it. If the particle, the hole and the total angular momentum lay in one plane (planar tilt) the kinematic moment of inertia is a decreasing function of I, like in the familiar case of rotational alignment of a high-j particle in an axial nucleus. The I-independence of J 1 as an evidence for an aplanar geometry of the angular momentum as was first pointed out by Vaman et al. [9], who used S(I) = 1/(2J 1 ) as a measure.

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The pattern of the electromagnetic decays depends sensitively on the the mixing matrix element that couples the left-handed with the right-handed configuration. Since the left- and right-handed configurations have the same energy, already a small matrix element determines the phase of the mixing amplitude. If this phase is similar in the initial and final states, the transitions remain in the bands and there is no cross talk, as observed in our case. If the phases differ substantially, then there will be strong interband transitions. Koike et al. [14] discussed recently such a case. However, the peculiar staggering pattern reflects the special symmetry of their model and cannot be expected to be observed in other chiral configurations that do possess the symmetry, like the one suggested in this paper. In summary, bands (4) and (5) in 106 Mo are proposed as the first chiral vibrational bands in an even-even nucleus. The TAC calculations strongly support this interpretation. A different mechanism (as compared to the known cases) generates chirality, which proves the general nature of the concept. Fig. 3. Plots of moment of inertia (J 1 ) versus I for 104 Rh (top pannel) and 106 Mo (bottom pannel).

Work at Tsinghua was supported by the Major State Basic Research Development Program Cont. G2000077405, the National Natural Science Foundation of China Grant 10375032 and the Special Program of Higher Education Science Foundation Grant 20030003090. Work at Vanderbilt, Mississippi State and Notre Dame was supported by the U.S. DOE Grants DE-FG-05-88ER40407, DE-FG05-95ER40939 and DEFG02-95ER40934. Idaho, Lawrence Berkeley and Lawrence Livermore National Labs’ work was supported by DOE Contracts DE-AC07-761DO1570, DE-AC03-76SF00098, and W7405-ENG48, respectively.

References Fig. 4. Energy level differences (keV).

Figure 4 shows that the energy difference between the same spin levels in the two doublet bands is small at the bottom and decreases slowly with I. This is consistent with the observation that J 1 is constant for the band. For the known examples of chirality, one sees a transition from chiral vibrations at the bottom to stable chirality at the top of the bands: the energy difference is large at the bottom and decreases to a small value, where simultaneously the kinematic moment of inertia approaches a constant value. Our case looks like a very soft chiral vibration or a chiral configuration with substantial left-right tunneling, which do not change very much with I.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

A.G. Smith et al., Phys. Rev. Lett. 77, 1711 (1996). D. Troltenier et al., Nucl. Phys. A 601, 56 (1996). H. Hua et al., Phys. Rev. C 69, 014317 (2004). Y.X. Luo et al., Phys. Rev. C 69, 024315 (2004). A. Guessous et al., Phys. Rev. Lett. 75, 2280 (1995). S. Frauendorf et al., Rev. Mod. Phys. 73, 463 (2001). V. Dimitrov, F. D¨ onau, S. Frauendorf, Frontiers of Nuclear Structure, AIP Conf. Proc. 656, 151 (2003). K. Starosta et al., Phys. Rev. Lett. 86, 971 (2001). C. Vaman et al., Phys. Rev. Lett. 92, 032501 (2004). C. Hutter et al., Phys. Rev. C 67, 054315 (2003). R. Bengtsson et al., Phys. Scr. 29, 402 (1984). V.I. Dimitrov, S. Frauendorf, F. D¨ onau, Phys. Rev. Lett. 84, 5732 (2000). S. Frauendorf, Nucl. Phys. A 677, 115 (2000). T. Koike et al., Phys. Rev. Lett. 93, 172502 (2004).

Eur. Phys. J. A 25, s01, 463–464 (2005) DOI: 10.1140/epjad/i2005-06-033-1

EPJ A direct electronic only

Half-life measurement of excited states in neutron-rich nuclei J.K. Hwang1,a , A.V. Ramayya1 , J.H. Hamilton1 , D. Fong1 , C.J. Beyer1 , K. Li1 , P.M. Gore1 , E.F. Jones1 , Y.X. Luo1 , J.O. Rasmussen2 , S.J. Zhu3 , S.C. Wu2 , I.Y. Lee2 , M.A. Stoyer4 , J.D. Cole5 , G.M. Ter-Akopian6 , A. Daniel6 , and R. Donangelo7 1 2 3 4 5 6 7

Physics Department, Vanderbilt University, Nashville, TN 37235, USA Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Department of Physics, Tsinghua University, Beijing 100084, PRC Lawrence Livermore National Laboratory, Livermore, CA 94550, USA Idaho National Engineering and Environmental Laboratory, Idaho Falls, ID 83415, USA Flerov Laboratory for Nuclear Reactions, Joint Institute for Nuclear Research, Dubna, Russia Universidade Federal do Rio de Janeiro, CP 68528, RG, Brazil Received: 28 October 2004 / c Societ` Published online: 20 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Half-lives (T1/2 ) of several states which decay by delayed γ transitions were determined from time-gated triple γ coincidence method. We determined, for the first time, the half-life of 330.6 + x state in 108 Tc and the half-life of 19/2− state in 133 Te based on the new level schemes. Five half-lives of 95,97 Sr, 99 Zr, 134 Te and 137 Xe are consistent with the previously reported ones. These results indicate that this new method is useful for measuring the half-lives. PACS. 21.10.Tg Lifetimes – 25.85.Ca Spontaneous fission – 27.60.+j 90 ≤ A ≤ 149

Since the classification of delayed γ-rays by Goldhaber and Sunyar [1], half-life (T1/2 ) measurements of nuclear states have been a major source of information on nuclear deformations, shell structures, and validity of nuclear models. Previously, half-lives of several states in neutronrich nuclei have been determined by single-γ or γ-γ coincidence relations for the delayed γ transitions emitted from the isotopes produced in the fission of 235 U, 239 Pu, 248 Cm, and 252 Cf [1, 2]. Most of the previous results were obtained from the coincidence measurement between the γ transition and the fission fragment after fission. And some of them were obtained from the delayed time measurement of the γ transition following the β-decay after fission. Usually, more than 100 isotopes are produced in the fission of these heavy nuclei, with each isotope emitting many γ-rays. Because several new nuclei and many new levels in the known nuclei have been identified in the spontaneous fission (SF) of 252 Cf, the present time-gated triple γ coincidence method is very useful for the half-life measurements of nuclear states in neutron-rich nuclei. The γ-γ-γ coincidence measurements were done by using the Gammasphere facility with 72 Ge detectors and a 252 Cf SF source of strength ∼28 μCi at LBNL. Several γ-γ-γ coincidence cubes with different time windows, tw , [1,2] were built for the three- and higher-fold data by using the Radware format. That is, a time-gated cube a

e-mail: [email protected]

will contain all triple-coincidence events for which all these time differences are less than the specified time value. Let us consider a downward cascade consisting of γ3 -γ2 -γ1 -γ0 transitions where γ0 is the outgoing transition from a state with long half-life and γ1 is the incoming transition into the same state. Other higher states in this cascade are assumed to have very short lifetimes. We set a double gate on Eγ3 and Eγ1 and compare the intensities of transitions, γ0 and γ2 , N (γ0 ) and N (γ2 ) in the spectra. In the present work, γ1 , γ2 , and γ3 , are in prompt coincidence. Therefore, the delay-time between γ1 and γ3 will be negligible. Since γ0 is the ending transition in this cascade, the coincidence time window (tw ) limits the TDC time difference, t10 , between the γ1 and γ0 transitions, and the intensity N (γ0 ) observed from the state with the long lifetime. The N (γ0 ) intensity determines the fraction of N (γ2 ) intensity observed from the state with the long half-life with decay constant, λ. Therefore, N (γ0 )/N (γ2 ) = C(1 − e−λtw ) can be applied in this case, where C is a constant. We applied this method, for the first time, to extract the half-lives of two states in 95,97 Sr [2]. Later, five other cases namely 99 Zr, 133,134 Te, 137 Xe and 108 Tc are investigated as shown in table 1 [1]. Recently, the new level schemes of 133 Te and 108 Tc have been reported from the SF work of 252 Cf. Based on these new level schemes, the half-lives of 1610.4 keV state in 133 Te and 330.6 + x keV

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Table 1. Half-lives (T1/2 ns) of several states (EIS , keV) [1, 2]. E(γ1 )/E(γ3 ) are the double-gated transition energies. For 97 Sr, E(γ2 )/E(γ3 ) and E(γ1 ) are used instead. Half-lives of delayed γ-rays without the mass identification were reported to be 110 ns for 154.0 keV γ-ray and 115 ns and 81.6(114) ns for 125.5 keV γ-ray [1]. The half-life of the 1610.4 keV state in 133 Te is the average value extracted from 125.5 and 1150.6 delayed transitions.

Nuclei 95

Sr 97 Sr 99 Zr 108 Tc 133 Te 134 Te 137 Xe

EIS

E(γ1 )/E(γ3 )

E(γ2 )

E(γ0 )

Present T1/2

Reference’s T1/2 [1]

ENSDF [3]

556.1 830.8 252.0 330.6 + x 1610.4 1692.0 1935.2

682.4/678.6 239.6/272.5 426.4/415.2 123.4/341.6 721.1/933.4 2322.0/516.0 311.3/304.1

427.1 205.9 142.5 125.7 738.6 549.7 1046.4

204.0 522.0 130.2 154.0 125.5 115.2 314.1

23.6(24) 265(27) 316(48) 94(10) 99(6) 197(20) 10.1(9)

24, 21, 21.8(11) 382(11), 255(10) 294(10), 375(11)

21.7(5) 255(10) 293(10)

161(4), 196(7), 175(6) 8.1(4)

164(1) 8.1(4)

Fig. 1. Coincidence spectra with double gate on 682.4 and 678.6 keV transitions in 95 Sr.

Fig. 2. Count ratio versus coincidence time window (tw ) plot for 95 Sr. The curve is the fitted line to C(1 − e−λtw ).

state in 108 Tc are reported in the present work. As one example, coincidence spectra with double gate on 682.4 and 678.6 keV transitions in 95 Sr [2] is shown in fig. 1. And the plots for the count ratio versus coincidence time window are shown in figs. 2 and 3. The more details for this time-gated triple-coincidence method to determine the level half-life can be seen in refs. [1,2]. In summary, we report half-lives of five states in 95,97 Sr, 99 Zr, 108 Tc, 133 Te, 134 Te, and 137 Xe by using the new time-gated triple-coincidence method. We determined, for the first time, half-lives of 108 Tc and 133 Te based on the new level schemes. The half-lives of states

Fig. 3. Count ratio versus coincidence time window (tw ) plots for 108 Tc and 137 Xe. The curves are the fitted lines to C(1 − e−λtw ).

in 95,97 Sr, 99 Zr, 134 Te, and 137 Xe are consistent with the previously reported ones. These results indicate that this new method is useful for the half-life measurements.

References 1. J.K. Hwang et al., Phys. Rev. C 69, 57301 (2004) and references therein. 2. J.K. Hwang et al., Phys. Rev. C 67, 54304 (2003) and references therein. 3. ENSDF in http://www.nndc.bnl.

Eur. Phys. J. A 25, s01, 465–466 (2005) DOI: 10.1140/epjad/i2005-06-176-y

EPJ A direct electronic only

252

Investigations of short half-life states from SF of

Cf

D. Fong1,a , J.K. Hwang1 , A.V. Ramayya1 , J.H. Hamilton1 , C.J. Beyer1 , K. Li1 , P.M. Gore1 , E.F. Jones1 , Y.X. Luo1 , J.O. Rasmussen2 , S.J. Zhu3 , S.C. Wu2 , I.Y. Lee2 , P. Fallon2 , M.A. Stoyer4 , S.J. Asztalos4 , T.N. Ginter2 , J.D. Cole5 , G.M. Ter-Akopian6 , A. Daniel6 , and R. Donangelo7 1 2 3 4 5 6 7

Physics Department, Vanderbilt University, Nashville, TN 37235, USA Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA Department of Physics, Tsinghua University, Beijing 100084, PRC Lawrence Livermore National Laboratory, Livermore, CA 94550, USA Idaho National Engineering and Environmental Laboratory, Idaho Falls, ID 83415, USA Flerov Laboratory for Nuclear Reactions, Joint Institute for Nuclear Research, Dubna, Russia Universidade Federal do Rio de Janeiro, CP 68528, RG Brazil Received: 26 October 2004 / Revised version: 5 May 2005 / c Societ` Published online: 21 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. By using different time-gated triple γ coincidence data, the half-lives (T 1/2 ) of several short lived states in neutron-rich nuclei have been studied. The first excited states in the ground state bands often decay by delayed γ emission. By creating triple γ coincidence spectra with time windows of 8, 16, 20, 28, and 48 ns, we have studied states with half-lives below 10 ns. The estimated half-lives of 102 Zr, 137 Xe, and 143 Ba are in reasonable agreement with previously reported values. We extract the first estimates of the half lives of the 2+ states in 104 Zr and 152 Ce. PACS. 21.10.Tg Lifetimes – 25.85.Ca Spontaneous fission – 27.60.+j 90 ≤ A ≤ 149

1 Introduction Half-lives of excited states provide important information on the deformation of nuclei. We have investigated whether a new technique of using triple γ coincidence data as a function of time applied to long-lived states [1] can be used for states with half-lives less than 10 ns. If so, then the technique may be used to determine deformations of other neutron-rich nuclei populated in spontaneous fission.

1431.4

8 565.1

866.3

6 433.0

433.3

4

2 Technique We estimated half-lives of excited states in neutron-rich nuclei populated in the spontaneous fission of 252 Cf by measuring the ratio of intensities for transitions populating and de-populating the state of interest. A schematic level scheme of the cascade in 98 Sr is shown in fig. 1 as an example. For this nucleus, we applied a double gate on the 565.1 and 289.0 keV transitions. Then we measured the ratio of intensities for the 144.3 and 433.0 keV transitions. The time resolution from constant fraction timing in our spectra is on the order of 10 ns. By varying the width of the coincidence time window, we can estimate a

Conference presenter; e-mail: [email protected]

2 0

289.0

144.3 L.O.I. 0.0

144.3 98

Sr

Fig. 1.

98

Sr Cascade.

the half-life of the level of interest, labeled as “L.O.I”. As the time window is opened wider and wider, the intensity of the de-populating transition increases with respect to the intensity of the populating transitions. This relationship follows an exponential curve that can be fitted to estimate the half-life. Fitted curves are presented in fig. 2.

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Table 1. Estimated half-lives (T1/2 ns) of several states.

Nuclei 98

Sr Zr 104 Zr 137 Xe 143 Ba 152 Ce 102

(a )

Fig. 2. Half-life curve fitting.

The technique gives good agreement with a previously known half-life below 10 ns for a transition of 314 keV in 137 Xe [2]. At energies of 80–200 keV, the measured half-lives are longer by a factor of 2–3 when compared to known results in this region. As a first estimate for transitions of 80–200 keV, a linear correction factor was applied and brought the measured values into good agreement with known values. Previously unknown half-lives for excited states in 104 Zr and 152 Ce were estimated with this technique.

3 Results Our results are shown in table 1, along with values from the Evaluated Nuclear Structure Data Files (ENSDF) [3]. There is only one accurate value known for neutron-rich nuclei with a half-life less than 10 ns, the 2+ state in 98 Sr. A systematic correction must be applied to our results because of time walk and other short-time corrections. This is a consequence of charge collection effects at the limits of our time resolution for these low-energy transitions. Thus, the correction depends on the energy of the de-populating transition. There is good agreement with previous results for the estimated half-life of the excited state in 137 Xe with a de-populating transition of 314.1 keV [2]. Thus we assume any time correction is small at these energies and higher. Also, good agreement is found with this measurement technique between our data and known values for longer-lived states [1]. Because of the lack of several precise measurements for half-lives under 10 ns as a function of energy, the exact nature of the correction is unknown. We hypothesize as the simplest assumption that the ratio of true half-life to our measured half-life is given as a linear function of the energy of the transition de-exciting the state over the short range of 80–200 keV. The only precisely known result is for 98 Sr, where the ENSDF value is

The

98

Energy

T1/2 UE

T1/2 CE

ENSDF

144.3 keV 151.8 keV 140.3 keV 314.1 keV 117.7 keV 81.7 keV

5.6(2) 5.7(4) 4.8(6) 7.8(8) 9.0(8) 8.9(6)

2.8(a) 3.0 2.3

2.78(8) 1.91(25) N/A 8.1(4) 3.5(8) N/A

3.7 2.5

Sr estimate was matched to the ENSDF value.

2.78(8) ns and our estimated value is 5.6 ns. We fitted our correction to match this value and pass through the origin. The corrected estimate is derived from the uncorrected estimate by the following: T1/2 CE = T1/2 UE ×Eγ /288.6 keV. In table 1, the energy of the de-exciting transition is given, along with the uncorrected estimated (UE) and corrected estimated (CE) half-lives. The uncertainties in the uncorrected estimated values are statistical errors from the curve-fitting to the data. The uncertainties associated with the correction factor are unknown. Note that no corrected value is given for 137 Xe, as no correction is needed for that energy.

4 Discussion and summary These new results provide the first estimates of the halflives of the first excited state in 104 Zr and 152 Ce. These are in the range of several nanoseconds. However, a more complete understanding of the nature of the correction is necessary to reduce the uncertainty in our result. Our new triple γ coincidence method allows one to examine halflives of many states populated in the SF of 252 Cf that have not been previously measured or have only imprecise measurements. We plan to investigate fully the timing problem and correction factor for low energy transitions to make this an accurate technique for half-lives below 10 ns. The work at Vanderbilt, Lawrence Berkeley National Laboratory, Lawrence Livermore National Laboratory, Idaho Engineering and Environmental Laboratory, and JINR are supported in part by the U.S. DOE under Grant and Contract Nos. DE-FG05-88ER40407, DE-AC03-76SF00098, W-7405Eng-48, and DE-AC07-76ID01570, DE-AC011-00NN4125, BBW1 Grant No. 3498 (CRIDF Grant RPO-10301-INEEL) and the joint RFBR-DFG grant (RFBR Grant No. 02-0204004, DFG Grant No. 436RUS 113/673/0-1(R)).

References 1. J.K. Hwang et al., Phys. Rev. C 69, 057301 (2004). 2. R.G. Clark, PhD Thesis, 1974. 3. Evaluated Nuclear Structure Data Files, National Nuclear Data Center, http://www.nndc.bnl.gov/index.jsp.

Eur. Phys. J. A 25, s01, 467–468 (2005) DOI: 10.1140/epjad/i2005-06-181-2

EPJ A direct electronic only

Identification of levels in 162,164Gd and decrease in moment of inertia between N = 98–100 E.F. Jones1,a , J.H. Hamilton1 , P.M. Gore1 , A.V. Ramayya1 , J.K. Hwang1 , and A.P. deLima2 1 2

Department of Physics, Vanderbilt University, Nashville, TN 37235, USA Department of Physics, University of Coimbra, 3000 Coimbra, Portugal Received: 16 December 2004 / Revised version: 3 May 2005 / c Societ` Published online: 11 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. From prompt γ-γ-γ coincidence studies with a 252 Cf source, the yrast levels were identified from 2+ to 16+ and 14+ in neutron-rich 162,164 Gd, respectively. Transition energies between the same spin states are higher and moments of inertia lower at every level in N = 100 164 Gd than in N = 98 162 Gd. These observations are in contrast to the continuous decrease in the 2 + energy to a minimum at neutron midshell (N = 104) in Er, Yb, and Hf nuclei. PACS. 21.10.Re Collective levels – 27.70.+q 150 ≤ A ≤ 189

A γ-γ-γ coincidence study of prompt γ rays emitted in the spontaneous fission of 252 Cf was carried out using Gammasphere [1] with 5.7 × 1011 triples and higher coincidences recorded. Further experimental details are found in Luo et al. [2]. The yrast levels in neutron-rich 162,164 Gd were identified for the first time from 2+ to 16+ in 162 Gd and from 2+ to 14+ in 164 Gd. The 162 Gd transitions were established from our earlier 1995 Gammasphere data [3]. We searched with our new high-statistics data for 164 Gd. We expected to find γ transistions with energies slightly below the energies in 162 Gd by double gating on its 84 Se partner, whose first two transistions are well known. We found no transitions with energies below those of 162 Gd. Instead, we found γ transitions with energies above those of 162 Gd. The 162,164 Gd intensities were checked against the relative yields as a function of neutron emission number. The transitions in 162,164 Gd are seen in double coincidence gates on the transitions identified in our work as the 6+ → 4+ and 8+ → 6+ in transitions 162 Gd and 164 Gd, as shown in fig. 1. The 2+ energy in known 160 Gd is at 75.3 keV and, from our data, in 162,164 Gd at 71.6 and 73.3 keV, respectively. The transition energies from every level in 164 Gd are higher than those from the same levels in 162 Gd. These data show that there is the same decrease at every level of the moment of inertia in N = 100 164 Gd compared to N = 98 162 Gd. There is at least a local minimum in the 2+ energies and local maximum in the moments of inertia in Gd nuclei at N = 98 (see fig. 2). The N = 98, 100 164,166 Dy [4] transition energies likewise a

Conference presenter; e-mail: [email protected]

Fig. 1. Top: double gate on 253.6 keV and 336.2 keV in 162 Gd. Bottom: double gate on 261.3 keV and 348.5 keV in 164 Gd. All gates have gate width = 0.33 keV.

increase from N = 98 to 100, and the J1 and J2 values of 166 Dy similarly fall between those of 162,164 Dy from 2+ → 0+ up to 12+ → 10+ , then become less than those of 162 Dy at 12+ . However, Asai et al. [5] found that the 2+ and 4+ energies in 168 Dy are lower than those of 166 Dy, so the J1 values of 168 Dy for N = 102 are above the N = 100 values but still below the N = 98 values. In constrast, the 2+ energies for Hf and Yb isotopes have a minimum at N = 104 (midshell). Also, the Er values out to N = 104 follow this trend (see fig. 2). The energies from 2+ → 0+ to 14+ → 12+ all decrease from N = 94 to 98 in 156,158,160 Sm, and their J1 and J2 MOIs increase in a systematic pattern. Unfortunately, the levels

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Fig. 2. Plot of 2+ level energies vs. neutron number.

ω than their lighter-mass isotopes. In addition to at least a local minimum in N = 98 for 162 Gd and 164 Dy, one also notes that Er and Yb have a kink and change of slope above N = 98. This suggests an unusual effect, maybe a change in structure, at N = 98. Looking at the trends of the Gd and Dy 2+ energies in fig. 2, one would expect that their N = 100 and 102 2+ energies would fall below those for similar-N Sm, and perhaps even those of Nd nuclei. With the new Gd and Dy data, the lowest known E(2+ )s in this region for N = 92–110 now are for Z = 60 Nd, followed by Z = 62 Sm and then Z = 64 Gd, with Z = 58 Ce E(2+ )s [6] curiously falling between the Gd and Dy values at N = 92 and 94 and with a much steeper slope. The Nd isotopes, with Z = 60, are well removed from the proton midshell at Z = 66, and the most neutronrich N = 96 is 8 neutrons away from midshell. Thus, our 162,164 Gd data, along with the 164,166 Dy [4] and 168 Dy [5] data, raise a new question of why is it that the most neutron-rich known Z = 60, 62 Nd, Sm isotopes have the lowest 2+ energies, largest MOI, and presumably the largest deformation in the deformed region bounded by Z = 50–82 and N = 82–126. In summary, from our work we identified levels in 162 Gd and 164 Gd. Each level and transition energy in 164 Gd is higher than its counterpart in 162 Gd. Although the known 2+ level energies have a minimum at midshell (N = 104) for Er, Yb, and Hf, our new data yield at least a local 2+ minimum at N = 98 for Gd. A local minimum also is seen there in Dy 2+ transitions established by Wu et al. [4]. Our 162,164 Gd data likewise make clear that the known minimum 2+ energies in this region surprisingly 160 are for 156 60 Nd96 and 62 Sm98 . There is at least a local minimum (maybe total minimum) in E(2+ ) at N = 98 for Gd and Dy nuclei and a kink in Er and Yb nuclei there. Thus there is some new microscopic effect taking place at N = 98 that challenges microscopic theories. Work at Vanderbilt University is supported by U.S. DOE grant and contract DE-FG05-88ER40407. The authors are indebted for the use of 252 Cf to the office of Basic Energy Sciences, U.S. DOE, through the transplutonium element production facilities at ORNL. The authors would also like to acknowledge the essential help of I. Ahmad, J. Greene, and R.V.F. Janssens in preparing and lending the 252 Cf source we used in the year 2000 runs.

160,162,164

Fig. 3. Plot of J1 (upper) and J2 (lower) vs. ω for Gd.

References

of N = 100 162 Sm are not yet known. In the Gd nuclei, the J1 and J2 moments of inertia as shown in fig. 3 for N = 100 fall between the N = 96 and 98 values at low spin and then drop below the N = 96 values above 10+ . Similar behavior was found for Dy nuclei. In Er, the N = 100 J1 values are systematically below the N = 102 values. Thus, 164 Gd and 166 Dy are more rigid with less stretching, i.e., less change in J1 and J2 with increasing

1. I-Yang Lee, Nucl. Phys. A 520, c641 (1990). 2. Y.X. Luo et al., Phys. Rev. C 64, 054306 (2001). 3. E.F. Jones et al., in Proceedings of ENAM98: 2nd International Conference on Exotic Nuclei and Atomic Masses, edited by B.M. Sherrill, D.J. Morrissey, C.N. Davids (AIP, New York, 1998) p. 523. 4. C.Y. Wu et al., Phys. Rev. C 57, 3466 (1998). 5. M. Asai et al., Phys. Rev. C 59, 3060 (1999). 6. S.J. Zhu et al., J. Phys. G 21, L75 (1995).

Eur. Phys. J. A 25, s01, 469–470 (2005) DOI: 10.1140/epjad/i2005-06-044-x

EPJ A direct electronic only

Shape transitions and triaxiality in neutron-rich odd-mass Y and Nb isotopes Y.X. Luo1,2,a , J.O. Rasmussen2 , J.H. Hamilton1 , A.V. Ramayya1 , A. Gelberg3 , I. Stefanescu3 , J.K. Hwang1 , S.J. Zhu4 , P.M. Gore1 , D. Fong1 , E.F. Jones1 , S.C. Wu2 , I.Y. Lee2 , T.N. Ginter2 , W.C. Ma5 , G.M. Ter-Akopian6 , A.V. Daniel6 , M.A. Stoyer7 , and R. Donangelo8 1 2 3 4 5 6 7 8

Physics Department, Vanderbilt University, Nashville, TN 37235, USA Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Institut f¨ ur Kernphysik, Universit¨ at zu K¨ oln, 50937 K¨ oln, Germany Department of Physics, Tsinghua University, Beijing 100084, PRC Department of Physics, Mississippi State University, MS 39762, USA Flerov Laboratory for Nuclear Reactions, Joint Institute for Nuclear Research, Dubna, Russia Lawrence Livermore National Laboratory, Livermore, CA 94550, USA Universidade Federal do Rio de Janeiro, CP 68528, RG, Brazil Received: 15 October 2004 / c Societ` Published online: 3 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. New level schemes of 99,101 Y and 101,105 Nd are established based on the measurement of prompt γ-rays from the fission of 252 Cf at Gammasphere. Triaxial-rotor-plus-particle model calculations and fitting suggest that in the A ≈ 100 neutron-rich nuclei triaxial shape is prevalent in the region with Z > 41. PACS. 21.10.Tg Lifetimes – 25.85.Ca Spontaneous fission – 27.60.+j 90 ≤ A ≤ 149

a

e-mail: [email protected]

0.8 103

Tc

N = 60

0.6 Signature Splitting S(I)

Studies of shape transitions and shape coexistence in neutron-rich nuclei with A ≈ 100 has long been of major importance [1, 2]. Large quadrupole deformations, onset of superdeformed ground states and identical bands, shape evolutions and shape coexistence were observed in the even-even Sr (Z = 38)-Zr (Z = 40)-Mo (Z = 42) region, and evidence of triaxiality was reported in Mo and Ru nuclei, e.g. [3, 4]. However, less has been reported for the odd-Z nuclei in this region so far. Evidence of triaxiality was observed in Tc (Z = 43) and Rh (Z = 45) isotopes, e.g. [5,6]. A shape transition from axially-symmetric to triaxial deformation in odd-Z nuclei of this region is of particular interest. New level schemes of odd-Z 99,101 Y (Z = 39) and 101,105 Nb (Z = 41) are established in the present work based on the measurement of prompt gamma rays from the fission of 252 Cf at Gammasphere [6]. It was found that the quadrupole deformations of the N = 60 (and N = 62) isotones with Z = 39–45 follows a similar trend in the neighboring even-even neutron-rich nuclei of Z = 38–42. The very small signature splitting and delay of band crossing observed for Y isotopes are in pronounced contrast to the results in Tc and Rh isotopes, and provide spectroscopic information concerning shape transition regarding triaxiality in this important region. Figure 1 shows

0.4 0.2 99

Y

0 -0.2

101

Nb

-0.4 105

Rh

-0.6 -0.8 4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

2I

Fig. 1. Experimental signature splitting S(I) of the groundstate bands in N = 60 isotones with odd-Z = 39–45. Data for 103 Tc and 105 Rh are taken from refs. [7] and [8].

the pronounced difference in experimental signature splittings between Y, Nb, Tc and Rh isotopes. Triaxial-rotor-plus-particle calculations [5] were performed to reproduce the level excitations, signature splittings and branching ratios of the observed bands in Y and Nb isotopes. The model calculations strongly support a pure axially symmetric shape with large quadrupole deformation, 2 = 0.41, γ = 0◦ and 2 = 0.39, γ = 0◦ in the 5/2+ [422] ground-state band of 99 Y and 101 Y isotopes,

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101

Y

5/2+[422] band Theory

Experiment

Y

5/2+[422] band Experiment

Theory

3354 27/2+ 3179.0

Eexc (MeV)

3

2

25/2+ 2717.9

2749

23/2+ 2332.3

2365

21/2+ 1933.3

1887

19/2+ 1596.0

1

1552

17/2+

1259.3

15/2+

976.0

13/2+ 11/2+

706.4

645

482.5

9/2+ 7/2+ 5/2+

284.0 125.3 0

434 252 109 0

0

1187 911

γ = 0 0, ε 2 = 0.41, Ε(2 +) = 0.14 ΜeV

2661 23/2+

2396.1

21/2+

1994.3

19/2+

1639.3

17/2+

1291.2

1303

15/2+

1001.4

1009

13/2+

725.0

700

11/2+ 9/2+ 7/2+ 5/2+

494.4

474

291.7 128.4 0

270 118 0

γ = 0 0, ε 2 = 0.39, Ε(2 +) = 0.16 ΜeV

Fig. 2. Experimental and theoretical excitation energies of ground-state bands of of 99 Y, all the spin/parity assignments are tentative.

0.4

99,101

Y. Except for the 5/2+ , 7/2+ and 9/2+

0.5

*URXQGVWDWHEDQGRI<

0.3

0.45

99,101

Y

101-105

Nb

0.4

107

ε2

0.2

0.35

Tc 111,113

0.3

0.1

Rh

0.25

0 37

-0.1

38

39

40

41

42

43

44

45 111,113

20

-0.2 Ŷ

-0.3

7KHRU J  H 



Ɣ 7KHRU

J 



H 

10

12

14

16

18

46

47

Rh

Tc

101-105

Nb

0

8

47

107

10

-0.4 6

46

30

Ƈ ([S

γ

6LJQDWXUH6SOLWWLQJ6,

2087 1735

20

22

24

26

28

30

-10 37

respectively. Figures 2 and 3 compare experimental results with model calculations for the excitations of the groundstate bands of 99,101 Y and for the signature splittings of the band of 99 Y, respectively. The model calculations yielded γ values ranging from −19◦ to −13◦ for the 5/2+ [422] ground-state bands of 101 Nb, 103 Nb and 105 Nb, and a γ value of −5◦ for the two negative-parity bands in 101 Nb. The Nb isotopes are transitional nuclei regarding triaxial deformation. An anticorrelation of quadrupole deformation and triaxiality is seen in nuclei with Z ranging from 39 to 45 (see fig. 4). One may conclude that in the A ≈ 100 neutron-rich nuclei triaxial shape is prevalent for the bands based on a onequasiparticle g9/2 proton state in the region with Z > 41.

38

39

Y 40

41

42

43

44

45

Z

I

Fig. 3. Experimental and theoretical signature splittings of the ground-state band of 99 Y.

99,101

Fig. 4. Systematics of triaxiality and quadrupole deformations observed in the neutron-rich Z = 39, 41, 43, 45 isotopes. Data of 111,113 Rh and 107 Tc are taken from refs. [5] and [6], respectively.

References 1. J. Skalski et al., Nucl. Phys. A 617, 282 (1997). 2. J.H. Hamilton, in Treatise on Heavy Ion Science, edited by Allan Bromley, Vol. 8 (Plenum Press, New York, 1989) p. 2. 3. J.H. Hamilton et al., Prog. Part. Nucl. Phys. 35, 635 (1995). 4. H. Hua et al., Phys. Rev. C 69, 014317 (2004). 5. Y.X. Luo et al., Phys. Rev. C 69, 024315 (2004). 6. Y.X. Luo et al., Phys. Rev. C 70, 044310 (2004). 7. A. Bauchet et al., Eur. Phys. J. A 10, 145 (2001). 8. F.R. Espinoza-Quinones et al., Phys. Rev. C 55, 2787 (1997).

Eur. Phys. J. A 25, s01, 471–472 (2005) DOI: 10.1140/epjad/i2005-06-178-9

EPJ A direct electronic only

Unexpected rapid variations in odd-even level staggering in gamma-vibrational bands P.M. Gore1,a , E.F. Jones1 , J.H. Hamilton1 , A.V. Ramayya1 , X.Q. Zhang1 , J.K. Hwang1 , Y.X. Luo1,2 , K. Li1 , S.J. Zhu3 , W.C. Ma4 , J.O. Rasmussen2 , I.Y. Lee2 , M. Stoyer5 , J.D. Cole6 , A.V. Daniel7 , G.M. Ter-Akopian7 , Yu.Ts. Oganessian7 , R. Donangelo8 , and J.B. Gupta9 1 2 3 4 5 6 7 8 9

Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, USA Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Department of Physics, Tsinghua University, Beijing, PRC Department of Physics, Mississippi State University, MS 39762, USA Lawrence Livermore National Laboratory, Livermore, CA 94550, USA Idaho National Laboratory, Idaho Falls, ID 83415, USA Flerov Laboratory for Nuclear Reactions, JINR, Dubna, Russia Universidade Federal do Rio de Janeiro, CP 68528, RG Brazil Ramjas College, University of Delhi, Delhi 110 007, India Received: 16 December 2004 / Revised version: 2 May 2005 / c Societ` Published online: 11 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Triple-γ coincidence data were used to study the γ-vibrational bands to 14 + in 104–106 Mo, to 13+ in 108,110 Ru and 17+ in 112 Ru, and to 13+ , 15+ in 112−116 Pd. The even-odd spin energy level splittings show rapid variations with spin and neutron number in these nuclides. With one exception, the Sm-Pt nuclei show no such reversal and much smaller staggering. PACS. 21.10.Re Collective levels – 27.60.+j Properties of specific nuclei listed by mass ranges: 90 ≤ A ≤ 149

We used our γ-γ-γ data (5.7 × 1011 triples and higher folds) from the spontaneous fission of 252 Cf to study the γ-type vibrational bands in 104–106 Mo, 108–112 Ru, and 112–116 Pd. The γ bands are extended from 8+ , 8+ [1] to + 14 , 14+ in 104–106 Mo, from 9+ [2] to 13+ , 13+ , 17+ in 108,110,112 Ru, and from 6+ , 5+ to 15+ , 15+ in 114–116 Pd. Lalkovski et al. [3] looked at the γ-band systematics in the 104–110 Ru to the 8+ levels and in 108,110,116 Pd to 8+ and 112,114 Pd to 11+ and 10+ . They noted that there were definite signature splittings in the γ bands in both these Ru and Pd nuclei and drew several conclusions. We have likewise analyzed the signature splittings in 104,106 Mo, 108,110,112 Ru, and 112,114,116 Pd to higher spin. As we will show, some of their conclusions [3] are not correct, in particular their conclusions “iii.) the even-spin levels in the γ band are depressed with respect to the odd-spin levels (staggering effect) for all Ru and Pd nuclei”, “iv.) the energy of transitions between states with even spin increases with the angular momentum (with exception of 104 Ru, 108 Pd, 112 Pd)” and their later conclusions “The staggering amplitude in Ru isotopes is lower than that in Pd isotopic chain” and “the irregular behavior of the odd-spin levels of the γ bands in 112,114,116 Pd can be explained by a

Conference presenter; e-mail: [email protected]

the back bending effect”. Our higher-spin data are important in changing some of the conclusions and in giving a clearer picture of what is happening in these γ bands. The even-odd spin energy level splittings, e.g. ΔE = E3+ -E2+ , E4+ -E3+ , . . . , show striking and rapid variations with N to indicate the need for a microscopic description. Gupta and Kavathekar [4] investigated the the K π = 2+ γ-vibrational bands and odd-even staggering from Sm to Pt nuclei. They conclude that “The sign of the odd-even energy staggering (OES) index in the γ bands distinguishes between the rigid triaxial rotor shape and the γ-soft vibrator or the O(6) symmetry. Its absolute magnitude indicates the degree of deviation from an axial rotor. This OES index S(4) is large for the shapetransitional nuclei and is much reduced for well-deformed nuclei.” Similar conclusions about the changing usefulness of the above models because of a prolate-oblate phase transition in the Hf-Hg region were discussed recently [5]. We analyzed the γ-vibrational bands in Sm to Pt nuclei and came to similar conclusions. With one exception, the Sm-Pt nuclei show no such reversal in staggering pattern as seen in Mo, Ru, and Pd, and much smaller staggering. In fig. 1(a), a comparison of the γ bands of 104,106,108 Mo shows a clear difference between 104 Mo and 106 Mo, with 104 Mo showing a marked staggering to spin + 12 . A little of this effect is seen at low spins in 106 Mo but

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The European Physical Journal A

Fig. 1. Energy-level differences of the γ bands of (a) 104,106,108 Mo, (b) 108,110,112 Ru, (c) 112,114,116 Pd, and (d) 156–170 Er.

it smoothes out at higher spins until spin 13+ . The 108 Mo staggering starts similar to 104 Mo and then smoothes out. For the γ bands of 108,110,112 Ru in fig. 1(b), the staggering in 108 Ru is the same as in 104 Mo with the oddspin levels pushed up to the even-spin levels. The 110 Ru staggering starts out similar to 108 Ru, then smoothes out like 108 Mo, and then looks like 112 Ru at higher spins. The 112 Ru staggering starts smooth but, starting at 4+ , exhibits an opposite staggering to 108 Ru with the evenspin levels pushed up to the odd-spin levels. At high spin, 112 Ru has the largest energy staggering seen in these nuclei. While 112 Pd looks similar to 104 Mo and 108 Ru, 114 Pd starts smooth then exhibits the opposite staggering to 112 Pd but similar to 112 Ru. These data clearly suggest the role of triaxial shapes, but the fluctuations indicate

that it is a very microscopic phenomenon. In going from 108 Ru to 112 Ru, we see a clearly changing pattern that is not easily reproduced within any one theoretical model. As noted in refs. [3] and [4], the Davydov and Fillipov model has the (2+ ,3+ ), (4+ ,5+ ) grouping while the Wilets and Jean model has (3+ ,4+ ), (5+ ,6+ ). One would need the Wilets and Jean model for 104 Mo, 108 Ru, and 112 Pd, and the Davydov and Fillipov model for 112 Ru and 114 Pd. Actually the low-spin data analyzed by Lalkovski et al. [3] already showed this effect but it was ignored in their summary (iii.)). Moreover their iv.) conclusion is also not true for 114 Pd and 116 Pd (see fig. 1(c)). Both the even- and odd-spin Pd sequences are irregular. The back bending of the γ bands cannot explain the switch in staggering patterns. Finally, one notes that the staggering in fact is greater at high spin in 112 Ru, not less than in the Pd as earlier claimed [3]. The region of Sm to Pt level energies were taken from [6]. For 154–166 Dy level-energy differences, strong oscillation is seen only in N = 88 154 Dy, which is outside the region of well-deformed nuclei. The others all vary smoothly with no staggering, as expected in the collective model, except at the highest spin. In a comparison of 156–170 Er level-energy differences shown in fig. 1(d), there is strong oscillation again in N = 88 156 Er, which is outside the region of deformed nuclei. There are small oscillations above spin 6+ in 162,164 Er. We found that 170 Er has the opposite oscillation to 162,164 Er, as found in the Ru and Pd nuclei. This is the only case of reversal in the oddeven spin staggering found in the Sm to Pt nuclei. Note 170 Er is 6–8 neutrons above 162,164 Er, to be compared to only 2, 4 neutron separation for reversal in Ru and Pd. The three largest energy differences are at the highest spins in 112 Ru, 570 keV, 114 Pd, 480 keV, and 166 Yb, 640 keV. Stable triaxial deformation is likely playing an important role in the rapidly varying and large odd-even spin staggering. It is not clear what causes the sudden complete reversal as found for 108,112 Ru and 112,114 Pd. This is a new phenomenon not generally seen for Sm to Pt γ bands, except for 170 Er. Clearly, the data call for a more microscopic description of γ-vibrational bands, including γ-soft and stable triaxial deformations. Work at VU, INEEL, LBNL, and LLNL is supported by U.S. DOE grants and contracts DE-FG05-88ER40407, DE-AC0799ID13727, W-7405-ENG48, and DE-AC03-76SF00098; Tsinghua by State Basic Res. Dev. Prog. G2000077400 and National Natural Science Foundation of China, 19775028.

References 1. 2. 3. 4.

A. Guessous et al., Phys. Rev. C 53, 1191 (1996). J.A. Shannon et al., Phys. Lett. B 336, 136 (1994). S. Lalkovski et al., Eur. Phys. J. A 18, 589 (2003). J.B. Gupta, A.K. Kavathekar, Pramana J. Phys. 61, 167 (2003). 5. J. Jolie, A. Linnemann, Phys. Rev. C 68, 031301(R) (2003). 6. Brookhaven National Laboratory Data Retrieval Website.

7 Nuclear structure theory 7.1 Ab initio

Eur. Phys. J. A 25, s01, 475–480 (2005) DOI: 10.1140/epjad/i2005-06-214-x

EPJ A direct electronic only

Ab initio No-Core Shell Model —Recent results and future prospects J.P. Vary1,a , O.V. Atramentov1 , B.R. Barrett2 , M. Hasan3 , A.C. Hayes4 , R. Lloyd5 , A.I. Mazur6 , P. Navr´atil7 , A.G. Negoita8 , A. Nogga9 , W.E. Ormand7 , S. Popescu8 , B. Shehadeh1 , A.M. Shirokov10 , J.R. Spence1 , I. Stetcu2 , S. Stoica8 , T.A. Weber1 , and S.A. Zaytsev6 1 2 3 4 5 6 7 8 9 10

Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA Department of Physics, University of Arizona, Tucson, AZ 85721, USA Department of Physics, University of Jordan, Amman, Jordan Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Department of Physics and Chemistry, Arkansas State University, State University, AR 72467, USA Physics Department, Khabarovsk State Technical University, Khabarovsk 680035, Russia Lawrence Livermore National Laboratory, Livermore, CA 94551, USA Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania Institut f¨ ur Kernphysik, Forschungszentrum J¨ ulich, 52425 J¨ ulich, Germany Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119992, Russia Received: 14 January 2005 / Revised version: 16 March 2005 / c Societ` Published online: 10 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The ab initio No-Core Shell Model (NCSM) adopts an intrinsic Hamiltonian for all nucleons in the nucleus. Realistic two-nucleon and tri-nucleon interactions are incorporated. From this Hamiltonian, an Hermitian effective Hamiltonian is derived for a finite basis space conserving all the symmetries of the initial Hamiltonian. The resulting finite sparse matrix problem is solved by diagonalization on parallel computers. Applications range from light nuclei to multiquark systems and, recently, to similar problems in quantum field theory. We present this approach with a sample of recent results. PACS. 21.60.Cs Shell model – 23.20.-g Electromagnetic transitions – 23.20.Js Multipole matrix elements

1 Introduction In the ab initio No-Core Shell Model (NCSM), we define an Intrinsic “bare” Hamiltonian to include a realistic nucleon-nucleon (NN) interaction and, in some cases, include a theoretical tri-nucleon (NNN) interaction. We utilize an NN interaction model that describes the NN data to high precision. This can be phenomenologically inspired or based on chiral field theory. These interactions may feature charge-symmetry breaking, may be non-local, and may be strongly repulsive at short distances. Recently obtained NN potentials from inverse scattering theory are also investigated and applied to light p-shell nuclei. The NNN interactions are taken from either meson-exchange theory or chiral field theory. In order to accommodate the strong short-range correlations, we adopt an effective Hamiltonian approach, outlined below, in which a 2-body or 3-body cluster subsystem of the full A-body problem is solved exactly. From the exact solutions of the cluster subsystem, an effective a

Conference presenter; e-mail: [email protected]

Hamiltonian is evaluated in a model space appropriate to the no-core many-body application at hand. The full Hamiltonian is then approximated as a proper superposition of these cluster effective Hamiltonians and the nocore many-body problem is then solved in the chosen basis space [1]. The effective Hamiltonian and its eigensolutions respect the symmetries of the underlying NN and NNN interactions. In this work, we indicate the utility of the ab initio NCSM for solving quantum many-body problems in other fields of physics. This utility is manifest when a limited number of fermions and/or bosons represents well the system of interest or a useful approximation to it. Specific references are made to multi-quark plus multi-antiquark systems and Hamiltonian formulations of quantum field theory. Indeed, initial applications to these systems have been published.

2 Ab initio No-Core Shell-Model The method involves a similarity transformation of the “bare” Hamiltonian to derive an effective Hamiltonian for

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a finite model space based on realistic NN and NNN interactions [2, 3, 4, 5,6,7,8]. Diagonalization and the evaluation of observables from effective operators created with the same transformations are carried out on highperformance parallel computers. For pedagogical purposes, we outline the ab initio NCSM approach with NN interactions alone and point the reader to the literature for the extensions to include NNN interactions. Note that another paper in these proceedings addresses results with NNN interactions in more detail [9]. We begin with the purely intrinsic Hamiltonian for the A-nucleon system, i.e., HA = Trel + V =

A A  1  (pi − pj )2 VN (ij) , (1) + 2m A i<j i<j=1

where m is the nucleon mass and VN (ij), the NN interaction, with both strong and electromagnetic components. Note the absence of a phenomenological singleparticle (sp) potential. We may use either coordinatespace NN potentials, such as the Argonne potentials [10] or momentum-space dependent NN potentials, such as the CD-Bonn [11]. Next, we add the center-of-mass HO Hamiltonian to the Hamiltonian (1) HCM = TCM + UCM , where UCM = A 1 1 2 2 i=1 ri . At convergence, the added 2 AmΩ R , R = A HCM term has no influence on the intrinsic properties. However, when we introduce our cluster approximation below, the added HCM term facilitates convergence to exact results with increasing basis size. The modified Hamiltonian, with a pseudo-dependence on the HO frequency Ω, can be cast into the form Ω HA

1 2 2 + mΩ ri = HA + HCM = 2m 2 i=1

A  mΩ 2 2 (ri − rj ) . VN (ij) − + 2A i<j=1 A 2  p i

(2)

Next, we introduce a unitary transformation, which is designed to accommodate the short-range two-body correlations in a nucleus, by choosing an antihermitian operator S, acting only on intrinsic coordinates, such that Ω S e . H = e−S HA

(3)

In our approach, S is determined by the requirements Ω have the same symmetries and eigenthat H and HA spectra over the subspace K of the full Hilbert space. In general, both S and the transformed Hamiltonian are Abody operators. Our simplest, non-trivial approximation to H is to develop a two-body (a = 2) effective Hamiltonian, where the upper bound of the summations “A” is replaced by “a”, but the coefficients remain unchanged. The next improvement is to develop a three-body effective Hamiltonian, (a = 3). This approach consists then of an approximation to a particular level of clustering with

a ≤ A, H=H

(1)

+H

(a)

=

A 

 A

A 

2  hi + A a

i=1

a

2

V˜i1 i2 ...ia ,

i1
(4) with (a) (a) V˜12...a = e−S HaΩ eS −

a 

hi ,

(5)

i=1 Ω and S (a) is an a-body a operator; Ha = h1 + h2 + h3 + . . . + ha +Va , and Va = i<j Vij . Note that there is no sum over “a” in eq. (4). Also, we adopt the HO basis states that are A eigenstates of the one-body Hamiltonian i=1 hi . If the full Hilbert space is divided into a finite model space (“P -space”) and a complementary infinite space (“Q-space”), using the projectors P and Q with P +Q = 1, it is possible to determine the transformation operator Sa from the decoupling condition

Qa e−S

(a)

HaΩ eS

(a)

Pa = 0 ,

(6)

and the simultaneous restrictions Pa S (a) Pa = Qa S (a) Qa = 0. Note that a-nucleon-state projectors (Pa , Qa ) appear in eq. (6). Their definitions follow from the definitions of the A-nucleon projectors P , Q. We note that in the limit a → A, we obtain the exact solutions for dP states of the full problem for any finite basis space, with flexibility for choice of physical states subject to certain conditions [12]. Note that this approach has a significant residual freedom. There is an arbitrary residual Pa -space unitary transformation that leaves the a-cluster properties invariant. There is a similar freedom for the Qa -space. Of course, the A-body results are not invariant under this residual transformation. An effort is underway to exploit this residual freedom to accelerate convergence in practical applications. The model space, P2 , is defined by Nm via the maximal number of allowed HO quanta of the A-nucleon basis states, NM , using the condition that the sum of the nucleons’ 2n + l ≤ Nm + Nspsmin = NM , where Nspsmin denotes the minimal possible HO quanta of the spectators, i.e., nucleons not affected by the interaction process. For example, 10 B, Nspsmin = 4 as there are 6 nucleons in the 0p-shell in the lowest HO configuration and, e.g., Nm = 2+Nmax , where Nmax represents the maximum HO quanta of the many-body excitation above the unperturbed ground-state configuration. For 10 B, in our nomenclature, NM = 12, Nm = 8 for an Nmax = 6 or “6Ω” calculation. On account of our cluster approximation, a dependence of our results on Nmax (or equivalently, on Nm or on NM ) and on Ω arises. The residual Nmax and Ω dependences can be used to infer the uncertainty in our results arising from effects associated with increasing a. We input the effective Hamiltonian, now consisting of a relative 2-body operator and the pure HCM term introduced earlier, into an m-scheme Lanczos diagonalization process to obtain the P -space eigenvalues and eigenvectors. At this stage we also add the term HCM again with

J.P. Vary et al.: Ab initio No-Core Shell Model —Recent results and future prospects

a) b) c) d) e) f) g) h) i) j)

spectra and transition rates in p-shell nuclei; comparisons between NCSM and Hartree-Fock [15]; di-neutron correlations in the 6 He halo nucleus [16]; neutrino cross sections on 12 C [17]; using inverse scattering theory plus NCSM to obtain novel NN interactions [18]; spectra of 16 C and 16 O [19]; spectroscopy of the A = 47–49 nuclei [20, 21]; statistical properties of nuclei based on NCSM and approximations thereto [22]; exotic multiple quark systems [23]; plus others in quantum field theory that will not be discussed due to time limitations.

Let us survey some of these applications and rely on labels and captions to convey key information. The ground-state energy of 6 Li [18] as a function of Ω provides a gauge of the rate of convergence with increasing model space as illustrated in fig. 1. The flatter the curve and the more densely packed the curves become with increasing basis space, then, the closer we are to the converged result. Note that the JISP6 interaction has been adjusted through a phase equivalent transformation, so as to retain its excellent description of the NN data and to provide a better fit to the properties of the p-shell nuclei up through A = 6 [18]. A family of such potentials is now under development that extend the range of nuclei well-described while retaining NN phase shift equivalence and the deuteron properties. We use another member of this family, called JISP16, to display in fig. 2 an observable related to elastic electron scattering, the RMS point proton radius of 4 He. Each curve again represents the results in a fixed model space ranging over 0–14Ω. The convergence with increasing model space, the tendency towards independence of the oscillator parameter, is good enough that by 8Ω the final result is obtained to within a few percent. While the convergence of the RMS is a demanding test of our approach, the results for 4 He should not be considered as typical. We expect that the convergence of the RMS neutron radius of a halo nucleus will be slower than for this tightly bound nucleus due to the fact that we work within an oscillator basis.

–25

–27

E (MeV)

A

CD-Bonn: 8Ω 10Ω 12Ω A A 14Ω

–26

A

JISP6:

A

–28

6Ω

A A A

–29

A

A

A

A

8Ω

–30

10Ω

–31

Exp. 30

–32 10

20 Ω (MeV)

Fig. 1. Ground-state energy (MeV) of 6 Li with the CDBonn [11] and JISP6 [18] effective interactions in various basis spaces as a function of the oscillator parameter. 2.1 2.0

0Ω 2Ω 4Ω 6Ω 8Ω 10Ω 12Ω 14Ω Experiment

1.9

RMS (fm)

a large positive coefficient (constrained via Lagrange multiplier) to separate the physically interesting states with 0s CM motion from those with excited CM motion. All observables that are expressible as functions of relative coordinates, such as the rms radius and radial densities, are then evaluated free of CM motion effects. Note that all observables require the same transformation as implemented for the Hamiltonian. We obtain small effects on long range operators such as the rms radius operator and the B(E2) operator when we transform them to P -space effective operators at the a = 2 cluster level [1, 13]. On the other hand, substantial renormalization was observed for the kinetic energy operator when using the a = 2 transformation to evaluate its expectation value [14]. Recent applications include:

477

1.8 1.7 1.6 1.5 1.4 1.3 1.2

5

10

15

20 25 Ω (MeV)

30

35

40

Fig. 2. Point proton root-mean-square (RMS) radius of 4 He with the JISP16 [18] effective interactions in various basis spaces as a function of the oscillator parameter.

The ground-state energies obtained in the ab initio NCSM often follow smooth trends as a function of both Ω and Nmax as seen, for example, in fig. 1. We display the minima of such sequences of curves for 16 O in fig. 3 for four NN potentials. These minima also follow smooth trajectories and allow a good fit with a constant plus exponential function for each NN potential as shown. This extrapolation method has proven successful in lighter nuclei where results closer to convergence are used to test its accuracy. The obtained constants yield our predictions for the fully converged binding energies which are −117(3), −116(5), −138(3), −111(5) MeV for the CD-Bonn, AV8’, INOY-3, N3LO potentials respectively. Our uncertainty in the last digit is indicated in parenthesis and is based on experience with different extrapolation strategies with these results. The results straddle the experiment (−127.619 MeV) and indicate the possible role of NNN potentials which are, in principle, different for each NN potential.

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-120

through the 6Ω model spaces. This trend suggests a converging spectra yet the rms differences from the experimental spectra are large (1.1 MeV) compared to the change in the last model space increase (0.25 MeV). From the sizable residual disparity with experiment, we conclude there is a need for genuine NNN potentials.

-125 Experiment

Ground state energy (MeV)

-130 -135 -140 -145

3 Phenomenological No-Core Shell Model

16O

-150

NN Potential -155

CDB-2000 AV8'

-160

INOY-3 N3LO

-165 -170 0

1

2

3

4

5

6

7

8

Nmax

Fig. 3. Ground-state energy of 16 O [19] in the ab initio NCSM with 4 realistic NN potentials as a function of basis space size [11, 24, 25, 26]. The points correspond to the minimum energy as a function of Ω at fixed Nmax . The smooth curves are constants plus exponentials fit to these results with Nmax = 2–8. 00

18

16O

20 20

16

40 30 40

14

(0 0) 20

12

E [MeV]

00 20

10

10 40

8

0 5

6

4(+) 60

4 2

2

RMS change using 18 states 1084keV 250 keV 541keV

0 2 (0) 3

0

11

EXP

6hΩ

4hΩ

2hΩ

6

Fig. 4. Low-lying positive-parity 16 O states from the CD-Bonn interaction at the a = 2 cluster approximation in the NCSM with Ω = 15 MeV. The spectra are aligned with the experimental first-excited 0+ state.

The positive-parity excitation spectra of 16 O in fig. 4 show a favorable convergence trend when proceeding to larger basis spaces. In particular, we note that the rms difference between spectra in successive model spaces decreases significantly when progressing from the 2Ω up

We now turn to heavier systems and select the 48 Ca region since the lightest nuclear candidate for neutrinoless double beta-decay is 48 Ca. Given the intense interest in this process as a method of inferring the Majorana mass of the neutrino or for indicating the presence of processes beyond the Standard Model, it is important that we focus considerable effort on this nucleus and its neighbors. At present, computational limits prevent a sequence of multi-Ω basis space evaluations so we resort to small no-core basis spaces (0–1Ω) and introduce phenomenological two-body terms to correct for the expected deficiencies. We use the name “ab initio NCSM” solely for results obtained within the framework outlined above. When we resort to phenomenological adjustments of the Hamiltonian, we will omit the label “ab initio” and simply refer to the results as obtained within the “NCSM”. Even with the phenomenological adjustments, our results are obtained with a pure two-body Hamiltonian, i.e. without single particle energies, and in a no-core model space leading to significant differences from traditional shell-model calculations in valence spaces. The specific forms we found adequate in fits to the low-lying the spectra of 48 Ca, 48 Sc and 48 Ti consist of finite-range central and tensor potentials as follows: V (r) = V0 e−(r/R) /r2 + V1 e−(r/R) /r2 + Vt S12 /r3 , (7) 2

2

where the isospin-dependent central strengths, VT , are set at V0 = −14.40 MeV fm2 and V1 = −22.61 MeV fm2 with R = 1.5 fm, the tensor strength Vt = −52.22 MeV fm3 , and S12 is the conventional tensor operator. Good spectra emerge [20, 21] as well as good total binding energies shown in fig. 5 with the added terms. The foremost deficiency of the CD-Bonn Heff in these small model spaces is traced to insufficient splitting between the 0f7/2 and the 1p3/2 orbits as seen in the rightmost column of fig. 6. This is repaired well by the addition of the phenomenological two-body interaction terms. (Note that 47 Ca was not involved in our fitting procedures.) This defect appears to be a continuation of the insufficient spin-orbit splitting problem well-documented in a variety of light nuclei results. Hence, it is likely that the resolution of this problem will ultimately come from the addition of genuine NNN interactions.

4 Further applications of the ab initio No-Core Shell-Model We have investigated the use of the ab initio NCSM to predict level densities for nuclei and to compare with simpler

J.P. Vary et al.: Ab initio No-Core Shell Model —Recent results and future prospects

479

A=48 Ground State Energies

-370

Ground state energy (MeV)

-380

-390

-400

-410

Experiment

-420

CD-Bonn CD-Bonn + 3terms

-430 48-Ar

48-K

48-Ca

48-Sc

48-Ti

48-V

48-Cr

48-Mn

Fig. 5. Ground-state energies in MeV of A = 48 nuclei. At the extremes of the valley of stability, these experimental energies are determined by only systematics. The ab initio NCSM results labelled “CD-Bonn” are obtained with Heff in the 1Ω model space, Ω = 10 MeV and isospin breaking in the P -space, as appropriate to 48 Ca. The same Heff with an added Gaussian central T = 0 term, a similar central T = 1 term and a tensor force is used for the results labeled “CDBonn + 3 terms”. 5

-

-

13/2 7/2

-

1/2 3/2 (13/2) -

-

-

(5/2 7/2

Excitation Energy (Mev)

4

-

5/2 7/2 11/2 7/2 9/2 1/2

)

)

(5/2 +

-

(7/2 11/2 -

(9/2

)

-

5/2 3/2

)

-

3

7/2 -

-

(5/2 7/2 -

47

Ca

) -

(1/2 3/2 )

-

11/2 3/2 11/2

+

1/2

-

2

3/2 +

-

3/2

7/2 13/2 -

7/2

-

1

5/2

-

9/2 3/2 -

5/2

0

1/2-

-

7/2

7/2

Exp

CD-Bonn CD-Bonn + 3 terms

Fig. 6. Negative-parity spectra of 47 Ca obtained with the same Hamiltonians as for fig. 5.

methods [22], one of which we have developed specifically for no-core models. The initial results are very encouraging. We find that a mean-field treatment with the derived Heff to generate the self-consistent single-particle spectrum [15], followed by statistical occupancy of those levels, can well-reproduce the ab initio NCSM results especially at higher excitation energies or higher temperatures. One subtlety, that we are currently studying, concerns the role of the spurious CM excitation which is absent in

Fig. 7. Three low-lying meson masses as a function of Nmax /2. Both the bare Hamiltonian (points following curved trajectories) and the effective Hamiltonian (points following straight lines) are solved in an oscillator basis.

the NCSM but present in models based on single-particle spectra. In order to provide a sense of the wide range of applications for the ab initio NCSM emerging in nuclear physics, we present in fig. 7 a constituent-quark model mass spectrum for three light mesons as a function of Nmax /2. The Hamiltonian consists of a potential derived from a relativistic wave equation treatment motivated by QCD and supplemented with traditional assumptions of massive constituent quarks [27]. It contains a term resembling one-gluon exchange and a term with behavior close to linear confinement. One major goal of this effort is to predict masses for exotic multiquark systems with sufficient precision to guide experimental searches as we have demonstrated for allcharm tetraquarks [23]. For this reason, all the techniques of the ab initio NCSM are needed, including the effective Hamiltonian treatment, as seen by the slow convergence of the bare Hamiltonian mass spectra with increasing basis size. Note that the inclusion of the flavor degree of freedom here is analogous to our isospin treatment in the case of nucleons. However, the introduction of color represents a major additional degree of freedom as we seek to predict global color singlet states which are antisymmetric under that exchange of color, and which lie below breakup thresholds into known mesons and baryons. Given the rapid progress of the ab initio NCSM in the last four years, one anticipates additional applications and extensions. It should have continuing impact on developing the nuclear many-body “standard model” including improvements in the NN and NNN interactions. It should contribute high-precision results for the determination of fundamental symmetries in nature such as nuclear double beta decay and the neutrino mass determination. Extensions to scattering theory and to the

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structure of heavier nuclei are underway. Recently, applications to non-perturbative solutions of quantum field theory have appeared [28] and underscore the potential for cross-disciplinary applications. This work was supported by the U.S. Department of Energy Grant Nos. DE-FG02-87ER40371, DE-F02-01ER41187, DEFG02-00ER41132, and Contract No. W-7405-Eng-48, by the U.S. National Science Foundation, Grant Nos. PHY0070858, PHY0244389, PHY0071027, INT0070789, RFBR, and by Lawrence Livermore National Laboratory LDRD contract No. 00-ERD-028.

References 1. P. Navr´ atil, J.P. Vary, B.R. Barrett, Phys. Rev. Lett. 84, 5728 (2000); Phys. Rev. C 62, 054311 (2000); P. Navr´ atil, G.P. Kamuntaviˇcius, B.R. Barrett, Phys. Rev. C 61, 044001 (2000). 2. S. Okubo, Prog. Theor. Phys. 12, 603 (1954). 3. J. Da Providencia, C.M. Shakin, Ann. Phys. (N.Y.) 30, 95 (1964). 4. S.Y. Lee, K. Suzuki, Phys. Lett. B 91, 79 (1980). 5. K. Suzuki, S.Y. Lee, Prog. Theor. Phys. 64, 2091 (1980). 6. K. Suzuki, Prog. Theor. Phys. 68, 246 (1982). 7. K. Suzuki, Prog. Theor. Phys. 68, 1999 (1982). 8. K. Suzuki, R. Okamoto, Prog. Theor. Phys. 70, 439 (1983). 9. P. Navr´ atil, these proceedings. 10. B.S. Pudliner, V.R. Pandharipande, J. Carlson, S.C. Pieper, R.B. Wiringa, Phys. Rev. C 56, 1720 (1997). 11. R. Machleidt, Phys. Rev. C 63, 024001 (2001).

12. C.P. Viazminsky, J.P. Vary, J. Math. Phys. 42, 2055 (2001). 13. I. Stetcu, B.R. Barrett, P. Navr´ atil, J.P. Vary, Phys. Rev. C 71, 044325 (2005); I. Stetcu, B.R. Barrett, P. Navr´ atil, C.W. Johnson, Int. J. Mod. Phys. E 14, 95 (2005), nuclth/0409072. 14. H. Kamada, et. al, Phys. Rev. C 64 044001 (2001). 15. M.A. Hasan, J.P. Vary, P. Navr´ atil, Phys. Rev. C 69, 034332 (2004). 16. O. Atramentov, J.P. Vary, P. Navr´ atil, in preparation. 17. A.C. Hayes, P. Navr´ atil, J.P. Vary, Phys. Rev. Lett. 91, 012502 (2003). 18. A.M. Shirokov, A.I. Mazur, S.A. Zaytsev, J.P. Vary, T.A. Weber, Phys. Rev. C 70, 044005 (2004); A.M. Shirokov, J.P. Vary, A.I. Mazur, S.A. Zaytsev, T.A. Weber, Phys. Lett. B 621, 96 (2005). 19. P. Navr´ atil, J.P. Vary, in preparation. 20. S. Popescu, S. Stoica, J.P. Vary, P. Navr´ atil, submitted for publication. 21. A. Negoita, S. Stoica, J.P. Vary, P. Navr´ atil, in preparation. 22. B. Shehadeh, J.P. Vary, in preparation. 23. R.J. Lloyd, J.P. Vary, Phys. Rev. D 70, 014009 (2004); R.J. Lloyd, J.R. Spence, J.P. Vary, to be published. 24. R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Phys. Rev. C 51, 38 (1995). 25. P. Doleschall, I. Borb´ely, Phys. Rev. C 62, 054004 (2000). 26. D.R. Entem, R. Machleidt, Phys. Lett. B 524, 93 (2002). 27. J.R. Spence, J.P. Vary, Phys. Rev. C 59, 1762 (1999); to be published. 28. D. Chakrabarti, A. Harindranath, J.P. Vary, Phys. Rev. D 69, 034502 (2004); D. Chakrabarti, A. Harindranath, L. Martinovic, J.P. Vary, Phys. Lett. B 582, 196 (2004).

Eur. Phys. J. A 25, s01, 481–484 (2005) DOI: 10.1140/epjad/i2005-06-145-6

EPJ A direct electronic only

Ab initio no-core shell model calculations using realistic two- and three-body interactions P. Navr´atil1,a , W.E. Ormand1 , C. Forss´en1 , and E. Caurier2 1 2

Lawrence Livermore National Laboratory, L-414, P.O. Box 808, Livermore, CA 94551, USA Institut de Recherches Subatomiques, IN2P3-CNRS, Universit´e Louis Pasteur, F-67037 Strasbourg, France Received: 30 November 2004 / c Societ` Published online: 13 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. There has been significant progress in the ab initio approaches to the structure of light nuclei. One such method is the ab initio no-core shell model (NCSM). Starting from realistic two- and threenucleon interactions this method can predict low-lying levels in p-shell nuclei. In this contribution, we present a brief overview of the NCSM with examples of recent applications. We highlight our study of the parity inversion in 11 Be, for which calculations were performed in basis spaces up to 9Ω (dimensions reaching 7 × 108 ). We also present our latest results for the p-shell nuclei using the Tucson-Melbourne TM  three-nucleon interaction with several proposed parameter sets. PACS. 21.60.-n Nuclear structure models and methods – 21.30.Fe Forces in hadronic systems and effective interactions

1 Introduction In recent years, construction of accurate nucleon-nucleon potentials and increases in computing power have led to new methods capable of solving the nuclear-structure problem for systems of more than four nucleons [1, 2]. One such method is the ab initio no-core shell model (NCSM) [2]. The principal foundation of this approach is the use of effective interactions appropriate for the large, but finite, basis spaces employed in the calculations. These effective interactions are derived from the underlying realistic inter-nucleon potentials by a unitary transformation in a way that guarantees convergence to the exact solution as the basis size increases. In this contribution, we briefly discuss the NCSM theory, present a convergence test of the method as well as selected nuclear-structure results for light nuclei up to A = 13. We highlight our recent study of the parity inversion in 11 Be, for which calculations were performed using several modern nucleon-nucleon potentials in basis spaces up to 9Ω (dimensions reaching 7 × 108 ). At present, the ab initio NCSM is capable of including the much-less-explored genuine three-nucleon forces [3, 4]. An important result of these nuclear-structure studies is the significance of the three-nucleon interaction in determining not only the binding energy, but also the excitation spectra and other observables. Consequently, nuclear-structure calculations are becoming a tool in disa

Conference presenter; e-mail: [email protected]

criminating different three-body interaction models and at the same time can put constraints on the three-body force parameters. As a step in this direction, we have improved the accuracy of our three-body interaction calculations and obtained results for the p-shell nuclei using the Tucson- Melbourne TM three-nucleon interaction [5] with several proposed parameter sets [6].

2 Ab initio no-core shell model We consider a system of A point-like non-relativistic nucleons that interact by realistic two- or two- plus threenucleon interactions. As the simpler case, when just the two-nucleon interaction is considered, was discussed in several papers, see, e.g., ref. [2], we focus here on the more general case when both two- and three-nucleon interactions (TNI) are included. The starting Hamiltonian is then HA =

1  (pi − pj )2 2m A i<j

+

A  i<j

VNN,ij +

A 

VNNN,ijk ,

(1)

i<j
where m is the nucleon mass, VNN,ij is the nucleon-nucleon (NN) interaction, and VNNN,ijk is the three-nucleon interaction. In the NCSM, we employ a large but finite

The European Physical Journal A

harmonic-oscillator (HO) basis. Due to properties of the realistic nuclear interaction in eq. (1), we must derive an effective interaction appropriate for the basis truncation. To facilitate the derivation of the effective interaction, we modify the Hamiltonian (1) by adding to it the center-ofmass (CM) HO Hamiltonian HCM = TCM + UCM , where A 1 UCM = 12 AmΩ 2 R2 , R = A i=1 ri . The effect of the HO CM Hamiltonian will later be subtracted out in the final many-body calculation. Due to the translational invariance of the Hamiltonian (1) the HO CM Hamiltonian has in fact no effect on the intrinsic properties of the system in the infinite basis space. The modified Hamiltonian can be cast into the form Ω = HA + HCM = HA

=

A 

A  i=1

hi +

A 

VijΩ,A +

i<j

A 

VNNN,ijk

i<j
1 p2i + mΩ 2 ri2 2 2m i=1

A  mΩ 2 (ri − rj )2 VNN,ij − + 2A i<j

+

A 

VNNN,ijk .

(2)

i<j
Next we divide the A-nucleon infinite HO basis space into the finite active space (P ) comprising of all states of up to Nmax HO excitations above the unperturbed ground state and the excluded space (Q = 1 − P ). The basic idea of the NCSM approach is to apply a unitary transΩ S e such that formation on the Hamiltonian (2), e−S HA Ω S e P = 0. If such a transformation is found, the Qe−S HA effective Hamiltonian that exactly reproduces a subset of eigenstates of the full space Hamiltonian is given by Ω S e P . This effective Hamiltonian contains Heff = P e−S HA up to A-body terms and to construct it is essentially as difficult as to solve the full problem. Therefore, we apply this basic idea on a sub-cluster level. When a genuine TNI is considered, the simplest approximation is to use a three-body effective interaction. The NCSM calculation is then performed with the following four steps: i) We solve a three-nucleon system for all possible Ω , i.e., usthree-nucleon channels with the Hamiltonian HA Ω,A Ω,A Ω,A ing h1 + h2 + h3 + V12 + V13 + V23 + VNNN,123 . It is necessary to separate the three-body effective interaction contributions from the TNI and from the two-nucleon interaction. Therefore, we need to find three-nucleon solutions for the Hamiltonian with and without the VNNN,123 TNI term. The three-nucleon solutions are obtained by procedures described in refs. [7] (without TNI) and [8] (with TNI). We note that we made some improvements and simplifications to the precedure described in ref. [8], which allowed us to reach a larger basis size and, consequently, lead to an improved accuracy of our results. ii) We construct the unitary transformation corresponding to the choice of the active basis space P from the three-nucleon solutions using the Lee-Suzuki procedure [9, 10].

E [MeV]

482

10 8 6 4 2 0 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22 -24 -26 -28 -30 -32 -34 -36

40; 0+0 exc 28; 0+0 exc 19; 0+0 exc 40; 0+0 gs 28; 0+0 gs 19; 0+0 gs



+H&'%RQQ

0

2

4

6

8

10

12

14

16

18

20

22

24

N max

Fig. 1. Ground state and the first 0+ 0 excited state energy of 4 He calculated using the CD-Bonn 2000 NN potential. Dependence on the NCSM model-space size Nmax for three different HO frequencies, Ω = 19, 28 and 40 MeV, is presented.

iii) As the three-body effective interactions are derived in the Jacobi-coordinate HO basis but the Anucleon calculations will be performed in a Cartesiancoordinate single-particle Slater-determinant m-scheme basis, we need to perform a suitable transformation of the interactions. This transformation is a generalization of the well-known transformation on the two-body level that depends on HO Brody-Moshinsky brackets. iv) We solve the Schr¨ odinger equation for the A nuA Ω = i=1 hi + cleon system using the Hamiltonian HA,eff A A 1 1 NN NNN i<j
3 Convergence test: 4 He with the CD-Bonn 2000 By construction, the ab initio NCSM calculation will converge to the exact result of the starting Hamiltonian with the increase of the model space, P → 1, that is with Nmax → ∞. Obviously, the idea is that the use of the effective interaction will speed up the convergence significantly compared to a calculation with the starting bare Hamiltonian. Consequently, the hope is that converged results can be obtained with model spaces that are reachable with present computers. An example of a succcesfully converged NCSM calculation is shown in fig. 1. We present the dependence of the 4 He ground state and the first 0+ 0 excited state energy on the model space size, defined by Nmax , for three different HO frequencies. The CD-Bonn 2000 NN potential was used [11]. The calculations were performed with the no-core version of the shell-model code Antoine [12]. We observe a fast convergence for the ground state for all three frequencies, with the final result −26.15(10) MeV

in good agreement with a Faddeev-Yakubovsky calculation [13]. The excited state convergence is slower with a stronger frequency dependence due to the more complex structure of this state. Still, we are able to extrapolate the excitation energy to −7.1(4) MeV. Although the CDBonn 2000 NN potential underbinds 4 He by about 2 MeV, the 0+ 2 0 excitation energy is described rather well. It is interesting to note that the convergence rate for the ground state is the fastest for the highest HO frequency while the convergence rate for the excited state is the fastest for the lowest HO frequency employed in our presented calculations. Clearly, the optimal frequency for convergence is state dependent and correlated with the radius of the state, the smaller the radius the higher optimal frequency.

4 Natural- vs. unnatural-parity states in

11

Be

Studies on light neutron-rich nuclei has attracted an increasing amount of theoretical and experimental effort ever since the advent of radioactive nuclear beams. One reason for this is the fact that substantial deviations from regular shell structure has been observed in these fewbody systems. The A = 11 isobar is of particular interest in this respect since it exhibits some anomalous features that are not easily explained in a simple shell-model framework. Most importantly, the parity-inverted 1/2+ ground state of 11 Be was noticed by Talmi and Unna [14] already in the early 1960s, and it still remains one of the best examples of the disappearance of the N = 8 magic number. The ability to explain this level inversion within a microscopic theory, such as the ab initio NCSM, is a true challenge of our understanding of nuclear forces. Unfortunately, a shortcoming of the NCSM method is the fact that the HO basis functions have incorrect asymptotics. This might be a problem when trying to describe loosely-bound systems. Therefore, it is desirable to include as many terms as possible in the expansion of the total wave function. By restricting ourselves to the use of NN interactions, we are able to maximize the model space and to better observe the convergence of our results. In order to study the level ordering in 11 Be, and in particular the relative position of natural- and unnatural-parity states, we have performed large-basis ab initio NCSM calculations using four different high-precision NN interactions [15]. One of these, the non-local INOY interaction [16], has never before been used in nuclear-structure calculations. Although it is formally a two-body potential, it does reproduce the binding energies of 3 H and 3 He and, to some extent, 3N scattering data. Remember that the underbinding of A > 2 systems is a deficiency of all other realistic NN interactions. However, this achievement comes with the cost of having to sacrifice some of the accuracy of the fit to NN scattering data. In particular, the 3P interactions are slightly modified in the IS-M version of the potential that we are using. In fig. 2 we show the excitation spectrum for 11 Be calculated using the INOY interaction. We were able to reach the 9Ω model space, which corresponds to a matrix with dimension exceeding 7 × 108 . Although we do not reproduce the anomalous 1/2+ ground state with any of the NN

E (MeV)

P. Navr´ atil et al.: Ab initio no-core shell model calculations using realistic two- and three-body interactions

15 14 11 13 Be 12 11 10 9 8 7 − 3/2 6 5 3.89 4 3.41 3 2.69 2 + (5/2,3/2) 1 − 1/2 + 0 1/2

483

+

5/2

INOY hΩ =17 MeV

1/2+

−

5/2 − 3/2 −

1/2

Exp (8−9)hΩ(6−7)hΩ(4−5)hΩ(2−3)hΩ(0−1)hΩ

Fig. 2. Excitation spectrum for 11 Be calculated using the INOY interaction in 0Ω–9Ω model spaces with a fixed HO frequency of Ω = 17 MeV. The experimental values are from ref. [17].

interactions being used, we do observe a dramatic drop of the positive-parity excitation energies with increasing model space. This observation is particularly prominent for the INOY results, shown in fig. 2; which in turn suggests that a realistic 3N force will be needed in order to reproduce the parity inversion in microscopic approaches. In this study we observe a remarkable agreement between the predictions of different standard high-precision NN interactions. In particular, the relative level spacings observed when plotting positive- and negative-parity states separately, were found to be very stable. The INOY interaction gives a larger binding energy and a stronger spin-orbit splitting than the other NN interactions. Note that both these effects would be expected from a genuine TNI, but with INOY they are achieved by the use of shortrange, non-local terms in the NN interaction.

5 Results with a genuine three-nucleon interaction It is well established that standard accurate NN potentials, like AV8 [1] or CD-Bonn 2000 [11], must be augmented by realistic three-body interactions in order to reproduce experimental binding energies, scattering observables and nuclear structure of A > 2 nuclei. An interesting example which demonstrates the importance of the TNI is the ground-state spin inversion in 10 B. The ground state of 10 B is 3+ 0. Calculations with standard accurate NN potentials, however, predict a 1+ 0 ground state [1,18, 19]. By including the TucsonMelbourne TM TNI, the problem is resolved, see fig. 3. In the figure, three parameter sets denoted as 81, 93 and 99 [6] are considered for the TM TNI. All give similar results, but dramatically different compared to the calculation with only the two-nucleon potential. In 13 C, a less dramatic but still significant effect of the TNI is apparent in the excitation spectra shown in fig. 4. A calculation with the two-nucleon interaction un− − − − derestimates the level splittings of 32 1 − 12 1 and 52 1 − 12 1 .  Including the TM TNI significantly improves agreement of these level splittings with experiment. We can also see a higher sensitivity of the excitation energies to the choice

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8.0 7.5 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5

V3eff hΩ=15 MeV

AV8'

10

B

AV8' AV8' AV8' +TM'(99) +TM'(93) +TM'(81)

3+ 0

2+ 1 4+ 2+ 3+ 2+

2+ 1

2+ 1

0 1 0 0

4+ 0 2+ 0

2+ 0 1+

0 2+ 0 0+ 1

1+ 0

0+ 1 1+ 0 3+ 0

3+ 0 1+ 0

4hΩ

Exp

4hΩ

4hΩ

4hΩ

Fig. 3. Excitation spectra of B obtained using the AV8 NN interaction and AV8 + TM interactions, respectively, are compared to experiment. Three parameter sets denoted as 81, 93 and 99 are considered for the TM TNI. The 4Ω basis space with Ω = 15 MeV HO frequency were employed.

The effects of the TNI in p-shell nuclei are not only limited to an increase of binding energies and changes in excitation spectra. In the A = 10–13 region, we also observe a significant TNI influence on the Gamow-Teller and B(M 1) transitions. An intresting example is the 0+ 0 → 1+ 1 transition in A = 12 [3] known to be highly sensitive to the strength of the spin-orbit force. An improved description of this transition with the TNI demonstrates that the TNI, here in particular the TM (99), increases the spin-orbit force strength. Similarly, we observe significant TNI effects for Gamow-Teller transistions in 11 B → 11 C [4] and in transitions from the 13 C ground state to low-lying excited states in 13 N. Concerning the 11 B → 11 C transitions, recent experimental data agree much better with our calculated results when the TNI is included [20].

E [MeV]

10

16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

13 5/2- 1/2

C

3/2- 3/2 1/2- 1/2 7/2- 1/2

3/2- 3/ 5/2- 1/2 1/2- 1/2 3/2- 1/2 7/2- 1/2 3/2- 1/2

3/2- 1/2 1/2- 1/2

1/2- 1/2

5/2- 1/2 5/2- 1/2

AV8' AV8' AV8' +TM'(99) +TM'(93) +TM'(81)

AV8'

3/2- 1/2

V3eff 3/2- 1/2 1/2- 1/2

4hΩ

Exp

4hΩ

4hΩ

4hΩ

1/2- 1/2

Fig. 4. Excitation spectra of 13 C obtained using the AV8 NN interactions and AV8 + TM interactions, respectively, are compared to experiment. Three parameter sets denoted as 81, 93 and 99 are considered for the TM TNI. The 4Ω basis space and the Ω = 15 MeV HO frequency were employed.

of the TNI parameter set compared to 10 B. Contrary to the two-nucleon interaction, the form and parameters of the TNI are much less established. A sensitivity of nuclear structure to the form and parameters of the TNI can then be helpful in determining the fine details of the TNI itself. Obviously, before any conclusions can be drawn, the convergence of the nuclear-structure results must be verified. Concerning the NCSM calculations with a two-nucleon interaction, we were able to reach the 10Ω and 8Ω model spaces for 10 B and 13 C, respectively. This was sufficient for the convergence of excitation energies of low-lying levels. Unfortunately, the NCSM calculations with the TNI are much more involved. Currently, we are limited to 4Ω model spaces for the A = 9–16 nuclei. It is imperative to increase the basis to at least 6Ω in order to establish the convergence of the excitation energies.

This work was performed in part under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. Support from the LDRD contract No. 04ERD-058, and from U.S. Department of Energy, Office of Science (Work Proposal Number SCW0498) is acknowledged.

References 1. B.S. Pudliner et al., Phys. Rev. C 56, 1720 (1997); R.B. Wiringa, Nucl. Phys. A 631, 70c (1998); R.B. Wiringa et al., Phys. Rev. C 62, 014001 (2000); S.C. Pieper et al., Phys. Rev. C 64, 014001 (2001). 2. P. Navr´ atil, J.P. Vary, B.R. Barrett, Phys. Rev. Lett. 84, 5728 (2000); Phys. Rev. C 62, 054311 (2000). 3. A.C. Hayes, P. Navr´ atil, J.P. Vary, Phys. Rev. Lett. 91, 012502 (2003). atil, W.E. Ormand, Phys. Rev. C 68, 034305 4. P. Navr´ (2003). 5. S.A. Coon et al., Nucl. Phys. A 317, 242 (1979). 6. S.A. Coon, H.K. Han, Few-Body Syst. 30, 131 (2001). 7. P. Navr´ atil, G.P. Kamuntaviˇcius, B.R. Barrett, Phys. Rev. C 61, 044001 (2000). 8. D.C. J. Marsden, P. Navr´ atil, S.A. Coon, B.R. Barrett, Phys. Rev. C 66, 044007 (2002). 9. K. Suzuki, S.Y. Lee, Prog. Theor. Phys. 64, 2091 (1980). 10. K. Suzuki, R. Okamoto, Prog. Theor. Phys. 92, 1045 (1994). 11. R. Machleidt, Phys. Rev. C 63, 024001 (2001). 12. E. Caurier, F. Nowacki, Acta Phys. Pol. 30, 705 (1999). 13. A. Nogga, private communication. 14. I. Talmi, I. Unna, Phys. Rev. Lett. 4, 469 (1960). atil, W.E. Ormand, E. Caurier, Phys. 15. C. Forss´en, P. Navr´ Rev. C 71, 044312 (2005). 16. P. Doleschall, Phys. Rev. C 69, 054001 (2004). 17. F. Ajzenberg-Selove, Nucl. Phys. A 506 1 (1990), (April 2004 revised manuscript, http://www.tunl.duke.edu/ nucldata/fas/11 1990.pdf). 18. P. Navr´ atil, W.E. Ormand, Phys. Rev. Lett. 88, 152502 (2002). 19. E. Caurier, P. Navr´ atil, W.E. Ormand, J.P. Vary, Phys. Rev. C 66, 024314 (2002). 20. Y. Fujita et al., Phys. Rev. C 70, 011306(R) (2004).

Eur. Phys. J. A 25, s01, 485–488 (2005) DOI: 10.1140/epjad/i2005-06-062-8

EPJ A direct electronic only

Ab initio coupled cluster calculations for nuclei using methods of quantum chemistry M. Wloch1 , D.J. Dean2,3,4 , J.R. Gour1 , P. Piecuch1,5,a , M. Hjorth-Jensen4,5,6,b , T. Papenbrock2,3 , and K. Kowalski1,c 1 2 3 4 5 6

Department of Chemistry, Michigan State University, East Lansing, MI 48824, USA Physics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831, USA Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA Center of Mathematics for Applications, University of Oslo, N-0316 Oslo, Norway Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA Department of Physics, University of Oslo, N-0316 Oslo, Norway Received: 13 January 2005 / Revised version: 4 February 2005 / c Societ` Published online: 13 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We report preliminary large scale ab initio calculations of ground and excited states of 16 O using quantum chemistry inspired coupled cluster methods and realistic two-body interactions. By using the renormalized Hamiltonians obtained with a no-core G-matrix approach, we obtain the virtually converged results at the level of two-body interactions. Due to the polynomial scaling with the system size that characterizes coupled cluster methods, we can probe large model spaces with up to seven major oscillator shells, for which standard non-truncated shell-model calculations are not possible. PACS. 31.15.Dv Coupled cluster theory – 21.60.-n Nuclear structure models and methods

1 Introduction One of the biggest challenges in nuclear physics is to understand how various properties, such as masses and excitation spectra arise from the nucleon-nucleon interactions. In recent years, construction of realistic nucleon-nucleon potentials and progress in the development of Monte Carlo [1] and no-core shell-model [2] techniques, combined with improvements in computer technology, have enabled to obtain converged results for nuclei with up to A = 12 nucleons, but one has to explore alternative approaches that do not suffer from the exponential growth of the configuration space with the system size and that could eventually be applied to medium-size systems in the mass 50– 100 region. Coupled cluster theory [3,4] discussed in this paper is a particularly promising candidate for such an endeavor due to its ability to provide precise description of particle correlations at the relatively low computer cost when compared to shell-model or configuration interaction techniques aimed at similar accuracies [5,6]. Historically, coupled cluster theory originated in nuclear physics [3], but its applications to the nuclear manybody problem have been relatively rare (see, e.g., [7]). On a

Conference presenter; e-mail: [email protected]. Present address: PH Division, CERN, CH-1211 Geneva 23, Switzerland. c Present address: EMSL, Pacific Northwest National Laboratory, Richland, WA 99352, USA. b

the other hand, after the early introduction of the coupled cluster wave function ansatz and diagrammatic methods ˇ ıˇzek [4], of many-body theory into quantum chemistry by C´ coupled cluster methods have enjoyed tremendous success over a broad range of problems related to molecular structure, properties, and reactivity. All kinds of coupled cluster methods have been developed for closed-shell, openshell, nondegenerate, and quasidegenerate ground and excited states of many-electron systems [5, 6]. As a result, coupled cluster methods of the type of approximations discussed in this article can nowadays be routinely applied to many-electron systems containing dozens of light atoms, several transition metal atoms, hundreds of electrons and thousands of basis functions (see, e.g., [8]). Several coupled cluster methods are available in the popular quantum chemistry software packages, enabling highly accurate ab initio calculations of useful molecular properties by non-experts. Much of this impressive development in coupled cluster theory made in quantum chemistry in the last 30 years still awaits applications to the nuclear manybody problem. In our view, the field of nuclear physics may significantly advance by adapting coupled cluster algorithms, developed in the context of electronic structure calculations, to the nuclear many-body problem. Recent coupled cluster calculations for light nuclei using modern nucleon-nucleon interactions and methods similar to those used by quantum chemists show that one may be able to overcome the difficulties posed by the enormous dimensionalities of the shell-model eigenvalue

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problem. In particular, using bare interactions, Mihaila and Heisenberg performed large scale coupled cluster calculations for the binding energy and the electron scattering form factor of 16 O [9]. We used a few quantum chemistry inspired coupled cluster methods and the renormalized interactions to compute ground- and excited-state energies of 4 He and ground-state energies of 16 O in a small model space consisting of 4 major oscillator shells [10]. These calculations indicate that quantum chemical coupled cluster methods combined with realistic nucleonnucleon interactions and renormalized Hamiltonians can provide very good accuracies at the relatively low computer cost when compared to the exact shell-model diagonalization. This paper highlights the results of our preliminary large-scale calculations of ground- and excited-state energies and properties of the 16 O nucleus using a new system of efficient general-purpose coupled cluster computer programs for nuclear structure that we developed in recent months using the elegant diagram factorization techniques developed by quantum chemists [11,12]. While the earlier large-scale coupled cluster calculations of Mihaila and Heisenberg [9] used bare interactions, making the convergence with the number of single-particle basis states very slow, our calculations use the renormalized form of the Hamiltonian exploiting a no-core G-matrix approach [13], which allows us to obtain a rapid convergence with the number of major oscillator shells in a basis. The groundand excited-state energies of 16 O reported in this work were calculated in basis sets consisting of up to 7 major oscillator shells (336 single-particle states), whereas the properties other than energy, such as charge radius, were obtained in basis sets consisting of up to 6 major oscillator shells. This is a significant progress compared to our earlier calculations [10], in which we had to limit ourselves to 80 single-particle states and energy calculations only. The complete set of converged results will be reported elsewhere once we complete the calculations.

2 Theory and computational details We begin our discussion with the construction of the suitable form of the effective Hamiltonian (see fig. 1 for the key components of our coupled cluster “machinery”). 2.1 Effective Hamiltonian In this work, we use the Idaho-A nucleon-nucleon potential [14] which was produced using techniques of chiral effective field theory [15]. The modern nucleon-nucleon interactions, such as Idaho-A, include short-range repulsive cores that require calculations in extremely large model spaces to reach converged results [9]. In order to remove the hard-core part of the interaction from the problem and allow for realistic calculations in manageable model spaces, we renormalize the interactions through a nocore G-matrix procedure [13], which introduces a startingenergy dependence ω ˜ in the effective two-body matrix elements G(˜ ω ). We use the Bethe-Brandow-Petschek [16]

Bare Hamiltonian (N3LO, Idaho-A, etc.)

Effective Hamiltonian (e.g., G-matrix, Lee-Suzuki)

Center of mass corrections ( H ⇒ H +βcmHcm)

Sorting 1- and 2-body integrals of H

EOMCCSD r-amplitude equations

CCSD t-amplitude equations

“Triples” energy corrections

Properties Λ equations

CR-CCSD(T)

Properties l- and ramplitude equations

“Triples” energy corrections

CR-EOMCCSD(T)

Fig. 1. The key components of the system of nuclear-structure coupled cluster programs used in this work. Table 1. The excitation energies for the lowest 3− state of O obtained with the EOMCCSD approach and a basis set of 5 major oscillator shells for a few values of βc.m. (in MeV). 16

(a )

βc.m. = 0.5

βc.m. = 1.0

βc.m. = 1.5(a)

13.413

13.497

13.574

The optimum value of βc.m. giving the expectation value of Hc.m.

of 0.0 MeV.

theorem to alleviate much of the starting-energy dependence. As a result, the dependence of our results on ω ˜ is weak (see ref. [13] for details). After renormalization, our Hamiltonian is given by H  = t + G(˜ ω ), where t is the kinetic energy. We correct H  for center-of-mass contaminations using the formula H = H  + βc.m. Hc.m. , where βc.m. is chosen such that the expectation value of the center-of-mass Hamiltonian Hc.m. is 0.0 MeV. This simple method of correcting H  for center-of-mass contaminations has several advantages. One of them is the ease of separation of intrinsic and center-of-mass contaminated states by analyzing the dependence of the calculated coupled cluster energies on βc.m. . The physical eigenstates of the Hamiltonian are essentially independent of βc.m. (see table 1 for the example). The center-of-mass contaminated states show a strong, nearly linear dependence of excitation energies on βc.m. . We are currently working on the alternative approach, in which instead of the G-matrix method, we will construct the renormalized Hamiltonian with the help of the Lee-Suzuki approach [17], exploited in no core shell-model calculations [2], which will eliminate the starting-energy dependence from our calculations.

2.2 Coupled cluster calculations Once the one- and two-body matrix elements of the centerof-mass-corrected renormalized Hamiltonian H are determined, we solve the nuclear many-body problem using

M. Wloch et al.: Ab initio coupled cluster calculations for nuclei using methods of quantum chemistry

coupled cluster theory. In order to construct coupled cluster equations in the most efficient way, we first sort the one- and two-body matrix elements of H according to the particle-hole character of single-particle indices that label them (cf. fig. 1). This is a common practice in coding coupled cluster methods in quantum chemistry. Figure 1 provides information about the types of computations our system of nuclear-structure coupled cluster programs can perform at this time. We always begin with the basic CCSD (“coupled cluster singles and doubles”) calculations, which provide information about the correlated ground state |Ψ0 . The CCSD method [18] is obtained by truncating the many-body expansion for the cluster operator T in the exponential wave function ansatz exploited in coupled cluster theory, |Ψ0  = exp(T )|Φ, where |Φ is the reference determinant obtained by filling the lowest-energy oscillator states, at the 2-particle-2-hole (2p-2h) component T2 . Thus, the truncated cluster operator T usedin the CCSD calculations T 1 + T2 ,  is T = a b a a aj ai are where T1 = i,a tia aa ai and T2 = 14 ij,ab tij ab the singly and doubly excited clusters, i, j, . . . (a, b, . . .) are the single-particle states occupied (unoccupied) in the reference determinant |Φ, and ap (ap ) are the usual creation (annihilation) operators associated with the orthonormal single-particle states |p. We determine the singly and doubly excited cluster amplitudes tia and tij ab , defining T1 and T2 , respectively, by solving the nonlinear system of coupled, energy-independent, algebraic ¯ ¯ ¯ = 0, Φab equations, Φai |H|Φ ij |H|Φ = 0, where H = a a ab exp(−T ) H exp(T ), and |Φi  = a ai |Φ and |Φij  = aa ab aj ai |Φ are the singly and doubly excited determinants, respectively, relative to the Fermi vacuum |Φ. The explicit form of these and other equations used in coupled cluster calculations, in terms of matrix elements of the Hamiltonian and cluster amplitudes tia and tij ab , can be derived by applying diagram factorization methods which yield vectorized computer codes [11,12]. Once tia and tij ab are determined, the ground-state CCSD energy E0CCSD is ¯ calculated as E0 = Φ|H|Φ. For the excited states |Ψμ , we use the equation of motion (EOM) CCSD method [19] (equivalent to the linear response CCSD approach [20]), in which we write |Ψμ  = R(μ) exp(T )|Φ, where T = T1 + T2 and R(μ) = R0 + R1 + R2 is a linear excitation operator, with R0 , R1 , and R2 representing the relevant reference, one-body, and twobody components of R(μ) . Each n-body component of R(μ) with n > 0 is aparticle-hole excitation  operator similar to ij a b a a aj ai , Tn , i.e. R1 = i,a rai aa ai and R2 = 14 ij,ab rab ij i where ra and rab are the corresponding excitation amplitudes. These amplitudes and the corresponding excitation energies Eμ − E0 are obtained by diagonalizing the simi¯ in the relatively small larity transformed Hamiltonian H space of singly and doubly excited determinants |Φai  and ¯ |Φab ij . The similarity transformed Hamiltonian H is not hermitian, so that in addition to the right eigenstates ¯ R(μ) |Φ, we can also determine the left eigenstates of H, (μ)

Φ|L , which define the “bra” coupled cluster wave functions Ψ˜μ | = Φ|L(μ) exp(−T ). Here, L(μ) is a hole-particle

487

Table 2. The energies of the ground state and the lowest 3− state obtained with CCSD, CR-CCSD(T), and EOMCCSD, and N = 5, 6, and 7 major oscillator shells (in MeV) using the Idaho-A potential without Coulomb. The starting-energy value used in the calculations was ω ˜ = −80 MeV.

Ground state

The lowest 3− state

N

CCSD

CR-CCSD(T)

EOMCCSD

5 6 7

−125.92 −121.53 −120.16

−126.26 −121.76 −120.76

−112.35 −108.55 −108.20

 a i de-excitation operator, so that L1 = i,a li a aa and  ab i j a a ab aa . The right and left eigenstates L2 = 14 ij,ab lij ¯ form a biorthonormal set, Φ|L(μ) R(ν) |Φ = δμν . of H The left eigenstates Φ|L(μ) become important if we are to calculate properties other than energy, such as expectation values and transition matrix elements involving coupled cluster states Ψ˜μ | and |Ψν  [19]; Ψ˜μ |θ|Ψν  =

Φ|L(μ) θ R(ν) |Φ, where θ = exp(−T )θ exp(T ) is a similarity transformed property operator θ. In particular, when θ = ap aq and μ = ν, we can determine the CCSD or EOMCCSD one-body reduced density matrices in quantum states |Ψμ , which can in turn be used to calculate one-body properties, including charge and matter densities (in the CCSD ground-state case, where T = T1 + T2 , we have R(0) = 1 and L(0) = 1+Λ1 +Λ2 , where Λ1 and Λ2 are obtained by solving the CCSD left eigenvalue problem, often referred to as the “lambda equations”; cf. fig. 1). The CCSD and EOMCCSD methods capture the bulk of the correlation effects with the relatively inexpensive computational steps that scale as n2o n4u , where no (nu ) is the number of occupied (unoccupied) single-particle states, but there may be cases, where the effects of threebody clusters T3 and three-body components R3 and L3 on the calculated ground- and excited-state energies and properties become important. We can estimate the effects of T3 and R3 on ground- and excited-state energies by adding the a posteriori corrections to the CCSD and EOMCCSD energies Eμ , defining the CR-CCSD(T) and CR-EOMCCSD(T) approaches [6,12,21], which require the relatively inexpensive n3o n4u noniterative steps. These corrections can be calculated using the T and R(μ) operators obtained in the CCSD and EOMCCSD calculations. Here, we use variant “c” (or ID) of the ground-state CRCCSD(T) approach [10] (see [21] for the original work).

3 Results and discussion We discuss the preliminary large-scale coupled cluster calculations for 16 O using methods described in sect. 2. Shown in table 2 are the energies of the ground state and the lowest 3− state obtained with CCSD (ground state), EOMCCSD (the 3− state) and CR-CCSD(T) (ground state), and 5, 6, and 7 major oscillator shells. The triples corrections to the EOMCCSD energies of the 3− state will be calculated in the near future along with other excited

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states and larger numbers of single-particle states to verify the rapid convergence observed here. We demonstrated earlier [10] that the corrections due to T3 clusters resulting from CR-CCSD(T) calculations are small in a basis including 4 major oscillator shells. The same is true when larger basis sets are employed (see table 2). Our results indicate that triples corrections to the ground-state energy in 16 O are less than 1% of the total energy. For example, for the N = 7 calculation, the difference between the CCSD and CR-CCSD(T) results is 0.6 MeV. A simple extrapolation based on fitting the data in table 2 to E(N ) = E∞ + a exp(−b · N ), where E∞ is the extrapolated energy and a and b are coefficients for the fit shows that the extrapolated CR-CCSD(T) energy is −120.5 MeV. Coulomb adds to the binding approximately 11.2 MeV, so that our estimated Idaho-A ground state energy is −109.3 MeV, compared to an experimental value of −128 MeV. Thus, the two-body interactions underbind 16 O by approximately 1 MeV per particle, leaving room for extra binding to be produced by three-nucleon interactions. Our preliminary conclusions are that connected three-body clusters are small and that the basic CCSD approximation produces a highly accurate estimate of the binding energy in 16 O due to two-nucleon interactions. We plan to verify this statement by running calculations with 8 major oscillator shells and other interactions. The first-excited 3− state in 16 O, located experimentally at 6.12 MeV above the ground state, is thought to be a 1p-1h state [22]. The vast experience of quantum chemistry with the EOMCCSD calculations for 1p-1h electronic states is telling us that the EOMCCSD method should describe the 3− state of 16 O well, if indeed this is a 1p-1h state and provided that the three-body interactions in the Hamiltonian can be neglected (there are no threeelectron interactions in molecular systems). According to our EOMCCSD calculations, the largest excitation amplitudes for the 3− state of 16 O are for the 1p-1h excitations from the 0p1/2 orbital to the 0d5/2 orbital. The 2p-2h excitations in the EOMCCSD wave function are very small, confirming the 1p-1h nature of the lowest 3− state. If we again extrapolate the CCSD and EOMCCSD energies for the ground and 3− state, we obtain that the 3− state is located at −108.2 MeV, i.e. 11.3 MeV above the CCSD ground state. The ∼ 5 MeV difference between the extrapolated EOMCCSD and experimental results suggests that we may have to incorporate higher–than–two-body clusters and/or three-nucleon interactions in the future to explain the observed discrepancy between theory and experiment. If the 3− state is predominantly a 1p-1h state, triples effects should be small. This would mean that the observed discrepancy between theory and experiment may reside in the Hamiltonian. We plan to explore this issue by performing the CR-EOMCCSD(T) calculations for the first-excited 3− state and other interactions. We also performed the preliminary CCSD calculations of the ground-state density, using the recipe described in sect. 2. The resulting densities for the 5 and 6 major oscillator shells were used to determine the root-mean-square

(r.m.s.) charge radii. After correcting for the finite sizes of the nucleons and the center-of-mass motion, we obtained 2.45 fm and 2.50 fm, respectively, in good agreement with experimental charge radius of 2.73 ± 0.025 fm. In summary, we have developed a system of coupled cluster programs for nuclear structure calculations, using methods and algorithms developed in the context of electronic structure studies. We discussed our preliminary large scale calculations for the 16 O nucleus. These calculations are among the first to probe, from an ab initio point of view, the structure of both the ground and excited states of 16 O in enormous model spaces, for which non-truncated shell-model calculations are not possible. This work has been supported by the U.S. Department of Energy (Oak Ridge National Laboratory, Michigan State University, and University of Tennessee), the National Science Foundation (Michigan State University), and the Research Council of Norway.

References 1. R.B. Wiringa, S.C. Pieper, Phys. Rev. Lett. 89, 182501 (2002). 2. P. Navratil, W.E. Ormand, Phys. Rev. C 68, 034305 (2003). 3. F. Coester, Nucl. Phys. 7, 421 (1959). ˇ ıˇzek, J. Chem. Phys. 45, 4256 (1966). 4. J. C´ 5. J. Paldus, X. Li, Adv. Chem. Phys. 110, 1 (1999); T.D. Crawford, H.F. Schaefer III, Rev. Comput. Chem. 14, 33 (2000). 6. P. Piecuch et al., Theor. Chem. Acc. 112, 349 (2004). 7. H. K¨ ummel et al., Phys. Rep. 36, 1 (1978). 8. M. Sch¨ utz, J. Chem. Phys. 116, 8772 (2002); R.M. Olson et al., J. Am. Chem. Soc. 127, 1049 (2005). 9. J.H. Heisenberg, B. Mihaila, Phys. Rev. C 59, 1440 (1999); B. Mihaila, J.H. Heisenberg, Phys. Rev. Lett. 84, 1403 (2000); Phys. Rev. C 60, 054303 (2002); 61, 054309 (2002). 10. K. Kowalski et al., Phys. Rev. Lett. 92, 132501 (2004). 11. S.A. Kucharski, R.J. Bartlett, Theor. Chim. Acta 80, 387 (1991). 12. M. Wloch et al., to be published in J. Chem. Phys. 13. D.J. Dean, M. Hjorth-Jensen, Phys. Rev. C 69, 054320 (2004). 14. D.R. Entem, R. Machleidt, Phys. Lett. B 524, 93 (2002). 15. S. Weinberg, Phys. Lett. B 363, 288 (1990); U. van Kolck, Prog. Part. Nucl. Phys. 43, 337 (1999). 16. H.A. Bethe et al., Phys. Rev. 129, 225 (1963). 17. S.Y. Lee, K. Suzuki, Phys. Lett. B 91, 79 (1980); K. Suzuki, S.Y. Lee, Prog. Theor. Phys. 64, 2091 (1980). 18. G.D. Purvis, R.J. Bartlett, J. Chem. Phys. 76, 1910 (1982). 19. J.F. Stanton, R.J. Bartlett, J. Chem. Phys. 98, 7029 (1993). 20. H. Monkhorst, Int. J. Quantum Chem., Symp. 11, 421 (1977); K. Emrich, Nucl. Phys. A 351, 379 (1981). 21. K. Kowalski, P. Piecuch, J. Chem. Phys. 120, 1715 (2004). 22. E.K. Warburton, B.A. Brown, Phys. Rev. C 46, 923 (1992).

Eur. Phys. J. A 25, s01, 489–490 (2005) DOI: 10.1140/epjad/i2005-06-074-4

EPJ A direct electronic only

Effective operators in the NCSM formalism I. Stetcu1,a , B.R. Barrett1 , P. Navr´ atil2 , and J.P. Vary3 1 2 3

Department of Physics, University of Arizona, P.O. Box 210081, Tucson, AZ 85721, USA Lawrence Livermore National Laboratory, Livermore, CA 94551, USA Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA Received: 12 November 2004 / Revised version: 9 January 2005 / c Societ` Published online: 29 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. No-core shell model (NCSM) calculations using ab initio effective interactions are very successful in reproducing the experimental nuclear spectra. While a great deal of work has been directed toward computing effective interactions from bare nucleon-nucleon (NN) and three-nucleon forces, less progress has been made in calculating the effective operators. Thus, except for the relative kinetic energy, the proton radius, and the NN pair density, all investigations have used bare operators. We apply the Lee-Suzuki procedure to general one-body operators, investigating the importance of the approximations involved. In particular we concentrate on the limitations of the two-body cluster approximation. PACS. 21.60.Cs Shell model – 23.20.-g Electromagnetic transitions – 23.20.Js Multipole matrix elements

A long standing problem in the phenomenological shell model was the use of effective charges which arise, in principle, from the truncation of the space. Previous perturbation theory attempts to describe phenomenological charges needed to obtain correct transition strengths have been unsuccessful [1], but, on the other hand, recent investigations within the framework of the no-core shell model (NCSM) have reported some progress in explaining the large values of the effective charges [2]. In the NCSM, one starts from a nucleon-nucleon (NN) interaction which describes the NN scattering data, and derives an effective interaction in a restricted model space. Three-body interactions have been shown to be important in the correct description of the energy spectra in light nuclei, but they are computationally very demanding. Therefore, in the current investigation we restricted ourselves to two-body interactions. As a result of the space truncation, one should also compute effective operators. The Lee-Suzuki transformation [3] has been used in order to accommodate the short-range two-body correlations, with the condition that the model and excluded spaces are not coupled by the Hamiltonian. Thus, the transformed Hamiltonian is given by H = e−S HeS ,

(1)

with S determined so that the model space and the excluded space are decoupled, that is P HQ = 0, with P and Q the projectors onto the model and excluded spaces, a

Conference presenter; e-mail: [email protected]

respectively. Such a transformation ensures an energy independent effective interaction in the model space. If one determines the operator S so that the additional decoupling condition QHP = 0 is fulfilled, it can be shown that the effective operators determined by the transformation O = e−S OeS

(2)

are also energy independent [4,5]. Formally, the operator S can be written by means of another operator ω as S = arctanh(ω − ω † ), where the new operator fulfills QωP = ω. Hence, one obtains the energy-independent effective Hamiltonian in the model space P P + P ω † Q P + QωP , H√ Heff = P HP = √ P + ω†ω P + ω†ω

(3)

and, analogously, any observable can be transformed to the P space as [4, 5] P + P ω † Q P + QωP . O√ Oeff = P OP = √ P + ω†ω P + ω†ω

(4)

The operator ω can be computed simply by using the relation [6]  ˜ P ,

αQ |k k|α (5)

αQ |ω|αP  = k∈K

with |αP  and |αQ  the basis states of the P and Q spaces, respectively; |k denotes states from a selected set K of eigenvectors of the Hamiltonian H in the full A-body ˜ is the matrix element of the inverse space, and αP |k overlap matrix αP |k. Therefore, an exact determination

The European Physical Journal A

B(E2)

490

8 7 6 5 4 3 2 1 0

+

+

20 0 0

hΩ=15 MeV 12

C

0 4 8 12 16 20 24 28 NhΩ for the Q space

Fig. 1. B(E2) in 12 C using effective interaction derived from AV8 potential [7]. Results as a function of the dimension of the Q-space included (circles) are compared with the bare operator (square) and the experimental value (diamond).

of the operator ω necessary to obtain the effective operators requires the exact solution of the A-body problem, which is the final goal. For practical applications, we approximate the operator ω, by solving eq. (5) for a cluster of a < A particles. For further details, we refer the reader to previous publications, e.g., [6] and references therein. In the present paper, we restrict the investigation to the two-body cluster, that is a = 2. Since, in this case, the transformation ω is a two-body operator, we write the one-body operators in a two-body form, introducing a dependence upon the number of particles. In this paper, we obtain corrections to electromagnetic multipoles, and the results for a selected quadrupole transition strength are shown in fig. 1. We point out that, because non-scalar operators can connect different channels with good angular momentum, the procedure to obtain effective operators is more involved than for the Hamiltonian. Therefore, for general one and two-body operators, one has to restrict the number of states from the Q-space included in the calculation [8], checking the convergence of the many-body matrix elements with the number of states included. In fig. 1 we show how the renormalization of the E2 operator varies with the number of states in the Q-space included in the calculation. The B(E2) remains almost constant, with negligible contributions from the states in the Q-space. This is somehow surprising, as the quadrupole operator connects the model space with the excluded space, and the renormalization was expected to improve the B value obtained with the bare operator. The same result is obtained for the M 1 operator, but this result is easier to understand as this operator is defined completely in the model space. Generally, our calculations in large model spaces have shown that the theoretical M 1 strengths are often in reasonable accord with the experimental values. The quadrupole transitions involving collective states, however, are usually underestimated, even in the largest model spaces. The two-body cluster approximation is the main difference between our present approach and a previous NCSM calculation that reported effective charges for 6 Li in agreement with the phenomenological charges usually employed in shell model calculations. Thus, in ref. [2], the authors

have performed a Lee-Suzuki transformation which includes up to six-body correlations, by transforming the Hamiltonian from an initial 6¯ hΩ space to a 0¯ hΩ model space, equivalent to a core calculation which fixes four particles in the 0s shell. The electromagnetic operators which they calculated reproduced the transition strengths obtained with bare operators in 6¯hΩ, which were considered to be the correct values. This suggests that the higher-order clusters are important for renormalization of electromagnetic operators. By using a Gaussian operator of variable range, we can show that the renormalization, obtained at the two-body cluster level [6], depends strongly upon the range of the operator [9]. Thus, for short-range operators, such as the relative kinetic energy, the renormalization is strong, while for long-range operators, it is very weak. The quadrupole operator is infinite range and therefore very weakly renormalized at the two-body cluster level. In summary, we have implemented the Lee-Suzuki procedure for the renormalization of general one- and twobody operators, at the two-body cluster level. The renormalization is much more involved than for the Hamiltonian, so that we include in the renormalization states from the excluded space one shell at a time, observing the convergence of matrix elements. We have shown that the renormalization fails to improve the transition strengths obtained with bare operators, and we conclude that this is due to the two-body cluster approximation, which renormalizes short-range correlations. The electromagnetic multipoles, however, are infinite range and, thus, are very weakly renormalized. Work on renormalizing form factors is underway where we expect greater success, especially at higher momentum transfers. I.S. and B.R.B. acknowledge partial support by NFS grants PHY0070858 and PHY0244389. The work was performed in part under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. P.N. received support from LDRD contract 04-ERD-058. J.P.V. acknowledges partial support by USDOE grant No. DE-FG-02-87ER40371.

References 1. P.J. Ellis, E. Osnes, Rev. Mod. Phys. 49, 777 (1977). 2. P. Navr´ atil, M. Thoresen, B.R. Barrett, Phys. Rev. C 55, R573 (1997). 3. K. Suzuki, S.Y. Lee, Prog. Theor. Phys. 64, 2091 (1980); K. Suzuki, Prog. Theor. Phys. 68, 246 (1982). 4. S. Okubo, Prog. Theor. Phys. 12, 603 (1954). 5. P. Navr´ atil, H. Geyer, T.T.S. Kuo, Phys. Lett. B 315, 1 (1993). 6. P. Navr´ atil, J.P. Vary, B.R. Barrett, Phys. Rev. C 62, 054311 (2000). 7. R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Phys. Rev. C 51, 38 (1995). 8. I. Stetcu, B.R. Barrett, P. Navr´ atil, C.W. Johnson, Int. J. Mod. Phys. E 14, 95 (2005), arXiv:nucl-th/0409072. 9. I. Stetcu, B.R. Barrett, P. Navr´ atil, J.P. Vary, Phys. Rev. C 71, 044325 (2005), arXiv:nucl-th/0412004.

7 Nuclear structure theory 7.2 Shell model

Eur. Phys. J. A 25, s01, 493–498 (2005) DOI: 10.1140/epjad/i2005-06-136-7

EPJ A direct electronic only

Shell-model description of weakly bound and unbound nuclear states N. Michel1,2,3,a , W. Nazarewicz1,2,4 , M. Ploszajczak5,b , and J. Rotureau5 1 2 3 4 5

Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA Physics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831, USA Joint Institute for Heavy Ion Research, Oak Ridge, TN 37831, USA Institute of Theoretical Physics, Warsaw University, ul. Ho˙za 69, 00-681 Warsaw, Poland Grand Acc´el´erateur National d’Ions Lourds (GANIL), CEA/DSM-CNRS/IN2P3, BP 55027, F-14076 Caen Cedex 05, France Received: 20 March 2005 / c Societ` Published online: 8 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A consistent description of weakly bound and unbound nuclei requires an accurate description of the particle continuum properties when carrying out multiconfiguration mixing. This is the domain of the Gamow Shell Model (GSM) which is the multiconfigurational shell model in the complex k-plane formulated using a complete Berggren ensemble representing bound single-particle (s.p.) states, s.p. resonances, and non-resonant complex energy continuum states. We shall discuss the salient features of effective interactions in weakly bound systems and show selected applications of the GSM formalism to p-shell nuclei. Finally, a development of the new non-perturbative scheme based on Density Matrix Renormalization Group methods to select the most significant continuum configurations in GSM calculations will be discussed shortly. PACS. 21.60.Cs Shell model – 24.10.Cn Many-body theory – 27.20.+n Properties of specific nuclei listed by mass ranges: 6 ≤ A ≤ 19

1 Introduction The binding of nuclei close to the particle drip lines depends sensitively both on the coupling to scattering states and on the effective in-medium NN interaction which itself is modified by the continuum coupling [1]. Weakly bound nuclei are best described in the open quantum system formalism allowing for configuration mixing, such as the real-energy continuum shell model (see ref. [2] for a recent review) and, most recently, the complex-energy continuum Gamow Shell Model (GSM) [3, 4,5, 6,7] (see also refs. [8,9]). GSM is the multi-configurational shell model with a single-particle (s.p.) basis given by the Berggren ensemble [10] which consists of Gamow (or resonant) states and the complex non-resonant continuum. The s.p. Berggren basis is generated by a finite-depth potential, and the many-body states are obtained in shell-model calculations as the linear combination of Slater determinants spanned by resonant and non-resonant s.p. states. Hence, both continuum effects and correlations between nucleons are taken into account simultaneously. All details of the formalism can be found in refs. [4,5], in which the GSM was applied to many-neutron configurations in neutronrich helium, oxygen, and lithium isotopes. a b

e-mail: [email protected] Conference presenter; e-mail: [email protected]

Even though the effective interaction theory for open quantum many-body systems has not yet been developed (see, however, recent attempts in ref. [11]), recent investigations [12,13] in the framework of the Shell Model Embedded in the Continuum (SMEC) [14,2] established basic features of the correction to the eigenenergy of the closed quantum system due to the continuum coupling. The novel feature, absent in the standard SM, is a strong influence of the poles of the scattering (S) matrix on the weakly bound/unbound states. In particular, for nucleons in low- orbits ( = 0, 1), the coupling becomes singular at the particle emission threshold if the pole of the S-matrix lies at the threshold [12,13]. Such a coupling may induce the non-perturbative rearrangement of the wave function. Below, we shall illustrate this effect in the case of spectroscopic factors of 0+ states in 6 He.

2 Average spherical Gamow-Hartree-Fock potential In earlier studies [3,4], we have used the s.p. basis generated by a Woods-Saxon (WS) potential which was adjusted to reproduce the s.p. energies in 5 He (“5 He” parameter set [4]). This “5 He” WS basis is unsuitable when applied to the neutron-rich helium isotopes. Therefore, we use an optimized Berggren basis given by the Hartree-Fock (HF) method extended to unbound states (the so-called

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Gamow-Hartree-Fock (GHF) approach). This allows for a more precise description of heavier p-shell nuclei in the GSM calculations [5]. The spherical HF potential cannot be defined for openshell nuclei and one has to resort to approximations. The first ansatz is the usual uniform-filling approximation in which HF occupations are averaged over all magnetic substates of an individual spherical shell. In the second ansatz, the deformed HF potential corresponding to nonzero angular momentum projection is averaged over all the magnetic quantum numbers (the so-called M -potential). For closed-shell nuclei, both methods yield the true HF potential. To define the M -potential, one occupies the s.p. states in the valence shell that have the largest angular momentum projections on the third axis. The resulting Slater determinant corresponds to the angular momentum J = M . For closed-shell nuclei (M = 0) and for nuclei with one particle (or hole) outside a closed subshell (M = j), this Slater determinant can be associated with the ground state (g.s.) of the s.p. Hamiltonian. Spherical M -potential, UM , is defined by averaging the resulting HF potential over magnetic quantum number m: ˆ

α|UM |β = α|h|β +

1 Nl,j

j 



m=j+1−Nl,j

λ

αm λmλ |Vˆ |βm λmλ ,

(1)

ˆ is the s.p. Hamiltonian (given by a WS+Coulomb where h potential), λ is an occupied shell with angular quantum numbers (jλ , lλ ), N (λ) is the number of nucleons occupying this shell, and Vˆ is the residual shell-model interaction. In the above expression, Nl,j is the number of nucleons occupying the valence shell with quantum numbers l, j. While the HF procedure is well defined for the bound states, it has to be modified for the unbound s.p. states (resonant or scattering), even in the case of closed-shell nuclei. First, the effective nuclear two-body interaction has to be quickly vanishing beyond a certain radius; otherwise the resulting HF potential diverges, thus providing incorrect s.p. asymptotics. Moreover, as resonant states are complex, the resulting self-consistent HF potential is complex as well. This is to be avoided, as the Berggren completeness relation assumes a real potential. Therefore, we take the real part of the GHF potential to generate the s.p. basis.

3 Description of the Gamow Shell Model calculation 3.1 Choice of the average potential, the Hamiltonian and the valence space For the residual interaction, we take a finite-range Surface Gaussian Interaction (SGI) [7]: VJ,T (r1 , r2 ) =   2  r1 −r2 · δ(|r1 |+|r2 |−2 · R0 ), (2) V0 (J, T ) · exp − μ

which is used, together with the WS potential with the “5 He” parameter set, to generate an optimal GHF basis. The Hamiltonian employed can thus be written as: ˆ =H ˆ (1) + H ˆ (2) , where H ˆ (1) is the one-body Hamiltonian H described above augmented by a hard sphere Coulomb potential of radius R0 (corresponding to the 4 He core), and ˆ (2) is the two-body interaction among valence particles, H which can be written as a sum of SGI and Coulomb terms. The Coulomb two-body matrix elements are calculated using the exterior complex scaling as described in ref. [4] and can be treated as precisely as nuclear terms. The principal advantage of the SGI is that it is finiterange, so no energy cutoff is needed. Moreover, the surface delta term simplifies the calculation of two-body matrix elements, because they can be reduced to one-dimensional radial integrals. Consequently, a local adjustment of the Hamiltonian parameters in GSM/GHF calculations becomes feasible. In this chapter, the valence space for protons and neutrons consists of the 0p3/2 and 0p1/2 GHF resonant states, calculated for each nucleus, and the {ip3/2 } and {ip1/2 } (i = 1, · · · , n) complex and real continua generated by the same potential. These continua extend from [k] = 0 to [k] = 8 fm−1 , and they are discretized with 14 points (i.e., n = 14). The 0p1/2 resonance is taken into account only if it is bound or very narrow; otherwise we take a real {ip1/2 } contour. Another continua, such as s1/2 , d5/2 , · · · , are neglected, as they can be chosen to be real and would only induce a renormalization of the two-body interaction. Altogether, we have 15 p3/2 and 14 or 15 p1/2 GHF shells in the GSM calculation. Having defined a discretized GHF basis, we construct the many-body Slater determinants from all s.p. basis states (resonant and scattering), keeping only those with at most two particles in the nonresonant continuum. The weight of configurations involving more than two particles in the continuum is usually quite small in the optimal GHF basis. In the chain of helium isotopes, which are described assuming an inert 4 He core, there are only T = 1 twobody matrix elements: (J = 0, T = 1) and (J = 2, T = 1). We have adjusted V0 (J = 0, T = 1) to reproduce the experimental g.s. energy of 6 He relative to the g.s. of 4 He, whereas V0 (J = 2, T = 1) has been fitted to all g.s. energies from 7 He to 10 He. The adopted values are: V0 (J = 0, T = 1) = –403 MeV· fm3 and V0 (J = 2, T = 1) = –315 MeV· fm3 . Our previous analysis of T = 0 two-body matrix elements in the chain of lithium isotopes suggests that they are gradually reduced with an increasing number of valence neutrons Nn [5]: V0 (J = 1, T = 0) = α10 [1 − β10 (Nn − 1)] , V0 (J = 3, T = 0) = α30 [1 − β30 (Nn − 1)] , where α10 = −600 MeV fm3 , β10 = −50 MeV fm3 , α30 = −625 MeV fm3 , and β30 = −100 MeV fm3 . This finding agrees with the conclusion of recent SMEC studies of the binding energy systematics in the sd-shell nuclei [12]. In the SMEC, the reduction of the neutron-proton T = 0

N. Michel et al.: Shell-model description of weakly bound and unbound nuclear states Table 1. Binding energies of the He isotopes (in MeV) calculated in the GSM using the GHF basis with the M -potential are compared with experimental values.

Nucleus

BGSM (MeV) BExp (MeV)

6

He

−0.984 −0.972

7

He

−0.475 −0.537

8

He

−3.740 −3.112

9

He

−2.418 −1.847

Table 2. The same as in table 1 but for the Li isotopes.

Nucleus

BGSM (MeV) BExp (MeV)

6

Li

−4.820 −3.698

7

Li

−13.008 −10.948

8

Li

−15.094 −12.981

9

Li

−20.181 −17.044

495

the framework of SMEC. (The description of the SMEC formalism has been given elsewhere [14, 2].) In this formalism, the total Hamiltonian H is divided into the “unperturbed” Hamiltonians HQQ and HP P in the subspaces Q and P of (quasi-)bound (Q subspace) and scattering (P subspace) states, respectively, and the coupling terms HQP , HP Q between these subspaces. The “closed quantum system” approximation is based on replacing H by HQQ (the standard SM Hamiltonian). In the open quantum formalism, the dynamics in Q subspace is described by an energy-dependent effective Hamiltonian which includes the coupling to the scattering continuum: (+)

eff (E) = HQQ + HQP GP (E)HP Q , HQQ

(3)

(+)

interaction with respect to the neutron-neutron T = 1 interaction is associated with a decrease in the one-neutron emission threshold when approaching the neutron drip line, i.e., it is a genuine continuum coupling effect. To account for this effect in the standard Shell Model (SM), one would need to introduce a N -dependence of the T = 0 monopole terms which comes about naturally if one includes three-body interactions into the two-body framework of a standard SM [15]. The NN coupling via intermediate scattering states contributes to three-body correlations which are difficult to disentangle from effects generated by the genuine three-body force. Tables 1 and 2 display binding energies of several He and Li isotopes. The experimental binding energies relative to the 4 He core are reproduced fairly well with the SGI interaction. For instance, the g.s. of 6 He and 8 He are bound, whereas g.s. of 5 He and 7 He are unbound. Moreover, the so-called helium anomaly, i.e., the presence of the higher one- and two-neutron emission thresholds in 8 He than in 6 He, is well reproduced. Ground-state energies of lithium isotopes relative to the g.s. energy of 4 He are described reasonably well, but clearly the particle-number dependence of the matrix elements has to be further investigated in order to achieve a detailed description of the data.

4 Effective interactions in weakly bound systems In the presence of explicit coupling to the scattering continuum, the treatment of many-body correlations poses a challenge to traditional nuclear structure methods based on SM, and to the derivation of effective interactions in the space of bound states. For weakly bound nuclei, the natural basis for calculating in-medium effective interactions is the complete Berggren basis. The effective interaction consistent with the framework of GSM, depends on the positions of various particle emission thresholds as well as on the distribution and nature of the S-matrix poles. The genuine features of the continuum coupling correction to the eigenenergy of the closed quantum system near the one-particle emission threshold can be studied in

where GP (E) is a Green’s function for the motion of a single nucleon in P subspace. The effective Hamiltonian eff is a complex-symmetric matrix for E above the parHQQ ticle emission threshold (E (thr) ), and Hermitian below it. (i) eff (E) can be writAn eigenvalue Ei (E) = Ei + Ecorr of HQQ ten as a sum of a closed-system eigenenergy Ei given by HQQ and the correction due to the coupling to the decay channels, which depends on the distance of Ei from the one-particle threshold. In the one-channel case, and neglecting the off(+) diagonal terms of HQP GP (E)HP Q , the continuum correction to Ei can be studied analytically assuming a finitedepth, square-well potential for HP P and replacing Q-P couplings by a source term having a radial dependence, which is consistent with the radial dependence of s.p. wave functions which enter in the microscopic calculation of this term [14]. A so-defined model can be rigorously solved [13] to determine basic dependencies of the continuum correction to the eigenenergy of the closed system at the threshold (E = 0), as a function of the distance ε of the eigenvalue of HP P (a pole of the S-matrix) from the one-body continuum threshold. In the leading order in ε, one finds:   ( ) (4) Ecorr (ε) = − const |ε|−1+ /2 + O |ε|0 , i.e., the continuum correction at the threshold is singular for  = 0, 1 states in the limit of ε → 0, independently of whether the considered S-matrix pole is a bound s.p. state, a s.p. resonance or a virtual s.p. state [13]. In general, this behavior leads to the rearrangement of a HF particle vacuum and to the coexistence of two HF minima with different configurations of the S-matrix poles around the threshold. Moreover, the non-perturbative rearrangement of GSM many-body wave functions with a significant  = 0, 1 s.p. content is expected. Below, we will see an illustration of this genuine behavior in the spectroscopic factor of 6 He. The discussion of effects of continuum coupling on spin-orbit splitting in p-shell nuclei can be found in refs. [13, 16]. For higher -values ( ≥ 2), even though the continuum correction is often bigger than for  = 0, 1 [12], a singular dependence on the position of the S-matrix pole is absent. Therefore, the continuum coupling for high- orbitals can be mocked up in standard SM calculations by an

6

5 Spectroscopic factors: example of He As discussed above, the coupling to the particle continuum leads to a strong modification of wave functions in weakly bound/unbound nuclei. A sensitive probe of such modifications is the spectroscopic factor. In this study, we investigate the p3/2 spectroscopic factor S(0+ , p3/2 ) for the two lowest 0+ states of 6 He:   S 0+ i , p3/2 =    2 5  + 6

He(0i )| | Heg.s.  ⊗ |p3/2 (k) J=0  , (5) k

where i = 1, 2 and the sum runs over all |p3/2 (k) states, i.e., both the 0p3/2 pole and the non-resonant p3/2 continuum. (It is to be noted that the Gamow states are normalized using the squared wave function and not the modulus of the squared wave function.) The spectroscopic factors are very sensitive to discretization effects. Below, we take 26 points for the p3/2 contour, and 14 points for the p1/2 complex contour. The 0p1/2 resonant state has to be in6 cluded, as the 0+ 2 state of He in the pole approximation is built from two neutrons in 0p1/2 . In the quasi-stationary approach with Gamow states, the spectroscopic factor (5) is, in general, complex. An interpretation of these complex values has been given by Berggren [17]: the real part of the matrix element can be associated with the average value, while the imaginary part represents the uncertainty of the mean value. Therefore, if the overlap matrix element has a large imaginary value, the spectroscopic factor can become negative. Figure 1 shows the spectroscopic factor of the 6 He g.s. in the [|5 He ⊗ |p3/2 ]0 channel as a function of the position of the 0p3/2 pole of the S-matrix in 5 He. (The energy of the 0p3/2 pole is varied by changing the depth of the central part of the WS potential.) The results of the full GSM calculations in the model space, which includes 0p3/2 , 0p1/2 s.p. resonances and the states of the discretized complex continuum, exhibit an intricate dependence on the position of the 0p3/2 pole. If the 0p3/2 s.p. state of 5 He is bound, the spectroscopic factor decreases smoothly when 0p3/2 approaches the continuum threshold. At the threshold, where the coupling to the nonresonant continuum is strongest, the spectroscopic factor reaches its lowest value. The behavior of the spectroscopic factor changes dramatically if 0p3/2 becomes a resonance, as it grows with increasing energy of the 0p3/2 state. This is an illustration of how strongly the analytic features of the S-matrix may influence the spectroscopic observables in a weakly bound system. The role of the completeness of the s.p. basis can be assessed by comparing results of the full GSM calculation

GSM pole

6

1.0 0.9

HO-SM

0.8

5

adjustment of monopole terms in the effective interaction, in particular, by introducing a suitable particle-number dependence.

He

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0.7

GSM

0.6 -0.5 -0.4 -0.3 -0.2 -0.1

0

0.1 0.2 0.3 0.4 0.5

E0p (MeV) 3/2

Fig. 1. Spectroscopic factor of the 6 He ground state in the [|5 He ⊗ |p3/2 ]0 channel as a function of the energy of the 0p3/2 s.p. state in 5 He. Thick solid line: GSM results; thin solid line: the equivalent SM results in the HO-SM approximation; dashed line: restricted GSM calculations in the pole approximation, i.e., including resonances 0p3/2 and 0p1/2 only.

with the results obtained in the pole approximation (poleGSM), where the basis states of the non-resonant continuum are neglected. In the latter case, the spectroscopic factor changes smoothly with the energy of the 0p3/2 state. This clearly demonstrates that the complicated dependence of the spectroscopic factor found in GSM is the result of an interplay between discrete states and the nonresonant continuum states in the many-body wave function of 6 He. To compare the GSM results with the results of the standard SM procedure, we performed calculations in the harmonic oscillator basis. The s.p. energies in such “equivalent SM calculations” (HO-SM approximation) are given by the real parts of 0p1/2 and 0p3/2 eigenvalues of the WS potential generating the GSM basis. Such equivalent SM calculation yields, as expected, a smooth and monotonic energy variation of the spectroscopic factor. The GSM results are close to the HO-SM results for well bound 0p3/2 s.p. state, i.e., when the coupling to the non-resonant continuum states is weak. On the contrary, the difference between GSM and HO-SM is strongest if the 0p3/2 pole lies at the threshold. It is worth noting that there is a significant difference between the results of HO-SM and pole-GSM calculations. In both cases, the dimension of the model space is identical but the radial wave functions used to calculate the matrix elements of the two-body Hamiltonian are different. In particular, the 0p1/2 s.p. state is a broad resonance in GSM, and the matrix elements of the SGI interaction involving this state are noticeably reduced as compared to the HO-SM variant. Consequently, the configuration mixing in the (0p3/2 0p1/2 ) space is stronger in HO-SM. Figure 2 shows the spectroscopic factor (5) for the first 6 + excited 0+ 2 state of He. There are only two 0 states in the (0p3/2 0p1/2 ) model space of HO-SM and pole-GSM; hence the results of figs. 1 and 2 are strongly correlated. (The sum of both spectroscopic factors is equal to one.) A small value of the spectroscopic factor in GSM cannot

0.2

HO-SM

0.1

5

Sp. factor : He + p3/2

6

He*

N. Michel et al.: Shell-model description of weakly bound and unbound nuclear states

GSM pole

0 GSM

-0.5 -0.4 -0.3 -0.2 -0.1

0

0.1 0.2 0.3 0.4 0.5

E0p (MeV) 3/2

Fig. 2. The same as in fig. 1 except for the second 0+ excited state of the 6 He.

be explained in the same way. In fact, the configurations involving a 0p3/2 s.p. state (bound or resonance) are spread over a huge number of excited 0+ states, all of them unbound, having a dominant contribution from the non-resonant continuum basis states. Consequently, the spectroscopic factor is mainly concentrated in a single state, the g.s. of 6 He in the present case, and other 0+ states have negligibly small amplitudes. For the bound 0p3/2 s.p. state, the maximum value of the spectroscopic factor in the distribution over all 0+ states decreases when 0p3/2 approaches the continuum threshold. The mechanism of concentration of the spectroscopic factor in a single state discussed in this section is a genuine effect of the strong coupling to the continuum. Going away from the valley of stability towards drip lines, one should expect to see a gradual reduction of the spreading of spectroscopic factors over different J π , T states, which is characteristic of the gradual evolution of correlations in the many-body system due to the enhanced continuum coupling. Obviously, the description of such an evolution is beyond the scope of the standard SM.

6 Application of the density matrix renormalization group techniques for solving the GSM problem The complex Berggren ensemble of the GSM contains many states representing a discretized non-resonant continuum. Consequently, the dimension of the (nonHermitian) GSM Hamiltonian matrix grows extremely fast with the number of active shells, and this “explosive” growth is much more severe than in the standard SM which deals with the pole space only. In practice, most of the configurations involving many nucleons in the nonresonant continuum contribute very little to wave functions of low-energy physical states which are dominated by the pole space configurations and by configurations with a small number of nucleons in the non-resonant states in the neighborhood of these pole states. This feature of GSM calls for a development of a procedure for selecting the most important configurations involving continuum

497

states. A promising approach is the DMRG method developed originally in the context of quantum lattices [18] and recently applied to SM problems with schematic Hamiltonians [19]. The main idea is to gradually consider different s.p. shells in the configuration space and retain only Nopt the most optimal states dictated by the one-body density matrix. Below, we shall discuss the application of the DMRG method to the g.s. configuration of 6 He in GSM. In this case, the configuration space is divided into two subspaces: A (s.p. resonances 0pα , α = 1/2, 3/2) and B (s.p. states/shells representing the non-resonant continua {pα }, α = 1/2, 3/2). In the initial phase (the warm-up phase), one calculates and stores all the possible matrix elements of suboperators of the Hamiltonian in A: K  K L  † † K  K   K  / a/ a , a , a† a† , a† a† / a , a a a† , a† / and constructs all the states |k with 0, 1, 2 particles coupled to all possible j-values. Then, from each continuum {pα }, one picks up a s.p. state, calculates for this added pair of shells the matrix elements of suboperators, and constructs all the states |i with 0, 1, 2 particles coupled to all possible j-values. In the following, one adds “one by one” pairs of s.p. states in B and repeats the procedure until the number of states |i is larger than Nopt . Then the Hamiltonian is diagonalized in the space {|kA |iB }J made of vectors in A and B. Obviously, the number of particles in such states is equal to the total number of valence particles, and J is equal to the angular momentum of the state of interest (J = 0). From the eigenstates  (6) |Ψ  = cki {|kA |iB }J , one calculates the one-body density matrix,  ρB cki cki , ii =

(7)

k

in different blocks with a fixed value of j in states |i, |i . The density matrix is then blockwise diagonalized and Nopt eigenstates |uν  having the largest eigenvalues ωνB are retained. (In GSM, eigenvalues of the density matrix are complex and the eigenstates of ρB are selected according to the largest absolute value of the density eigenvalues.) Those eigenvalues correspond to the most important states of the enlarged set. All the matrix elements of suboperators for the optimized states are recalculated; they are linear combinations of previously calculated matrix elements. Then, the next pair of non-resonant continuum states is added and, again, only the Nopt states are kept. This procedure is repeated until the last shell in B is reached, providing a “first guess” for the wave function of the system. This ends a warm-up phase, and a sweeping phase begins. At this point, one constructs states with 0, 1, 2 particles and then the process continues in the reverse direction until the number of vectors becomes larger than Nopt . If the m-th shell in B is reached, the Hamiltonian is diagonalized in the set of vectors: {|k, iprev |i}J , where iprev is a previously optimized state (first m − 1 p-shells in B),

(εDMRG-εexact)/εexact

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6

GSM energy of 6He

4 2 0

0

50

Νstep

100

Fig. 3. The relative difference between the exact g.s. GSM energy of 6 He (εexact ) and the energy of this state calculated in GSM + DMRG approach (εDMRG ) as a function of the number of iteration steps. Solid (dashed) line marks the real (imaginary) part of the GSM + DMRG energy. See text for details.

strongly reduced by applying techniques of the DMRG in solving the GSM problem. The novel feature of GSM, absent in the standard SM, is a strong influence of S-matrix poles on the weakly bound/unbound many-body states. For the low- orbits ( = 0, 1), the continuum coupling may induce the instability of the HF vacuum and nonperturbative rearrangement of the wave function. We have demonstrated that this effect can be seen in the properties of spectroscopic factors. A similar mechanism may also influence the spin-orbit effects, pair-transfer amplitudes, nuclear collectivity, and properties of nuclear excitations. Further systematic investigations of weakly bound nuclei, both experimentally and theoretically, will undoubtedly shed new light on the salient features of the continuum coupling and will identify the most pertinent observables affected by a gradual appearance of open channels when moving towards particle drip lines. This work was supported in part by the U.S. Department of Energy under Contracts Nos. DE-FG02-96ER40963 (University of Tennessee), DE-AC05-00OR22725 with UT-Battelle, LLC (Oak Ridge National Laboratory), and DE-FG05-87ER40361 (Joint Institute for Heavy Ion Research).

References and i is a new state (i > m). The density matrix is then diagonalized and the Nopt i-states are kept. The procedure continues by adding the (m − 1)-th pair of shells, etc., until the first state in B is reached. Then the procedure is reversed again: the first pair of shells is added, then the second, the third, etc. The succession of sweeps is successful if the energy converges. Figure 3 illustrates the convergence of real and imaginary parts of the g.s. energy of 6 He calculated in the DMRG procedure as a function of the number of steps, Nstep . In this example, the number of shells included in blocks A and B are 2 and 50, respectively. At each step we keep Nopt = 6 states. For these parameters, the warmup phase is completed in 25 steps, and fully converged GSM + DMRG results are found in 15 steps, i.e. in less than one sweep. This example demonstrates that a finitesystem algorithm of DMRG is very efficient in selecting the most important GSM continuum configurations. In the considered example, a total dimension D of the GSM Hamiltonian is 702, and the rank of the biggest matrix to be diagonalized in GSM + DMRG is d = 32. The gain factor D/d grows very fast with the number of valence particles and with the number of shells in the non-resonant continuum (B block).

7 Conclusion Coupling to the non-resonant continuum and the multiconfiguration mixing can be consistently described in the framework of the GSM. The explosive growth of dimensionality in GSM, associated with the inclusion of a large number of states in the non-resonant continuum, can be

1. J. Dobaczewski, W. Nazarewicz, Philos. Trans. R. Soc. London, Ser. A 356, 2007 (1998). 2. J. Okolowicz, M. Ploszajczak, I. Rotter, Phys. Rep. 374, 271 (2003). 3. N. Michel, W. Nazarewicz, M. Ploszajczak, K. Bennaceur, Phys. Rev. Lett. 89, 042502 (2002). 4. N. Michel, W. Nazarewicz, M. Ploszajczak, J. Okolowicz, Phys. Rev. C 67, 054311 (2003). 5. N. Michel, W. Nazarewicz, M. Ploszajczak, Phys. Rev. C 70, 064313 (2004). 6. N. Michel, W. Nazarewicz, M. Ploszajczak, J. Okolowicz, J. Rotureau, Acta Phys. Pol. B 35, 1249 (2004). 7. N. Michel, W. Nazarewicz, M. Ploszajczak, J. Rotureau, arXiv:nucl-th/0401036. 8. R.I. Betan, R.J. Liotta, N. Sandulescu, T. Vertse, Phys. Rev. Lett. 89, 042501 (2002). 9. R.I. Betan, R.J. Liotta, N. Sandulescu, T. Vertse, Phys. Rev. C 67, 014322 (2003). 10. T. Berggren, Nucl. Phys. A 109, 265 (1968). 11. G. Hagen, M. Hjorth-Jensen, J.S. Vaagen, arXiv:nuclth/0410114. 12. Y. Luo, J. Okolowicz, M. Ploszajczak, N. Michel, arXiv:nucl-th/0201073. 13. N. Michel, W. Nazarewicz, J. Okolowicz, M. Ploszajczak, Proceedings of the International Nuclear Physics Conference (INPC 2004), (Elsevier B.V., Amsterdam, 2005). 14. K. Bennaceur, F. Nowacki, J. Okolowicz, M. Ploszajczak, Nucl. Phys. A 651, 289 (1999); 671 (2000) 203. 15. A. Zuker, Phys. Rev. Lett. 90, 042502 (2003). 16. N. Michel, W. Nazarewicz, M. Ploszajczak, these proceedings. 17. T. Berggren, Phys. Lett. B 373, 1 (1996). 18. S.R. White, Phys. Rev. B 48, 10345 (1993). 19. J. Dukelsky, S. Pittel, S.S. Dimitrova, M.V. Stoitsov, Phys. Rev. C 65, 054319 (2002).

Eur. Phys. J. A 25, s01, 499–502 (2005) DOI: 10.1140/epjad/i2005-06-032-2

EPJ A direct electronic only

Shell-model description of neutron-rich pf-shell nuclei with a new effective interaction GXPF1 M. Honma1,a , T. Otsuka2,3 , B.A. Brown4 , and T. Mizusaki5 1 2 3 4

5

Center for Mathematical Sciences, University of Aizu, Tsuruga, Ikki-machi, Aizu-Wakamatsu, Fukushima 965-8580, Japan Department of Physics and Center for Nuclear Study, University of Tokyo, Hongo, Tokyo 113-0033, Japan RIKEN, Hirosawa, Wako-shi, Saitama 351-0198, Japan National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824-1321, USA Institute of Natural Sciences, Senshu University, Higashimita, Tama, Kawasaki, Kanagawa 214-8580, Japan Received: 1 October 2004 / c Societ` Published online: 22 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The shell-model effective interaction GXPF1 is tested for the description of unstable pf -shell nuclei. The GXPF1 successfully describes the N = 32 shell gap in Ca, Ti and Cr isotopes, while the 56 deviation of predicted Ex (2+ Ti from the recent experimental data requires the modification of the 1 ) in Hamiltonian especially in the T = 1 matrix elements related to the p1/2 and f5/2 orbits. The modified interaction gives improved description simultaneously for all these isotope chains. PACS. 21.60.Cs Shell model – 21.30.Fe Forces in hadronic systems and effective interactions

1 Introduction The nuclear shell model has been one of the most powerful tools for the microscopic study of the nuclear structure. Owing to recent developments in computational facilities as well as numerical methods, most of the pf -shell nuclei are now in the scope of exact or nearly exact 0¯ hω calculations. The success of the shell model crucially depends on the choice of the effective interaction, however. For practical use in a wide region of the pf -shell, we have recently derived an effective interaction GXPF1 [1]. Starting from the microscopic effective interaction [2] derived from the Bonn-C potential (it is simply referred as G hereafter), we modified 70 well-determined linear combinations of 4 single-particle energies and 195 two-body matrix elements by iterative fitting calculations to about 700 experimental energy data out of 87 nuclei. The GXPF1 interaction was tested [3] extensively from various viewpoints such as binding energies, electormagnetic moments, energy-levels and transitions, revealing its predictive power in the wide region of the pf -shell. At the same time, it was found that the deviation of the shell-model prediction from available experimental data appeared to be sizable in binding energies of N ≥ 35 nuclei and in magnetic moments of Z ≥ 32 even-even nuclei. This observation suggests the limitation of its applicability near the end of the pf -shell. a

Conference presenter; e-mail: [email protected]

Since the GXPF1 was determined by using the experimental energy data mainly of stable nuclei, it is a challenging test to apply this interaction to describe/predict the structure of unstable nuclei. Recent data of such unstable nuclei may provide crucial information for clarifying possible problems in some parts of the effective interaction. This paper is organized as follows: In sect. 2, we clarify the problem in GXPF1 revealed by new experimental data of neutron-rich nuclei around Ti isotopes. In sect. 3, we investigate possible modifications of GXPF1 so as to improve the description, and the validity of such modifications is examined. Several results obtained with the modified interaction are presented in sect. 4. The shell-model calculations were carried out by using the code MSHELL [4]. We also consider the KB3G [5] interaction as a reference, because it gives an excellent description for light pf -shell nuclei (A ≤ 52). The KB3G interaction is the latest version of the family of the KB3 [6] interaction. Both GXPF1 and KB3G predict similar structure for light stable nuclei, but they give rather different results in several cases of neutron-rich nuclei.

2 Shell evolution One of the interesting results obtained by the GXPF1 for the neutron-rich nuclei is the shell evolution, i.e., the change of the shell structure due to the occupation of single-particle orbits. Figure 1 shows the excitation energies Ex (2+ 1 ) for Ca, Ti and Cr isotopes as a function of

500

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2 1 0

Ti

Ex (MeV)

22

Cr

f5 4

f5

3

p1

2

p1 1

1

0

Exp. GXPF1 KB3G GXPF1A

28

GXPF1 KB3G GXPF1A

30 32 34 36 28 30 32 34 36 28 30 32 34 36 Neutron Number Neutron number Neutron number

Fig. 2. Effective single-particle energies of the neutron p1/2 and f5/2 orbits relative to the p3/2 orbit calculated by three effective interactions: GXPF1 (solid lines), KB3G (dashed lines) and GXPF1A (dot-dashed lines).

0

Cr

24

Ex (MeV)

Ti

5

3

ESPE(j) − ESPE(p3/2) (MeV)

Ex (MeV)

6

Ca

4

1

0

20

24

28 32 Neutron Number

36

40

Fig. 1. Systematics of Ex (2+ 1 ) for even-even Ca, Ti, and Cr isotopes. Experimental data (closed circles) are compared to shell-model results obtained with three effective interactions: GXPF1 (dod-dashed line), KB3G (dashed line) and GXPF1A (solid line). Experimental data are taken from refs. [7, 8, 9, 10].

the neutron number N . It can be seen that the GXPF1 successfully describes the variation of Ex for all these isotope chains, including the increase of Ex at N = 28 shell closure. In addition, one can find a remarkable increase in Ex from N = 30 to 32 for all these isotopes, which has been interpreted as an indication of another shell closure. Since the experimental energy data included in the fitting calculations for the derivation of GXPF1 were limited to N ≤ 31, 30 and 32 for Ca, Ti and Cr, respectively, it turns out that the prediction for Ex of 54 Ti was in good agreement with the experiment [9]. In order to illustrate the shell evolution, it is useful to consider the effective single-particle energy (ESPE) for pf -shell nuclei [1]. The ESPE contains the effects of both bare single-particle energy and the angular-momentum averaged two-body interaction. We focus on the behavior of the p1/2 and f5/2 orbits relative to the p3/2 orbit as a function of N , which is shown in fig. 2 for even-even Ca, Ti and Cr isotopes. The N = 32 shell gap is a result of the large spin-orbit splitting between the p3/2 and p1/2 orbits. In fact, as seen in fig. 2, both GXPF1 and KB3G predict no single-particle orbit between these two orbits, which are separated by about 2 MeV in Ca and Ti. The shell gap disappears as more and more protons are added in the f7/2 orbit, because the neutron f5/2 orbit rapidly comes down well below the p1/2 orbit due to the large attractive proton-

neutron interaction between the member of the spin-orbit partner j> -j< [11]. As for Cr, GXPF1 predicts that the f5/2 orbit is still higher than the p1/2 orbit by 1.5 MeV and there exists a corresponding increase in Ex at N = 32. On the other hand, KB3G produces almost degenerate f5/2 and p1/2 orbits, and accordingly, the increase of Ex can hardly be seen. Nevertheless, the formation mechanism of N = 32 shell gap is robust and the jump of Ex (2+ 1 ) at N = 32 is, at least qualitatively, predicted by various effective interactions such as KB3, KB3G and FPD6 [12]. In addition to N = 32, GXPF1 predicts another increase in Ex at N = 34 for Ca and Ti, which is attributed to the large energy gap between the neutron f5/2 and p1/2 orbits [11]. However, in the recent experiment for 56 Ti [10], it turned out that the measured Ex (2+ 1 ) is lower than the GXPF1 prediction by 0.4 MeV, indicating a problem of GXPF1 for the description of neutron-rich nuclei. In contrast with the N = 32 shell gap, the persistence of the shell gap with N > 32 and Z > 20 is more complex: it is predicted by GXPF1 and KB3, while not by FPD6 and KB3G. It can be seen in fig. 2 that, in the case of Ti, the difference of the ESPE between the f5/2 and p1/2 orbits at N = 34 is only 0.7 MeV in KB3G, while it is 3.2 MeV in GXPF1. This gap is already about 1.3 MeV at N = 28 and rapidly increases toward N = 34. Since the N -dependence of the p1/2 orbit is modest in both interactions, the behavior of the f5/2 orbit is of great interest.

3 Modification of GXPF1 In order to improve the description of Ex (2+ ) for 56 Ti, one possible choice is to lower the single particle energy of the f5/2 orbit by 0.8 MeV, as suggested in ref. [10]. In fact it remedies this discrepancy by about 0.2 MeV. However, such a modification affects the description of other neighboring nuclei. For example, in fig. 3, energy levels of 54 Ti are compared with experimental data including highspin states. One can find that the correspondence between

M. Honma et al.: Shell-model description of neutron-rich pf -shell nuclei with a new effective interaction GXPF1 8

54

56

Ti

Table 1. Summary of modified two-body matrix elements V (2ja 2jb 2jc 2jd ; JT ) (in MeV). Those of other effective interactions are also shown for comparison.

Ti

7

6

Ex (MeV)

5

(8+) (7+)

10+ 9+ 8+ 8+ 7+

6+

6+

4+

4+

2+

2+

(10+) (9+) (8+)

10+ 8+ 9+ 7+ 9+ 8+

9+ 7+ 8+

4

3

GXPF1

GXPF1A

V (7777; 01) V (5511; 01) V (1111; 01) V (5151; 21) V (5151; 31)

−2.439 −0.809 −0.447 −0.152 +0.238

−2.239 −0.309 +0.053 −0.502 +0.488

G

KB3G

−2.045 −0.450 −0.308 −0.174 +0.207

−1.920 −0.392 +0.151 −0.135 +0.205

4+

(2+)

2+

1

0+ 0+ Exp. GXPF1A GXPF1 KB3G

V

6+

2

0

501

0+ 0+ Exp. GXPF1A GXPF1 KB3G

Fig. 3. Energy levels of 54,56 Ti. Experimental data [9, 10] are compared to shell-model results with three effective interactions GXPF1, KB3G and GXPF1A.

the experimental data and the GXPF1 prediction is very good. It was argued in ref. [9] that the energy gap above the yrast 6+ state is one evidence of the N = 32 shell closure. In the shell model results, the leading configura+ 2 8 3 1 tion of 7+ 1 and 81 states is πf7/2 νf7/2 p3/2 p1/2 , while it is + + 2 8 3 1 πf7/2 νf7/2 p3/2 f5/2 for 91 and 101 . The lowering of the f5/2 orbit affects only the latter two states, giving rise to worse agreement between the shell model results and the experimental data. It is also the case for high-spin states in 53 Ti [13], suggesting that the ESPE for the p3/2 and f5/2 orbits predicted by GXPF1 is reasonable at least near N = 32. Therefore, we search for another way to solve the problem in 56 Ti. Since the experimental data included in the derivation of GXPF1 were limited to Z ≤ 32, it is natural to anticipate that there remains relatively large uncertainty in the matrix elements which are related to the p1/2 and f5/2 orbits. It can be seen in fig. 1 that GXPF1 predicts slightly higher Ex (2+ ) than experimental data commonly for almost all nuclei. This is naturally understood by recalling that we have adopted the few-dimensional-bases approximation (FDA) [14] for deriving GXPF1 in order to obtain shell-model wave functions for all states included in the fit. Since the FDA wave function is a superposition of several angular-momentum projected Slater determinants, the pairing correlations cannot be described accurately. Therefore, the determined “strengths” (i.e. two-body matrix elements) for the pairing interaction become relatively stronger than they should be in the exact calculations. Thus we change the following pairing matrix elements to be less attractive. The increments are   ΔV f7/2 f7/2 f7/2 f7/2 ; J = 0, T = 1 = +0.2 MeV, (1)   ΔV f5/2 f5/2 p1/2 p1/2 ; J = 0, T = 1 = +0.5 MeV, (2)   ΔV p1/2 p1/2 p1/2 p1/2 ; J = 0, T = 1 = +0.5 MeV. (3)

Here, we consider only these three matrix elements, because they are enough to improve the results for all nuclei discussed in the present study, and we should keep the modifications minimal. The modification (1) accounts only for the systematic error due to the FDA. On the other hand, the shift is relatively large in (2) and (3), which are related to the p1/2 and f5/2 orbits, allowing additional 0.3 MeV uncertainty due to the lack of data for determining these matrix elements. The modification (3) affects the monopole matrix element and therefore changes the ESPE of the p1/2 orbit for N > 32, as shown in fig. 2 with dot-dashed lines. The energy gap between f5/2 and p1/2 is made narrower at N = 34 by 0.5 MeV, promoting the mixing between these orbits. Such a modification is reasonable from the viewpoint of systematics in the monopole part after the subtraction of the tensor force [15]. In ref. [3], we have pointed out that the strength of quadrupole-quadrupole (QQ) interaction p3/2 )](2) · [(p3/2 )† (f˜7/2 )](2) in GXPF1 is made to [(f7/2 )† (˜ be much stronger than the original G as well as KB3G, leading to successful description of 2+ states on top of the 56 Ni closed core. In fact, the strength of this term is −0.81, −0.38, and −0.34 MeV for GXPF1, G, and KB3G, respectively. In the case of 56 Ti, we can consider 8 p43/2 core, and expect that the similar correca νf7/2 tion takes effects for lowering Ex (2+ ). The strength of p1/2 )](2) · [(p1/2 )† (f˜5/2 )](2) term is −0.23, −0.22, [(f5/2 )† (˜ and −0.20 MeV for GXPF1, G, and KB3G, respectively. Then, the relevant matrix elements are changed by   ΔV f5/2 p1/2 f5/2 p1/2 ; J = 2, T = 1 = −0.35 MeV, (4)   ΔV f5/2 p1/2 f5/2 p1/2 ; J = 3, T = 1 = +0.25 MeV. (5) This modification keeps the monopole centroid unchanged, and the strength of the QQ term is now −0.58 MeV. The modified matrix elements are summarized in table 1. These modifications are typically within about 0.3 MeV in comparison with other effective interactions. This modified GXPF1 is referred to as GXPF1A hereafter.

4 Results and discussions It can be seen in fig. 1 that GXPF1A gives better description of the systematics of Ex (2+ ) than GXPF1 for almost

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55

Ti

Ti

7

21/2− 6

19/2− 21/2−

19/2−

Ex (MeV)

5

17/2− 4

15/2− 17/2−

15/2− 3

2

9/2−

11/2− 13/2− 9/2− 7/2−

1

7/2− 5/2− 1/2−

3/2− 5/2−

3/2−

1/2−

0

13/2− 11/2−

GXPF1A GXPF1 KB3G

GXPF1A GXPF1 KB3G

and p1/2 orbits is reduced from 4.1 MeV (GXPF1) to 3.6 MeV (GXPF1A) and, correspondingly, Ex (2+ ) is decreased from 3.8 MeV to 3.0 MeV. Nevertheless, this excitation energy is higher than that of 52 Ca (2.56 MeV experimentally), suggesting the N = 34 shell closure in the Ca isotopes as predicted in ref. [11]. In 49 Ca, the single-particle strength of the neutron p1/2 orbit is lower in energy than that of f5/2 by about 1.8 MeV [18], which appears rather close to the predictions of GXPF1 and KB3G. The size of this energy gap is large enough to be comparable to that between the p3/2 and p1/2 orbits at N = 32. As more neutrons are put into the p3/2 and p1/2 orbits toward N = 34, this gap significantly widens in GXPF1A, while it is almost constant in KB3G. This difference is due to the T = 1 monopole effect. Therefore, Ex (2+ ) of 54 Ca reflects the T = 1 part of the monopole property. The experimental determination of Ex (2+ ) will provide crucial information.

53,55

Fig. 4. Calculated energy levels of Ti with three effective interactions GXPF1, KB3G and GXPF1A.

all nuclei. There still remains a large deviations from experiment in 60 Cr (N = 36), but it has been shown that a (9/2+ ) state appears at 503 keV in 59 Cr [16] and the pf -shell space is already insufficient at N = 35. Therefore we do not expect the accurate description for N ≥ 35, consistently with the systematics in binding energies and electromagnetic moments mentioned before. We have confirmed that GXPF1A improves the agreement with experimental data also for high-spin states in 54 Ti, as shown in fig. 3. The difference between GXPF1A and KB3G is apparent in 9+ and 10+ states, which can be understood as a result of the difference in the position of f5/2 orbit (see fig. 2). As for 56 Ti, GXPF1A and KB3G predict very different excitation energy for 10+ state by 0.9 MeV. The leading configuration of this state 2 8 2 νf7/2 p43/2 f5/2 (46% and 62% for GXPF1A and is πf7/2 KB3G, respectively) and the difference reflects again the position of the f5/2 orbit. The information of the f5/2 orbit is obtained also from odd-A nuclei. Figure 4 shows the calculated yrast energy levels of 53 Ti and 55 Ti. In 53 Ti, the similarity between the results of GXPF1A and KB3G can be seen for low-spin states, where the dominant configuration is 2 8 νf7/2 p33/2 . A sizable difference appears first in 17/2− πf7/2 2 8 1 state with a dominant configuration πf7/2 νf7/2 p23/2 f5/2 . 55 There exist remarkable differences in Ti. The groundstate spin-parity is predicted to be 1/2− by GXPF1A, while it is 5/2− by KB3G. It is discussed [17] that the branching pattern of the β-decay is consistent with the ground-state spin greater than 1/2. If it is the case, the lower f5/2 is favored. However, the arguments of 2+ in 56 Cr and 10+ in 54 Ti suggest higher f5/2 than the KB3G prediction at N = 32. Definite assignment of the spinparity is desired for further discussions. Finally, we come back to N = 34 shell closure. In 54 Ca, the difference of the ESPE between the f5/2

5 Summary We have considered possible modifications of GXPF1 in order to improve the description of neutron-rich pf -shell nuclei. By changing five two-body matrix elements within reasonable amount, the discrepancy between the recent experimental data and theoretical prediction in 56 Ti can be remedied. Therefore the problem can be attributed to uncertainties in several matrix elements which could not be well determined in the fitting calculations for deriving GXPF1 because of the insufficient data. The modified 54 Ca, interaction still predicts an increase of Ex (2+ 1 ) at suggesting the appearance of the N = 34 shell gap in Ca isotopes.

References 1. M. Honma, T. Otsuka, B.A. Brown, T. Mizusaki, Phys. Rev. C 65, 061301(R) (2002). 2. M. Hjorth-Jensen, T.T.S. Kuo, E. Osnes, Phys. Rep. 261, 125 (1995). 3. M. Honma, T. Otsuka, B.A. Brown, T. Mizusaki, Phys. Rev. C 69, 034335 (2004). 4. T. Mizusaki, RIKEN Accel. Prog. Rep. 33, 14 (2000). 5. A. Poves, J. S´ anchez-Solano, E. Caurier, F. Nowacki, Nucl. Phys. A 694, 157 (2001). 6. A. Poves, A.P. Zuker, Phys. Rep. 70, 235 (1981). 7. Data extracted using the NNDC WorldWideWeb site from the ENSDF database. 8. P.F. Mantica et al., Phys. Rev. C 67, 014311 (2003). 9. R.V.F. Janssens et al., Phys. Lett. B 546, 55 (2002). 10. S.N. Liddick et al., Phys. Rev. Lett. 92, 072502 (2004). 11. T. Otsuka et al., Phys. Rev. Lett. 87, 082502 (2001). 12. W.A. Richter, M.G. van der Merwe, R.E. Julies, B.A. Brown, Nucl. Phys. A 523, 325 (1991). 13. B. Fornal, private communication. 14. M. Honma, B.A. Brown, T. Mizusaki, T. Otsuka, Nucl. Phys. A 704, 134c (2002). 15. T. Otsuka, in preparation. 16. S.J. Freeman et al., Phys. Rev. C 69, 064301 (2004). 17. P.F. Mantica et al., Phys. Rev. C 68, 044311 (2003). 18. T.W. Burrows, Nucl. Data Sheets 76, 191 (1995).

Eur. Phys. J. A 25, s01, 503–504 (2005) DOI: 10.1140/epjad/i2005-06-213-y

EPJ A direct electronic only

Effects of the continuum coupling on spin-orbit splitting N. Michel1,2,3,a , W. Nazarewicz1,2,4 , and M. Ploszajczak5 1 2 3 4 5

Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA Physics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831, USA Joint Institute for Heavy Ion Research, Oak Ridge, TN 37831, USA Institute of Theoretical Physics, Warsaw University, ul. Ho˙za 69, 00-681 Warsaw, Poland Grand Acc´el´erateur National d’Ions Lourds (GANIL), CEA/DSM-CNRS/IN2P3, BP 55027, F-14076 Caen Cedex 05, France Received: 24 November 2004 / c Societ` Published online: 9 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Recently, the shell model in the complex k-plane (the so-called Gamow Shell Model) has been formulated using a complex Berggren ensemble representing bound single-particle states, single-particle resonances, and non-resonant continuum states. The single-particle basis used is that of the HartreeFock potential generated self-consistently by a finite-range residual interaction. In this framework, we shall − 7 discuss the “spin-orbit splitting” of the 3/2− 1 and 1/21 states in He. It is demonstrated that the continuum effects are very important and cannot be taken into account in standard shell-model calculations. PACS. 21.60.Cs Shell model – 24.10.Cn Many-body theory – 27.20.+n 6 ≤ A ≤ 19

1 Introduction It is extremely difficult to describe weakly bound states or resonances in a closed-system formalism such as the nuclear Shell Model (SM). The binding of nuclei close to the particle drip lines depends sensitively both on the coupling to the scattering continuum and on the detailed features of an effective NN interaction [1]; hence it has to be described in the open-system formalism allowing for configuration mixing, such as the continuum shell model (see ref. [2] for a recent review) and, most recently, the Gamow Shell Model (GSM) [3,4, 5, 6] (see also refs. [7, 8, 9]). GSM is the multi-configurational shell model with a single-particle (s.p.) basis given by the Berggren ensemble [10, 11, 12] which consists of Gamow (or resonant) states and the complex non-resonant continuum. The s.p. Berggren basis is generated by a finite-depth potential, and the many-body states are obtained in shell-model calculations as the linear combination of Slater determinants spanned by resonant and non-resonant s.p. basis states. Hence, both continuum effects and correlations between nucleons are taken into account simultaneously. All details of the formalism can be found in ref. [4], in which the GSM was applied to many-neutron configurations in neutron-rich helium and oxygen isotopes. Even though the effective interaction theory for open quantum many-body systems has not yet been developed, recent investigations [13,14] in the framework of the Shell Model Embedded in the Continuum (SMEC) [15, 2] detera

Conference presenter; e-mail: [email protected]

mined basic features of the correction to the eigenenergy of the closed quantum system due to the continuum coupling. The novel feature, absent in the standard SM, is a strong influence of the poles of the scattering (S) matrix on the weakly bound/unbound states. In particular, for nucleons in low- orbits ( = 0, 1), the coupling is singular at the particle emission threshold if the pole of the Smatrix lies at the threshold [13,14]. Such a coupling may induce the non-perturbative rearrangement of the wave function. Below, we shall illustrate this effect in the case of the spin-orbit splitting in 7 He.

2 Description of the calculation In our previous studies [3,4], we have used the s.p. basis generated by a Woods-Saxon (WS) potential which was adjusted to reproduce the s.p. energies in 5 He. This potential (“5 He” parameter set [4]) is characterized by the radius R = 2 fm, the diffuseness d = 0.65 fm, the strength of the central field V0 = 47 MeV, and the spin-orbit strength Vso = 7.5 MeV. We use a finite-range residual interaction, the Surface Gaussian Interaction (SGI) [6]: VJ,T (r1 , r2 ) = V0 (J, T ) · e−(

r1 −r2 μ

2

) · δ(|r | + |r | − 2 · R ) 1 2 0

together with the WS potential with the “5 He” parameter set. The “5 He” WS basis is undesirable when applied to the neutron-rich isotopes of He. Therefore, we use an optimized s.p. basis, i.e., the Hartree-Fock basis extended to unbound states. Such an optimal Berggren basis which

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in such “equivalent SM calculations” (HO-SM approximation) are given by real parts of 0p1/2 and 0p3/2 eigenvalues of the WS potential generating the GSM basis. One can see that the 3/2− –1/2− splitting is enhanced by the coupling to the non-resonant continuum states. The discontinuity seen between the two GSM results (GSM1 and GSM2 ) is an artifact of truncations used, especially neglect of 3p-3h excitations to the non-resonant continuum [16].

1.8

E1/2- - E3/2- splitting

) 2 M S

5

He

1.4

G

7

( He

3 Conclusions

G

1

1

SM

)

1.2

e(

Energy (MeV)

1.6

0.6

)

-SM e (HO

7

H

0.8

7 4

5

6

H

7

8

9

10

11

Vso (MeV) Fig. 1. Energy splitting of the lowest 3/2− and 1/2− states of 5 He and 7 He as a function of the spin-orbit strength Vso . The solid lines with filled symbols show the truncated GSM results (see ref. [16] for details of calculations). The 0p3/2 state of the GHF basis is unbound in the GSM1 branch and bound in the GSM2 branch. The solid line with empty squares represents the SM results for 7 He obtained in the HO-SM approximation. The solid line with empty circles shows the splitting of the 5 He 3/2− and 1/2− states, i.e., the 0p1/2 and 0p3/2 eigenstates of the WS potential.

is generated in the Gamow-Hartree-Fock (GHF) approach allows for a more precise description of heavier p-shell nuclei [16]. In the chain of helium isotopes, which are described assuming an inert 4 He core, there are only T = 1 twobody matrix elements. Consequently, only (J = 0, T = 1) and (J = 2, T = 1) couplings come into play. We have adjusted V0 (J = 0, T = 1) to reproduce the experimental ground state (g.s.) energy of 6 He relative to the g.s. of 4 He, whereas V0 (J = 2, T = 1) has been fitted to all g.s. energies from 7 He to 10 He. The adopted values are: V0 (J = 0, T = 1) = −403 MeV · fm3 and V0 (J = 2, T = 1) = −315 MeV · fm3 . The experimental g.s. binding energies relative to the 4 He core are reproduced fairly well with this interaction. For instance, the g.s. of 6 He and 8 He are bound, whereas g.s. of 5 He and 7 He are unbound. Moreover, the so-called helium anomaly [17], i.e., the presence of the higher one- and two-neutron emission thresholds in 8 He than in 6 He, is well reproduced. 2.1 Spin-orbit effects: example of 7 He The coupling to the particle continuum may be singular for  = 0, 1 orbits. In p-shell nuclei, this effect may lead to strong modifications of spin-orbit effects. In fig. 1 we show the energy splitting between the lowest 3/2− and 1/2− states of 7 He as a function of Vso (all details of calculations follow ref. [16]). To compare the GSM results with standard SM, we calculate matrix elements of the SGI interaction in the harmonic-oscillator basis. The s.p. energies

The coupling to the non-resonant continuum increases when approaching the particle emission thresholds. The novel feature, absent in the standard SM, is a strong influence of S-matrix poles on the weakly bound/unbound many-body states. For the low- orbits ( = 0, 1), the continuum coupling may induce the non-perturbative rearrangement of the wave function. We have demonstrated that the continuum coupling may be seen in the enhancement of spin-orbit effects for nuclei close to the driplines. A similar mechanism may also influence other observables such as the spectroscopic factors, pair-transfer amplitudes, nuclear collectivity, and properties of nuclear excitations. This work was supported in part by the U.S. Department of Energy under Contract Nos. DE-FG02-96ER40963 (University of Tennessee), DE-AC05-00OR22725 with UT-Battelle, LLC (Oak Ridge National Laboratory), and DE-FG05-87ER40361 (Joint Institute for Heavy Ion Research).

References 1. J. Dobaczewski, W. Nazarewicz, Philos. Trans. R. Soc. London, Ser. A 356, 2007 (1998). 2. J. Okolowicz, M. Ploszajczak, I. Rotter, Phys. Rep. 374, 271 (2003). 3. N. Michel, W. Nazarewicz, M. Ploszajczak, K. Bennaceur, Phys. Rev. Lett. 89, 042502 (2002). 4. N. Michel, W. Nazarewicz, M. Ploszajczak, J. Okolowicz, Phys. Rev. C 67, 054311 (2003). 5. N. Michel et al., Acta Phys. Pol. B 35, 1249 (2004). 6. N. Michel, W. Nazarewicz, M. Ploszajczak, J. Rotureau, arXiv:nucl-th/0401036. 7. R.I. Betan et al., Phys. Rev. Lett. 89, 042501 (2002). 8. R.I. Betan et al., Phys. Rev. C 67, 014322 (2003). 9. R.I. Betan et al., Phys. Lett. B 584, 48 (2004). 10. T. Berggren., Nucl. Phys. A 109, 265 (1968). 11. T. Berggren, P. Lind, Phys. Rev. C 47, 768 (1993). 12. P. Lind, Phys. Rev. C 47, 1903 (1993). 13. Y. Luo, J. Okolowicz, M. Ploszajczak, N. Michel, arXiv:nucl-th/0201073. 14. N. Michel, W. Nazarewicz, J. Okolowicz, M. Ploszajczak, Proceedings of the International Nuclear Physics Conference (INPC 2004) (Elsevier B.V., Amsterdam 2005). 15. K. Bennaceur, F. Nowacki, J. Okolowicz, M. Ploszajczak, Nucl. Phys. A 651, 289 (1999). 16. N. Michel, W. Nazarewicz, M. Ploszajczak, Phys. Rev. C 70, 064313 (2004). 17. A.A. Oglobin, Y.E. Penionzhkevich, in Treatise on HeavyIon Science, Nuclei Far From Stability, edited by D.A. Bromley, Vol. 8 (Plenum, New York, 1989) p. 261.

Eur. Phys. J. A 25, s01, 505–506 (2005) DOI: 10.1140/epjad/i2005-06-135-8

EPJ A direct electronic only

Study of drip-line nuclei with a core plus multi-valence nucleon model H. Masui1,a , T. Myo2 , K. Kat¯ o3 , and K. Ikeda1 1 2 3

The Institute of Physical and Chemical Research (RIKEN), Wako, 351-0198, Japan Research Center for Nuclear Physics, Osaka University, Osaka, 567-0047, Japan Division of Physics, Graduate School of Science, Hokkaido University, Sapporo, 060-8810, Japan Received: 21 October 2004 / Revised version: 25 February 2005 / c Societ` Published online: 4 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We study neutron- and proton-rich nuclei with an extended cluster-orbital shell model (COSM) approach, which we call Neo-COSM. The binding energies and r.m.s. radii of oxygen isotopes are reproduced. For N = 8 isotones, the tendency of the abrupt increase of the r.m.s. radii is qualitatively improved. PACS. 21.10.-k Properties of nuclei; nuclear energy levels – 21.60.-n Nuclear structure models and methods

1 Introduction New techniques and other experimental developments have widen the area of observation near the neutron drip line [1]. Exotic phenomena such as halo structures and the inversion of single-particle orbits have been observed and can be considered a new aspect of nuclear structure which differs greatly from that observed from stable nuclei. For example, the observed 23 O r.m.s radius is large compared with the empirical A1/3 scaling. An analysis using the Glauber theory suggests that 23 O is not a simple 22 O core plus one valence neutron structure, and the spin parity of the 23 O ground state is determined to be 5/2+ [2] or 1/2+ [3]. Therefore, a theoretical study which is able to describe the halo structure of 23 O is required.

2 Model and method To study such a complex halo structure, we develop a method using the cluster-orbital shell model (COSM) approach and extend it so as to be able to treat the dynamics of the total system. For treating the dynamics of the core, we introduce the degrees of freedom for the width parameter b. In the case that we use the lowest configuration of the core wave function, the energy of the core can be calculated analytically [4]. The potential between the core and the valence nucleon (the core-N potential) is a folding-type potential, which is constructed microscopically using the core density. Hence, the change in b affects a

Conference presenter; Present address: Information Processing Center, Kitami Institute of Technology, Kitami 0908507, Japan; e-mail: [email protected]

both the core energy and the core-N potential. Therefore, the optimum value of b can be determined by combining the energies of the core and core-N parts. Further, to reproduce the asymptotic shape of the core-N wave function, the radial part is expressed by a linear combination of the Gaussian basis functions. The motion of valence nucleons is solved by using the same technique of the stochastic variational method (SVM) [5]. We call this approach “Neo-COSM”. We use the effective nucleon-nucleon potential, Volkov No. 2 [6] with the exchange parameter mk = 0.58:   (k)  2 wk +mk PˆM +bk PˆB −hk PˆH e−βk r . (1) v(r) = V0 k

For valence nucleons, we artificially introduce non zero hk and bk parameters, as hk = bk = 0.07 to adjust the ground state energy of 18 O. Note that we do not introduce any other adjustable parameters in the calculation.

3 Results 3.1 Calculation with fixed and changed b parameters First, we perform calculations at a fixed b. For oxygen isotopes (16 O + Xn systems), calculated binding energies show good agreement to the experiments. And, the r.m.s. radii are well reproduced as shown in fig. 1. On the other hand, for N = 8 isotones (16 O + Xp systems), calculated r.m.s. radii are much smaller than the observed values in 18 Ne and 20 Mg, while the binding energies are well reproduced. The calculated and observed r.m.s. radii are shown in fig. 2.

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(fm) 3.4

2.8

R r.m.s.

Rrms (fm)

3.0

A1/3 2.8

2.7

16

2.9

16

O+Xp

2.7 16

2.53

2.5

O+Xn

2.6

2.5

2.4

15

2.4

2.4

18

17

16

20

19

22

21

23

24

Fig. 1. The calculated r.m.s. radii of the oxygen isotopes with a fixed core b parameter. The experimental values [1] are shown with error bars. 3.1 3.0 20 19

2.9 18

Na

Mg

Ne

2.8 2.7

Rrms

17

F

16

O

2.5 15

N

2.4 2.3 2.2 14

15

16

17

A

18

19

20

Fixed-b :b = 1.723 (fm)

15

16

18

17

19

20

21

A

15

16

25

A

2.6

O+Xn

2.8

Rrms (fm)

2.6

O+Xp

2.6

2.71 2.64 2.67

2.59

16

O-isotopes

3.2

17

A

18

19

20

21

Fig. 3. The calculated r.m.s. radii by Neo-COSM by changing the core b parameter.

We make a comparison between the Neo-COSM and GSM calculations in two systems, 18 O and 6 He, which are tightly bound and loosely bound (Borromean) systems, respectively. In 18 O, the Neo-COSM calculation gives almost the same result as the GSM one. A difference appears in the result of 6 He. The contribution of (0p3/2 )2 , which is the largest one, is the same in both calculations. But contribution of (0p1/2 )2 , which is the second largest one, becomes different each other. The Neo-COSM calculation shows that the contribution of (0p1/2 )2 is almost the same as that of (0p3/2 )2 . However, the contribution of (0p1/2 )2 of the GSM calculation is much smaller than that of (0p3/2 )2 .

21

Fig. 2. The calculated r.m.s. radii of N = 8 isotones with a fixed core b parameter. The experimental values [1] are shown with error bars.

The difference for the r.m.s. radii between 16 O + Xn and 16 O+Xp systems suggests that we need to introduce a new mechanism or improve the description of the system, which includes the improvement of the interaction. Therefore, to reproduce the difference, we perform the Neo-COSM calculation by changing the core b parameter. We calculate the energies of the core and valence nucleons and determine the optimum value of the core b width parameter. The obtained r.m.s. radii are qualitatively improved from the fixed b calculation, see fig. 3. 3.2 Comparison with the Gamow shell model If we expand the wave function obtained by the NeoCOSM approach in terms of the components of the single-particle eigen functions, each component corresponds to the weight calculated by the Gamow shell model (GSM) [7] approach.

4 Summary In summary, we developed a new method of studying the particular structures of the neutron- and proton-rich nuclei. The essential point of our method is that we treat the total system by introducing the degrees of freedom of the core b parameter in the COSM formalism. The Neo-COSM approach showed the promising results. In the future, calculations for systems of larger number of valence nucleons are hopeful.

References 1. 2. 3. 4.

A. Ozawa et al., Nucl. Phys. A 691, 559 (2001). R. Kanungo et al., Phys. Rev. Lett. 88, 142502 (2002). D. Cortina-Gil et al., Phys. Rev. Lett. 93, 062501 (2004). T. Ando, K. Ikeda, A. Tohsaki-Suzuki, Prog. Theor. Phys. 64, 1608 (1980). 5. V.I. Kukulin, V.M. Krasnopol’sky, J. Phys. G 3, 795 (1977). 6. A.B. Volkov, Nucl. Phys. 74, 33 (1965). 7. N. Michel, W. Nazarewicz, M. Ploszajczak, J. Okolowicz, Phys. Rev. C 67, 054311 (2003).

Eur. Phys. J. A 25, s01, 507–508 (2005) DOI: 10.1140/epjad/i2005-06-059-3

EPJ A direct electronic only

Wave function factorization of shell-model ground states T. Papenbrocka Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA and Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Received: 14 January 2005 / c Societ` Published online: 3 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The wave function factorization method determines an optimal basis of correlated proton and neutron states, and accurately approximates low-lying shell-model states by a rather small number of suitable product states. The optimal basis states result from a variational principle and are the solution of relatively low-dimensional eigenvalue problems. The error involved in this truncation decreases exponentially fast as more basis states are included. PACS. 21.60.Cs Shell model – 21.10.Dr Binding energies and masses

1 Introduction

2 Wave function factorization

The shell-model can now routinely be applied up to f p shell nuclei [1, 2], and no-core shell-model calculations accurately describe p-shell nuclei [3]. In other mass regions, the dimensionality of the model space is often too large, and exact diagonalizations can only be carried out for a small number of nuclei in the region of interest. To deal with the increasingly large model-space sizes, various approximation techniques have been developed and applied. Some of them are based on extrapolation schemes [4], while others involve a basis state selection. In many methods, this selection is based on what are perceived to be the relevant states, e.g. low-energy eigenstates of the proton Hamiltonian and the neutron Hamiltonian [5], energy expectation values of configurations [6], or state selection based on symmetry arguments [7]. In other methods, the relevant states are selected by the Hamiltonian itself. In the Monte Carlo shell-model [8], for instance, a good basis is selected stochastically by random walks through the Hilbert space. In the density matrix renormalization group [9, 10], relevant basis states are obtained from a density matrix. Recently, we proposed the wave function factorization [11]. In this method, the most important proton and neutron states are determined from a variational principle. This results in an accurate approximation of low-lying states states, and the dimensionality of the eigenvalue problem is reduced by orders of magnitudes. In this note, we briefly review the the wave function factorization and present future opportunities.

In the wave function factorization we approximate the shell-model ground state as a sum over Ω products of correlated proton states |pj  and neutron states |nj 

a

Conference presenter; e-mail: [email protected]

|Ψ  =

Ω 

|pj |nj .

(1)

j=1

The expansion (1) becomes exact for sufficiently large Ω and is based on the singular value decomposition of amplitude matrices [11]. The states |pj  and |nj  are not normalized. Variation of the energy yields the following set of eigenvalue equations that determine the states |pj  and |nj  Ω  

 ˆ i  − E nj |ni  |pi  = 0,

nj |H|n

i=1 Ω  

 ˆ i  − E pj |pi  |ni  = 0.

pj |H|p

(2)

i=1

This system of equations is solved iteratively as follows. A random set of Ω neutron states is fixed and the eigenvalue problem for the proton states is solved for the lowest energy E. The resulting proton states are the input to the eigenvalue problem for the neutron states. Typically, the energy converges within 5–10 iterations for fixed Ω. Then, Ω is increased and the calculations are repeated. One empirically finds that the resulting function E(Ω) is of the form E(Ω) = E0 +b exp (−cΩ), and a fit of the parameters E0 , b and c yields the estimate E0 for the ground-state energy. For f p-shell nuclei, this estimate might deviate about

508

The European Physical Journal A

3 Summary and outlook (E0 + 46.03) / MeV

1

We have briefly reviewed the wave function factorization as an accurate approximation for large-scale nuclear structure calculations, and applied it to the f p-shell nucleus 51 Mn. Highly accurate approximations can be obtained from the solution of eigenvalue problems of relatively small dimension. Up to now, the wave function factorization has been tested mainly for sd-shell and f p-shell nuclei, and the results have been very encouraging. Studies of larger shell-model problems (with tens of billions of configurations) are currently under way. Such dimensions are out of reach for exact diagonalization methods and have so far been the realm of the Monte Carlo methods [8,16].

0.1

0.01 0

100

Ω

200

300

Fig. 1. Ground-state energy as a function of the number Ω of kept proton and neutron states obtained from the wave function factorization (data points) and exponential fit (line).

100 keV from the results obtained from full space diagonalizations, while the dimension of the eigenvalue problem (2) is considerably smaller than in the full space matrix diagonalization. For the mid-shell f p-shell nuclei, for instance, the reduction in dimension reaches three orders of magnitude. For details we refer the reader to ref. [12]. As an example we consider 51 Mn in the 0f 1p-shell and use the KB3 interaction [13,14]. The Hilbert space consists of products of 38746 and 15504 Slater determinants for the neutrons and protons, respectively. The ground-state energy obtained from exact diagonalization is E = −46.17 MeV [1]. Figure 1 shows the result obtained from the wave function factorization. The estimate E0 = −46.03 MeV deviates only 140 keV from the exact result and is obtained from Ω ≈ 250 proton and neutron states. This number is about a factor 60 smaller than the number of available proton states, and the 45 × 106 dimensional eigenvalue problem encountered in the exact diagonalization is reduced by the same factor in the wave function factorization. Note that the rotational symmetry is restored to a good approximation. The angular momentum expectation value of the approximated ground state is J 2  ≈ 8.9 compared to 8.75 (corresponding to spin J = 5/2) of the exact ground state. These results show that the method works quite well also for odd-mass nuclei. Our experience shows that shell-model states of odd mass systems and deformed nuclei are harder to factorize than their even-even neighbors or less deformed nuclei [12,15]. This is due to the fact that such systems exhibit stronger proton neutron correlations than more spherical and/or even-even nuclei. Note that low-lying excited states can also be computed by wave function factorization [12].

This research was supported in part by the U.S. Department of Energy under Contract Nos. DE-FG02-96ER40963 (University of Tennessee) and DE-AC05-00OR22725 with UT-Battelle, LLC (Oak Ridge National Laboratory).

References 1. E. Caurier, G. Mart´ınez-Pinedo, F. Nowacki, A. Poves, J. Retamosa, A.P. Zuker, Phys. Rev. C 59, 2033 (1999), nuclth/9809068. 2. M. Honma, T. Otsuka, B.A. Brown, T. Mizusaki, Phys. Rev. C 65, 061301(R) (2002), nucl-th/0205033. 3. P. Navr´ atil, J.P. Vary, B.R. Barrett, Phys. Rev. Lett. 84, 5728 (2000), nucl-th/0004058. 4. T. Mizusaki, M. Imada, Phys. Rev. C 65, 064319 (2002), nucl-th/0203012. 5. F. Andreozzi, A. Porrino, J. Phys. G 27, 845 (2001). 6. M. Horoi, B.A. Brown, V. Zelevinsky, Phys. Rev. C 50, R2274 (1994), nucl-th/9406004. 7. V.G. Gueorguiev, W.E. Ormand, C.W. Johnson, J.P. Draayer, Phys. Rev. C 65, 024314 (2002), nuclth/0110047. 8. M. Honma, T. Mizusaki, T. Otsuka, Phys. Rev. Lett. 75, 1284 (1995). 9. S.R. White, Phys. Rev. Lett. 69, 2863 (1992). 10. J. Dukelsky, S. Pittel, Rep. Prog. Phys. 67, 513 (2004), cond-mat/0404212. 11. T. Papenbrock, D.J. Dean, Phys. Rev. C 67, 051303(R) (2003), nucl-th/0301006. 12. T. Papenbrock, A. Juodagalvis, D.J. Dean, Phys. Rev. C 69, 024312 (2004), nucl-th/0308027. 13. T.T.S. Kuo, G.E. Brown, Nucl. Phys. A 114, 241 (1968). 14. A. Poves, A.P. Zuker, Phys. Rep. 70, 235 (1980). 15. T. Papenbrock, D.J. Dean, nucl-th/0412112. 16. S.E. Koonin, D.J. Dean, K. Langanke, Phys. Rep. 278, 1 (1997), nucl-th/9602006.

Eur. Phys. J. A 25, s01, 509–510 (2005) DOI: 10.1140/epjad/i2005-06-207-9

EPJ A direct electronic only

Shell model analysis of intruder states and high-K isomers in the fp shell G. Stoitcheva1,2,a , W. Nazarewicz1,2,3 , and D.J. Dean1 1 2 3

Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Department of Physics, University of Tennessee, Knoxville, TN 37996, USA Institute of Theoretical Physics, Warsaw University, ul. Ho˙za 69, 00-681 Warsaw, Poland Received: 12 September 2004 / c Societ` Published online: 15 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We perform a systematic shell-model study of collective intruder structures and fully aligned high-spin states in nuclei from the lower-f p shell in the sdf p configuration space. We analyze the intruder structures associated with the 1p-1h cross-shell excitations from the sd shell that have been observed in several nuclei from this region, including 44 Ti and 44 Sc. We compare the shell-model calculations to the recent mean-field work (H. Zdu´ nczuk, W. Satula, R.A. Wyss, nucl-th/0408018) and experimental data (M. Lach, J. Stycze´ n, private communication). The high-spin behavior may be understood in terms of the competing cross-shell proton and neutron excitations. The interplay between proton and neutron intruder states is reflected in the angular-momentum dependence of electromagnetic rates. PACS. 21.60.Cs Shell model – 21.10.Ky Electromagnetic moments – 21.10.Pc Single-particle levels and strength functions – 27.40.+z 39 ≤ A ≤ 58

1 Introduction

Energy (MeV)

The nuclei of the f7/2 shell are of special interest due to the presence of intruder states which can give rise to shape coexistence phenomena. These nuclei lie close to the doubly magic 40 Ca and 56 Ni, and therefore their structure can often be interpreted in terms of the competition between collective or single-particle excitations. One objective of this work is to analyze high-spin states of the lower-f p shell nuclei based on large-scale shell-model (SM) calculations using the code ANTOINE [1]. In particular, we are interested in the intruder structures associated with cross-shell excitations across the N = Z = 20 gap.

(f7/2)n

SM Exp

(d3/2)-1(f7/2)n+1

2 Shell model analysis In this work, we study high-spin excitations in A ∼ 44, 20 ≤ Z ≤ N ≤ 24 nuclei. An excellent agreement is observed between experiment and SM for the energies n (fig. 1, top) and at the maximally aligned states of f7/2 −1 n+1 d3/2 f7/2 (fig. 1, bottom) structures. The black bars represent our SM calculations in which 1p-1h cross-shell excitations were allowed. They are compared to experimental data given by grey bars. We used the interaction of a

e-mail: [email protected]

Fig. 1. Comparison between SM and experiment for the maxn+1 n imum spin states in f7/2 (top) and d−1 3/2 f7/2 (bottom) configurations in several N = Z (left) and N > Z (right) nuclei in the f p shell.

ref. [2] where the mass scaling of the SM matrix elements was done consistently, thus reducing the sd interaction channel by ∼ 4% as compared to the previous work [2].

The European Physical Journal A

Occupations

510

B(E2) (e2fm4)

Fig. 2. Energy differences, ΔE − ΔEexp , for SM and HF [3] calculations.

E (MeV)

44Sc

44Sc

Angular Momentum

Exp

SM

Exp

Fig. 4. Top: proton and neutron SM occupations in the π = − intruder structure of 44 Sc. Bottom: calculated B(E2) rates within the intruder structure.

SM

Fig. 3. Calculated negative-parity yrast structures in compared to experimental data [4].

44

Sc

Figure 2 shows the SM and Skyrme Hartree-Fock (HF) [3] n+1 n energy differences, ΔE ≡ E(d−1 3/2 f7/2 ) − E(f7/2 ), of the maximally aligned states, relative to experimental values. While for the N = Z nuclei, the SM calculations overestimate the data by ∼ 10%, HF underestimates them by ∼ 10%. However, it is interesting to see that the resulting energy difference patterns in the SM and HF are indeed very similar. In general, excellent agreement between the SM and experiment was obtained. High-spin states of the odd-odd 44 Sc nucleus have been studied in a recent experiment [4]. In the SM description, the positive-parity yrast structure of 44 Sc has one proton and three neutrons in the f7/2 shell, and the maximum aligned state has I π = 11+ . The negative-parity states up to I π = 15− can be associated with the holes in the sd shell. A comparison between the experimental and calculated negative-parity band is given in fig. 3, while fig. 4 (bottom) shows the predicted B(E2) transition rates. The effective proton and neutron charges that are used in the calculations, ep = 1.33e and en = 0.64e, have been determined from E2 transitions in lower-f p shell nuclei [5]. The transition rates and the shell occupations in the wave function (fig. 4, top) nicely show the interplay between proton and neutron intruder configurations for a given angular

momentum I π . It is predicted that the lower spin states as well as the highest I π = 15− spin state, are dominated by proton excitations. The intermediate angular-momentum spin states between I π = 8− up to I π = 13− are fairly equal mixtures of proton and neutron excitations. As our present calculations are limited to 1p-1h crossshell excitations only, some correlations are missing in our SM description. In particular, the structure N = Z nuclei can be affected by an explicit absence of the 2p-2h cross-shell T = 0 excitations. This is shown in fig. 2, which clearly demonstrates a different behavior of ΔE for N = Z and N = Z nuclei. Detailed studies of this effect are in progress [6]. Discussions with Wojtek Satula and Jan Stycze´ n are gratefully acknowledged. This work was supported in part by the U.S. Department of Energy under Contract Nos. DE-AC0500OR22725 with UT-Battelle, LLC (Oak Ridge National Laboratory), and DE-FG02-96ER40963 (University of Tennessee).

References 1. 2. 3. 4. 5. 6.

E. Caurier, F. Nowacki, Acta Phys. Pol. 30, 705 (1999). P. Bednarczyk et al., Phys. Lett. B 393, 285 (1997). H. Zdu´ nczuk, W. Satula, R.A. Wyss, nucl-th/0408018. M. Lach, J. Stycze´ n, private communication. W.A. Richter et al., Nucl. Phys. A 523, 325 (1991). G. Stoitcheva et al., to be published.

Eur. Phys. J. A 25, s01, 511–513 (2005) DOI: 10.1140/epjad/i2005-06-174-1

EPJ A direct electronic only

Extended pairing model revisited J.P. Draayer1,a , Feng Pan2 , and V.G. Gueorguiev1 1 2

Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA Department of Physics, Liaoning Normal University, Dalian, 116029, PRC Received: 22 October 2004 / Revised version: 22 December 2004 / c Societ` Published online: 21 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The mean-field plus extended pairing model proposed by the authors for describing welldeformed nuclei (F. Pan, V.G. Gueorguiev, J.P. Draayer, Phys. Rev. Lett. 92, 112503 (2004)) is revisited. Eigenvalues of the model can be determined by solving a single transidental equation. Results to date show that even through the model includes many-body interactions, the one- and two-body terms continue to dominate the dynamics for small values of the pairing strength; however, as the strength of the pairing interaction grows, the higher-order terms grow in importance and ultimately dominate. Attempts to extend the theory to the prediction of excited zero plus states did not produce expected results and therefore requires additional consideration. PACS. 21.10.Dr Binding energies – 71.10.Li Pairing interactions in model systems – 21.60.Cs Shell model

Pairing is an important residual interaction in nuclear physics. Much attention and progress, building on Richardson’s early work [1] and various extensions to it based on the Bethe ansatz, has been made in the past few years. Solutions are provided by a set of non-linear Bethe Ansatz Equations (BAEs) [2]. Though these applications show that the pairing problem is exactly solvable, solutions of the BAEs are not trivial. This limits the applicability of the methodology to relatively small systems; it cannot be applied to large systems such as well-deformed nuclei. As an extension of the standard pairing interaction, we constructed the following new Hamiltonian: ˆ = H

p 

j nj − G

j=1

p 

a+ i aj

i,j=1

×



i1 =··· =i2μ

−G

p  μ=2

i1 <···
1

(μ!)

2

×

(1)

+ a+ i1 · · · aiμ aiμ+1 · · · ai2μ ,

where p is the total number of levels considered, G > 0 is the pairing strength, j single-particle energies taken, for example, from the Nilsson model, nj = c†j↑ cj↑ + c†j↓ cj↓ is the fermion number operator for the j-th level, and † † + † a+ i = ci↑ ci↓ (ai = (ai ) = ci↓ ci↑ ) are pair creation (annihilation) operators. The up and down arrows refer to time-reversed states. Since each level can only be occupied by one pair due to the Pauli Principle, the operaa

tors a+ i , ai , and ni satisfy the hard-core boson algebra: + + + 2 [ai , a+ j ] = δij (1 − ni ), [ai , aj ] = 0 = (ai ) . Besides a mean-field and standard pairing, the interaction includes multi-pair hopping terms that allow pairs to simultaneously scatter (hop) between and among different levels. With this extension in place, the model can be shown to be exactly solvable [3]. If |j1 , · · · , jm  is the pairing vacuum, where j1 , · · · , jm are levels occupied by single nucleons, thus blocked by the Pauli principle, then the k-pair eigenstate is  (ζ) + |k; ζ; j1 · · · jm  = Ci1 ···ik a+ i1 · · · aik |j1 · · · jm , (2)

Conference presenter; e-mail: [email protected]

where Ci1 i2 ···ik are expansion coefficients that are to be determined. It is assumed that the indices j1 , · · · , jm should be excluded from the summation. Since the formalism for even-odd systems is similar, we focus on the even-even seniority zero case where the exci(ζ) (ζ) tation energies Ek and expansion coefficients Ci1 i2 ···ik of the k-pair eigenstates are given by (ζ)

Ek (ζ)

Ci1 i2 ···ik

2 − G(k − 1), x(ζ) 1 , = k (ζ) 1−x μ=1 iμ

(3)

=

(4)

and the variable x(ζ) is determined by 2

x(ζ)

+

 1≤i1
(1 −

x(ζ)

G k

μ=1 iμ )

= 0.

(5)

512

The European Physical Journal A

Fig. 2. Ratios Rμ (%) with μ = 1, 2, · · · , 5 as a function of the pairing interaction strength G for k = 2, · · · , 5 for p = 10 levels.

Fig. 1. (a) Spectral structure of the standard pairing interaction, and (b) spectral structure of the extended pairing interaction given by eq. (1), as functions of the pairing interaction strength G for k = 5 pairs for a system with p = 10 levels, where the single-particle energies and G are given in arbitrary units. The straight dash line is the expectation value of the Hamiltonian in the pure pairing (i = 0) ground state.

The label ζ = 1, 2, 3, · · · in this expression can be understood as the ζ-th solution of (5). For even-odd systems the level js occupied by the single nucleon should also be excluded from the summation in (2) and the single-particle energy term js contributing to the eigenenergy from the first term of (1) should be included. Although these eigenstates (2) are not normalized, they can be normalized easily; the eigenstates (2) with different roots given by (5) are of course mutually orthogonal. Extensions of this to many broken-pair cases are straightforward. To gain a better understanding of the extended pairing theory, we considered an example of p = 10 levels with single-particle energies given by i = i + χi for i = 1, 2, · · · , 10, where χi are random numbers within the interval (0, 1) and the pairing strength G varies from 0.01 to 0.10. Figure 1 shows the lowest few energies of the standard and extended pairing models for this case. It is clear that there are essential differences in the spectra. As shown in fig. 1(b), the extended pairing model rapidly develops a paired ground-state configuration and the transition from mean-field eigenstates to pairing eigenstates is sharp and rapid, while standard pairing, fig. 1(a), exhibits a slower and smoother transition. The differences in the spectra is a distinguishing characteristic that can be used to explore cases where the extended pairing concept might be more relevant and appropriate than the standard pairing model. Since there are higher order terms involved in (1), it is important to know whether the dynamics is still dominated by the one- and two-body interactions or if the

presence of the higher-order terms alters this picture. To explore this, we calculated as a function of G the expectation value of each higher order term Vμ  defined by:  a+ V1 = i aj , i,j

Vμ =

1 (μ!)2

 i1 =··· =i2μ

+ a+ i1 · · · aiμ aiμ+1 · · · ai2μ

with μ = 2, 3, · · · , for k-pair ground states. We calculated the ratio Rμ = Vμ / Vtotal , where Vtotal  is the sum of all terms above. The results, which are shown in fig. 2, indicate that the two-body pairing interaction (V1 ) dominates the dynamics of the system for small interaction strength G. With increasing interaction strength, the system is driven increasingly by the higher-order terms. Returning to eq. (3), it is natural to consider excited as well as ground state solutions. Once the coupling strength is fixed from the ground state, excited states can also be calculated. However, initial calculations suggest they do not agree well with the experimentally observed values; that is, the dependence of the strength on the particle number that is required to make the extended theory reproduce first excited states seems to be different than for the ground state. This poses a dilemma; namely, whether or not the agreement for ground states was fortuitous rather than fundamental. This and other matters, such as whether or not the extended Hamiltonian has a special coherent-state–like solution, remain under investigation. Financial support for this project was provided by the U.S. National Science Foundation (0140300), the Natural Science Foundation of China (10175031), and the Education Department of Liaoning Province (202122024). One of the authors (J.P.D.) acknowledges special support from the Southeastern Universities Research Association.

References 1. R.W. Richardson, Phys. Lett. 3, 277 (1963); R.W. Richardson, N. Sherman, Nucl. Phys. 52, 221 (1964).

J.P. Draayer et al.: Extended pairing model revisited 2. J. Dukelsky, V.G. Gueorguiev, P. Van Isacker, nuclth/0406001. 3. F. Pan, V.G. Gueorguiev, J.P. Draayer, Phys. Rev. Lett. 92, 112503 (2004).

513

4. P. M¨ oller, J.R. Nix, K.L. Kratz, At. Data Nucl. Data Tables 66, 131 (1997). 5. G. Audi, O. Bersillon, J. Blachot, A.H. Wapstra, Nucl. Phys. A 624, 1 (1997).

Eur. Phys. J. A 25, s01, 515–516 (2005) DOI: 10.1140/epjad/i2005-06-108-y

EPJ A direct electronic only

Application of the extended pairing model to heavy isotopes V.G. Gueorguiev1,2,a , Feng Pan3 , and J.P. Draayer2 1 2 3

Lawrence Livermore National Laboratory, Livermore, CA 94550, USA Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA Department of Physics, Liaoning Normal University, Dalian, 116029, PRC Received: 21 October 2004 / Revised version: 11 November 2004 / c Societ` Published online: 22 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Relative binding energies (RBEs) within three isotopic chains ( 100–130 Sn, 152–181 Yb, and 181–202 Pb) have been studied using the exactly solvable extended pairing model (EPM) (F. Pan, V.G. Gueorguiev, J.P. Draayer, Phys. Rev. Lett. 92, 112503 (2004) (see also these proceedings)). The unique pairing strength G, which reproduces the experimental RBEs, has been determined. Within EPM, log(G) is a smooth function of the model space dimension dim(A), as expected for an effective coupling strength. In particular, for the Pb and Sn isotopes G can be described by a two parameter expression that is inversely proportional to the dimensionality of the model space, G = α dim(A)−β with β ≈ 1. PACS. 21.10.Dr Binding energies and masses – 71.10.Li Excited states and pairing interactions in model systems – 21.60.Cs Shell model

In many applications the infinite dimensionality of the quantum mechanical Hilbert space is an obstacle; to overcome it, one has to restrict the model space to a finite dimensional subspace and construct an appropriate effective Hamiltonian. This in turn leads from a two-body to a many-body interaction terms. Nonetheless, the effective Hamiltonian approach has been very successful and even pointed to the importance of three-body nuclear interactions [1]. The recently introduced exactly solvable extended pairing model [2] provides a framework for study of Hamiltonians with many-body interaction terms: ˆ = H

p 

j nj − G

j=1

p 

Bi+ Bj − G

i,j=1

×



i1 =··· =i2μ

p  μ=2

1

(μ!)

2

×

Bi+1 · · · Bi+μ Biμ+1 · · · Bi2μ .

(1)

Ideally, one should be able to calculate binding energies and other observables ab initio using the exact nucleon interaction. However, we are still lacking this capability. Instead, we use different models for binding energies and excitation energies. Conventionally, the liquid-drop model is the zeroth order approximation to the binding energies while the two-body pairing interaction gives the shell model corrections. The extended pairing model (EPM) (1) has terms beyond the standard Nilsson plus pairing Hamiltonian; these terms provide an alternative description of the relative binding energies (RBEs) of neighboring nuclei within the same valence space. As we will discuss below, a

Conference presenter; e-mail: [email protected]

EPM is well suited to provide description of the RBEs only within the shell-model since the equations are insensitive to the binding energy of the core nucleus. Beside the first two terms, Nilsson plus standard pairing interaction, the Hamiltonian in (1) contains manypair interactions which connect configurations that differ by more than a single pair. Here p is the total number of single-particle levels considered, j are single-particle energies, G is the overall pairing strength (G > 0), nj = c†j↑ cj↑ + c†j↓ cj↓ is the number operator for the j-th single-particle level, Bi+ = c†i↑ c†i↓ are pair creation opera-

tors where c†j creates a fermion in the j-th single-particle level. The up and down arrows refer to time-reversed states. Since each Nilsson level can only be occupied by one pair due to the Pauli Exclusion Principle, the operators Bi+ , Bi , and ni form a hard-core boson algebra: [Bi , Bj+ ] = δij (1 − ni ), [Bi+ , Bj+ ] = 0 = (Bi+ )2 . The pairing vacuum state |j1 , · · · , jm  is defined so that: Bi |j1 , · · · , jm  = 0 for 1 ≤ i ≤ p and i = js , where j1 , · · · , jm indicate those m levels that are occupied by unpaired nucleons. Any state that is occupied by a single nucleon is blocked to the hard-core bosons due to the Pauli principle. The k-pair eigenstates of (1) has the form  (ζ) |k; ζ; j1 · · · jm  = Ci1 ···ik Bi+1 · · · Bi+k |j1 · · · jm , (2) i1 <···
where are expansion coefficients to be determined. It is assumed that the level indices j1 , · · · , jm should be excluded from the summation in (2). For simplicity, we focus only on the seniority zero case (m = 0).

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= z (ζ) − G(k − 1), k  1 (ζ) , Ei1 ···ik = 2iμ , Ci1 i2 ···ik = (ζ) z − Ei1 ...ik μ=1  G . 1= (ζ) E i1 ···ik − z i
2

(3)

(4)

(5)

k

Due to the space limitations many details and results of the current application of this exactly solvable model are omitted, however, a more detailed paper is available [3]. For the current application the single-particle energies are calculated using the Nilsson deformed shell model with parameters from [4]. Experimental BEs are taken from [5]. Theoretical RBE are calculated relative to a specific core, 152 Yb, 100 Sn, and 208 Pb for the cases considered. The RBE of the nucleus next to the core is used to determine an energy scale for the Nilsson single-particle energies. For an even number of neutrons, we considered only pairs of particles (hard bosons). For an odd number of neutrons, we apply Pauli blocking to the Fermi level of the last unpaired fermion and considered the remaining fermions as if they were an even fermion system. The valence model space consists of the neutron single-particle levels between two closed shells with magic numbers 50–82 and 82–126. By using (3) and (5), values of G are determined so that the experimental and theoretical RBE match exactly. Figure 1 shows results for the 181–202 Pb isotopes. The RBEs are relative to 208 Pb which is set to zero, and the core nucleus is chosen to be 164 Pb. For the Yb and Sn isotopes the core nucleus is also the zero RBE reference nucleus (100 Sn and 152 Yb). In this regard, the calculations for the Pb-isotopes are different because the core nucleus (164 Pb) and the zero binding energy reference nucleus (208 Pb) are not the same. One can see from fig. 1 that a quadratic fit to ln(G) as function of A fits the data well. In this particular case, the pairing strength G(A) for all 21 nuclei in the range A = 181–202 was also fit to a simple two-parameter function that is inversely proportional to the dimensionality of the model space dim(A), namely, by G(A) = α dim(A)−β . Similar results have been obtained for the Sn-isotopes relative to 132 Sn. In conclusion, we studied RBEs of nuclei in three isotopic chains, 100–130 Sn, 152–181 Yb, and 181–202 Pb, within the recently proposed EPM [2] by using Nilsson singleparticle energies as the input mean-field energies. Overall, the results suggest that the model is applicable to neighboring heavy nuclei and provides, within a shell-model approach, an alternative means of calculating RBEs. In order to achieve that, the pairing strength is allowed to change as a smooth function of the model space dimen-

BE Nilsson BE theory BE experiment

Pairing Strength 1

Log[G] Exact

0

-50

Log[G] fit

-1 -2 -3 -4

-100

5

10

15

Log(Dim)

Pairing Strength 1

-150

Log[G] Exact

0

Log(G)

(ζ)

Ek

0

Log(G)

Although Hamiltonian (1) contains many-body interaction terms that are non-perturbative, the contribution of the higher and higher energy configurations is more and more suppressed due to the structure of the equation that needs to be solved to determine the eigensystem of (ζ) (ζ) the Hamiltonian (1). The eigensystem Ek and Ci1 i2 ···ik depend on only one parameter z (ζ) , where the quantum number ζ [2] is understood as the ζ-th solution of (5):

Relative BE (MeV)

516

-200

Log[G] fit -odd A

-1

Log[G] fit -even A

-2 -3 -4 180

190

200

A

-250 180

185

190

A

195

200

Fig. 1. The solid line gives the theoretical RBEs for the Pb isotopes relative to the 208 Pb nucleus. The insets show the fit to the values of G that reproduce exactly the experimental data using a 164 Pb core. The lower inset shows the two fitting functions: log(G(A)) = 382.3502−4.1375A+0.0111A2 for even values of A and log(G(A)) = 391.6113 − 4.2374A + 0.0114A 2 for odd values of A. The upper inset shows a fit to G(A) that is inversely proportional to the size of the model space, (dim(A)), that is valid for even as well as odd values of A: G(A) = 366.7702 dim(A)−0.9972 . The Nilsson BE energy is the lowest energy of the non-interacting system.

sion. It is important to understand that the A-dependence of G is indirect, since G only depends on the model space dimension, which by itself is different for different nuclei. In particular, in all the cases studied ln(G) has a smooth quadratic behavior for even and odd A with a minimum in the middle of the model space where the dimensionality of the space is a maximal; ln(G) for even A and odd A are very similar which suggests that further detailed analyses may result in the same functional form for even-A and odd-A isotopes as found in the case of the Pb-isotopes and Sn-isotopes. It is a non-trivial result that G is inversely proportional to the space dimension dim in the two cases considered (Pb-isotopes and Sn-isotopes), which requires further studies. Financial support provided by the U.S. National Science Foundation, the Natural Science Foundation of China, and the Education Department of Liaoning Province. Some of the work was also performed under the auspices of the U. S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.

References 1. P. Navratil, W.E. Ormand, Phys. Rev. C 68, 034305 (2003). 2. F. Pan, V.G. Gueorguiev, J.P. Draayer, Phys. Rev. Lett. 92, 112503 (2004), (see also these proceedings). 3. V.G. Gueorguiev, F. Pan, J.P. Draayer, nucl-th/0403055. 4. P. M¨ oller, J.R. Nix, K.L. Kratz, At. Data Nucl. Data Tables 66, 131 (1997). 5. G. Audi, O. Bersillon, J. Blachot, A.H. Wapstra, Nucl. Phys. A 624, 1 (1997).

7 Nuclear structure theory 7.3 Mean field and beyond

Eur. Phys. J. A 25, s01, 519–524 (2005) DOI: 10.1140/epjad/i2005-06-011-7

EPJ A direct electronic only

Microscopic models for exotic nuclei M. Bender1,a and P.-H. Heenen2 1 2

Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA Service de Physique Nucl´eaire Th´eorique, Universit´e Libre de Bruxelles, CP 229, B-1050 Brussels, Belgium Received: 16 November 2004 / c Societ` Published online: 15 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Starting from successful self-consistent mean-field models, this paper discusses why and how to go beyond the mean-field approximation. To include long-range correlations from fluctuations in collective degrees of freedom, one has to consider symmetry restoration and configuration mixing, which give access to ground-state correlations and spectroscopy. PACS. 21.60.-n Nuclear structure models and methods – 21.60.Jz Hartree-Fock and random-phase approximations – 21.10.-k Properties of nuclei; nuclear energy levels – 21.10.Dr Binding energies and masses

1 Self-consistent mean-field models Self-consistent mean-field models are one of the standard approaches in nuclear structure theory, see ref. [1] for a recent review. For heavy nuclei, they are the only fully microscopic method that can be applied systematically.

1.1 Ingredients There are three basic ingredients of self-consistent meanfield models: (see ref. [1] for references) 1) The many-body state is assumed to be an independent-quasi-particle state of the BCS type. Degrees of freedom are a set of orthonormal single-particle states φk with corresponding operators a ˆk and occupation amplitudes vk . The generalized one-body density matrix is idempotent   †   ˆ ˆ aa ˆ

ˆ a a ρ κ 2 = . (1) R =R= −κ∗ 1 − ρ∗

ˆ a† a ˆ†  ˆ aa ˆ†  2) An effective interaction tailored for the purpose of mean-field calculations has to be used. It incorporates the short-range correlations induced by the strong interaction. The actually used effective interactions are parametrized and adjusted phenomenologically. They are formulated either as a density-dependent two-body force or as an energy functional E depending on the density matrix in the spirit of density functional theory. 3) The equations-of-motion for the single-particle states and the occupation amplitudes are determined selfconsistently from the variation of the total energy adding a

Conference presenter; e-mail: [email protected]

constraints on the particle number ! !   ˆ − λZ Zˆ + · · · = 0. δ E − λN N

(2)

This leads to the Hartree-Fock-Bogoliubov (HFB) equations, or, using a common approximation, the HF+BCS equations. The Lagrange parameters λi are adjusted to ˆ = N meet conditions for the constraint, for example N for the average neutron number. The main ingredients of the HFB equations are the single-particle Hamiltonian and the pairing field, which are obtained as first functional derivatives of the total energy ˆ = δE , h δρ

δE Δˆ = ∗ . δκ

(3)

1.2 Typical applications Mean-field models can be used to describe a manifold of phenomena and experimental data: – Nuclear masses or binding energies, and all difference quantities derived from them, like one- and two-particleseparation energies, Q values for α and β-decay. – Deformation energy surfaces can be mapped by adding one or more constraints on a multipole moment ˆ m  to the variational equation (2). −λ m Q – The radial density distribution and quantities derived from it as the mean-square radii of the charge and neutron distributions, the neutron skin, the surface thickness, or the full charge form factor at low momentum transfer. – The spatial density distribution, for example multipole moments of well-deformed nuclei. – The very concept of a single-particle energy, associated ˆ with the eigenvalues of the single-particle Hamiltonian h,

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eq. (3), refers to an underlying mean-field picture of the nucleus. Experimental single-particle energies, however, are obtained as an energy difference between the groundstate of an even-even nucleus on one the hand and states in adjacent odd-A nuclei on the other, the latter having a different structure due to the unpaired nucleon, which adds significant corrections. – Rotational bands of well-deformed nuclei can be obtained by adding a constraint on one component of the angular momentum −ωi Jˆi  to the variational equation (2), which is equivalent to solving the mean-field equations in a rotating frame. This adds inertial forces to the modeling, which align the angular momenta of the singleparticle states and weaken pairing with increasing total angular momentum. 1.3 Prospects – Mean-field models offer an intuitive interpretation of their results in terms of the shapes of a nuclear liquid and of shells with single-particle states. – The full model space of occupied states can be used, removing any distinction between core and valence particles and the need for effective charges. – This allows the use of a universal effective interaction, universal in the sense that it can be applied for all nuclei throughout the periodic chart. There is, however, no consensus among practitioners of the field about a unique effective interaction. Many different functional forms have been proposed —for example non-relativistic Skyrme and Gogny interactions and finite-range as well as point-coupling relativistic interactions —and parameterizations thereof to be found in the literature [1]. 1.4 Difficulties and problems – An independent particle description establishes a bodyfixed intrinsic frame of the nucleus. The connection of mean-field results to spectroscopic observables in the laboratory frame of reference relies on additional assumptions like the rigid-rotor model, which are not valid, for example, at small deformation or in soft nuclei. – By construction, a mean-field state breaks symmetries in the laboratory frame. Examples are given in table 1. On the one hand, symmetry breaking is a desired feature of mean-field models. In the language of the spherical shell model (using a spherically symmetric Slater determinant as reference state) the symmetry-breaking in mean-field models adds the most important n-particle-nhole and particle-particle correlations to the modeling at very moderate computational cost. On the other hand, a broken symmetry mixes excitations related to the symmetry operator into the mean-field state. For example, broken rotational symmetry mixes states with different values of J 2 , i.e. the members of a rotational band. Broken parity mixes states of opposite parity, broken translational symmetry admixes states with different center-of-mass motion. Restoring the symmetries decomposes the mean-field states into states with proper quantum numbers.

Table 1. Examples for symmetries broken in the intrinsic frame of the nucleus.

Symmetry

Generator

Which states

U (1) gauge translational rotational parity

particle number momentum angular momentum parity

pairing finite nuclei deformation octupole deformation

– The mean-field approach becomes ill-defined when the binding energy changes slowly with a collective degree of freedom. This is a common situation in transitional nuclei. – It is tempting to associate two or more local minima in the potential energy landscape that are separated by a substantial barrier with different physical states, so-called shape coexistence. This interpretation might not always be valid as two different mean-field states are not orthogonal, and they might well be coupled by the interaction.

2 Going beyond the mean field The idea is to start from self-consistent mean-field models as described above, keeping their advantages and successes, and to resolve the remaining problems in an efficient, systematic and consistent manner. This will add long-range correlations to the model, where “long-range” does not refer to the range of an interaction, but to collective correlations that involve the nucleus as a whole. Two kinds of correlations have to be distinguished. As outlined above, a mean-field state describes static correlations related to deformation or pairing. These have to be distinguished from the dynamical correlations we will discuss below. They are also related to deformation and pairing, but describe fluctuations in collective degrees of freedom. The dynamical correlations cannot be described by a state for which R2 = R holds and therefore require to go beyond the mean field. 2.1 Projection methods As a first-order approximation to projection, corrections to the energy are used in self-consistent mean-field models. Most prominent examples are the center-of-mass correction and the Lipkin-Nogami scheme to calculate the occupation amplitudes. Both are approximations to projection before variation (on zero momentum and particle number, respectively), when consistently included in the variation, eq. (2). Sometimes a rotational correction to the binding energy is also applied. The corrections work best when the symmetry breaking is large, which is often not the case. It is, therefore, desirable to restore broken symmetries of the mean-field states exactly by projecting on good quantum numbers after variation. The projection might be combined with some of the correction schemes. ˆ , with Eigenstates of the particle-number operator N eigenvalue N0 , are obtained applying the particle-number

M. Bender and P.-H. Heenen: Microscopic models for exotic nuclei

. . ..

.

.... .. ..

.. . . .

Fig. 1. Decomposition of the energy into angular-momentum components (upper left), collective wave function (upper right) and energy (lower right) for the mixed J = 0 states, and complete spectrum of low-J states (lower left) for 188 Pb. All curves are plotted against the mass quadrupole deformation β2 of the unprojected mean-field states.

projection operator 1 PˆN0 = 2π



2π

dφN eiφN (N −N0 ) , ˆ

(4)

0

while eigenstates of the angular momentum operators Jˆ2 and Jˆz , with eigenvalues J(J + 1) and M , are obtained applying the operator   π  2π 2J + 1 4π ∗J J ˆ ˆ dα dβ sin(β) dγ DM PM K = K R, (5) 16π 2 0 0 0

for 188 Pb (thin solid line) into its angular-momentum components (thick curves). All energies are normalized to the spherical state. The intrinsic spherical state is a pure J = 0 state by construction. The difference between the mean-field and projected J = 0 states is the rotational energy. It increases rapidly to about 3 MeV at small β2 , and then grows at a slower rate with deformation. The example of 188 Pb demonstrates that projection after variation of the mean-field ground-state might not lead to the lowest projected state as it is not a variational procedure. Instead, one has to consider a set of states with different deformations and search for the energy minimum. In particular, the lowest projected state of a nucleus with a spherical mean-field ground-state is usually obtained from a deformed state. For such nuclei, there is the additional peculiarity that one obtains two J = 0 minima at small oblate and prolate deformation, see fig. 1. Closer examination reveals that they represent the same state, as their overlap is very close to one. 2.2 Variational configuration-mixing The ambiguities of many near-degenerated states with different deformation can be overcome by diagonalizing the Hamiltonian in the space of these states within the Generator Coordinate Method (GCM). The mixed projected many-body state is set-up as a coherent superposition of projected mean-field states |JM q with different intrinsic deformations q  fJk (q) |JM q, (7) |JM k = q

where fJ,k (q) is a weight function which is determined from the stationarity of the states

ˆ k δ JM k|H|JM = 0, ∗ δfJk JM k|JM k

−iαJˆz −iβ Jˆy −iγ Jˆz

ˆ = e e e is the rotation operator where R ∗J a Wigner function. Both depend on the Euler and DM K J angles α, β, γ. PˆM picks the component with angular K momentum projection K along the intrinsic z-axis. The projected state is then obtained by summing over all K components with weights determined from a variational J equation. Note that PˆM K is not a projection operator in the strict mathematical sense [2]. In the current implementation of our model, we start with HF+BCS or HFB states |q for which we assume even particle numbers, good parity, axial and time-reversal symmetry. This allows for the analytical evaluation of the α and γ integration in eq. (5) at the price of restricting the projected states to positive parity P = +1, even integer total angular momentum J, and intrinsic angular momentum projection K = 0 |JM q =

J ˆ ˆ PˆM 0 PN0 PZ0 |q . J ˆ ˆ

q|P PN PˆZ |q1/2

00

0

(6)

0

As an example, the upper left panel of fig. 1 shows the decomposition of the particle-number projected energy curve

521

(8)

which leads to the Hill-Wheeler-Griffin equation [3]  ! !   ˆ JM q|H|JM q  − Ek JM q|JM q  fJ,k q  = 0, q

that gives a correlated ground state for each value of (9) J, and, in addition, a spectrum of excited states. The weight functions fJk (q) are not orthonormal. A set of orthonormal collective wave functions gJk (q) = JM k|q in the basis of the intrinsic states is obtained from a transformation involving the square root of the norm kernel. The actual choice for the generator coordinate depends on the mode to be described, for example, the quadrupole or octupole moment of the mass density, or the monopole moment of the pair density, which then delivers a description of quadrupole, octupole or pairing vibrations, respectively. Examples for such calculations, without angular-momentum projection, can be found in ref. [4]. Several generator coordinates can be easily combined for multi-dimensional calculations, although this has been rarely done so far. For all results shown here, the axial quadrupole moment of the mass distribution serves as

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the generator coordinate. Hence, the excited states are either quadrupole vibrational or rotational states. The right panels of fig. 1 show as an example the mixing of the J = 0 states with different quadrupole moments in 188 Pb. The upper right panel shows the collective wave functions g0k (q) for the five lowest collective J = 0 states, the lower right panel the corresponding energies drawn in the same line style by horizontal lines centered at the average deformation of the mean-field states they are composed of together with the projected J = 0 energy curve. The energies are now normalized to the projected GCM ground state. Combining such calculations for all values of J gives then the the entire spectrum of low-J states, most of which can be clearly grouped into rotational bands, see the lower left panel of fig. 1. The projected energy curves in fig. 1 are the diagonal matrix elements entering the Hill-Wheeler equation. They should not be confused with a collective potential, which does not exist in the GCM framework —nor does a collective mass. Both appear in approximations like the Bohr-Hamiltonian [5,6]. Owing to the energy gain from configuration mixing, the GCM ground state is located below the energy curves. Projection is a special case of the GCM, where exactly degenerate states are mixed. The generators of the group involved define the collective path, and the weight functions are determined by the restored symmetry. Angularmomentum projection is part of the quadrupole correlations, as it mixes states with different orientations of the quadrupole tensor. Therefore the GCM mixing of states with respect to the quadrupole moment should be performed together with angular-momentum projection. For a state resulting from the mixing of different meanfield states, the mean particle number is not anymore equal to the particle number of the original mean-field states. Projection, as done here, eliminates this problem, otherwise a constraint on the particle number has to be added to the Hill-Wheeler-Griffin equation (9). We also perform an approximate particle-number projection before variation in the Lipkin-Nogami approach to ensure that pairing correlations are present in all meanfield states. The angular-momentum projected GCM allows to calculate transition moments directly in the lab frame for in-band and out-of-band transitions, for example B(E2) values   B E2; Jk  → Jk = +J  e2 2J  + 1

M =−J



+J 

+2 

M  =−J 

μ=−2

ˆ 2μ |J  M  k  |2 . (10) | JM k|Q

The B(E2) value scales with mass and angular momentum. A more intuitive measure is the transitional quadrupole deformation obtained from the B(E2) using the static rotor model +  B(E2; Jk → Jk − 2) 4π (t)   , (11) β2 Jk → Jk = 2 (J 0 2 0|J − 2 0)2 e2 3R A

Fig. 2. Experimental (left) and calculated (right) excitation spectra and selected transition quadrupole moments (t) β2 (Jk  → Jk ) for 188 Pb.

with R = 1.2 A1/3 . The method gives also the spectroscopic quadrupole moments in the lab frame ˆ 20 |J M = J k, Qs (Jk ) = J M = J k|Q

(12)

which again scale with mass and angular momentum and might be given in a more intuitive measure through a dimensionless deformation parameter $ 4π 5 2J + 3 (s) Qs (Jk ), (13) β2 (Jk ) = − 16π 3R2 A J

again with R = 1.2 A1/3 and assuming axial symmetry. For a given rotational band in the rigid rotor, one has (t) (s) (s) β2 (J + 2 → J) ≈ β2 (J + 2) ≈ β2 (J) for J > 0. Deviations from this behavior point at a more complicated situation. An example is given in fig. 2. For high-J states, (t) the β2 values within a band are constant, while with the mixing of the low-lying states they are significantly decreased.

3 Examples of applications All results discussed here were obtained by configuration mixing of particle-number and angular-momentumprojected HF+BCS states with different axial mass quadrupole moments. We chose the Skyrme interactions SLy4 or SLy6 [7] for the particle-hole channel and a density-dependent delta pairing interaction (“surface pairing”) [8] for the particle-particle channel. A group in Madrid uses the Gogny force in a similar model [9].

3.1 Spectroscopy Results for spectroscopic observables obtained with our method for 24 Mg have been published in [10], for 16 O in [11], for 32 S, 36,38 Ar, 40 Ca in [12], for 186 Pb in [13], for 182–194 Pb in [14], and for 240 Pu in [15].

M. Bender and P.-H. Heenen: Microscopic models for exotic nuclei

523

Fig. 3. Mean-field deformation energy curves for Pb isotopes.

Fig. 5. Upper two panels: difference between calculated and experimental masses. Lower two panels: mean-field deformation energy Edef and beyond-mean-field quadrupole correlation energy Ecorr . All panels share the same energy scale in MeV.

3.2 Mass systematics Fig. 4. Lowest collective states in the Pb isotopes.

The neutron-deficient Pb isotopes show unique spectroscopic features, which are associated with a spherical ground state, an oblate minimum present above A = 188 but disappearing below, a prolate minimum present below A = 188 and disappearing above, and a superdeformed minimum, that is confirmed down to A = 192, see fig. 3. Projected GCM then delivers collective states that can be associated with a spherical ground state and excited prolate, oblate and superdeformed bands. There is a nice qualitative agreement with experimental data, see fig. 4, but the calculated transition energies within the bands are too dilute, see also fig. 2 for 188 Pb. For more details and further discussion of other observables, see refs. [13,14]. An example with very different spectroscopic features is the well-deformed nucleus 240 Pu, see ref. [15]. Projection does not alter the topology of the potential energy curve, but gives about 3 MeV additional binding for the ground state and about 4 MeV for the fission isomer which has now an excitation energy that is 1 MeV lower compared to mean-field calculations. Projection lowers the outer barrier as much as 2 MeV. GCM does not substantially mix states. Again, the excitation energies within the rotational bands are too large, while the deformation is well described on all levels of approximation: we obtain β2 = 0.29 for the mean-field ground (t) state, β2 (J + 2 → J) = 0.30 for all E2 transitions within the ground-state band, where all excited states have spectroscopic quadrupole moments corresponding to (s) β2 (J) = 0.30, in agreement with the experimental value + of 0.29 deduced from the B(E2; 0+ 1 → 21 ).

Mass formulas based on self-consistent mean-field models using Skyrme interactions have reached a quality where they compete with the best available microscopic-macroscopic models [16]. A key to this success is to add various correlation energies phenomenologically through correction terms, as a Wigner energy term or a rotational correction. There is no correction for vibrations, as it cannot be formulated in terms of a simple expression. Our model allows us to consistently calculate the quadrupole correlation energy from symmetry restoration and fluctuations of the quadrupole moment. For the calculation of a mass table including correlations, it was necessary to use an approximation to the method described above. For this purpose, we implemented the Gaussian overlap approximation (GOA) into our method [17]. While most applications of the GOA use it as an intermediate step to derive a BohrHamiltonian [5,6], we use the GOA solely as a numerical tool: a topological GOA to estimate the integrals over Euler angles from two or three exactly calculated points, and a second GOA to construct the matrices entering the HillWheeler equation from diagonal matrix elements and matrix elements between nearest neighbors only. The GOA puts emphasis on the correlated 0+ ground state; most information for spectroscopy is lost. Particle-number projection is still performed exactly. The accuracy of the GOA is better than 300 keV, which is sufficient for a study of the systematics of quadrupole correlation energies, which are an order of magnitude larger. Figure 5 shows some results [18]. The overall erroneous trend with A, that was already observed in ref. [19], can be removed with a slight refit of the coupling constants of SLy4 on the mean-field level [20]. The quadrupole correlation energy improves the masses by reducing the

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Fig. 6. Two-proton gap δ2p for Sn and Pb isotopes.

oscillations between the closed shells, but without removing them completely. Still, there is a substantial improvement, which becomes obvious when looking at energy differences like the two-proton gap δ2p (N, Z) = E(N, Z − 2) − 2E(N, Z) + E(N, Z + 2), see fig. 6. Spherical meanfield calculations (open squares) give near-constant δ2p in accordance with the stable Z = 82 shell. Allowing for deformation (open triangles) and adding correlations (open circles) substantially reduces δ2p for mid-shell nuclei far from 208 Pb, in agreement with experiment (full diamonds). Similar results were obtained in ref. [21]. The lower panels of fig. 5 compare mean-field deformation and beyond-mean-field quadrupole correlation energies. While heavy nuclei are dominated by the deformation energy, light nuclei are dominated by the correlation energy.

4 Summary and outlook Projection and configuration mixing significantly improve the modeling of nuclei in self-consistent mean-field approaches and give access to spectroscopy. Masses are significantly improved around closed shells, and the overall structure of collective bands is reproduced, even in complicated systems like neutron-deficient Pb isotopes where many structures coexist. On the quantitative level, neither masses nor excitation spectra are yet described with the desired precision. This might be for a number of origins. There will be imperfections of the effective interactions that we use. Some aspects of the effective interaction might be much more sensitive to spectroscopy than to the ground states they are fitted to. For consistency, the effective interaction should be refitted including the correlations. To obtain a more robust extrapolation of the interaction into the unknown, it is desirable to establish a link between the effective interaction needed for calculations as done here, and more ab-initio methods. On the other hand, the modeling of the configuration mixing might still have some deficiencies as well. There are additional modes like pairing vibrations, triaxial quadrupole deformations, or octupole vibrations, which might play a role for certain nuclei and, therefore, should be included in a unified model. The determination of the

collective path has to be re-examined, and diabatic states may play a role in some situations. An interesting insight comes from self-consistent, cranked mean-field calculations: for 240 Pu, the excitation energies from cranked HFB are in much better agreement with experiment than our projected values when using the same interaction [15]. Cranked mean-field states break time-reversal invariance and have the proper angular momentum on the average, which might be crucial for excitation energies. A generalization of our model to use cranked states as a starting point for projected GCM is currently underway. This will also allow to describe nuclei with an odd nucleon number in our framework. A lot of work is left for the future, but present results are most encouraging. The results discussed here were obtained in collaboration with G.F. Bertsch, P. Bonche, T. Duguet, and H. Flocard. We thank T. Duguet and R.V.F. Janssens for critical reading of the manuscript. MB thanks for the warm hospitality at the Service de Physique Nucl´eaire Th´eorique at the Universit´e Libre de Bruxelles, Belgium, and the Institute for Nuclear Theory, Seattle, USA, where parts of the research presented here were carried out. This work was supported in parts by the U.S. Department of Energy, Office of Nuclear Physics, under Grant W-31-109-ENG-38 (Argonne National Laboratory) and the Belgian Science Policy Office under contract PAI P5-07.

References 1. M. Bender, P.-H. Heenen, P.-G. Reinhard, Rev. Mod. Phys. 75, 121 (2003). 2. P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer Verlag, New York, Heidelberg, Berlin, 1980) p. 438. 3. D.L. Hill, J.A. Wheeler, Phys. Rev. 89, 1106 (1953); J.J. Griffin, J.A. Wheeler, Phys. Rev. 108, 311 (1957). 4. P.-H. Heenen et al., Eur. Phys. J. A 11, 393 (2001). 5. J. Libert et al., Phys. Rev. C 60, 054301 (1999). 6. P. Fleischer et al., Phys. Rev. C 70, 054321 (2004). 7. E. Chabanat et al., Nucl. Phys. A 635, 231 (1998). 8. C. Rigollet et al., Phys. Rev. C 59, 3120 (1999). 9. R. Rodriguez-Guzman et al., Phys. Rev. C 62, 054319 (2002). 10. A. Valor et al., Nucl. Phys. A 671, 145 (2000). 11. M. Bender, P.-H. Heenen, Nucl. Phys. A 713, 390 (2003). 12. M. Bender et al., Phys. Rev. C 68, 044321 (2003). 13. T. Duguet et al., Phys. Lett. B 559, 201 (2003). 14. M. Bender et al., Phys. Rev. C 69, 064303 (2004). 15. M. Bender et al., Phys. Rev. C 70, 054304 (2004). 16. M. Samyn et al., Nucl. Phys. A 700, 142 (2002); Phys. Rev. C 70, 044309 (2004). 17. M. Bender et al., Phys. Rev. C 69, 034340 (2004). 18. M. Bender et al., Phys. Rev. Lett. 94, 102503 (2005). 19. M.V. Stoitsov et al., Phys. Rev. C 68, 054312 (2003). 20. G.F. Bertsch et al., preprint nucl-th/0412091. 21. P. Fleischer et al., Eur. Phys. J. A 22, 363 (2004).

Eur. Phys. J. A 25, s01, 525–526 (2005) DOI: 10.1140/epjad/i2005-06-003-7

EPJ A direct electronic only

Breathing mode energy and nuclear matter incompressibility coefficient within relativistic and non-relativistic models B.K. Agrawal1,2,a , S. Shlomo1 , and V. Kim Au1 1 2

Cyclotron Institute, Texas A&M University, TX, USA Saha Institute of Nuclear Physics, Kolkata, India Received: 1 October 2004 / Revised version: 4 November 2004 / c Societ` Published online: 11 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Seemingly large differences (∼ 20%) in the value of the nuclear matter incompressibility coefficient K obtained from relativistic and non-relativistic models have been systematically investigated. For an appropriate comparison with the relativistic mean-field (RMF) based random phase approximation (RPA) calculations, we obtain the parameters of the Skyrme force used in the non-relativistic model by adopting the same experimental data and procedure employed in the determination of the NL3 parameter set of the effective Lagrangian used in the RMF model. Our investigation suggests that the discrepancy between the values of K predicted by the relativistic and non-relativistic models is less than 10%. PACS. 21.65.+f Nuclear matter – 24.30.Cz Giant resonances – 21.60.Jz Hartree-Fock and random-phase approximations

1 Introduction The Hartree-Fock (HF) based random phase approximation (RPA) provides a microscopic description of the nuclear compression modes such as the isoscalar giant monopole resonance (ISGMR), also referred to as the breathing mode. The centroid energy E0 of the ISGMR allows us to determine the value of nuclear matter incompressibility coefficient K which plays an important role in understanding a wide variety of phenomena. Currently, the uncertainty in the experimental data [1] for the E0 in heavy nuclei is ∼ 0.1–0.3 MeV. The uncertainty δE0 associated with E0 is approximately related to the uncertainty δE0 δK in K by δK K = 2 E0 , the value of δK is only about 10 MeV, for K = 250 MeV and E0 = 14.17 ± 0.28 MeV for the 208 Pb nucleus. The theoretical scenario for K is [2,3], 0 250–270 MeV Relativistic models, K= (1) 205–212 MeV Non-relativistic models.

In eq. (1), the “relativistic” model refers to the calculations carried out using an effective Lagrangian which describes the nucleon-nucleon interaction through exchange of σ, ω and ρ mesons. Whereas, the “non-relativistic” models refer to the calculations carried out using a Skyrme type nucleon-nucleon effective interaction. The difference K[Relativistic] − K[Non-relativistic] ≈ 50–60 MeV was a

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claimed to be due to the model dependence [3]. Some preliminary work to resolve this discrepancy was presented in ref. [4]. Our motivation is to investigate systematically the issue of the model dependence of K [5].

2 New Skyrme parameters (SK255) As a first step toward resolving the issue of the model dependence of K we would like to match the typical differences between the relativistic and non-relativistic meanfield models. Most of the mean-field calculations carried out using the Skyrme interaction (non-relativistic) and the effective Lagrangian (relativistic) differ in the ways the contributions from the center-of-mass motion, Coulomb interaction and density dependence of the symmetry energy are dealt with [5]. For an appropriate comparison with the relativistic mean-field (RMF) based RPA calculations, we obtain the parameters of the Skyrme force used in the non-relativistic model by adopting the same experimental data and procedure employed in the determination of the NL3 parameter set of the effective Lagrangian used in the RMF model. In table 1 we have compared the nuclear matter properties obtained for the SK255 interaction with those for the NL3 parameter. Similar results for the binding energies and charge rms radii are presented in table 2 along with the experimental data.

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Table 1. Comparison of the nuclear matter properties for the SK255 and NL3 interactions.

NL3 −16.30 271.76 0.148 37.4 118.5

SK255 −16.33 254.96 0.157 37.4 95.0

18 116

Sn

Table 2. Binding energy and charge rms radii for the SK255 and NL3 interactions.

Nuclei 16 O 40 Ca 48 Ca 90 Zr 116 Sn 132 Sn 208 Pb

Binding energy (MeV) Expt. NL3 SK255 −127.6 −128.8 −128.1 −342.1 −342.0 −342.5 −416.0 −415.2 −413.9 −783.9 −782.6 −783.3 −988.7 −987.7 −984.5 −1102.9 −1105.4 −1100.0 −1636.5 −1639.5 −1637.5

rms charge radii (fm) Expt. NL3 SK255 2.73 2.73 2.81 3.45 3.47 3.50 3.45 3.47 3.53 4.26 4.29 4.29 4.63 4.61 4.62 4.71 4.73 5.50 5.52 5.50

208

Pb

14 80

120

160

200

A

Fig. 2. Comparison of the results for the breathing mode energies obtained using the SK255 and NL3 interactions.

∼ 0.3 MeV, which is on the level of the uncertainty associated with the experimental data for E0 .

4 Conclusions 208

Pb

Ca

0.2

Δr (fm)

116

Sn

90

Zr

0.1

16

O 40

Ca

0

Sm

16

Sn

48

0

144

132

NL3 SK255

0.3

Zr

E0(MeV)

E/A (MeV) Knm (MeV) ρ0 (fm−3 ) J (MeV) L (MeV)

NL3 SK255 Expt.

90

50

100

150

200

A

Fig. 1. Neutron skin versus mass number A for the SK255 and NL3 interactions.

3 Neutron skin and breathing mode energy In fig. 1 we display our results for Δr = rn − rp , the difference between the neutron and proton rms radii (the so-called neutron skin). The values of Δr for the SK255 and NL3 interactions are quite close to each other. For instance, in the case of 208 Pb nucleus Δr = 0.25 (0.28) fm for the SK255 (NL3) interactions. Most of the calculations using a Skyrme interaction having the value of K ∼ 210 MeV yield Δr ∼ 0.16 fm. The value of Δr is mainly governed by the values of J and L. For the SK255 interaction we have taken exactly the same value of J as obtained for the NL3 interaction (see table 1). In fig. 2 we display our results for the breathing mode energy obtained using the SK255 interaction and compare them with those obtained using the NL3 interactions. We see that the maximum difference between the values of E0 obtained from the parameter sets SK255 and NL3 is

We have analyzed in detail the claim that the nuclear matter incompressibility coefficient K deduced from the breathing mode energy calculated within the relativistic and non-relativistic based RPA models differ by about 20%. For a meaningful comparison, we have generated a set of the Skyrme parameters SK255 (K = 255 MeV) by using the same procedure and the experimental data for the bulk properties of nuclei considered in ref. [6] for determining the NL3 parameterization (K = 272 MeV) of an effective Lagrangian used in the relativistic mean-field models. We have used the SK255 interaction to calculate the breathing mode energies for the several nuclei. We find that our results for the breathing mode energies are quite close to those obtained for the NL3 parameters of the relativistic model. This clearly demonstrates that for appropriately calibrated relativistic and non-relativistic models, the difference in the value of K is less than 10%. This work was supported in part by the US Department of Energy under grant No. DOE-FG03-93ER40773 and the National Science Foundation under grant No. PHY-0355200.

References 1. D.H. Youngblood, H.L. Clark, Y.W. Lui, Phys. Rev. Lett. 82, 691 (1999). 2. D. Vretenar, T. Niksick, P. Ring, Phys. Rev. C 68, 024310 (2003). 3. Nguyen Van Giai, P. F. Bortignon, G. Colo, Zhongyu Ma, M. Quaglia, Nucl. Phys. A 687, 44c (2001). 4. J. Piekarewicz, Phys. Rev. C 66, 034305 (2002). 5. B.K. Agrawal, S. Shlomo, V. Kim Au, Phys. Rev. C 68, 031304R (2003). 6. G.A. Lalazissis, J. Konig, P. Ring, Phys. Rev. C 55, 540 (1997).

Eur. Phys. J. A 25, s01, 527–529 (2005) DOI: 10.1140/epjad/i2005-06-052-x

EPJ A direct electronic only

Unrestricted TDHF studies of nuclear response in the continuum T. Nakatsukasaa and K. Yabana Center for Computational Science and Institute of Physics, University of Tsukuba, Tsukuba 305-8571, Japan Received: 7 October 2004 / c Societ` Published online: 6 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The TDHF dynamics in the small-amplitude regime is studied in the real-space and real-time representation. The continuum is taken into account by introducing a suitable complex potential. This is equivalent to the continuum random-phase approximation and applicable to deformed nuclei. PACS. 21.60.Jz Hartree-Fock and random-phase approximations – 24.30.Cz Giant resonances

1 Introduction The time-dependent Hartree-Fock (TDHF) theory is a dynamical theory and takes care of both collective and single-particle excitations. Its small-amplitude regime is known as the random-phase approximation (RPA) for the effective density-dependent forces. The spreading width, which is partially described in the TDHF (one-body dissipation), is known to be important for the broadening of giant resonances. However, for light nuclei, the escape width gives a dominant contribution and becomes even more important near the drip line. Recently, we have proposed a feasible method to treat the continuum in the real-space TDHF calculation [1,2, 3]. That is the absorbing-boundary condition (ABC) approach. We studied photoabsorption in molecules [4] and nuclear breakup reaction [5, 6] with the similar technique. The method, we call TDHF + ABC, is simple and accurate enough to calculate nuclear response in the continuum for spherical and deformed nuclei. Its small amplitude limit is equivalent to the continuum RPA [7]. An advantage over the continuum RPA is its applicability to nonspherical systems. In addition, the TDHF wave function in the coordinate space provides us with an intuitive picture of nuclear collective motion and the damping mechanism of particle escaping. The time evolution of the TDHF states is calculated following the prescription in ref. [8]. The trick to treat the continuum is introduction of an absorbing complex potential outside of the interacting region. The potential must be properly chosen so as to make the minimum reflection. We would like readers to refer to our recent paper [3] for computational details.

2 Octupole states in

16

O

In this section, we discuss the isoscalar octupole resonances in 16 O with the simple BKN interaction. A pera

Conference presenter; e-mail: [email protected]

turbative external field is chosen as Vext (r) = r 3 Y30 . The time evolution is determined by the TDHF equation with the complex absorbing potential, −iη(r), i

∂ ψi (r, t) = {h[ρ] + Vext (r)δ(t) − iη(r)} ψi (r, t), (1) ∂t

where i = 1, · · · , A/4 and  is a small parameter to validate the linear response approximation. The BKN interaction assumes the exact spin-isospin symmetry, thus each orbital has a four-fold degeneracy. η(r) is zero in the physically relevant region of space. The single-particle wave functions are represented on the three-dimensional coordinate space. See ref. [3] for details. The time evolution of the density calculated with and without the ABC is shown in fig. 1. The horizontal axis is z-axis. There is no difference up to t < 0.8 /MeV between the box (left panel) and absorbing boundary condition (right). However, the waves reflected at the edge of the space return to the nucleus for t > 1 /MeV (left). As a result, the time-dependent octupole moment shows a beating pattern created by the reflected waves. The reflection is a consequence of the discretized continuum in the energy representation. In fig. 1, we can also see that, the octupole resonance emits particles along the z-axis and to the diagonal direction. This can be understood in terms of the pear shape of Y30 mode. In the numerical calculation, we stop the time evolution at t = 30 /MeV. The Fourier transform of the time-dependent octupole moment leads to the octupole strength function in fig. 2. We use a smoothing parameter Γ = 0.2 MeV to make low-energy peaks below the particle threshold with a finite width. The octupole oscillation with E = 11.3 MeV is stable with respect to the particle decay. On the other hand, the high-energy resonance is in the continuum. The particle escape almost ceases by t = 1 /MeV and only a low-frequency octupole oscillation survives after that (fig. 1). Taking into account the particle continuum properly, the high-frequency octupole

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16

600

6

Octupole strength [ fm /MeV ]

Octupole strength in O

400

200

0

0

10

20

30

40

50

E [ MeV ]

Fig. 2. Isoscalar octupole strength for 16 O as a function of excitation energy, being calculated with the ABC.

Vext (r). See ref. [3] for full details. For 12 Be, we obtain the ground state with a small prolate deformation. The lowest dipole state appears near the threshold, at E ≈ 4.5 MeV, with B(E1; 0+ → 1− ) = 0.023 e2 fm2 . The corresponding experimental data [9] indicate E = 2.68 MeV with B(E1) = 0.051(13) e2 fm2 . Some experiments suggest that 12 Be has a large deformation in the ground state [10]. Since the ground-state deformation is very small in this calculation, this might be a reason of the discrepancy. For 14 Be, the HF ground state has a superdeformed prolate shape (β ≈ 0.75). The low-energy dipole state is embedded in the continuum at E ≈ 5 MeV having a significant E1 strength, B(E1) ≈ 0.26 e2 fm2 . The peak position is almost at the same energy as that in 12 Be, however, the strength is about 10 times larger. Experiment seems to suggest some enhancement of Coulomb dissociation crosssection around E ≈ 2 and ≈ 5 MeV [11].

4 Conclusion

Fig. 1. Density plots in the zx plane in the logarithmic scale. The times t is given in units of /MeV. The box boundary condition is used in the left panel, while the ABC is applied in the right one.

resonance is significantly broadened by the particle escape. Note that the peak at E ≈ 2.5 MeV is due to small admixture of the translational mode.

3 Low-energy dipole states in Be isotopes We study E1 responses in neutron-rich Be isotopes using the same technique as in sect. 2. The full Skyrme functional (SIII) is used in the calculation. The TDHF equation, eq. (1), is solved with the E1 external field for

We have studied nuclear response in the continuum for spherical and deformed nuclei. The absorbing boundary condition approach is utilized in the TDHF simulation in the small amplitude regime. This is equivalent to the continuum RPA, but easier to apply to deformed nuclei. In this paper, we have shown the application to octupole states in 16 O and dipole states in 12,14 Be. Strong enhancement of the E1 strength at the neutron drip line is obtained for 14 Be. This work is supported by the Grant-in-Aid for Scientific Research in Japan (Nos. 14540369 and 14740146).

References 1. T. Nakatsukasa, 146, 447 (2002). 2. T. Nakatsukasa, (2004). 3. T. Nakatsukasa, (2005). 4. T. Nakatsukasa, (2001).

K. Yabana, Prog. Theor. Phys. Suppl. K. Yabana, Eur. Phys. J. A 20, 163 K. Yabana, Phys. Rev. C 71, 024301 K. Yabana, J. Chem. Phys. 114, 2550

T. Nakatsukasa and K. Yabana: Unrestricted TDHF studies of nuclear response in the continuum 5. M. Ueda, K. Yabana, T. Nakatsukasa, Phys. Rev. C 67, 014606 (2002). 6. M. Ueda, K. Yabana, T. Nakatsukasa, Nucl. Phys. A 738, 288 (2004). 7. S. Shlomo, G.F. Bertsch, Nucl. Phys. A 243, 507 (1975).

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8. H. Flocard, S.E. Koonin, M.S. Weiss, Phys. Rev. C 17, 1682 (1978). 9. H. Iwasaki et al., Phys. Lett. B 491, 8 (2000). 10. A. Navin et al., Phys. Rev. Lett., 85, 266 (2000). 11. M. Labiche et al., Phys. Rev. Lett. 86, 600 (2001).

Eur. Phys. J. A 25, s01, 531–534 (2005) DOI: 10.1140/epjad/i2005-06-057-5

EPJ A direct electronic only

Self-consistent relativistic QRPA studies of soft modes and spin-isospin resonances in unstable nuclei N. Paar1,2,3,a , T. Nikˇsi´c2,3 , T. Marketin2 , D. Vretenar2 , and P. Ring4 1 2 3 4

Institut f¨ ur Kernphysik, Technische Universit¨ at Darmstadt, Schlossgartenstrasse 9, D-64289 Darmstadt, Germany Physics Department, Faculty of Science, University of Zagreb, Croatia Institute for Nuclear Theory, University of Washington, Seattle WA, 98195, USA Physik-Department der Technischen Universit¨ at M¨ unchen, D-85748 Garching, Germany Received: 14 October 2004 / c Societ` Published online: 6 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The excitation phenomena in unstable nuclei are investigated in the framework of the relativistic quasiparticle random-phase approximation (RQRPA) in the relativistic Hartree-Bogoliubov model (RHB) which is extended to include effective interactions with explicit density-dependent meson-nucleon couplings. The properties of the pygmy dipole resonance (PDR) are examined in 132 Sn and within isotopic chains, showing that already at moderate proton-neutron asymmetry the PDR peak energy is located above the neutron emission threshold. A method is suggested for determining the size of the neutron skin within an isotopic chain, based on the measurement of the excitation energies of the Gamow-Teller resonance relative to the isobaric analog state. In addition, for the first time the relativistic RHB + RQRPA model, with tensor ω meson-nucleon couplings, is employed in calculations of β-decay half-lives of nuclei of the relevance for the r-process. PACS. 21.60.Jz Hartree-Fock and random-phase approximations – 21.30.Fe Forces in hadronic systems and effective interactions – 24.10.Jv Relativistic models

1 Introduction Studies of excitation phenomena and β-decay rates in nuclei away from the valley of β-stability provide a sensitive test for theoretical models of nuclear structure, and relevant input for nuclear astrophysical applications. Of particular importance is a quantitative description of nuclear masses, (n, γ) and (γ, n) rates, α- and β-decay half-lives, fission probabilities, electron and neutrino capture rates, and excitations. A well known example of an exotic excitation mode is the low-lying 1− excited state in neutron-rich nuclei. As one moves away from the valley of β-stability towards the neutron-rich side, modification of the effective nuclear potential results with the appearance of the neutron skin and halo structures. Excitations in these nuclei may give rise to the existence of pygmy dipole resonance (PDR), when loosely bound neutrons coherently oscillate against the isospin saturated proton-neutron core [1,2,3]. The evidence of the low-energy E1 strength has been provided in electromagnetic excitations in heavy-ion collisions in oxygen isotopes [4], and via (γ, γ  ) scattering in lead isotopes [5, 6,7], and N = 82 [8,9,10] isotone chain. The a

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properties of PDR are closely related to the size of the neutron skin [11,12], and are of a particular importance in the calculations of cross-sections for radiative neutron capture in the r-process [13,14]. There is still some discussion on the issue whether the PDR corresponds to a collective, or non-collective excitation phenomena [15,16,17, 18,19]. The β-decay process in neutron-rich nuclei is of a particular importance, because it generates elements with higher Z-values, and sets the time scale for the r-process. Due to the lack of experimental data, β-decay rates of most r-process nuclei have to be determined from various theoretical models. A consistent microscopic treatment of the β-decay in exotic nuclei is therefore necessary. Two microscopic approaches have been successfully applied in large-scale modeling of weak interaction rates: the shell-model [20,21,22] and the proton-neutron quasiparticle random-phase approximation (PN-QRPA) [23, 24]. In comparison to the shell model, there are important advantages of a QRPA approach based on the microscopic self-consistent mean-field framework: it includes the use of global effective nuclear interactions and enables the treatment of arbitrarily heavy systems. In this work we present an analysis of the low-lying excitation modes, spin-isospin resonances, and β-decay process in the framework of the relativistic quasiparticle random-phase approximation.

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2 The relativistic quasiparticle random-phase approximation A consistent and unified treatment of mean-field and pairing correlations is crucial for a quantitative analysis of ground state properties and multipole response of nuclei away from the line of β-stability. In ref. [19], we have formulated the relativistic quasiparticle random-phase approximation (RQRPA) in the canonical single-nucleon basis of the relativistic Hartree-Bogoliubov (RHB) model. The RHB model presents the relativistic extension of the Hartree-Fock-Bogoliubov framework, and provides a unified description of particle-hole (ph) and particle-particle (pp) correlations. In this framework the ground state of a nucleus can be written either in the quasiparticle basis as a product of independent quasiparticle states, or in the canonical basis as a highly correlated BCS-state. By definition, the canonical basis diagonalizes the density matrix and it is always localized. It describes both the bound states and the positive-energy single-particle continuum. The formulation of the RQRPA in the canonical basis is particularly convenient because, in order to describe transitions to the low-lying excited states in weakly bound nuclei, the two-quasiparticle configuration space must include states with both nucleons in the discrete bound levels, states with one nucleon in a bound level and one nucleon in the continuum, and also states with both nucleons in the continuum. The pairing correlations in the RHB model are described by the finite range Gogny interaction D1S [25]. The relativistic QRPA of ref. [19] is fully selfconsistent. For the interaction in the particle-hole channel effective Lagrangians with nonlinear meson selfinteractions have been used, and pairing correlations have been described by the pairing part of the finite range Gogny interaction. Both in the ph and pp channels, the same interactions are used in the RHB equations that determine the canonical quasiparticle states, and in the matrix equations of the RQRPA. This is an essential feature of our calculations, and it ensures that RQRPA amplitudes do not contain spurious components associated with the mixing of the nucleon number in the RHB ground state (for 0+ excitations), or with center-of-mass translational motion (for 1− excitations). The RQRPA configuration space includes also the Dirac sea of negative energy states. Relativistic mean-field and RPA calculations based on effective Lagrangians with nonlinear meson selfinteractions present not only a number of technical problems, but also the description of finite nuclei obtained with these effective interactions is not satisfactory, especially for isovector properties. Several recent analyses have shown that relativistic effective interactions with explicit density dependence of the meson-nucleon couplings provide an improved description of asymmetric nuclear matter, neutron matter, and nuclei far from stability. In ref. [26] we have extended the RHB model to include density dependent meson-nucleon couplings. The effective Lagrangian is characterized by a phenomenological density dependence of the σ, ω, and ρ meson-nucleon vertex functions, adjusted to properties of nuclear matter

and finite nuclei. It has been shown that, in comparison with standard RMF effective interactions with nonlinear meson-exchange terms, the new density-dependent meson-nucleon force DD-ME1 significantly improves the description of asymmetric nuclear matter and of groundstate properties of N = Z nuclei. This is, of course, very important for the extension of RMF-based models to exotic nuclei far from β-stability, and for applications in the field of nuclear astrophysics.

3 Soft dipole mode in neutron rich nuclei The dipole response of very neutron-rich isotopes is characterized by the fragmentation of the strength distribution, its spreading into the low-energy region, and by mixing of isoscalar and isovector modes. The structure of the low-lying dipole strength changes with mass. While in relatively light nuclei the onset of dipole strength in the lowenergy region is due to non-resonant independent single particle excitations of the loosely bound neutrons, in heavier nuclei low-lying dipole states appear that are characterized by a more distributed structure of the RRPA amplitude [18]. Among several peaks characterized by single particle transitions, a single collective dipole state, known as the pygmy dipole resonance (PDR) is identified below 10 MeV. Its amplitude represents a coherent superposition of many neutron particle-hole configurations. A typical example of PDR is obtained in 132 Sn. The corresponding strength distribution for DD-ME1 interaction results with a characteristic peak of the isovector giant dipole resonance (IVGDR) at 15.2 MeV. In addition, among several dipole states in the low-energy region between 7 MeV and 10 MeV that are characterized by single particle transitions, at 7.8 MeV a single pronounced peak is found with a more distributed structure of the RQRPA amplitude, exhausting 1.6% of the energy weighted sum rule (EWSR), where EWSR = (1 + κ)TRK. Here TRK corresponds to the classical Thomas-Reiche-Kuhn sum rule [27], and the enhancement factor from calculation equals κ = 0.35. The peak at 7.8 MeV is composed mainly of 11 neutron ph transitions from loosely bound orbits, each contributing more than 0.1% to the total RRPA amplitude  υ 2 υ 2 υ υ are RRPA ˜ | − |Yph ˜ | = 1, where X and Y ph ˜ |Xph eigenvectors. The low-lying pygmy state does not belong to statistical E1 excitations sitting on the tail of the GDR, but represents a fundamental structure effect: the neutron skin oscillates against the core. The fully self-consistent RHB + RQRPA model with DD-ME1 + D1S combination of effective interactions is also employed in a microscopic description of low-lying dipole excitations for Pb isotopic chain. The PDR strength in Pb isotopes is always concentrated in one peak. The corresponding peak energies are displayed in fig. 1, together with the neutron separation energies. The RQRPA calculations predicts a very weak mass dependence of the PDR excitation energies. The interesting result here is that for Pb isotopes A < 208 the PDR excitation energies are lower than the corresponding one-neutron separation energies, whereas for A > 208 the pygmy resonance is located above

N. Paar et al.: Self-consistent relativistic QRPA studies . . . 10

4 EGTR-EIAR (MeV)

EPYG-RQRPA EPYG-EXP Sn-RHB Sn-EXP

9

8

E[MeV]

533

7

DD-ME1 EXP

3 2 1

Sn

0.06

0.08

0.10

0.12

0.14 rn-rp (fm)

0.16

0.18

0.20

0.22

6

Pb

0.25

rn-rp (fm)

5

200

204

208

212

216

A

Fig. 1. The calculated PDR peak energies and the oneneutron separation energies for Pb isotopes, as functions of the mass number. The open square denotes the experimental position of the PDR in 208 Pb [5]. The RHB results for the neutron separation energies are compared with the experimental values [28].

the neutron emission threshold. These results imply that in isotopes heavier than 208 Pb the observation of the PDR in (γ, γ  ) experiments will be strongly hindered. The crossing point between the PDR and the one-neutron separation energy, which is calculated at A = 208, is in excellent agreement with the recent experimental data on the PDR in 208 Pb [5]. Future (γ, γ  ) experiments on Pb nuclei could confirm the other predictions of the RHB + RQRPA analysis [29].

4 Spin-isospin resonances and the neutron skin in nuclei The determination of neutron density distribution in nuclei provides not only basic nuclear structure information, but it also places important additional constraints on effective interactions used in nuclear models. Recently, we have suggested a new method for determining the difference between the radii of the neutron and proton density distributions along an isotopic chain, based on measurement of the excitation energies of the Gamow-Teller resonances (GTR) relative to the isobaric analog resonances (IAR) [30]. In this analysis we employ the self-consistent RHB plus proton-neutron (PN) RQRPA [31] to calculate the GTR and IAR in the Sn isotopic chain. The RMF effective interaction is DD-ME1. The π- and ρ-meson exchange generate the spin-isospin dependent terms in the ph residual interaction (mπ = 138 MeV, fπ2 /4π = 0.08). The Landau-Migdal zero-range force in the spin-isospin channel is also included in the residual interaction with the strength parameter g  = 0.55. In the T = 1 pp channel of the PN-RQRPA we use the D1S Gogny interaction. For the T = 0 proton-neutron pairing we employ a similar interaction which consists of a short-range repulsive Gaussian with a weaker longer-range attractive Gaussian. The only free parameter, the overall strength, is set to V0 = 250 MeV. In fig. 2 we display the

0.20 0.15 0.10 0.05 112

114

116

118 A

120

122

124

Fig. 2. The PN-RQRPA and experimental [32] differences between the excitation energies of the GTR and IAR, as a function of the calculated differences between the r.m.s. radii of the neutron and proton density distributions of even-even Sn isotopes (upper panel). In the lower panel the calculated differences rn − rp are compared with experimental data [33].

calculated differences between the centroids of the direct spin-flip GT strength and the respective isobaric analog resonances for the sequence of even-even Sn target nuclei in comparison with experimental data [32]. The energy difference between the GTR and the IAR reflects the magnitude of the effective spin-orbit potential, and therefore it is closely related to the proton and neutron density distributions in nuclei. A uniform dependence of the energy spacings between the GTR and IAR on the size of the neutron skin can be observed. In principle, therefore, the value of rn − rp can be determined from the theoretical curve for a given value of EGTR − EIAR . Of course, this necessitates implementation of a model which reproduces the experimental values of the rn − rp , as it is displayed for Sn isotopes in the lower panel of fig. 2.

5 β-decay rates of r-process nuclei The low-lying GT strength distribution, crucial in the description of the β-decay lifetimes, is very sensitive to the single-quasiparticle levels that enter the calculations. In order to reproduce the data on β-decay lifetimes, the relativistic description of single-particle energies around the Fermi surface has to be improved. The inclusion of the ω-meson tensor coupling to nucleon enables the enhancement of the nucleon effective mass, while still retaining a good description of the spin-orbit splitting. We have constructed a new density-dependent effective interaction DD-ME1*, with the value of the nucleon effective mass m∗ = 0.76m. In addition, the low-lying Gamow-Teller strength strongly depends on the proton-neutron pairing in the residual pp QRPA interaction [23]. In the T = 0 and T = 1 pp channel of the residual interaction we use the force described in sect. 4. The overall strength parameter V0 = 225 MeV is adjusted to reproduce the half-life of 130 Cd.

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134

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Te 138

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1. 2. 3. 4.

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193, and by the Gesellschaft f¨ ur Schwerionenforschung (GSI) Darmstadt. N.P. acknowledges support from the Deutsche Forschungsgemeinschaft (DFG) under contract SFB 634. We thank the (Department of Energy’s) Institute for Nuclear Theory at the University of Washington for its hospitality and the Department of Energy for partial support during the completion of this work.

-1

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1

10 10

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136 138 140 142 144 146

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Fig. 3. Calculated half-lives of Sn and Te isotopes with (V0 = 225 MeV), and without (V0 = 0 MeV) T = 0 pairing, in comparison with experimental data [34, 35]. In the right panel the results for the N = 82 isotones are compared with the shellmodel [36], and non-relativistic HFB + QRPA results [23].

In fig. 3 we display β-decay half-lives in Sn and Te isotopes, and N = 82 isotones, in comparison to the available empirical data and the results of similar nonrelativistic mean-field [23] and shell-model [36]. The particular choice of the T = 0 pairing strength V0 = 225 MeV results in β-decay half-lives which overestimate the empirical data for Sn isotopes, while the ones for Te isotopes are slightly underestimated. For N = 82 isotones, our results are in good agreement with the results obtained in similar nonrelativistic QRPA study [23], whereas the shell-model predicts somewhat shorter half-lives [36].

5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

16. 17. 18. 19.

6 Conclusions

20.

The RHB + (PN-)RQRPA model with density dependent effective meson-nucleon couplings has been employed in an analysis of the low-lying excitation modes, spin-isospin resonances, and β-decay process. We have demonstrated that the one-neutron separation energies along Pb isotope chain decrease much faster than the PDR excitation energies. As a result, the PDR energy is located above the neutron emission threshold for A > 208. This implies that the experimental observation of the PDR will be strongly hindered in these isotopes. In addition, it has been shown that the energy spacings between the GTR and IAR provide direct information on the evolution of neutron skinthickness along the Sn isotopic chain. In principle, the value of rn − rp could be determined from the theoretical curve for a given value EGTR − EIAR . Finally, we have applied the PN-RQRPA in the description of the weak interaction rates. The resulting β-decay half lives are in good agreement with both the available empirical data and the results obtained in previous studies of the β-decay process.

21.

This work has been supported in part by the Bundesministerium f¨ ur Bildung und Forschung under project 06 MT

22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36.

Y. Suzuki et al., Prog. Theor. Phys. 83, 180 (1990). J. Chambers et al., Phys. Rev. C 50, R2671 (1994). M. Matsuo, Prog. Theor. Phys. Suppl. 146, 110 (2002). A. Leistenschneider et al., Phys. Rev. Lett. 86, 5442 (2001). N. Ryezayeva et al., Phys. Rev. Lett. 89, 272502 (2002). J. Enders et al., Nucl. Phys. A 724, 243 (2003). A. Richter, Nucl. Phys. A 731, 59 (2004). A. Zilges et al., Phys. Lett. B 542, 43 (2002). T. Hartmann et al., Nucl. Phys. A 719, 308c (2003). A. Zilges, Nucl. Phys. A 731, 249 (2004). N. Tsoneva, H. Lenske, Ch. Stoyanov, Phys. Lett. B 586, 213 (2004). H. Lenske, C.M. Keil, N. Tsoneva, Prog. Part. Nucl. Phys. 53, 153 (2004). S. Goriely, Phys. Lett. B 436, 10 (1998). S. Goriely, E. Khan, Nucl. Phys. A 706, 217 (2002). J. Enders, T. Guhr, A. Heine, P. von Neumann-Cosel, V.Y. Ponomarev, A. Richter, J. Wambach, Nucl. Phys. A 741, 3 (2004). D. Sarchi, P.F. Bortignon, G. Colo, Phys. Lett. B 601, 27 (2004). J.P. Adams, B. Castel, H. Sagawa, Phys. Rev. C 53, 1016 (1996). D. Vretenar, N. Paar, P. Ring, G.A. Lalazissis, Nucl. Phys. A 692, 496 (2001). N. Paar, P. Ring, T. Nikˇsi´c, D. Vretenar, Phys. Rev. C 67, 034312 (2003). K. Langanke, G. Mart´inez-Pinedo, Rev. Mod. Phys. 75, 819 (2003). N. Michel, J. Okolowicz, F. Nowacki, M. Ploszajczak, Nucl. Phys. A 703, 202 (2002). E. Caurier, P. Navr´ atil, W.E. Ormand, J.P. Vary, Phys. Rev. C 66, 024314 (2002). J. Engel, M. Bender, J. Dobaczewski, W. Nazarewicz, R. Surman, Phys. Rev. C 60, 014302 (1999). I.N. Borzov, Phys. Rev. C 67, 025802 (2003). J.F. Berger, M. Girod, D. Gogny, Nucl. Phys. A 428, 25c (1984). T. Nikˇsi´c et al., Phys. Rev. C 66, 024306 (2002). H. Sagawa, T. Suzuki, Nucl. Phys. A 687, 111c (2001). G. Audi, A.H. Wapstra, Nucl. Phys. A 595, 409 (1995). N. Paar, T. Nikˇsi´c, D. Vretenar, P. Ring, Phys. Lett. B 606, 288 (2005). D. Vretenar, N. Paar, T. Nikˇsi´c, P. Ring, Phys. Rev. Lett. 91, 262502 (2003). N. Paar, T. Nikˇsi´c, D. Vretenar, P. Ring, Phys. Rev. C 69, 054303 (2004). K. Pham et al., Phys. Rev. C 51, 526 (1995). A. Krasznahorkay et al., Phys. Rev. Lett. 82, 3216 (1999). NUBASE database, http://csnwww.in2p3.fr/amdc. I. Dillmann et al., Phys. Rev. Lett. 91, 162503 (2003). G. Martinez-Pinedo, K. Langanke, Phys. Rev. Lett. 83, 4502 (1999).

Eur. Phys. J. A 25, s01, 535–538 (2005) DOI: 10.1140/epjad/i2005-06-065-5

EPJ A direct electronic only

Deformations and electromagnetic moments of light exotic nuclei H. Sagawa1,a , X.R. Zhou2,b , X.Z. Zhang3 , and Toshio Suzuki4 1 2 3 4

Center for Mathematical Sciences, University of Aizu, Aizu-Wakamatsu, Fukushima 965-8560, Japan Department of Physics, Tsinghua University, Beijing, PRC China Institute of Atomic Energy, Beijing, PRC Department of Physics, College of Humanities and Sciences, Nihon University, Sakurajosui 3-25-40, Setagaya-ku, Tokyo 156-8550, Japan Received: 12 November 2004 / Revised version: 14 February 2005 / c Societ` Published online: 29 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Structure of carbon and neon isotopes is investigated by deformed Skyrme Hartree-Fock and shell model calculations. We point out that the quadrupole deformations of C and Ne isotopes have strong isotope dependence as a typical example of the evolution of deformations in nuclei. It is shown also that the quadrupole moments and the magnetic moments of the odd C isotopes depend clearly on assigned configurations, and their experimental data will be useful to determine the spin-parities and the deformations of the ground states of these nuclei. The electric quadrupole (E2) transitions in even C and Ne isotopes are also studied. The isotope dependence of the E2 transition strength is reproduced properly, although the calculated strength overestimates an extremely small observed value in 16 C. PACS. 21.10.Ky Electromagnetic moments – 21.60.-n Nuclear structure models and methods

1 Introduction Nuclei far from the stability lines open a new test ground for nuclear models. Recently, many experimental and theoretical efforts have been paid to study the structure and reaction mechanism in nuclei near drip lines. Modern radioactive nuclear beams and experimental detectors reveal several unexpected structure of light nuclei with the mass number A ∼ (10–24) such as existence of halo and skin [1], modifications of shell closures [2] and Pigmy resonances in electric dipole transitions [3]. One of the current topics is a large quenching of the electric quadrupole (E2) transition between the first excited 2+ state and the ground state in 16 C [4,5]. The isotope dependence of deformation is an interesting subject to study in relation to the evolution of deformation in quantum many-body systems as a manifestation of spontaneous symmetry breaking effect. To this end, C and Ne isotopes are promising candidates since all isotopes between the proton and neutron drip lines will be available in future experiments within next few years. The effect of spontaneous symmetry breaking effect is a general phenomenon known in many fields of physics. In molecular physics, the spontaneous symmetry breaking was disa

Conference presenter; e-mail: [email protected] b Present address: Department of Physics, Liaoning Normal University, Dalian, PRC.

covered by Jahn and Teller in 1937 [6]. The coupling to the quadrupole vibration is the main origin of the static deformation in both molecules and atomic nuclei [7]. On the other hand, the pairing correlations in nuclei work to stabilize the spherical symmetry. A unique and essential feature of the evolution of deformation in atomic nuclei will appear in the competition between the deformation deriving particle-vibration coupling and the pairing correlations [8].

2 Deformations of carbon and neon isotopes We investigate the neutron number dependence of deformations along the chains of C and Ne isotopes. For this purpose, we perform deformed HF+BCS calculations with a Skyrme interaction SGII. The axial symmetry is assumed for the deformed HF potential. The pairing interaction is taken to be a density-dependent pairing interaction in the BCS approximation;   ρ(r) δ(r1 − r2 ), (1) V (r1 , r2 ) = V0 1 − ρ0

where ρ(r) is the HF density at r = (r1 + r2 )/2 and ρ0 is chosen to be 0.16 fm−3 . The pairing strength is taken to be −410 MeV · fm3 for both neutrons and protons. A smooth energy cut-off is employed in the BCS calculations [9].

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Fig. 2. Isotope dependence of deformations of C and Ne isotopes with SGII interaction. The points with error bars show the cases in which two deformation minima are found within the energy difference of 0.1 MeV.

Fig. 1. Deformed HF + BCS calculations with SGII interaction; (a) for C isotopes and (b) for Ne isotopes. The densitydependent pairing interaction (1) is adopted in the calculations. The strength of spin-orbit force is modified to be 60% of the original one in the HF calculations of C isotopes. See the text for details.

Figure 1 shows the binding energy surfaces for evenmass C and Ne isotopes as a function of the quadrupole deformation parameter β2 with SGII interaction. The spin-orbit interaction of SGII interaction is reduced to be 60% of the original strength to enhance the deformation effect [10]. The energy minimum in 12 C appears at oblate deformation with β2 = −0.32. The energy minimum becomes spherical in 14 C because of the neutron closed shell effect. For heavier C isotopes 16 C and 18 C, two minima appear both in the prolate and oblate sides. In 18 C, the ground state has the largest deformation at β2 = 0.36, while the local minimum appears at the oblate side with β2 ∼ −0.3. The deformations become oblate in 20 C and 22 C. The HF calculation with the original spinorbit strength gives a spherical shape for 22 C. The deformations of Ne isotopes are shown in fig. 1(b). The similar neutron number dependence to that of C isotopes is found in Ne isotopes. In general, the energy surfaces are shallow in even Ne isotopes. The energy minimum of 18 Ne is very close to the spherical shape as ex-

pected due to the N = 8 shell closure. The prolate deformations are found in 20 Ne and 22 Ne and then the deformation minimum is oblate in 24 Ne. The spherical and oblate energy minima are almost degenerate in energy in 26 Ne. The energy minimum of 28 Ne is very flat and depends on the adopted interaction. Namely the SGII interaction gives a prolate minimum, while the SIII interaction gives an oblate minimum. The nucleus 30 Ne is found to show a spherical shape due to another shell closure N = 20. We can see also a prolate local minimum in the case of 30 Ne, whose binding energy is very close to that of the spherical minimum. Then, 32 Ne becomes prolate again as a typical nucleus next to the closed shell nucleus. Figure 2 shows the isotope dependence of the quadrupole deformation parameter β2 at the binding energy minima for C and Ne isotopes. Blocked deformed Skyrme HF + BCS calculations are performed for odd carbon isotopes. The results show that the ground state of + 17 C is prolate with J π = 32 while that of 19 C is oblate + + with J π = 32 . In 19 C, the energy minimum of J π = 12 + is very close to that of J π = 32 having almost the same oblate deformation β2 ∼ −0.36. These spin-parities of the ground states are consistent with our shell model calculations [11]. The spin of the ground state of 17 C was assigned + as 3/2 in the magnetic moment measurement [12]. The + spin of 19 C was assigned as 1/2 in the Coulomb break-up reactions [13], while there is still controversial argument on the experimental assignment in ref. [14]. In fig. 2, the two isotopes show a clear manifestation of the evolution of the nuclear deformation induced by the deformation driving force in the mean field potential [8]. The deformation effect in the C and Ne isotopes is unique compared with that in rare-earth nuclei in a sense that both prolate and oblate deformations appear clearly in the beginning of the closed shell and at the end of the closed shell.

H. Sagawa et al.: Deformations and electromagnetic moments of light exotic nuclei

with a = 0.82, b = −0.25, c = 0.12 and d = −0.36 to reproduce the calculated values for 12 C and 16 C in ref. [16]. Both the neutron (ν) and proton (π) polarization charges decrease as the neutron excess increases. The effective charges are given by eeff = e(1/2 − tz ) + epol .

(3)

The Q-moments obtained by using these polarization charges are shown in fig. 3(a). Open circles denote results of the shell model calculations with the use of epol . Single-particle or -hole values with the use of epol are given by open triangles. The configurations for 9 C and 11 C are 17 C νp3/2 and νp−1 3/2 , respectively. The configurations for −1 19 2 5 and C are νd5/2 1s1/2 and νd5/2 (νd5/2 ), respectively, + + for the 5/2 state. For the 3/2 state of 17 C, a case for a single particle configuration of νd3/2 is given. Filled triangles are obtained for νd±2 5/2 1s1/2 configuration with the use of epol . The νd25/2 (J = 2)1s1/2 and νd−2 5/2 (J = 2)1s1/2 are possible simple configurations for 17 C and 19 C, respectively, since the νd35/2 or νd35/2 1s21/2 configuration corresponding to the middle of the d5/2 shell results in the vanishing of the Q-moments. The + Q-moments are given by ∓ 25 enpol Qsp (d5/2 ) for 3/2 and + ∓ 47 enpol Qsp (d5/2 ) for 5/2 in the case of the νd±2 5/2 (J = 2)1s1/2 configuration. Here, enpol is the neutron polarization charge and Qsp (d5/2 ) is the single particle value of the Q-moment for d5/2 . Note that the signs of the Q-moments for 17 C and 19 C are opposite. The shell model values of the Q-moments are obtained by the admixture among these configurations, and their magnitudes are usually enhanced compared to those of the simple configurations. Nevertheless, the difference of the signs between 17 C and 19 C can be understood from those of the simple configurations. Calculated values for the magnetic (μ) moments are shown in fig. 3(b). Here, gseff /gsfree = 0.9 is used for neutron. The values of the μ-moments are found to be sensitive to the configurations as in the case for the Q-moments, which is useful to find out the spin-parities and the deformations of the ground states of these nuclei. Especially, the spin assignments of 17 C and 19 C are quite consistent between the deformed HF and the shell model

Q(mb)

We study electromagnetic moments and transitions in C and Ne isotopes by the shell model calculations [15] in comparison with the deformed HF results [10]. We first discuss the Q-moments. The WBP interaction is used as an effective interaction within the 0¯hω space. We adopt state-dependent polarization charges which are obtained by the microscopic particle vibration coupling model (Hartree-Fock + Random Phase Approximation [16]). These polarization charges can be parameterized as   Z N −Z N −Z Z epol τz (2) + c+d =a +b A A A A e

80

(a)

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s.p. (s.h.) +- 2 1 d5/2 s 1/2 HF (SGII)

20 0 -20 -40 -60 -80

A 9 11 π - J 3/2 3/2

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g (μ Ν )

3 Q-moments, μ-moments and E2 transitions

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17 17 + + 3/2 5/2

19 19 + + 3/2 5/2

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A

9 11 13 15 17 17 17 19 19 19 π J 3/2- 3/2 - 1/2 1/2+1/2+ 3/2+5/2+1/2+ 3/2+5/2+

Fig. 3. Q-moments and magnetic moments for the odd C isotopes. (a) Open triangles denote Q-moments of single-particle or -hole values, while filled triangles give the results of the 0d±2 1s1/2 configuration. These values include the effects of 5/2 the polarization charges, epol in eq. (2). (b) Open circles denote the results of the magnetic g-factors of shell model calculations obtained with the use of WBP interaction and gseff = 0.9gs , while the HF results are obtained by using deformed HF wave functions and shown by open boxes. The filled circles are the experimental values taken from refs. [17, 18, 19, 12, 20].

+

results. The 5/2 state is excluded from the ground state by the β-decay experiment. Let us now discuss the E2 transitions in the even C and Ne isotopes. Calculated and experimental B(E2) val+ ues for the 2+ 1 → 0g.s. transitions are shown in fig. 4. The shell model values obtained with the use of epol are larger than the experimental values except for 10 C, for which larger effective charges of eqs. (2) and (3) epeff = 1.38 and eneff = 0.71 are needed. For 12–16 C, the isotope dependence of the observed values [20, 4] is well explained by that of epol , but their magnitudes are smaller than the calculations. In particular, the observed B(E2) value is quite small for 16 C–[4], which suggests some exotic structure yet unknown in the isotopes, for example, the shape coexistence of prolate and oblate deformations expected

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(a) C isotopes

16

The configuration dependence of the Q-moments and μ-moments in the odd C isotopes, which can be attributed to the deformation effects, is also pointed out by using the shell model wave functions. This dependence can be used to determine the spin-parities as well as the deformation properties of the ground states of the isotopes. The isotope dependence of the B(E2) values in even C and Ne isotopes is reproduced well by the calculations, while the experimental values are found to be smaller in 12–16 C, in particular, in 16 C where the observed B(E2) value almost vanishes. This suggests an exotic structure of 16 C still to be found out.

Exp. WBP HO WBP HF+PV MK HO

14

+

B(E2:2 −>0 )

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+

10 8 6 4 2 0

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This work is supported in part by the Japanese Ministry of Education, Culture, Sports, Science and Technology by Grantin-Aid for Scientific Research under the program No. (C(2)) 16540259.

References

Fig. 4. B(E2) values of the 2+ 1 → 0g.s. transitions; (a) C isotopes and (b) Ne isotopes. Filled and open squares show the results of the shell model calculations with the use of the coneff stant effective charges eeff p = 1.3, en = 0.5 and the harmonicoscillator wave functions with b = 1.64 fm for C isotopes and b = 1.83 fm for Ne isotopes. The WBP and MK interactions are used to calculate the shell model wave functions for the filled and open squares, respectively. Filled (WBP) and open (MK) diamonds are obtained with the use of HF wave functions and the isotope-dependent polarization charges epol given by eq. (2). Filled circles show experimental values [20, 4].

from the deformed HF calculations. It would be also interesting to find out if the B(E2) value increases for 18 C as the calculation predicts. This increase comes from that of the neutron contribution.

4 Summary We have studied the isotope dependence of deformation in C and Ne isotopes by using the deformed HF calculations with BCS approximation. We found clear isotope dependence of the deformation change as a manifestation of the dynamical evolution of nuclear deformation.

1. I. Tanihata et al., Phys. Rev. Lett. 55, 2676 (1985). 2. A. Ozawa et al., Phys. Rev. Lett. 84, 5493 (2000). 3. A. Leistenschneider et al., Phys. Rev. Lett. 86, 5442 (2001). 4. N. Imai et al., Phys. Rev. Lett. 92, 062501 (2004). 5. Z. Elekes et al., Phys. Lett. B 586, 34 (2004). 6. H.A. Jahn, E. Teller, Proc. R. Soc. London, Ser. A 161, 220 (1937). 7. P.-G. Reinhard, E.W. Otten, Nucl. Phys. A 420, 173 (1984). 8. W. Nazarewicz, Int. J. Mod. Phys. E 2, 51 (1993); Nucl. Phys. A 574, 27c (1994). 9. M. Bender, K. Rutz, P.-G. Reinhard, J.A. Maruhn, Eur. Phys. J. A 8, 59 (2000); P.-G. Reinhard, the computer code SKYAX, unpublished. 10. H. Sagawa, X.R. Zhou, X.Z. Zhang, T. Suzuki, to be published in Phys. Rev. C. 11. T. Suzuki, H. Sagawa, K. Hagino, in the Proceedings of the International Symposium on “Frontiers of Collective Motions (CM2002)”. (World Scientific, 2003) p. 236; H. Sagawa, T. Suzuki, K. Hagino, Nucl. Phys. A 722, 183 (2003). 12. H. Ogawa et al., Eur. Phys. J. A 13, 81 (2002). 13. D. Bazin et al., Phys. Rev. C 57, 2156 (1998); T. Nakamura et al., Phys. Rev. Lett. 83, 1112 (1999); V. Maddalena et al., Phys. Rev. C 63, 024613 (2001). 14. Rituparna Kanungo, I. Tanihata, Y. Ogawa, H. Toki, A. Ozawa, Nucl. Phys. A 677, 171 (2000). 15. E.K. Warburton, B.A. Brown, Phys. Rev. C 46, 923 (1992); OXBASH, the Oxford, Buenos-Aires, Michigan State, Shell Model Program; B.A. Brown et al., MSU Cyclotron Laboratory Report No. 524, 1986. 16. H. Sagawa, K. Asahi, Phys. Rev. C 63, 064310 (2001). 17. K. Matsuta et al., Nucl. Phys. A 588, 153c (1995). 18. P. Raghaven, At. Data Nucl. Data Tables 42, 189 (1989). 19. K. Asahi et al., AIP Conf. Proc. 570, 109 (2001). 20. S. Raman et al., At. Data Nucl. Data Tables 36, 1 (1987).

Eur. Phys. J. A 25, s01, 539–540 (2005) DOI: 10.1140/epjad/i2005-06-082-4

EPJ A direct electronic only

Skyrme-QRPA calculations of multipole strength in exotic nuclei J. Terasaki1,2,3,4,a , J. Engel1 , M. Bender5 , J. Dobaczewski2,3,4,6 , W. Nazarewicz2,3,6 , and M. Stoitsov2,3,4,7 1 2 3 4 5 6 7

Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599-3255, USA Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA Physics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831, USA Joint Institute for Heavy-Ion Research, Oak Ridge, TN 37831, USA Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA Institute of Theoretical Physics, Warsaw University, ul. Ho˙za 69, 00-681 Warsaw, Poland Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Science, Sofia 1784, Bulgaria Received: 18 October 2004 / Revised version: 25 January 2005 / c Societ` Published online: 11 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We present test calculations of the quasiparticle random-phase approximation with Skyrme and delta-pairing forces. We examine the convergence of solutions in the isoscalar 0 + channel as we increase the number of single-quasiparticle states, and the separation of spurious states from physical excited states in the isoscalar 1− channel. Our calculation is fully self-consistent as it neglects no component of the interaction. We focus on Sn isotopes near the two-neutron drip line. PACS. 21.30.Fe Forces in hadronic systems and effective interactions – 21.60.Jz Hartree-Fock and randomphase approximations – 24.30.Cz Giant resonances

1 Introduction One of the most important subjects in nuclear structure is the nature of nuclei near the particle drip lines. In these regions, some of the basic concepts developed in studies of stable nuclei may need to be modified. An urgent task for theoreticians is to develop methods which are reliable enough to investigate those unstable nuclei. The Quasiparticle Random-Phase Approximation (QRPA) is one of the general and well-developed methods for calculating excited states, and we expect it to work well in all nuclei. (The approximation is reliable only in the small-amplitude limit [1].) A fully self-consistent QRPA calculation with a Skyrme force, however, is not easy because of technical difficulties, and in typical applications self-consistency is broken and/or some components of the interaction neglected (see [2]). In this paper, we exhibit a self-consistent QRPA calculation and examine its accuracy. This is important preparation for an investigation of exotic nuclei that is free from theoretical ambiguities. In the next section, we explain our procedure for solving the QRPA equations and results of calculations, while sect. 3 contains conclusions.

2 Calculation Our QRPA calculation is based on the “matrix formulation” (see, e.g., [1]), with spherical symmetry assumed. a

Conference presenter; e-mail: [email protected]

The explicit expressions for the dynamical equations and matrix elements of the interactions, as well as the definitions of the transition operators, are given in [2]. First, we solve the Hartree-Fock-Bogoliubov (HFB) equation with the method of ref. [3], in which discretized continuumenergy quasiparticle wave functions are obtained in a spherical box. Then we obtain canonical-basis wave functions by diagonalizing the nuclear one-body density matrix. We calculate the quasiparticle energies, matrix elements of the interaction, and uv-factors of the special Bogoliubov transformation within this basis (the transformation connects the canonical basis to a quasiparticle basis associated with the HFB ground state), and then use those quantities to obtain the Hamiltonian matrix of the QRPA, which we diagonalize to get QRPA wave functions. Because the box makes our continuum solutions discrete, we introduce a width parameter1 when we display strength functions. To test the applicability of our method near the neutron drip line, we performed calculations for 174 Sn, which the Skyrme parameter set SkM∗ with volume-type delta pairing interaction places very close to the two-neutron drip line. The results in the isoscalar 0+ channel are shown in fig. 1, which displays three curves calculated within different single-particle spaces. We include single-particle 1 This parameter depends on the eigenvalue Ek of the QRPA solution; it is constant (100 keV) if Ek is lower than the neutron threshold energy, and increases above threshold (to 3 MeV around Ek = 20 MeV) [2].

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Fig. 1. Strength functions in the isoscalar 0+ channel of 174 Sn. 2 The thick (thin) line was obtained with vcrit = 10−16 (10−8 ), for the neutrons, and εcrit = 200 (100) MeV, for the protons. 2 The result with vcrit = 10−12 and εcrit = 150 MeV is almost identical to the thick line.

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states for which occupation probabilities are larger than a 2 (which is set to a very small value cutoff parameter vcrit so that we omit little of physical significance) if the system is paired in the HFB ground state, or those for which the Hartree-Fock (HF) energies are lower than a cutoff parameter εcrit , if the system is unpaired. In 174 Sn, the neutrons are paired, and protons are unpaired in the HFB calculation. Figure 1 demonstrates that our solution con2 small enough and εcrit large verges when we make vcrit enough. Since the neutrons of 174 Sn are paired, there is a spurious state associated with particle-number nonconservation. We checked that the transition strengths for the particle-number operator are smaller than 10−5 to the real excited states. The isoscalar 1− mode is challenging technically because of spurious center-of-mass motion; a careful calculation is necessary to accurately separate the spurious state from real excited states. In calculations that are not fully self-consistent, the strength is often corrected by including a term −ηrY1M (Ω) (where η = (5/3) r 2  with r 2  the mean value in the HFB ground state) in the isoscalardipole transition operator (see [4] for derivation of η). We performed calculations of the strength functions with and without the correction term and obtained identical results for real excited states; our 1− solutions are therefore essentially free from contamination. In a perfect calculation, the spurious state would have zero energy and the correction term would remove strength only from this state. In our calculation of 174 Sn (120 Sn), even though the spurious state energy is 0.319 (0.713) MeV, the correction removes almost no strength except from this spurious state. This check is important for proving that the strong enhancement of strength at low energy in nuclei near the neutron drip line, illustrated in fig. 2, is not an artifact of the calculation. Finally we mention that the energy-weighted sum rules of the 0+ , 1− , and 2+ modes of 120,174 Sn are satisfied with errors of ±1% at most.

0

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Fig. 2. Strength function in the isoscalar 1− channel of 174 Sn (upper) and 120 Sn (lower). The low-energy strength is greatly enhanced in the drip-line nucleus.

3 Conclusion We have performed fully self-consistent QRPA calculations with Skyrme and delta-pairing interactions, without neglecting any of their components, and showed them to be numerically accurate. Investigations of the structure of excited states near the neutron drip line, as well as more systematic calculations, are in progress. This work was supported in part by the U.S. Department of Energy, Contract Nos. DE-FG02-97ER41019 (University of North Carolina), DE-FG02-96ER40963 (University of Tennessee), DE-AC05-00OR22725 with UT-Battelle, LLC (Oak Ridge National Laboratory), DE-FG05-87ER40361 (Joint Institute for Heavy Ion Research), and W-31-109-ENG-38 (Argonne National Laboratory); by the National Science Foundation, Contract No. 0124053 (U.S.-Japan Cooperative Science Award); by the Polish Committee for Scientific Research (KBN), Contract No. 1 P03B 059 27; and by the Foundation for Polish Science (FNP).

References 1. D. Rowe, Nuclear Collective Motion, Methods and Theory (Mathuen, London, 1970). 2. J. Terasaki, J. Engel, M. Bender, J. Dobaczewski, W. Nazarewicz, M. Stoitsov, Phys. Rev. C 71, 034310 (2005). 3. J. Dobaczewski, H. Flocard, J. Treiner, Nucl. Phys. A 422, 103 (1984). 4. B. Agrawal, S. Shlomo, A. Sanzhur, Phys. Rev. C 67, 034314 (2003).

Eur. Phys. J. A 25, s01, 541–542 (2005) DOI: 10.1140/epjad/i2005-06-151-8

EPJ A direct electronic only

On the non-unitarity of the Bogoliubov transformation due to the quasiparticle space truncation J. Dobaczewski1,2,3,4,a , P.J. Borycki2,5,b , W. Nazarewicz1,2,4 , and M. Stoitsov2,3,4,6 1 2 3 4 5 6

Institute of Theoretical Physics, University of Warsaw, ul. Ho˙za 69, PL 00681 Warsaw, Poland Department of Physics, University of Tennessee, Knoxville, TN 37996, USA Joint Institute for Heavy Ion Research, Oak Ridge, TN 37831, USA Physics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831, USA Institute of Physics, Warsaw University of Technology, ul. Koszykowa 75, PL 00662 Warsaw, Poland Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Science, Sofia-1784, Bulgaria Received: 18 January 2005 / Revised version: 10 March 2005 / c Societ` Published online: 11 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We show that due to the energy cutoff in the Hartree-Fock-Bogoliubov quasiparticle space, the Bogoliubov transformation becomes non-unitary. We propose a method of restoring the unitarity by introducing a truncated single-particle Hilbert space, in which the HFB equations are to be solved. PACS. 21.30.Fe Forces in hadronic systems and effective interactions – 21.60.Jz Hartree-Fock and randomphase approximations – 24.30.Cz Giant resonances

1 Introduction

2 Method

Skyrme energy density functionals are among the most commonly used in the self-consistent mean-field nuclear structure calculations. The pairing component of the functional usually corresponds to a zero-range interaction in the coordinate space [1], which is equivalent to a constant (infinite range) interaction in the momentum space. Therefore, an energy cutoff followed by a pairing strength refit is necessary to regularize the results, and the number of active quasiparticle states becomes finite. On the other hand, the dimension of the particle space is either infinite (coordinate representation) or truncated for reasons that are not related to the pairing regularization. This implies different dimensions of particle and quasiparticle spaces and, therefore, renders the Bogoliubov transformation non-unitary. As a result, the pairing tensor is no longer antisymmetric, but it acquires a finite symmetric component. In this work, we propose a method of restoring the unitarity of the Bogoliubov transformation, while keeping the number of quasiparticle states limited. The method is based on a truncation of the particle space and solving the Hartree-Fock-Bogoliubov [2] (HFB) equations in this truncated Hilbert space. The proposed truncation scheme accommodates all the particle states that are needed within a given truncation of the quasiparticle space.

By using the code HFBTHO [3], we perform the HFB calculations within the particle space of 20 harmonic oscillator shells, which leads to the single-particle energies of 200 MeV and above. When no truncation is performed in the quasiparticle space, the Bogoliubov transformation is unitary, and this guarantees that the pairing tensor κ is antisymmetric. This is no longer true for the finite energy cutoff. The inset in fig. 1 shows the maximum matrix element of the symmetric and antisymmetric parts of the pairing tensor as functions of the cutoff energy Ec in the quasiparticle space. Typically, the former does not exceed 1% of the latter; however, a non-zero symmetric component means that the fermion quasiparticle state representing the HFB ground state does not exist. Usually one simply disregards this symmetric part in the Skyrme-HFB calculations. Our method ensures the antisymmetricity of the pairing tensor and, at the same time, keeps the number of quasiparticle states limited. The approach is based on finding an optimal truncated particle space, dictated by a given quasiparticle truncation, in which the HFB equations are solved without any further cutoff. Full-space diagonalization of the HFB equations is necessary only to provide the aforementioned optimal basis. The Singular Value Decomposition (SVD) [4] is an algebraic method, which, by means of finding the so-called singular values, orders orthonormal basis states according to their importance for decomposition of a rectangular matrix into a sum of components. We use it to decompose

a b

e-mail: [email protected] Conference presenter.

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Number of States Fig. 1. Total energies of 120 Sn obtained for the Sly4 Skyrme functional and different values of the energy and SVD cutoffs. Stars correspond to the standard HFB solutions and diamonds to two values of the SVD cutoff: vc = 10−3 and 10−2 . The maximum matrix element of the antisymmetric (left scale) and symmetric (right scale) parts of the pairing tensor are shown in the inset.

the combined matrix [B ∗ A∗ ], where B and A are the Bogoliubov matrices corresponding to a non-unitary transformation, and assemble the optimal basis by taking only those particle states which have the corresponding singular values above a certain SVD cutoff, vc . Since for each value of the SVD cutoff the dimension of the resulting particle space is different, one has to refit the pairing strength as function of vc . We do it so that the pairing gap is the same in both steps: in the full-space solution obtained for a given energy cutoff and in the truncated-space solution. Our calculations are carried out according to the following scheme: a Self-consistent solution of the HFB equations in the full space. b Singular Value Decomposition of the combined matrix [B ∗ A∗ ] corresponding to the full-space solution. c Defining the truncated particle space by keeping the SVD states that correspond to singular values above the SVD cutoff vc . d Self-consistent solution of the HFB equations in the truncated particle space. e Fitting the pairing strength by repeating step (d) with different pairing strengths until the pairing gaps in the full and truncated spaces are equal.

-3

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SVD cutoff Fig. 2. Number of neutron particle states in 120 Sn in the truncated spaces (solid lines) and numbers of quasiparticle states below the cutoff energies (dotted lines) as functions of the SVD cutoff, for different values of the energy cutoff.

For cutoff energies above 30 MeV, the total energy is stable up to about 200 keV. For any fixed cutoff energy, the method is also very stable (< 100 keV) with respect to the SVD cutoff. Therefore, our method allows us to perform the HFB calculations with satisfying precision for relatively small cutoff energies and dimensions of the particle space. While the two-step character of the method, and necessity to refit the pairing strength, makes the method significantly more computationally extensive than the standard HFB approach, the procedure allows for usual interpretation in terms of Bogoliubov product states. In order to implement the pairing readjustments, one could use the Green-function regularization methods [5], which will be considered in future work. This work was supported in part by the U.S. Department of Energy under Contract Nos. DE-FG02-96ER40963 (University of Tennessee), DE-AC05-00OR22725 with UT-Battelle, LLC (Oak Ridge National Laboratory); by the National Nuclear Security Administration under the Stewardship Science Academic Alliances program through DOE Research Grant DEFG03-03NA00083; by the Polish Committee for Scientific Research (KBN) under contract No. 1 P03B 059 27; and by the Foundation for Polish Science (FNP).

References 3 Results Figure 2 shows the number of states in the truncated particle spaces as functions of the SVD cutoff vc for various cutoff energies Ec . For large vc or Ec , these numbers are close to the numbers of quasiparticle states (shown by dotted lines); however, for small vc , additional particle states are necessary to properly represent the kept quasiparticle states. Total energies obtained by solving the HFB equations in the truncated particle spaces are shown in fig. 1.

1. J. Dobaczewski, W. Nazarewicz, T.R. Werner, J.F. Berger, C.R. Chinn, J. Decharg´e, Phys. Rev. C 53, 2809 (1996). 2. P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, New York, 1980). 3. M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, P. Ring, to be published in Comput. Phys. Commun. 4. W.H. Press, B.P. Flannery, P.A. Teukolsky, W.T. Vetterling, Numerical Recipies (Cambridge University Press, Cambridge, 1986). 5. A. Bulgac, Y. Yu, Phys. Rev. Lett. 88, 042504 (2002).

Eur. Phys. J. A 25, s01, 543–544 (2005) DOI: 10.1140/epjad/i2005-06-100-7

EPJ A direct electronic only

2-D lattice HFB calculations for neutron-rich zirconium isotopes A. Blazkiewicza , V.E. Oberacker, and A.S. Umar Department of Physics and Astronomy, Vanderbilt University, Nashville, TN, 37235, USA Received: 20 October 2004 / Revised version: 23 March 2005 / c Societ` Published online: 13 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Using the Hartree-Fock-Bogoliubov (HFB) mean-field theory in coordinate space, we investigate ground-state properties of the zirconium isotopes from the line of stability up to the two-neutron dripline (102–122 Zr). In particular, we calculate two-neutron separation energies, quadrupole moments, and r.m.s. radii for protons and neutrons. We find large prolate ground-state deformations for the isotopes 102 Zr through 112 Zr, and the spherical shapes starting from 114 Zr up to the dripline nucleus 122 Zr. PACS. 21.60.-n Nuclear structure models and methods – 21.60.Jz Hartree-Fock and random-phase approximations

1 Introduction

2 Results

The neutron-rich A ∼ 100 region is known for its competition between various coexisting nuclear shapes. The isotopes in this region are produced in the fission of transuranic elements and have been studied via γ-ray spectroscopy techniques. Among these are the zirconium isotopes which possess rapidly changing nuclear shapes when the neutron number changes from 56 to 60 [1]. In this paper we study the ground-state properties of neutron-rich zirconium nuclei. For this purpose, we solve the Hartree-Fock-Bogoliubov (HFB) equations for deformed, axially symmetric nuclei in coordinate space on a 2-D lattice [2, 3]. Recently, triple-gamma coincidence experiments have been carried out with Gammasphere at LBNL [4] which have determined half-lives and quadrupole deformations of several neutron-rich zirconium, cerium, and samarium isotopes. Furthermore, laser spectroscopy measurements [5] for zirconium isotopes have yielded precise r.m.s. radii in this region. These mediummass nuclei are among the most neutron-rich isotopes (N/Z ≈ 1.6) for which spectroscopic data are available. It is therefore of great interest to compare these data with the predictions of the self-consistent HFB mean-field theory. In our calculations we find large ground-state prolate deformations and the spherical shapes as well. The same results were also obtained by calculations, which utilize the Transformed Harmonic Oscillator basis (THO) approach [6].

We have solved, for the first time, the computationally challenging Hartree-Fock-Bogoliubov (HFB) continuum problem for deformed, axially symmetric even-even nuclei in coordinate space on a 2-D lattice, without any further approximations. Our computational technique (Basis-Spline collocation and Galerkin method) [7,8,9,10, 11, 12] is particularly well suited to study ground-state properties of nuclei near the driplines. The unique feature of our HFB code is that it treats the continuum wave functions consistently on the lattice and takes into account the strong coupling to high-energy continuum states, up to an equivalent single-particle energy of 60 MeV or higher. For the p-h channel, the Skyrme (SLy4) effective N-N interaction is utilized, and for the p-p and h-h channel we use a delta interaction. For axially symmetric nuclei, we diagonalize the HFB Hamiltonian separately for fixed isospin projection q and angular-momentum quantum number Ω (typically up to 21/2). For fixed values of q and Ω, we obtain 4 · Nr · Nz eigenstates, typically up to 1000 MeV. In particular, we recently calculated the properties of the zirconium (102–122 Zr) isotope chain up to the two-neutron dripline. Figure 1 shows the calculated two-neutron separation energies for the zirconium isotope chain. The dripline is located where the separation energy becomes zero. As one can see our HFB calculations predict the dripline nucleus to be at mass number 122. We also give a comparison with the latest available experimental data up to the isotope 110 Zr [13]. In fig. 2 we show the intrinsic proton and neutron quadrupole moments. We find very strong prolate deformations for the 102–112 Zr isotopes and the spherical shapes for the remaining isotopes in the chain including

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References

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Fig. 3. The root-mean-square radii for the chain of zirconium isotopes.

Fig. 1. Two-neutron separation energy.

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the dripline nucleus 122 Zr. Our HFB lattice code predicts the 112 Zr isotope to have the largest intrinsic ground-state quadrupole moment; for the corresponding quadrupole deformation parameter β2 of the neutron density distribution we find the value 0.47. The experimental deformations for protons are available for two isotopes, 102 Zr and 104 Zr [4]. Our theoretical results for these two nuclei (β2 = 0.42, 0.43) agree very well with the experimental data of β2102 = 0.42, and β2104 = 0.45. In fig. 3 we plot the root-mean-square radii of protons and neutrons. We can clearly observe the presence of the neutron-skin manifested by the large differences between the neutron and proton r.m.s. radii for all of the isotopes in the chain. As expected the neutron-skin becomes “thicker” as we approach the dripline. Starting at the mass number A = 114 up to the dripline the nuclei prefer a spherical ground-state shape (fig. 2) which results in the sudden shrinking of the r.m.s. radius at A = 114.

1. S. Rinta-Antila, S. Kopecky, V.S. Kolhinen, J. Hakala, J. ¨ o, Phys. Rev. C Huikari, A. Jokinen, A. Nieminen, J. Ayst¨ 70, 011301(R) (2004). 2. E. Ter´ an, V.E. Oberacker, A.S. Umar, Phys. Rev. C 67, 064314 (2003). 3. V.E. Oberacker, A.S. Umar, E. Ter´ an, A. Blazkiewicz, Phys. Rev. C 68, 064302 (2003). 4. J.K. Hwang, A.V. Ramayya, J.H. Hamilton, D. Fong, C.J. Beyer, P.M. Gore, E.F. Jones, E. Ter´ an, V.E. Oberacker, A.S. Umar, Y.X. Luo, J.O. Rasmussen, S.J. Zhu, S.C. Wu, I.Y. Lee, P. Fallon, M.A. Stoyer, S.J. Asztalos, T.N. Ginter, J.D. Cole, G.M. Ter-Akopian, R. Donangelo, Half lives of isomeric states from SF of 252 Cf and large deformations in 104 Zr and 158 Sm, submitted to Phys. Rev. C (July 2003). 5. P. Campbell et al., Phys. Rev. Lett. 89, 082501 (2002). 6. M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, S. Pittel, D.J. Dean, Phys. Rev. C 68, 054312 (2003), arXiv:nuclth/0307049. 7. C. De Boor, Practical Guide to Splines (Springer Verlag, New York, 1978) and references therein. 8. A.S. Umar, J. Wu, M.R. Strayer, C. Bottcher, J. Comput. Phys. 93, 426 (1991). 9. A.S. Umar, M.R. Strayer, J.-S. Wu, D.J. Dean, M.C. G¨ uc¸l¨ u, Phys. Rev. C 44, 2512 (1991). 10. J.C. Wells, V.E. Oberacker, M.R. Strayer, A.S. Umar, Int. J. Mod. Phys. C 6, 143 (1995). 11. D.R. Kegley, V.E. Oberacker, M.R. Strayer, A.S. Umar, J.C. Wells, J. Comput. Phys. 128, 197 (1996). 12. V.E. Oberacker, A.S. Umar, Mean-field nuclear structure calculations on a Basis-Spline-Galerkin lattice, book chapter in “Perspectives in Nuclear Physics”, edited by J.H. Hamilton, H.K. Carter, R.B. Piercey (World Scientific, 1999) pp. 255-266. 13. G. Audi, A.H. Wapstra, C. Thibault, The 2003 atomic mass evaluation*1: (II). Tables, graphs and references, Nucl. Phys. A 729, 337 (2003).

Eur. Phys. J. A 25, s01, 545–546 (2005) DOI: 10.1140/epjad/i2005-06-111-4

EPJ A direct electronic only

Soft octupole vibrations on superdeformed states in nuclei around 40Ca suggested by Skyrme-HF and self-consistent RPA calculations T. Inakura1,a , H. Imagawa2 , Y. Hashimoto2 , M. Yamagami3 , S. Mizutori4 , and K. Matsuyanagi5 1 2 3 4 5

Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan Institute of Physics, University of Tsukuba, Tsukuba 305-8571, Japan Heavy Ion Nuclear Physics Laboratory, RIKEN, Wako, Saitama 351-0198, Japan Department of Human Science, Kansai Women’s College, Osaka 582-0026, Japan Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan Received: 15 January 2005 / c Societ` Published online: 9 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We present the results of fully self-consistent RPA calculation for low-frequency negative-parity modes built on superdeformed states in the 40 Ca region. The RPA calculation was carried out using the mixed representation on the three-dimensional Cartesian mesh in a box. The SD shell structure provides a very favorable situation for octupole shape fluctuations, and we show that the coherent excitation of protons and neutrons play an important role in the emergence of strongly collective octupole vibrations buit on the SD states in the N = Z nuclei, 32 S, 36 Ar, 40 Ca and 44 Ti. In particular, the calculation suggests that a low-frequency, strongly collective K π = 1− octupole vibration appears on the SD state in 40 Ca. PACS. 21.60.-n Nuclear structure models and methods – 21.60.Jz Hartree-Fock and random-phase approximations

Properties of low-frequency vibrational modes are sensitive to details of shell structure near the Fermi energy. The superdeformed (SD) shell structure is drastically different from the normal deformed one; each major shell at the SD shape consists of about equal numbers of positiveand negative-parity levels. Thus, we expect soft octupole surface vibrational modes to emerge in SD nuclei. Various mean-field calculations [1, 2,3] and quasiparticle RPA [4,5] on the basis of the rotating mean field (cranked shell model) indicate that SD nuclei are very soft against both axial and non-axial octupole deformations Accordingly, low-frequency octupole vibrations may appear near the SD yrast lines. In fact, such octupole vibrations have been discovered in heavy SD nuclei in the Hg-Pb region [6], and also in 152 Dy [7]. In recent years, the SD bands were discovered also in the 40 Ca region: 36 Ar [8], 40 Ca [9] and 44 Ti [10]. One of their important new features is that they are built on excited 0+ states and observed up to high spin, in contrast to the SD bands in heavier mass regions where their lowspin portions are unknown in almost all cases. Thus, in this SD region we can calculate vibrational modes built on superdeformed 0+ states and discuss their properties a

Conference presenter; e-mail: [email protected]

in the absence of rotational effects. Moreover, we can study coherent effects of proton and neutron excitations in these N = Z nuclei. In a recent paper [11], we reported results of the symmetry-unrestricted Skyrme-Hartree-Fock (SHF) calculations for these SD bands. Quite recently, Imagawa and Hashimoto [12, 13] constructed a new computer code that carries out a selfconsistent RPA in the mixed representation on the basis of the SHF mean field. In the mixed representation, particles are described in the coordinate representation, while holes are represented in the HF single-particle basis. This approach is fully self-consistent in that the same effective interction is used in both the mean field and the RPA calculations; i.e., all terms of the Skyrme force are taken into account as the residual interactions for the RPA. Furthermore, in this method, we can treat strongly deformed nuclei on the same footing as spherical nuclei. Figure 1 shows the low-frequency negative-parity intrinsic excitations on the SD states in 32 S, 36 Ar, 40 Ca, and 44 Ti, obtained by the mixed representation RPA calculation with the SkM∗ interaction. Although the SHF calculation yields small triaxiality for some of the SD states (see below), this calculation was done with the constraint γ = 0 for the mean fields. The RPA matrix was constructed using 30 and 50 mesh points in the

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-10 -12 -14

[200 12] [321 32]

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Fig. 2. Isoscalar octupole transition strengths and singleparticle levels near the Fermi surface for the SD state in 40 Ca. Numbers in the right panel indicate the asymptotic quantum numbers [N n3 ΛΩ]. The solid (dashed) lines are used for positive- (negative-) parity single-particle levels. The dotted line indicates the Fermi surface.

direction of the minor and major axes, respectively, with the mesh size h = 0.6 fm. We obtained the spurious mode associated with the center of mass motion in the energy region lower than 0.1 MeV. Numbers beside the arrows (in parentheses) indicate the squared transition matrix elements for the mass (electric) octupole operators in the Weisskopf unit (W.u.). Since we are interested in collective vibrations, only the modes having mass octupole transition probabilities greater than 10 W.u. are plotted here. As displayed in fig. 1, we obtained in 40 Ca a low-frequency K π = 1− mode possessing large octupole strength (26 W.u.) at 0.6 MeV above the SD band head. The RPA and the unperturbed isoscalar octupole transition strengths for the K π = 1− intrinsic excitations are compared in fig. 2. The unperturbed strengths at excitation energies about 1.3–1.4 MeV are associated with the proton and the neutron excitations from the [321 32 ] state to the [200 12 ] state. The fact that the RPA strength is significantly enhanced in comparison with the

unperturbed strength and the RPA energy is shifted down from the unperturbed particle-hole excitation energy indicates that this K π = 1− mode possesses strong collectivity. In addition to this K π = 1− mode, we obtained a number of axial and non-axial octupole vibrational modes buit on the SD states in the 40 Ca region: the K π = 2− mode at 1.8 MeV in 32 S, the 2− mode at 3.3 MeV in 36 Ar, the 0− mode at 3.4 MeV in 40 Ca, the 0− mode at 1.1 MeV and the 2− mode at 2.2 MeV in 44 Ti. The RPA strengths of these modes are enhanced more than 10 times the unperturbed strengths. Also, the RPA excitation energies are shifted down by 0.8–1.5 MeV from the unperturbed particle-hole excitation energies. In fact, the SD local minima for 40 Ca and 44 Ti obtained in the SHF mean-field calculation possess small triaxial deformations. Thus we also made the self-consistent RPA calculations taking into account the triaxial deformations. The results of this calculation were essentially the same as those presented in fig. 1, in which the axial symmetry constraint was imposed on the SD states, except that the K π = 0− modes split into the doublets. We also made the SHF + RPA calculations using the SIII and SLy4 interactions, and obtained results similar to those obtained with the SKM∗ interaction. Low-frequency collective octupole vibrational modes might mix with soft dipole modes in deformed unstable nuclei with neutron skins. Search for such a new kind of soft (dipole + octupole) vibrational modes of excitation in deformed unstable nuclei close to the neutron drip line is challenging both theoretically and experimentally. We gratefully acknowledge useful discussions with the members of the Japan-US cooperative project on Mean-Field Approach to Collective Excitations in Unstable Medium-Mass and Heavy Nuclei.

References 1. J. Dudek et al., Phys. Lett. B 248, 235 (1990). 2. J. Skalski, Phys. Lett. B 274, 1 (1992). 3. P.A. Butler, W. Nazarewicz, Rev. Mod. Phys. 68, 349 (1996). 4. S. Mizutori et al., Nucl. Phys. A 557, 125c (1993). 5. T. Nakatsukasa et al., Phys. Rev. C 53, 2213 (1996). 6. A. Korichi et al., Phys. Rev. Lett. 86, 2746 (2001); D. Rossbach et al., Phys. Lett. B 513, 9 (2001). 7. T. Lauritsen et al., Phys. Rev. Lett. 89, 282501 (2002). 8. C.E. Svensson et al., Phys. Rev. Lett. 85, 2693 (2000). 9. E. Ideguchi et al., Phys. Rev. Lett. 87, 222501 (2001). 10. C.D. O’Leary et al., Phys. Rev. C 61, 064314 (2000). 11. T. Inakura et al., Nucl. Phys. A 710, 261 (2002). 12. H. Imagawa, Doctor Thesis, University of Tsukuba (2003). 13. H. Imagawa, Y. Hashimoto, Phys. Rev. C 67, 037302 (2003).

Eur. Phys. J. A 25, s01, 547–548 (2005) DOI: 10.1140/epjad/i2005-06-039-7

EPJ A direct electronic only

Collective path connecting the oblate and prolate local minima in proton-rich N = Z nuclei around 68Se M. Kobayasi1,a , T. Nakatsukasa2 , M. Matsuo3 , and K. Matsuyanagi1 1 2 3

Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan Institute of Physics, University of Tsukuba, Tsukuba 305-8571, Japan Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan Received: 15 January 2005 / Revised version: 25 February 2005 / c Societ` Published online: 9 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. By means of the adiabatic self-consistent collective coordinate method and the pairing-plusquadrupole interaction, we have for the first time obtained a self-consistent collective path connecting the oblate and prolate local minima in 68 Se and 72 Kr. This self-consistent collective path is found to run approximately along the valley connecting the oblate and prolate local minima in the collective potential energy landscape. The result of this calculation clearly indicates the importance of triaxial deformation dynamics in oblate-prolate shape coexistence phenomena. PACS. 21.60.-n Nuclear structure models and methods – 21.60.Jz Hartree-Fock and random-phase approximations

a

e-mail: [email protected]

(a)

(b) V(q)(MeV)

0.5

γ

0

0.1

0.2

0.4 0.3

Oblate

0.2

Prolate

0.1 0

0.3

0

1

0.5

β

q

(d)

(c) 40

4

β

2

ω2 (MeV )

M(s(q))(1/MeV)

Shape coexistence phenomena are typical examples of large-amplitude collective motion in nuclei. These phenomena implies that different solutions of the HartreeFock-Bogoliubov (HFB) equations (local minima in the deformation energy surface) appear in the same energy region and that the nucleus exhibits large-amplitude collective motion connecting these different equilibrium points. Recently, we have proposed a new method of describing such large-amplitude collective motion, which is called adiabatic self-consistent collective coordinate (ASCC) method [1,2]. This method is formulated on the basis of the time-dependent HFB theory (TDHB), and consists of two basic equations: 1) the HFB equation in the moving frame and 2) the local harmonic equations in the moving frame, abbreviated to the “moving frame QRPA” below. It does not assume a single local minimum, so that it is expected to be suitable for the description of the shape coexistence phenomena. The ASCC method also enables us to self-consistently include the pairing correlations, removing the spurious number fluctuation modes. Quite recently, with use of the pairing-plus-quadrupole (P + Q) interaction, we have applied the ASCC method to the shape coexistence phenomena in 68 Se and 72 Kr, discovered by Fischer et al. [3] and Bouchez et al. [4], where the oblate ground band and the prolate excited bands compete in energy, and investigated the collective path connecting the oblate and prolate local minima in the collective potential energy landscape.

30 20 10

2 0

γ

-2

0

0

1

0.5

q

0

1

0.5

q

Fig. 1. The collective path (a), the collective potential (b), the collective mass (c), and the local eigen-frequencies squared, ω 2 (q) (d), of the moving frame QRPA as functions of the collective coordinate q, obtained by the ASCC calculation for 68 Se.

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(b)

(a)

1.2

V(q)(MeV)

1

γ

0.8

Oblate

0.6 0.4

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0.2 0

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0.1

0.3

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0 0.5 1 1.5 2 2.5

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q

(c)

(d)

100

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Δn

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120

80 60 40

2 0

20

γ

β

β

β γ

-2

0

0 0.5 1 1.5 2 2.5

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q

Fig. 2. The collective path (a), the collective potential (b), the collective mass (c), and the local eigen-frequencies squared, ω 2 (q) (d), of the moving frame QRPA as functions of the collective coordinate q, obtained by the ASCC calculation for 72 Kr.

The result of the calculation is shown in figs. 1 and 2. For 68 Se, because the γ-vibrational mode is the lowest frequency and most collective QRPA mode at the prolate and oblate local minima, we have chosen this mode as the initial condition, and successfully obtained the collective path connecting the oblate and prolate local minima, which is plotted in fig. 1(a). As we have extracted the collective path in the TDHB phase space, which has a very large number of degrees of freedom, the path drawn in this figure should be regarded as a projection of the collective path onto the (β, γ)-plane. Roughly speaking, the collective path goes through the valley that exists in the γ direction and connects the oblate and prolate minima. The potential energy curve V (q) along the collective path is displayed in fig. 1(b). Because the collective Hamiltonian, Hcoll = 12 B(q)p2 + V (q), is invariant under a point transformation, q → q  = q  (q), p → p = p(∂q  /∂q)−1 , with B(q) → B(q  )(∂q  /∂q)−2 , we can take the scale of q such that the collective mass is given by M (q) = B(q)−1 = 1 MeV−1 . The collective mass as a function of the geometrical length s along the collective path in the (β, γ)plane is then given by M (s(q)) = M (q)(ds/dq)−2 , with ds2 = dβ 2 +β 2 dγ 2 . This quantity is plotted in fig. 1(c) as a function of q. We see an appreciable increase of the collective mass in the vicinity of γ = 60◦ . This property might contribute to increase the stability of the oblate shape in the ground state. The eigen-frequencies of the moving frame QRPA along the collective path are plotted in fig. 1(d). The solid curve represents the frequency squared, ω 2 (q), given by the moving frame QRPA, which corre-

sponds to the γ-vibration in the oblate and prolate limits. ˆ This solution determines the infinitesimal generators Q(q) ˆ and P (q) along the collective path. For reference, we also present in this figure another solution of the moving frame QRPA, which possesses the β-vibrational properties and is irrelevant to the collective path in the case of 68 Se. In contrast to 68 Se, the lowest-frequency QRPA mode is the β-vibration at the prolate local minimum in 72 Kr. The collective path first goes in the direction of the β-axis in the (β, γ)-plane (see fig. 2(a)). As we go along the β-axis, we encounter a situation in which the two solutions (labeled by β and γ) of the moving frame QRPA compete in energy, and they eventually cross at q ∼ 0.8 (see fig. 2(d)). Using an efficient algorithm developed in ref. [5] to determine the collective path in the crossing region, we have successfully obtained the smooth deviation of the direction of the collective path from the β-axis toward the γ direction. We see that the properties of the lowest mode gradually changes from those of the β to the γ-vibrations. After a smooth turn in the γ direction, the collective path approaches the γ = 60◦ axis. Then, we again encounter the crossing at q ∼ 1.8, where the properties of the lowest solution of the moving frame QRPA change smoothly from those of the γ-vibrational to those of the β-vibrational case. The collective path thus runs along the γ = 60◦ axis and it finally reaches the oblate minimum. We have also carried out a calculation starting from the oblate minimum and proceeded in the inverse manner, obtaining the same collective path. The potential energy curve V (q) and mass parameter M (s(q)) along the collective path is displayed in fig. 2(b) and (c), respectively. We notice again a significant increase of M (s(q)) in the vicinity of the oblate minimum. Quite recently, Almehed and Walet found a collective path going from the oblate minimum over a spherical energy maximum into the prolate secondary minimum [6]. We also obtained such a collective path when we imposed axial symmetry on the solutions of the moving frame HB equation and always used only K = 0 solutions of the moving frame QRPA. For the first time, the self-consistent collective paths between the oblate and prolate minima have been obtained in realistic situations starting from the microscopic P + Q Hamiltonian. The result of our calculation strongly indicates the necessity of taking into account the γ degree of freedom, for the description of the oblate-prolate shape coexistence phenomena in 68 Se and 72 Kr.

References 1. M. Matsuo, T. Nakatsukasa, K. Matsuyanagi, Prog. Theor. Phys. 103, 959 (2000). 2. M. Kobayasi, T. Nakatsukasa, M. Matsuo, K. Matsuyanagi, Prog. Theor. Phys. 110, 61 (2003). 3. S.M. Fischer et al., Phys. Rev. Lett. 84, 4064 (2000); Phys. Rev. C 67, 064318 (2003). 4. E. Bouchez et al., Phys. Rev. Lett. 90, 082502 (2003). 5. M. Kobayasi, T. Nakatsukasa, M. Matsuo, K. Matsuyanagi, Prog. Theor. Phys. 113, 129 (2005), nucl-th/0412062. 6. D. Almehed, N.R. Walet, Phys. Lett. B 604, 163 (2004).

Eur. Phys. J. A 25, s01, 549–550 (2005) DOI: 10.1140/epjad/i2005-06-055-7

EPJ A direct electronic only

Light exotic nuclei studied with the parity-projected Hartree-Fock method H. Ohta1,a , T. Nakatsukasa2 , and K. Yabana2 1 2

Institute of Physics, University of Tsukuba, Tsukuba 305-8571, Japan Center for Computational Science and Institute of Physics, University of Tsukuba, Tsukuba 305-8571, Japan Received: 25 October 2004 / c Societ` Published online: 1 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Calculation of the variation after parity projection is performed in 3D Cartesian mesh representation for ground and excited states of even-even magnesium isotopes. The full 3D angular momentum projection after the variation provides rotational spectra for deformed nuclei. The method takes account of a part of octupole and rotational correlations beyond the mean field. We show the positive-parity ground band and the lowest negative-parity excited band in each isotope. Properties of the ground-state bands are in a good agreement with experiments. PACS. 21.60.Jz Hartree-Fock and random-phase approximations

1 Introduction Among theories beyond the mean field, the variation after projection (VAP) method is one of the simplest ones. Yet, practical applications with realistic effective interactions, such as the Skyrme interaction, have not been fully investigated even for projection with respect to just the parity. The variation after the parity projection (VAPP) with a symmetry-violating intrinsic state leads to the ground state including some octupole correlations. In addition, one can obtain a negative-parity excited state which is either a collective or non-collective excitation. Recently, we propose an algorithm to calculate the VAPP with the Skyrme interaction on the three-dimensional (3D) Cartesian coordinates [1]. The calculations with the simple BKN interaction were reported before [2]. In the ordinary mean-field calculations, one finds selfconsistent solutions with axial and reflection symmetries for most nuclei. However, in the VAPP calculations, the self-consistent solutions violate these symmetries. This symmetry violation in the intrinsic state is a consequence of the correlation beyond the mean field, which can be regarded as the octupole correlation. This is similar to cluster correlation in light systems. In ref. [1], we have shown that the cluster structure of α + 16 O appears in 20 Ne and the three α structure in 12 C, as a result of the VAPP using the Skyrme interaction. Simultaneously, we have obtained negative-parity excited bands with both well-developed cluster structures and shell-model-like particle-hole excitations in these nuclei. The angular momentum projection after the variation well reproduces experimental low-lying spectra and transition strengths. a

e-mail: [email protected]

In this paper, we apply the same method to Mg isotopes. Among those isotopes, neutron-rich nuclei in the neighborhood of the shell closure N = 20 are of significant interest. The observed low excitation energy of 2+ state and the enhanced B(E2; 0+ → 2+ ) for 32 Mg suggests an anomalous deformation and a quenching of the shell gap at N = 20 [3]. The deformation becomes more evident for 34 Mg, in which the 2+ excitation energy is even lower and the B(E2) is larger than those in 32 Mg [4].

2 VAP calculation in the 3D coordinate space In this section, we briefly summarize our method of VAP calculation. The details are given in refs. [1,2]. The method is based on minimization of the energy expectation value with respect to a parity projected Slater determinant, |Φ(±)  = √12 (1 ± Pˆ )|Φ, where Pˆ is the space √ inversion operator and |Φ = det{|φi }/ N ! represents an intrinsic Slater determinant. The variation with respect to the single-particle orbitals |φi  leads to " #  ˜ ˜ ˜ ˆ (h − η · r) |φi  ± Φ|P |Φ hP |φi  − |φj  φj |hP |φi  j

+(E

(±)

− E)|φ˜i  =



ij |φj ,(1)

j

where E = Φ|H|Φ and E (±) = Φ(±) |H|Φ(±) . h is the usual Hartree-Fock Hamiltonian. hP has the same structure as h, however, all the densities are replaced by the transition densities [2]. |φ˜i  is defined by  ˆ −1 )ji , with Bij = φi |Pˆ |φj . η and ij are the j P |φj (B

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Mg; the lowest π = +

π=− Excitation Energy ( MeV )

12

6+

32

34

Mg; the lowest π = +

Mg; the lowest π = +

π=−

π=−

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6

6−

2 0

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4+ EXP 2+

4+ CAL

0+ GROUND

odd-parity lowest band

6−

5−

5−

6+

−

4 3−

4−

0− 2−

CAL

CAL

EXP 2−

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CAL GROUND

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Mg

Mg

8−

8

34

32

10

odd-parity lowest band

CAL

3− 1−

4+ 2+ 0+

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GROUND

odd-parity lowest band

Fig. 2. Excitation spectra for the lowest positive- and negative-parity bands in 30,32,34 Mg. Fig. 1. Contour plots of intrinsic density in the xy-, yz-, and zx-planes for the lowest state in each parity sector.

Lagrange multipliers to fix the center of mass and to orthonormalize |φi , respectively. We solve eq. (1) using the imaginary-time method. The left-hand-side of eq. (1) plays a role of the gradient of the energy functional. Numerically, the 3D Cartesian coordinate space is discretized into uniform square grid points on which the single-particle wave functions are represented. The grid spacing is taken to be 0.8 fm, and the grid points inside a sphere of radius 8 fm are used in the calculations. After obtaining the self-consistent intrinsic solutions, |Φ, we make the angular momentum projection (AMP) to calculate rotational spectra. Since the VAP treatment leads to a triaxial solution in general, we perform the full 3D rotation in Euler angles.

3 Low-energy spectra in Mg isotopes We apply the VAPP method to Mg isotopes. The Skyrme functional with the SGII parameter set is used in the calculation. For the stable nucleus, 24 Mg, we obtain a deformed ground state with positive parity. The deformation is β2 = 0.52 with some octupole components, β30 = 0.17 and β31 = 0.12. The state has a dominant K π = 0+ character. The angular momentum projection reproduces experimental spectra and B(E2) for the ground band up to J π = 6+ . However, the well-known side band is not reproduced in the calculation because of the K π = 0+ character of the intrinsic state. The negative-parity solutions (K π = 0− , 3− , 1− ) also well correspond to experimental data, though calculated band-head energies are slightly higher than the experiments by 1–2.5 MeV. Next, let us discuss results for neutron-rich even-even Mg isotopes, 30,32,34 Mg. Calculated density distributions for the ground state and the lowest negative-parity state are shown in fig. 1. The rotational spectra obtained from these intrinsic states are displayed in fig. 2. Although we show only the lowest solutions in these figures, we have obtained quasi-stationary solutions as well both in the positive- and in the negative-parity sectors. In 30,32,34 Mg, there are two positive-parity solutions, one of which has a large quadrupole deformation of β ≈ 0.4–0.6 and the other has a small deformation of β ≈ 0.1–0.3. These two states are nearly degenerate in energy, and the interplay

between these two seems to be a characteristic feature in the neutron-rich Mg isotopes. In 30 Mg, the one with a small deformation is the ground state, while the one with a large deformation becomes the lowest in 32,34 Mg. The ground state in 30 Mg has a deformation of β2 = 0.22 and β33 = 0.14. In 32 Mg, we have the ground state with β2 = 0.44 and β33 = 0.12. The rotational correlation is essential to obtain the well-deformed ground state in 32 Mg. The deformation in 34 Mg is even larger, β2 = 0.53 with β30 = 0.17. This change of the ground-state character accounts for the experimental observation. The calculated B(E2; 0+ → 2+ ) are also consistent with the experiments. The moments of inertia are somewhat overestimated in 30,32 Mg, probably because the pairing correlation is neglected in the calculation. The calculation predicts lowenergy negative-parity bands in these isotopes. The octupole deformations for the negative-parity states turns out to be smaller than those in the ground states. This is different from what we observed for stable nuclei, 20 Ne and 12 C, in which the octupole deformation is enhanced in negative-parity solutions [1]. The lowest negative-parity excitations in 30,32,34 Mg seem to correspond neither to parity-inversion doublets nor to octupole vibrations.

4 Conclusion We have studied low-energy low-spin spectra for neutronrich Mg isotopes using the VAPP method. The groundstate deformation becomes larger as the neutron number increases. This is consistent with experimental data. For the lowest negative-parity bands, though there are no experimental information available, the calculation may suggest non-collective excitation character in 30,32,34 Mg. This work is supported by the Grant-in-Aid for Scientific Research in Japan (Nos. 14540369 and 14740146).

References 1. H. Ohta, K. Yabana, T. Nakatsukasa, Phys. Rev. C 70, 014301 (2004). 2. S. Takami, K. Yabana, K. Ikeda, Prog. Theor. Phys. 96, 407 (1996). 3. T. Motobayashi et al., Phys. Lett. B 346, 9 (1995). 4. H. Iwasaki et al., Phys. Lett. B 522, 227 (2001).

Eur. Phys. J. A 25, s01, 551–552 (2005) DOI: 10.1140/epjad/i2005-06-067-3

EPJ A direct electronic only

Using high-spin data to constrain spin-orbit term and spin-fields of Skyrme forces The need to unify the time-odd part of the local energy density functional W. Satula1,2,a , R. Wyss2 , and H. Zdu´ nczuk1 1 2

Institute of Theoretical Physics, University of Warsaw, ul. Ho˙za 69, PL-00 681 Warsaw, Poland KTH (Royal Institute of Technology), AlbaNova University Centre, S-106 91 Stockholm, Sweden Received: 15 November 2004 / c Societ` Published online: 10 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A method to study spin-fields and the spin-orbit potential within the local energy density approach is presented. The concept utilizes the intrinsic simplicity of terminating states in order to constrain certain parameters of the local nuclear energy functional. In particular, constraints on the isoscalar Landau parameter g0 and the strength of the spin-orbit potential are thoroughly discussed. PACS. 21.60.Jz Hartree-Fock and random-phase approximations

1 Introduction The terminating states are one of the purest examples of unperturbed single-particle (sp) motion. Hence, they are perfectly suited for unpaired Hartree-Fock (HF) calculations and, in turn, offer an excellent playground for testing and constraining various aspects of the effective NN interaction or local energy density functional (LEDF). In this contribution, see refs. [1, 2] for details, we present calculations of the energy differences, ΔE, n+1 n between terminating states within d−1 3/2 f7/2 and f7/2 configurations in 20 ≤ Z < N ≤ 24 nuclei, where n denotes the number of valence particles outside the 40 Ca core. The value of ΔE is dominated by the size of the magic gap 20, Δe20 . One can establish a hierarchy of the different contributions to Δe20 guided by the Nilsson model expression Δe20 = ¯hω0 (1 − 6κ − 2κμ). Indeed, it shows that: i) flat-bottom and surface effects, μ ∼ 0, are marginal in light nuclei ii) even small changes to low-energy nuclear physics energy scale, ¯hω0 , which is well established, is rather unlikely since it will impair the in general good agreement between theory and experiment, in particular, in heavy nuclei. Hence, the uncertainties in Δe20 are predominantly related to the uncertainties in the s-term enabling, in turn, a fine-tuning of its strength. This argumentation is general and pertains also to self-consistent approaches including, in particular, the Skyrme-HF (SHF) method used in this work. We will also demonstrate that thanks to the intrinsic simplicity of the terminating states one can reduce the a

Conference presenter; e-mail: [email protected]

arbitrariness of the time-odd (TO) channel in the Skyrmeforce (SF) induced LEDF (S-LEDF) by establishing a firm constraint on the isoscalar Landau parameter g0 .

2 The spin-fields Since the SF is fitted ultimately to the time-even (TE) channel, the TO components of the S-LEDF which are not related to the TE channel through the local gauge invariance appear to be completely accidental, see refs. [1,3]. This pertains to the spin-field coupling constants Cts and CtΔs in the TO part of the S-LEDF: (TO)

Ht

(r) = Cts s2t + CtΔs st Δst + CtT st · Tt + Ctj j2t + Ct∇j st · (∇ × jt ),

(1)

where t denotes isospin. The definition of the local densities and relations between coupling constants C and the auxiliary SF parameters can be found, for example, in [4]. The uncertainty in the spin-fields is reflected in fig. 1a, showing the calculated energy differences ΔEth relative to the experimental data ΔEexp . Indeed, even a small generalization of the S-LEDF by replacing the SF-induced coupling constants Cts with the following set of the Landau parameters (L-LEDF) recommended in ref. [3]: g0 = 0.4, g0 = 1.2 and g1 = −0.19, g1 = 0.62, and by setting CtΔs ≡ 0 provides a very consistent description of the experimental data by most of the tested parameterizations, as shown in fig. 1b. Most of the parameterizations deviate from the data by ∼ 10% (ΔE ≈ 500 keV). Only for SkP, MSk1, and SkM* it is unacceptably large, ∼ 20–30%. The

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The European Physical Journal A 2.0

Skyrme-LEDF SkM* MSk1 SkP SkXc SkO SLy4 SLy5 SIII

1.5

1.0

SkM* MSk1 SkP SkXc SkO SLy4 SLy5 SIII

1.0 0.5

MSk1 SkP

1.0

Sly..

0

b) 1.5

1.5

0.5

0.5

2.0

SkM*

W*0

ΔE [MeV]

ΔE=Δ ΔEexp - ΔEth [MeV]

2.0

a)

SkXc

SkO SIII 120

140 160 180 5 W* 0 [MeV fm ]

Fig. 2. The values of ΔE averaged over all nuclei considered in fig. 1, ΔE, as a function of the isoscalar strength W0∗ for different parameterizations of the SF.

tivistic models and seems to be more consistent with the data particularly in neutron rich nuclei [6,7].

47V 45Ti 46Ti 44Sc 42Ca 45Sc44Ca

Fig. 1. Calculated energy differences for terminating states n+1 n ΔEth = E[d−1 3/2 f7/2 ] − E[f7/2 ] relative to the experimental data ΔE ≡ ΔEexp − ΔEth . Upper part shows SHF calculations for various parameterizations while lower part illustrates calculations using a unified description of the spin-fields.

detailed analysis shows that the value of ΔE cannot be reduced by further tuning of g0 , and that the optimal value of g0 deduced from our calculations is only slightly larger than the value recommended in the literature [5].

3 The spin-orbit term The average discrepancy ΔE does not correlate directly with the bare isoscalar strength W0 of the s-term. However, the value of ΔE correlates nicely with the isoscalareffective-mass scaled isoscalar strength of the spin-orbit ∗ term W0∗ ≡ mm W0 , see fig. 2, which takes into account non-local effects. Indeed, the Skyrme forces having W0∗ ≈ 135 ± 10 MeV fm5 give similar level of agreement between theory and the data of the order of 10%. It can be shown that, by reducing the strength of the s-term by 5%, the deviation from the data can be lowered to below 5%. Let us also observe that the SF giving large disagreement to the data have W0∗ > 150 MeV fm5 . These SF cannot be corrected just by fine tuning of W0 . Further detailed study shows that our calculations give rather clear preference for the non-standard parameterizations of the s-term with a strong isovector dependence characterized by the ratio of the isovector to the isoscalar coupling constants W1 /W0 ∼ −1. Indeed, such forces tend to reduce the slope of ΔE versus the reduced isospin I = (N − Z)/A which is clearly seen in fig. 1. More detailed discussion can be found in refs. [1, 2]. Let us point out that the ratio W1 /W0 ∼ −1 is inspired by the rela-

4 Summary The objective of this analysis is to demonstrate that the terminating states, due to their intrinsic simplicity, offer a unique and so far unexplored opportunity to study different aspects of the effective NN interaction or nuclear local energy density functional within the self-consistent approaches. First of all our work demonstrates that the terminating states offer a unique playground for studying the TO components of the LEDF, allowing to set a firm constraint on the isoscalar Landau parameter g0 . Furthermore, it is shown that the ∼ 10% disagreement between theory and the data correlates nicely with the isoscalar-effective-mass scaled isoscalar spin-orbit strength. A 5% reduction of W0 appears to reduce the average discrepancy, ΔE, well below ∼ 5%. Our calculations give also certain preference for non-standard parameterizations of the spin-orbit term having W1 /W0 ∼ −1. This work has been supported by the Foundation for Polish Science (FNP), the G¨ oran Gustafsson Foundation, the Swedish Science Council (VR), the Swedish Institute (SI), and the Polish Committee for Scientific Research (KBN) under Contract No. 1 P03B 059 27.

References 1. H. Zdu´ nczuk et al., Phys. Rev. C 71, 024305 (2005). 2. H. Zdu´ nczuk et al., to be published in Int. J. Mod. Phys. E (2005). 3. M. Bender et al., Phys. Rev. C 65, 054322 (2002). 4. M. Bender et al., Rev. Mod. Phys. 75, 121 (2003). 5. F. Osterfeld, Rev. Mod. Phys. 64, 491 (1992). 6. P.G. Reinhard, H. Flocard, Nucl. Phys. A 584, 467 (1995). 7. P.G. Reinhard et al., Phys. Rev. C 60, 014316 (1999).

Eur. Phys. J. A 25, s01, 553–554 (2005) DOI: 10.1140/epjad/i2005-06-087-y

EPJ A direct electronic only

TDHF studies with modern Skyrme forces A.S. Umara and V.E. Oberacker Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, USA Received: 16 November 2004 / Revised version: 1 February 2005 / c Societ` Published online: 12 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We present preliminary results for TDHF studies of low-energy nuclear collisions involving deformed nuclei. The computations are performed using our highly accurate 3D TDHF code, with no assumed symmetries. The code uses Basis-Splines for discretization and is written in Fortran 95. PACS. 24.10.Cn Many-body theory – 25.70.Jj Fusion and fusion-fission reactions – 25.70.De Coulomb excitation

1 Introduction With the ever increasing availability of radioactive ionbeams, the study of heavy-ion fusion for exotic nuclei is becoming possible. In terms of theoretical studies it is generally acknowledged that the time-dependent HartreeFock (TDHF) method provides a useful foundation for a fully microscopic many-body theory of low-energy heavyion reactions [1]. The TDHF method is most widely known in nuclear physics in the small amplitude domain, where it provides a useful description of collective states. Most of the work on large amplitude dynamics have focused on studying low energy heavy-ion collisions and relating the properties of fusion and strongly damped collisions to the properties of the effective N-N interactions. The viability of this analysis depends on the overall accuracy of the TDHF calculations. Previously, the numerical complexity and demand of extensive computer time limited studies to simple systems and employed approximations and assumptions which were not present in the basic theory. For example, most static Hartree-Fock (HF) calculations have studied the ground state properties of even-even nuclei possessing spherical symmetry, while the study of deformed systems were limited [2], whereas most TDHF calculations have been limited to cylindrical symmetry with stripped down versions of the Skyrme effective interaction. In 1991, we have developed the world’s most accurate unrestricted 3-D TDHF code with spin-orbit coupling, using B-Spline techniques [3], and applied it to fusion and deep-inelastic heavy-ion reactions. This code does not make any spatial symmetry assumptions nor does it impose time-reversal invariance for the effective interaction. Given the experimental interest in fusion of neutron-rich nuclei we have updated this TDHF code. The code has a

Conference presenter; e-mail: [email protected]

been completely rewritten taking advantage of the array processing capabilities of Fortran 95, and using the modern versions of effective interactions. Recently, experiments have been performed at the Holifield Radioactive Ion-Beam Facility at ORNL to study fusion-evaporation residue cross-sections with neutronrich 132 Sn beams on 64 Ni. Using this inverse-kinematics fusion technique, surprisingly large sub-barrier fusion enhancement was observed [4]. Similar experiments are planned in the future, not only at ORNL but also at other RIB facilities. In general, the heavy-ion reactions of nuclei far from stability have not been theoretically explored and pose great challenges to our microscopic approaches.

2 TDHF studies for deformed nuclei Until today, we do not have a systematic study of TDHF collisions for deformed nuclei. This is due to the fact that if one or both of the nuclei are deformed the collision cross-sections need to be averaged over all possible orientations of the two nuclei. This is further complicated by the fact that the two nuclei approach each other on a Coulomb trajectory. This aspect is dealt with by using pure Coulomb kinematics to find out the location and the relative energy of the two nuclei at a finite separation and subsequently initializing the nuclei using these values. The two nuclei represented by Slater determinants are then boosted towards  each other by a plane wave exp(ik · R) where R = i ri , and leads to a translating solution due to the Galilean invariance of the equations of motion. However, any possible internal excitation during the Coulomb approach is ignored. In this work, we modify the initial Coulomb kinematics to include multiple E2/E4 Coulomb excitation of the g.s. rotational band, since this is the primary mechanism for

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Fig. 1. Diagram showing the three Euler angles for a deformed-spherical nuclear system.

nuclear alignment during this phase. There exists an extensive literature on the “semiclassical” theory of multiple Coulomb excitation of heavy ions [5]. In this approach [6], the excitation process is described quantum mechanically, and the relative motion of the nuclei is treated by classical mechanics. The total Hamiltonian consists of the free Hamiltonian of the target nucleus, H0 (X), and of the coupling potential for inelastic Coulomb excitation, VC (X, r(t)). The latter depends on the intrinsic coordinates of the target (X) and on the classical relative trajectory r(t), and the Coulomb excitation process is determined by the time-dependent Schr¨odinger equation. In the specific application of this formalism to dynamic nuclear alignment, we describe the free Hamiltonian and the corresponding wave functions in terms of the collective rotor model. The degrees of freedom are the three Euler angles X = (α, β, γ), depicted in fig. 1. H0 (X) = Trot (X).

(1)

In deformed even-even nuclei, the g.s. rotational band has an intrinsic total angular momentum projection K = 0; therefore, the collective wave functions are independent of the Euler angle γ which describes a rotation about the intrinsic symmetry axis z   φr (X) =

2J + 1 8π 2

= (2π)

1/2

−1/2

J ∗ DM,K=0 (α, β, γ)

YJM (β, α).

(2)

The probability density at time t to find the nucleus oriented with given Euler angles X = (α, β, γ) is given by |ψ(X, t)|2 ; by integration over γ we find the corresponding differential orientation probability dP (α, β; t) = sin β dβ dα



2π

dγ |ψ(α, β, γ; t)|

2

0

 2     −iEJ t/¯ h  −→  aJM (t)YJM (β, α)e  . J,M 

(3)

Fig. 2. TDHF collisions of 16 O + 22 Ne at E/A = 2.5 MeV. For the column on the left the neon is placed in perpendicular orientation, whereas in the right column the neon is horizontal. Both calculations cover a range of collisions time of about 450 fm/c. It is interesting to note that only the perpendicular configuration fuses, indicating the importance of orientation averaging.

3 Results We have performed a number of TDHF collisions for the O + 22 Ne system at a c.m. energy of 95 MeV. The two nuclei are initialized at a center-to-center separation of 16 fm and zero impact parameter (head-on). The classical Coulomb trajectory equations are solved to determine the kinematical values at this initial separation. We have used Basis-Splines of order 7, with a mesh spacing of 1.0 fm. The collision axis stretched from −16.0 fm to +16.0 fm, whereas the other two axes range from −10.0 fm to +10.0 fm. For the time spacing we have used Δt = 0.2 fm/c. The most striking result of our calculation is the dependence of fusion on the initial orientation of the 22 Ne nucleus. As shown in fig. 2 when the Ne is aligned with its long axis perpendicular to the collision axis the two nuclei fuse, whereas when the alignment is horizontal to the collision axis no fusion is seen. This is an indication that the calculation of fusion needs to include a weighted average over all possible orientations as well as impact parameter. Such calculations are presently underway as well as the application of TDHF for calculating fusion cross-sections along various isotope chains. 16

References 1. J.W. Negele, Rev. Mod. Phys. 54, 913 (1982). 2. P. Bonche, H. Flocard, P.-H. Heenen, S.J. Krieger, M.S. Weiss, Nucl. Phys. A 443, 39 (1985). 3. A.S. Umar, M.R. Strayer, J.-S. Wu, D.J. Dean, M.C. G¨ uc¸l¨ u, Phys. Rev. C 44, 2512 (1991). 4. J.F. Liang et al., Phys. Rev. Lett. 91, 152701 (2003). 5. K. Alder, A. Winther, Electromagnetic Excitation (North Holland, 1975). 6. V.E. Oberacker, Phys. Rev. C 32, 1793 (1985).

Eur. Phys. J. A 25, s01, 555–556 (2005) DOI: 10.1140/epjad/i2005-06-091-3

EPJ A direct electronic only

Relativistic mean-field models with medium-dependent meson-nucleon couplings D. Vretenar1,3,a , G.A. Lalazissis2,3 , T. Nikˇsi´c1,3 , and P. Ring3 1 2 3

Physics Department, Faculty of Science, University of Zagreb, Zagreb, Croatia Department of Theoretical Physics, Aristotle University of Thessaloniki, GR-54124, Thessaloniki, Greece Physik-Department der Technischen Universit¨ at M¨ unchen, D-85748 Garching, Germany Received: 10 November 2004 / c Societ` Published online: 13 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Microscopic structure models based on the relativistic mean-field approximation have been extended to include effective Lagrangians with explicit density-dependent meson-nucleon couplings. In a number of recent studies it has been shown that this class of global effective interactions provides an improved description of asymmetric nuclear matter, neutron matter and finite nuclei far from stability. PACS. 21.30.Fe Forces in hadronic systems and effective interactions – 21.60.-n Nuclear-structure models and methods – 21.60.Jz Hartree-Fock and random-phase approximations

The self-consistent mean-field framework enables a description of the nuclear many-body problem in terms of universal energy density functionals. By employing global effective interactions, adjusted to empirical properties of symmetric and asymmetric nuclear matter, and to bulk properties of few spherical nuclei, self-consistent meanfield models have achieved a high level of accuracy in the description of ground states and properties of excited states in arbitrarily heavy nuclei. A universal energy density functional theory should provide a basis for a consistent microscopic treatment of infinite nuclear and neutron matter, ground-state properties of all bound nuclei, low-energy excited states, small-amplitude vibrations, and reliable extrapolations toward the drip lines. An important class of self-consistent mean-field models belongs to the framework of relativistic mean-field theory (RMF). The RMF framework has recently been extended to include effective Lagrangians with density-dependent meson-nucleon vertex functions. The functional form of the meson-nucleon vertices can be deduced either by mapping the nuclear matter Dirac-Brueckner nucleon self energies in the local density approximation, or a phenomenological approach can be adopted, with the density dependence for the σ-, ω- and ρ-meson–nucleon couplings adjusted to properties of nuclear matter and a set of spherical nuclei. We have recently adjusted two new phenomenological density-dependent interactions to be used in RMF + BCS, relativistic Hartree-Bogoliubov (RHB), and quasiparticle random phase approximation (RQRPA) calculations of ground states and excitations of spherical and deformed a

Conference presenter; e-mail: [email protected]

nuclei. The eight independent parameters: seven coupling parameters and the mass of the σ-meson, have been adjusted to reproduce the properties of symmetric and asymmetric nuclear matter, binding energies, charge radii and neutron radii of spherical nuclei. In ref. [1] we introduced the density-dependent meson-exchange effective interaction (DD-ME1). It has been shown that, as compared to standard non-linear relativistic mean-field effective forces, the interaction DD-ME1 has better isovector properties and therefore provides an improved description of asymmetric nuclear matter, neutron matter and nuclei far from stability. The DD-ME1 interaction has recently been also tested in the calculation of deformed nuclei [2]. In refs. [3,4] we employed the RQRPA in a series of calculations of giant resonances in spherical nuclei. Starting from DD-ME1, and by constructing families of interactions with some given characteristic (compressibility, symmetry energy, effective mass), it has been shown how the comparison of the RQRPA results on multipole giant resonances with experimental data can be used to constrain the parameters that characterize the isoscalar and isovector channel of the density-dependent effective interactions. In particular, in ref. [4] we have shown that the comparison of the calculated excitation energies with the experimental data on the giant monopole resonances (GMR) restricts the nuclear matter compression modulus to Knm ≈ 250–270 MeV. The isovector giant dipole resonance (IVGDR) in 208 Pb, and the available data on differences between neutron and proton radii, limit the range of the nuclear matter symmetry energy at saturation (volume asymmetry) of these effective interactions to 32 MeV ≤ a4 ≤ 36 MeV. The interaction DD-ME1 has

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1450

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Eth = 15.28 MeV Eexp= 15.19 MeV

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2

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2

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2

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Fig. 2. The binding energies [5], charge isotope shifts [6], and quadrupole deformation parameters [7] of the Dy, Er and Yb isotopes, compared with predictions of the RHB model with the DD-ME2 plus Gogny D1S interactions.

also been employed in the proton-neutron RQRPA analysis of charge-exchange modes: isobaric analog resonances and Gamow-Teller resonances in spherical nuclei [8]. Taking into account these results, a new global effective interaction DD-ME2 has been tested in ref. [9]. Similar to the case of DD-ME1, the parameters have been adjusted to a set of twelve spherical nuclei. For DD-ME2, in addition, data on excitation energies of isoscalar GMR and IVGDR have been used. The interaction has been adjusted to the excitation energies of the ISGMR and IVGDR in 208 Pb, which practically do not display any fragmentation. The calculated centroid energy of 12.1 MeV for the isoscalar giant quadrupole resonance in 208 Pb, compared to the empirical excitation energy 10.9 ± 0.3 MeV [10], reflects the rather low effective nucleon mass. DD-ME1 and DD-ME2 display very similar equations of state for symmetric nuclear matter, the symmetry energies as function of the nucleon density, and the neutron matter equations of state. In general, when compared with the results obtained with DD-ME1 [1,2,3], DD-ME2 improves the agreement with experimental data on ground-state

properties of spherical and deformed nuclei, and excitation energies of giant resonances in spherical nuclei. In the following figures we present several illustrative results obtained with the DD-ME2 effective interaction. The theoretical binding energies of approximately 200 nuclei calculated in the RHB model with the DD-ME2 plus Gogny D1S interactions, are compared with experimental values in fig. 1. The rms error including all the masses shown in the figure is less than 900 keV. The predictions for the total binding energies, charge isotope shifts, and groundstate quadrupole deformation parameters of three rareearth isotopic chains Dy, Er and Yb, are shown in comparison with experimental results in fig. 2. Finally, in fig. 3 we compare the RQRPA results for the isovector dipole response of Sn isotopes with experimental data on IVGDR excitation energies [11].

References 1. T. Nikˇsi´c, D. Vretenar, P. Finelli, P. Ring, Phys. Rev. C 66, 024306 (2002). 2. T. Nikˇsi´c, D. Vretenar, G.A. Lalazissis, P. Ring, Phys. Rev. C 69, 047301 (2004). 3. T. Nikˇsi´c, D. Vretenar, P. Ring, Phys. Rev. C 66, 064302 (2002). 4. D. Vretenar, T. Nikˇsi´c, P. Ring, Phys. Rev. C 68, 024310 (2003). 5. G. Audi, A.H. Wapstra, C. Thibault, Nucl. Phys. A 729, 337 (2003). 6. E.G. Nadjakov, K.P. Marinova, Yu.P. Gangrsky, At. Data Nucl. Data Tables 56, 133 (1994). 7. S. Raman, C. Nestor, P. Tikkanen, At. Data Nucl. Data Tables 78, 1 (2001). 8. N. Paar, T. Nikˇsi´c, D. Vretenar, P. Ring, Phys. Rev. C 69, 054303 (2004). 9. G.A. Lalazissis, T. Nikˇsi´c, D. Vretenar, P. Ring, Phys. Rev. C. 71, 024312 (2005). 10. F.E. Bertrand, G.R. Satchler, D.J. Horen, A. van der Woude, Phys. Lett. B 80, 198 (1979). 11. B.L. Berman, S.C. Fultz, Rev. Mod. Phys. 47, 713 (1975).

Eur. Phys. J. A 25, s01, 557–558 (2005) DOI: 10.1140/epjad/i2005-06-142-9

EPJ A direct electronic only

Microscopic structure of negative-parity vibrations built on superdeformed states in sulfur isotopes close to the neutron drip line K. Yoshida1,a , T. Inakura2 , M. Yamagami3 , S. Mizutori4 , and K. Matsuyanagi1 1 2 3 4

Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan Heavy Ion Nuclear Physics Laboratory, RIKEN, Wako, Saitama 351-0198, Japan Department of Human Science, Kansai Women’s College, Osaka 582-0026, Japan Received: 13 January 2005 / Revised version: 14 March 2005 / c Societ` Published online: 5 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We study properties of the excitation modes built on the superdeformed states in sulfur isotopes close to the neutron drip line by means of the RPA based on the deformed Woods-Saxon potential in the coordinate mesh representation. We find that the low-lying state created by the excitation of a single neutron from a loosely bound low-Ω state to a high-Ω resonance state acquires an extremely strong octupole transition strength due to the spatially very extended structure of the particle-hole wave functions.

New features, such as neutron skin and shell structure near the continuum, of unstable nuclei close to the neutron drip line are nowadays under lively discussions both theoretically and experimentally. Because properties of lowfrequency excitation modes are quite sensitive to surface effects and details of shell structure, we expect that new kinds of excitations might emerge under such new situation of nuclear structure. We have been investigating such possibilities by means of the self-consistent RPA based on the Skyrme-Hartree-Fock (SHF) mean field. Although such RPA calculations for unstable nuclei are available (see, e.g., refs. [1]), most of them are restricted to the case of spherical nuclei, and low-frequency RPA modes in deformed unstable nuclei remain largely unexplored. In order to clearly see the deformation effects, Inakura et al. investigated properties of negative-parity collective excitations built on superdeformed (SD) states in neutron-rich sulfur isotopes by means of the mixed representation RPA [2], and found many low-energy modes possessing strongly enhanced mass octupole transition strengths. This approach is fully self-consistent in that the same effective interaction is used in both the mean-field and RPA calculations. On the other hand, it is not easy in this method to identify microscopic particle-hole configurations generating individual RPA modes. Therefore, with the use of deformed Woods-Saxon potential and the conventional matrix formulation of the RPA, we have carried out a detailed anala

e-mail: [email protected]

Strength (fm6)

PACS. 21.60.-n Nuclear structure models and methods – 21.60.Jz Hartree-Fock and random-phase approximations

7000 6000 5000 4000 3000 2000 1000 0

isoscalar 50

S Kπ=2−

0

1

3 2 ω (MeV)

4

Fig. 1. Isoscalar octupole transition strengths for the SD state in 50 S close to the neutron drip line, obtained by the RPA calculation with β2 = 0.54 and 0.73 for protons and neutrons, respectively, using the box of size ρmax × zmax = 14.25 fm × 22.0 fm. The arrow indicates the neutron threshold energy Eth = 1.43 MeV.

ysis of microscopic structure of negative-parity excitation modes built on the SD states in the 50 S region. In this approach, we can easily obtain a simple and transparent understanding of the particle-hole configurations generating the RPA eigenmodes. In this paper, as a typical example, we concentrate on the result of calculation for the SD state in 50 S. According to the SHF calculation by Inakura et al. [3], this nucleus

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Fig. 2. The neutron particle-hole excitation contributing to the strongly enhanced octupole transition strength of the K π = 2− state at 3.1 MeV. The particle and hole levels are labeled by the asymptotic quantum numbers [N n3 Λ]Ω. Their wave functions are drawn by the dotted and dash-dotted curves. The neutron single-particle potentials including the centrifugal barrier for Λ = 2 are plotted by solid curves; one as  a function of ρ along the ρ-axis, and the other as a function of ρ2 + z 2 along the θ = 45◦ line.

is situated close to the neutron drip line, and we have chosen the deformation parameter β2 of the SD state so as to approximately reproduce the single-particle spectrum near the Fermi surface obtained there. Figure 1 shows the isoscalar octupole transition strengths with K π = 2− . The highest peak at 3.1 MeV is associated with the excitation of a single neutron from the loosely bound [310]1/2 state to the resonance [422]5/2 state. We also obtain a peak of similar nature but with lower strength at 2.9 MeV, which is associated with the excitation of a single neutron from the loosely bound [431]3/2 state to the resonance [303]7/2 state. This difference in strength between the two peaks is understood from the asymptotic selection rule [4] valid for the lowest-energy particle-hole octupole excitations in the SD harmonic-oscillator potential; the former particle-hole excitation satisfies it whereas the latter does not. On the other hand, the second highest peak at 2.8 MeV is due to a neutron excitation from the loosely bound [431]3/2 state − to a discretized continuum state with Ω π = 1/2 . Therefore, its position and height do not have definite physical meanings. The highest peak at 3.1 MeV has an extremely strong isoscalar octupole transition strength B(QIS 3)  41 W.u. and a weak electric transition strength B(E3)  0.13 W.u. (1 W.u.  149 fm6 for 50 S). The wave functions of the major particle-hole configuration generating this RPA eigenmode are drawn in fig. 2. Because the [310]1/2 state is loosely bound and the [422]5/2 state is a resonance state, their wave functions are significantly extended outside of the half-density radius of this nucleus. This [422]5/2 state has an interesting property: Because the centrifugal barrier is angle dependent, it lies below the barrier for θ ≤ 60◦ while 0.2 MeV above along the ρ-axis (θ = 90◦ ). The resonance character of this state was confirmed by examining

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0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 z (fm) z (fm) z (fm)

Fig. 3. (a) The neutron density distribution of the SD state −3 in 50 S. The contour lines are drawn at intervals  of 0.003 fm . 2

r n = 4.46 fm. The neutron root-mean-square radius is (b) The spatial distribution function Qph 32 (ρ, z) of the octupole transition strength associated with the excitation of a single neutron from the loosely bound [310]1/2 state to the resonance [422]5/2 state on the SD state in 50 S. The contour lines are drawn at intervals of 0.02 fm. (c) The same as (b), but for the octupole excitation from the loosely bound [431]3/2 state to the resonance [303]7/2 state.

the box-size dependence of its energy and also by calculating the eigenphase sum following ref. [5]. It was also checked that this resonance state always exists for relevant values of β2 . We find that not only the resonance [422]5/2 state but also the weakly bound [310]1/2 state has a root-mean-square radius about 1 fm larger than the average value for neutrons. Together with the fact that this particle-hole configuration satisfies the asymptotic selection rule [4], the very extended spatial structures of their wave functions are the main reason why it has the extremely large transition strength. We plot in fig. 3 the spatial distributions of the strengths associated with individual particle-hole excitations, Qph 3K (ρ, z) = ρφp (ρ, z)Q3K (ρ, z)φh (ρ, z),

(1)

where Q3K (ρ, z) = r 3 Y3K e−iKϕ . It is clear that these particle-hole excitations have spatial distributions significantly extended outside of the nucleus. This spatially extended structure brings about the striking enhancement of the octupole transition strength, which may be regarded as one of the unique properties of excitation modes in nuclei close to the neutron drip line. Note that this mechanism of transition strength enhancement is different from the threshold effect associated with the excitation of a loosely bound neutron into the non-resonant continuum. Other examples suggesting that this kind of enhancement phenomena is not restricted to the SD states will be presented elsewhere.

References 1. I. Hamamoto, H. Sagawa, X.Z. Zhang, Phys. Rev. C 53, 765 (1996); 64, 024313 (2001). 2. T. Inakura et al., Int. J. Mod. Phys. E 13, 157 (2004). 3. T. Inakura et al., Nucl. Phys. A 728, 52 (2003). 4. S. Mizutori et al., Nucl. Phys. A 557, 125c (1993). 5. K. Hagino, Nguyen Van Giai, Nucl. Phys. A 735, 55 (2004).

Eur. Phys. J. A 25, s01, 559–562 (2005) DOI: 10.1140/epjad/i2005-06-068-2

EPJ A direct electronic only

Cranking in isospace Applications to neutron-proton pairing and the nuclear symmetry energy W. Satula1,2,a , R. Wyss2 , and M. Rafalski1 1 2

Institute of Theoretical Physics, University of Warsaw, ul. Ho˙za 69, PL-00 681 Warsaw, Poland KTH (Royal Institute of Technology), AlbaNova University Centre, S-106 91 Stockholm, Sweden Received: 8 December 2004 / c Societ` Published online: 6 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Isoscalar pairing interaction and nuclear symmetry energy are investigated by means of the iso-cranking technique. Iso-cranking represents the lowest order approximation to isospin projection after variation. Due to its internal simplicity, it offers a very intuitive understanding of the structure of the nuclear symmetry energy as well as the response of the isoscalar and isovector pairing versus isospin. PACS. 21.60.Jz Hartree-Fock and random-phase approximations

1 Introduction An adequate treatment of the isospin degree of freedom is crucial for our understanding of low-energy nuclear structure excitations. Hereafter, we shall present two applications of the isospin cranking model, which represents the lowest order approximation to isospin projection after variation. Because of its internal simplicity, iso-cranking offers an intuitive understanding to the underlying mechanisms of the isoscalar pairing phenomenon and allows to unveil the physical origin of the nuclear symmetry energy strength. We will start with a brief discussion of the isovector and isoscalar pair fields different response to rotation in isospace [1]. The destructive role of the isospin degree of freedom on the isoscalar pair field and, simultaneously, the neutrality of the isovector pair field can be easily and intuitively understood via a direct analogy between rotations in isospace and real space, respectively. In the second part we will focus on the microscopic structure of the nuclear symmetry energy (NSE) strength within the Skyrme-Hartree-Fock (SHF) method [2]. We will demonstrate that the strength of the NSE originates in part from the discreteness of the single-particle levels characterized by the mean level spacing ε which is governed essentially by the isoscalar mean-potential. We will discuss the influence of non-local effects on ε and, in turn, on the second component of the NSE, namely on the part related directly to the mean isovector potential. We will demonstrate that this part, in spite of the apparent complexity of the Skyrme mean isovector potential, can be characterized essentially by a single number, the strength a

Conference presenter; e-mail: [email protected]

of the effective isospin-isospin vT T = with surprisingly high accuracy.

1 ˆ2 2 κT

interaction,

2 Neutron-proton pairing Isoscalar (T = 0) np-pairing is expected to develop in N ≈ Z nuclei. In these nuclei, the neutron and proton wave functions overlap most strongly and the isoscalar two-body NN interaction is on the average stronger than the isovector (T = 1) NN interaction [3]. However, the T = 0 matrix elements (m.e.) are, unlike the T = 1 m.e., fragmented over different spin (J) values with almost equal preference for anti-parallel J = 1 and parallel J = 2j couplings and with sizable m.e. corresponding to intermediate J-coupling. Moreover, the (T = 0, J) m.e. are weaker than the dominant (T = 1, J = 0) m.e. These two facts tend to erode the potential fingerprints of the isoscalar np-paired condensate causing interpretational difficulties both on the experimental as well as theoretical side. In deformed nuclei, however, individual features of the (T = 0, J) m.e. are expected to become averaged. Hence, one can assume that the basic features of nuclear pairing in deformed N ≈ Z nuclei can be reasonably accounted for by using a standard seniority-type T = 1 pairing interaction and a schematic T = 0 np-pairing interaction:  † ˆ ˆ sp − G1 ˆ =h P1μ − G0 Pˆ0† Pˆ0 , P1μ (1) H where P0† =

√1 2



μ=0,±1

† † a†αn a ˆαp a†αp a ˆαn ¯ −ˆ ¯ ) α>0 (ˆ

denotes the T = 0  ˆ ˆ†ατ a ˆατ pair creation operator and hsp = α,τ =n,p eατ a stands for the deformed phenomenological Woods-Saxon potential. The pure HFB (or BCS) approximation to the

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(2)

20

This term, which is indeed due to the T = 0 interaction as indicated by shell-model studies [6], is essentially beyond the conventional mean-field and must be introduced as a phenomenological correction. Hence, as a first approximation one can ascribe its microscopic origin to the T = 0 pairing which, when strong enough, can naturally account for the missing binding energy, see ref. [5]. A fit to the Wigner energy allows the determination of the unknown strength of the T = 0 pairing interaction G0 . The consistency of this approach can be tested later by calculating the lowest T = 0, 1, 2 isobaric excitations in N = Z nuclei. Such an approach was undertaken in ref. [1] where an excellent agreement with the data was obtained. The key to this success was the proper treatment of both the quasi-particle (qp) excitations and the isospin degree of freedom. The latter was treated within the iso-cranking approximation to the isospin variation after projection: ˆ − ω Tˆx . ˆω = H H

experiment theory

15

36

A

44

52

ωcrit

3 2

48Cr

ΔT=0

ΔT=1

1 0

(3)

The results of our calculations are presented in fig. 1. To understand the role of qp and isospin degrees of freedom let us concentrate on the case of the T = 1 and T = 2 excitations in even-even (e-e) N = Z nuclei. The T = 2, Tz = 0 excitations belong to the isospin quintuplet T = 2, Tz = 0, ±1, ±2, of J = 0 states that include the ground states of N − Z = ±4 nuclei. Hence they are treated as 0qp HFB vacuum cranked  in isospace to√restore the proper value of isospin Tˆx [≡ T (T + 1)] = 6. The T = 1 states, on the other hand, belong to the Tz = 0, ±1 triplet of J = 0 states. Hence, their HFB treatment requires both time reversal symmetry breaking and the isospin symmetry restoration. This can be achieved by isocranking the appropriate√2qp excitation till the frequency is reached where Tˆx  = 2 . The model predicts that the T = 2 states are purely isovector-paired. √ The isocranking frequency necessary to reach Tˆx  = 6 is, in these cases, large enough to break the antiparallel (in isospace) coupled isoscalar pairs, causing a Meißner-type phase transition, see fig. 2. In spite of the good agreement to the data the model has a clear drawback; the isoscalar pair-gaps necessary to reproduce the data are nonphysically large. This is a direct consequence of the lack of the isovector mean-potential (in ex-

28

Fig. 1. The experimental (•) and calculated (◦) excitation energies of the lowest T = 2 states and the lowest T = 1 states in e-e N = Z nuclei, and the difference between the excitation energies of the lowest T = 1 and the lowest T = 0 states in o-o N = Z nuclei, see text and refs. [1, 7] for further details.

Δ [MeV]

Esym =

Excitation energy [MeV]

model Hamiltonian (1) essentially exclude the most interesting mixed-phases, quartetting-type solutions, see [4,5]. To obtain such a solution, the theory requires a supplementary spontaneous isospin symmetry breaking mechanism which can be introduced via the approximate particle-number symmetry projection of Lipkin-Nogami type [5]. A possible manifestation of the np-pairing collectivity is the so called Wigner effect, an extra binding energy in N = Z nuclei. Within the mean-field approach, the Wigner energy is associated with a linear (∼ T ) contribution to the symmetry energy:

0

1

2

3

hω ω [MeV] ] [

4

Fig. 2. Isoscalar (•) and isovector (◦) pair-gap parameters versus iso-cranking frequency calculated for 48 Cr. The figure shows the phase transition from mixed pairing phase to purely isovector pairing phase induced by the fast iso-rotation. Note that ΔT =1 stays fairly constant versus ω because iso-rotation cannot break isovector pairs having parallel coupled isospins.

cited states of N = Z nuclei) in the sp model Hamiltonian (1). Consequently, the additional binding energy due to the np-pairing is used partly to restore the symmetry energy strength asym , and partly to enhance the linear term to its empirical value of λ ≈ 1.25 in N ≈ Z nuclei [8, 9, 10] 1 .

3 The nuclear symmetry energy The missing isovector potential can be simulated by adding an isospin-isospin interaction, see [11], to the 1

See also J. J¨ anecke, these proceedings.

κ [MeV] ε [MeV] ε [MeV]

W. Satula et al.: Cranking in isospace

*

a)

The coupling constants C are either density independent or depend only on the isoscalar density. The definitions of all local densities as well as the relations between the coupling constants C and the auxiliary parameters of the Skyrme force (SF) can be found, for example, in ref. [12].

68

1.5 1.0

b)

SkP SLy4 SIII

1.5

In turn, the isoscalar Γ0 HF potential depends only on the isoscalar C0 coupling constants, while the isovector HF potential Γ1 is defined ultimately by the isovector C1 coupling constants. This property allows us to perform precise tests of eq. (5) using the following two-step procedure. In the first step we switch off the isovector potential Γ1 ≡ 0 by setting all C1 ≡ 0. The calculated excitation energy with respect to the N = Z (at A = const) nu(t=0) (t=0) = 12 εT 2 . cleus, ΔEHF , can be compared to ΔEHF In this way, one can extract the information about ε. In the next step, we perform full SHF calculations and (t=1) (t=0) ≡ ΔEHF − ΔEHF to compare the quantity ΔEHF (t=1) ΔEHF = 12 κT (T + 1), giving us information about κ.

SkO SkXc MSk3

1.0

1.4 1.2 1.0 0.8

c)

2

6

10

14

18

T Fig. 3. Part (a) shows the mean level spacing ε calculated using the isoscalar part of the SHF potential. Part (b) shows  the isoscalar effective mass scaled mean level spacing ε = mm ε.  Note that for larger T the value of ε is almost constant and lies in between the empirical limits for the mean level spacing marked by the shaded area. Part (c) shows the calculated value of κ(A). Note that this value is almost perfectly independent of T . The calculations were done for the A = 68 isobaric chain using several SF parameterizations as indicated in the legend.

Routhian (3):

ˆT ˆ −→ H ˆ T. ˆ ˆ + 1 κT ˆ − [ω − κ T] ˆ − ωT ˆω = H H 2

(4)

The Hartree approximation to (4) corresponds again to the isospin cranking model but with an effective, isospin dependent frequency. Within the HF approximation (no pairing) the model Routhian (4) gives rise to the following symmetry energy formula [2]: Esym =

1 1 (ε + κ)T 2 + κT. 2 2

561

(5)

Let us observe that, at variance with the standard textbook interpretation, part of the symmetry energy strength asym = ε + κ is related directly to the mean spacing of nuclear levels at the Fermi energy, ε, and not to the kinetic energy. The schematic formula (5), can be tested within the fully self-consistent Skyrme-Hartree-Fock (SHF) model. This is due to the fact that the Skyrme force induced local energy density functional can be divided into Skyrme = isoscalar t3= 0 and isovector t = 1 parts E  rH (r) where d t t=0,1 Ht (r) = Ctρ ρ2t +CtΔρ ρt Δρt +Ctτ ρt τt +CtJ J2t +Ct∇J ρt ∇·Jt . (6)

Our calculations, performed by using the code HFODD [13], show certain generic features which are illustrated in fig. 3. Namely, for a given value of A and for small values of N − Z, the values of ε(A, Tz ) change quite rapidly. They tend to stabilize for N − Z ≥ 8 where ε(A, Tz ) → ε(A). The value of the isoscalar-effective-mass  scaled ε (A) = mm ε(A) is 55/A < ε (A) < 66/A, i.e. it lies within the experimental limits. The values of κ(A, Tz ) stabilize much faster, already for N −Z > 4 κ(A, Tz ) → κ(A), showing that κ(A) is free from the kinematic (shell) effects with surprisingly high accuracy. Let us observe that these features are common for all the tested parameterizations of the SF. The only exception is the SkO force with its unconventionally strong isovector component of the spin-orbit term. Such a spin-orbit term is inspired by the relativistic mean-field (RMF) models [14], and indeed our recent study shows that the RMF results follow qualitatively the SkO results [15].

All these features are nicely confirmed by large-scale calculations including isobaric chains of even-even nuclei from A = 20 till A = 128, see [16]. These calculations were performed specifically to establish the mass-number dependence of the nuclear symmetry energy, see fig. 4. The figure clearly shows that i) the values of ε(A) heavily depend on the kinematics (shell effects); ii) in contrast, the values of κ(A) are almost unaffected by the kinematics; iii) both ε(A) and κ(A) show clear surface ∼ 1/A4/3 dependence reducing the dominant volume term ∼ 1/A. Considering only the two lowest-order expansion terms: ε(A) =

εS εV − 4/3 ; A A

κ(A) =

κS κV − 4/3 , A A

(7)

one can establish the volume and the surface contributions to ε and κ. For the case of the SLy4 force the ratio of the surface to the volume parameters equals rε ≡ εS /εV ≈ 1.56 and rκ ≡ κS /κV ≈ 1.45, i.e. rε ≈ rκ ≈ 3/2. The value of rε can be estimated based on the semi-classical formula of the level density developed for a diffuse-wall

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*

1.0

κ ,ε

[MeV]

2.0 1.5

rε ≈

SLy4

κ ~~

0.5

ε*~~

94.5

20

40

A

118.4

A

(1- A ) 1/3

(1- 1.56 ) A 1/3

60

80

100 120 A

ΔEkin [MeV]

Fig. 4. The values of ε (A) and κ(A) calculated for the isobaric chains of e-e nuclei from A = 20 till 128. The curves fitting the calculated points and their parameters are indicated in the figure. The differences between the smooth trends and the calculated points are also shown. These curves nicely illustrate that ε strongly depends on the shell effects while κ is essentially independent of the kinematics.

20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88

100 50 0 -50 0

5

10

15

Fig. 5. Expectation value of the kinetic energy with respect to N = Z nucleus, ΔEkin ≡ Ekin (N − Z, A) − Ekin (0, A), calculated using the SLy4-SHF approach for several isobaric chains of nuclei. Note that ΔEkin does not show any systematic trend when plotted versus N − Z.

potential well by Stocker and Farine [17]: ε(A) ∼ g(F )−1

 SM + ... , 1 − (B) VM 4k



π

4 Summary Applications of the isospin cranking model to np-pairing and the nuclear symmetry energy were briefly discussed. It is demonstrated that this generalized rotation gives an intuitive and simple understanding of the response of the isovector and isoscalar pair-fields with respect to the isospin degree of freedom. It is also shown that the predictions of the iso-cranking model concerning the nuclear symmetry energy are consistent with the self-consistent SHF results. The arguments are given, that part of the symmetry energy strength, which is traditionally connected to the kinetic energy, is related in fact to the mean-level spacing. Moreover, it is demonstrated that the SHF isovector mean-potential can be characterized by an effective two-body interaction ˆ 2 with unexpectedly high precision. vT T = 12 κT This work has been supported by the Foundation for Polish Science (FNP), the G¨ oran Gustafsson Foundation, the Swedish Science Council (VR), the Swedish Institute (SI), and the Polish Committee for Scientific Research (KBN) under Contract No. 1 P03B 059 27.

N-Z

1 ∼ A

≈ 1.52 which almost perfectly matches the

value calculated for the SLy4 force. All these facts seem to confirm very nicely the correctness of the symmetry energy formula (5), and in turn the reliability of the iso-cranking technique. Let us finally point out that the standard, Fermi gas model driven explanation of the symmetry energy coefficient as being partially due to the kinetic energy has no support in our calculations. Indeed, the expectation value of the SHF kinetic energy does not correlate with N − Z as shown in fig. 5.

1.45

0 0

3π (B) 4kF ro

(8)

F

where VM and SM denote the volume and the surface of nuclear matter distribution, respectively. The value of the (B) bulk Fermi momentum is kF ≈ 1.36 fm−1 . The volume coefficient evaluated according to eq. (8) is unrealistic since it corresponds to the Fermi gas model M ≈ estimate. However, assuming spherical geometry SVM 3 , one can expect a rather reliable estimate for the ro A1/3 ratio rε . Adopting for ro ≈ 1.14 fm, i.e. the value consistent with the standard Skyrme force saturation density ρ0 ≈ 0.16 fm−1 , one obtains the ratio of the surface to volume contribution to the symmetry energy equal to

References 1. W. Satula, R. Wyss, Phys. Rev. Lett. 86, 4488 (2001); 87, 052504 (2001). 2. W. Satula, R. Wyss, Phys. Lett. B 572, 152 (2003). 3. N. Anantaraman, J.P. Schieffer, Phys. Lett. B 37, (1971) 229. 4. J. Engel, K. Langanke, P. Vogel, Phys. Lett. B 389, 211 (1996). 5. W. Satula, R. Wyss, Phys. Lett. B 393, 1 (1997). 6. W. Satula et al., Phys. Lett. B 407, 103 (1997). 7. W. Satula, R. Wyss, Acta Phys. Pol. B 32, 2441 (2001). 8. J. J¨ anecke, Nucl. Phys. 73, 97 (1965). 9. J. J¨ anecke et al., Nucl. Phys. A 728, 23 (2003). 10. S. Glowacz et al., Eur. Phys. J. A 19, 33 (2004). 11. K. Neerg˚ ard, Phys. Lett. B 537, 287 (2002); 572, 159 (2003). 12. J. Dobaczewski, J. Dudek, Comput. Phys. Commun. 131, 164 (2000). 13. J. Dobaczewski et al., nucl-th/0501008. 14. P.-G. Reinhard, H. Flocard, Nucl. Phys. A 584, 467 (1995). 15. S. Ban, J. Meng, W. Satula, R. Wyss, in preparation. 16. W. Satula, R. Wyss, M. Rafalski, in preparation. 17. W. Stocker, M. Farine, Ann. Phys. (N.Y.) 159, 255 (1985).

Eur. Phys. J. A 25, s01, 563–565 (2005) DOI: 10.1140/epjad/i2005-06-045-9

EPJ A direct electronic only

Di-neutron correlations in medium-mass neutron-rich nuclei near the dripline M. Matsuoa , K. Mizuyama, and Y. Serizawa Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan Received: 21 October 2004 / c Societ` Published online: 29 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. On the basis of the coordinate-space Hartree-Fock-Bogoliubov and the continuum quasiparticle random phase approximation (QRPA) theories, we demonstrate that a di-neutron correlation exists in the ground states of medium-mass neutron-rich nuclei near the dripline, and we suggest that the soft dipole excitation has the character of di-neutron motion against the remaining A − 2 subsystem. PACS. 21.60.Jz Hartree-Fock and random-phase approximations

Our description of the correlated ground state is based on the formalism of the standard coordinate-space Hartree-Fock-Bogoliubov (HFB) theory [6], In the numerical calculation we adopt the mixed-type densitydependent delta-force as the effective pairing interaction [6], and a Woods-Saxon potential for the particlehole mean field. The spatial behavior of correlated neutron pairs in the ground state |Φ0  can be displayed by

a

Conference presenter; e-mail: [email protected]

(a)

(b)

0.004 0.002 0.000

-8 -4 x [fm] 0

0.006

4

ρ2 /ρn [fm−3]

Pairing among like nucleons is one of the most important many-body correlations in nuclei, influencing strongly properties of low-lying excitations and the ground state. This is true not only in stable nuclei but also in neutronrich nuclei near the drip-line where weak binding of the last neutrons may cause further characteristic behaviors. Indeed in light two-neutron halo nuclei, e.g. in 11 Li, the existence of spatial correlation among the halo neutrons at short relative distances —the di-neutron correlation— is predicted [1, 2,3]. In the present work, we generalize the concept of the di-neutron correlation in heavier neardripline systems, in particular in the medium-mass region, where, although the halo may not develop significantly, many-body coherency can be expected due to the presence of more than two valence neutrons. Here we look into not only the ground state but also the soft dipole excitation whose observation is recently extended up to the oxygen isotopes [4]. We have performed theoretical investigations for even-even 18–24 O, 50–58 Ca and 80–86 Ni. Although we here present figures only for 84 Ni, essentially the same results are obtained for the other isotopes and nuclides [5].

x 8

-8

-4

0 z [fm]

4

8

0.004

84

Ni

0.002 0.000 -10

-5

lcut=8 7 6 5 4 3 2

0

5

10

z [fm]

Fig. 1. (a) Neutron two-body correlation density ρ2 (r ↑, r  ↓)/ ρn (r  ↓) in the ground state of 84 Ni, plotted as a function r on the xz plane. Here the position r  of one reference neutron is fixed at the surface along the z-axis (at the radius Rsurf = 4.8 fm, marked by X). (b) The same quantity but along the z-axis, and the reference neutron is fixed at the exterior position Rsurf + 2 fm marked by the arrow. Here the results obtained by neglecting high-l quasineutron orbits with the cut-off lcut are also shown.

means of the two-body correlation density:  ρ2 (r ↑, r  ↓) = Φ0 | δ(r − ri )δ(r  − rj )δσi ↑ δσj ↓ |Φ0  i =j∈n

−ρn (r ↑)ρn (r  ↓).

(1)

It probes the probability distribution of the pair wave function as ρ2 ≈ | Φ0 |ψn† (r ↑)ψn† (r  ↓)|Φ0 |2 , where ψq† (rσ) is the nucleon creation operator (q = np, σ =↑↓). Figure 1 displays the apparent presence of the dineutron correlation in the ground state. Two neutrons with anti-parallel spins are correlated strongly at short relative distances |r − r  |  2–3 fm, where about a half

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The European Physical Journal A

(a)

(b) full pairing no pairing

5

84

4

Ni

3 2 1 0

25

20

15

10

5

0

E [MeV]

r2 Ppp [fm−1]

(c)0.15 lcut=9 84 lcut=7 lcut=5

Ni

0.10

Transition density [fm−3]

dB(E1)/dE [e2 fm2/MeV]

6

Ni

neutron full pairing no dynamical pairing

Ppp

0.003 0.002 0.001 0 -0.001 -0.002 0

(d)

0.05

84

ρph

0.003 0.002 0.001 0 -0.001 -0.002

5

proton

10

15

r [fm]

0.00

based on a time dependent extension of the coordinatespace HFB, describing a correlated response of a nucleus against an external field (the electric dipole field). Importantly, it takes into account escaping process of neutrons. As the soft dipole excitation often lies above the threshold, precise treatments of the neutron continuum states are necessary. The continuum QRPA facilitates such a description in a microscopic way, and takes into account the pair correlation in the continuum excited state, i.e., the correlation among two escaping neutrons. Figure 2(a) exhibits the presence of the soft dipole excitation in the calculated E1 strength function. We also plot in fig. 2(b) the particle-hole ρph (r) and the particlepair P pp (r) transition densities for this mode, defined respectively by  ψq† (rσ)ψq (rσ) |Φ0  , (2) ρph iq (r) = Φi |

-0.05 0

2

4

6

8

10

12

14

16

18

20

r [fm]

pp Piq (r)

Fig. 2. (a) The calculated E1 strength function in Ni. The threshold for neutron escaping is shown by the arrow. (b) The particle-hole ρph (r) and the particle-pair P pp (r) transition densities for the soft dipole excitation evaluated at E = 4 MeV in 84 Ni. The influence of the neutron pair correlation on P pp (r) is large as shown by the result (dashed line) neglecting the dynamical pair correlation. (c) The particle-pair transition density r 2 P pp (r) showing contributions of high-l quasiparticle states. The thick dashed line is obtained without the dynamical pair correlation. (d) A schematic drawing of the di-neutron picture.

=

σ

Φi | ψq† (r

↑)ψq† (r ↓) |Φ0  .

(3)

84

in the probability distribution of the pair is concentrated for a fixed r  . The localization is clearly seen also in the composition of the two-body correlation density with respect to the contributions of quasiparticle orbits involved; the quasiparticle states having large orbital angular momenta l ∼ 4–8 (about twice the maximum angular momenta of the bound orbits) contribute coherently to form the di-neutron correlation (fig. 1(b)). This is in accord with a relation rd ∼ 2R/lmax between the size of localization rd and the maximum angular momentum lmax (R being the distance from the origin to the center of mass of the di-neutron), which can be expected from the general uncertainty relation. It is found that the di-neutron correlation becomes strong at the surface and the skin regions although it prevails also inside the nuclear volume. The spatial correlation of the di-neutron type is generally seen also in more stable nuclei. In nuclei near the dripline, however, the pair correlation is more significant in the low-density skin region than in the external region of stable nuclei because the density-dependent pair force acts stronger on the neutrons there. The above observations suggest that the di-neutron correlation may be probed in characteristic surface excitation modes of near-dripline nuclei. Here we seek such possibility in connection with the soft isovector dipole mode. For this purpose, we describe the excitation by means of the recently developed continuum quasiparticle random phase approximation (the continuum QRPA) [7]. It is

The latter describes how neutron pairs in an anti-parallel spin configuration move in the excited state |Φi . The calculation (fig. 2(b)) shows that the transition amplitude for the particle-particle channel P pp (r) dominates over the particle-hole amplitude ρph (r) in the external region r  5 fm. Further, a strong enhancement of the neutronpair transition amplitude P pp (r) by about a factor of two is caused by a dynamical pair correlation acting among moving neutrons in the excited state (fig. 2(b)). This indicates that the soft dipole excitation is not a simple uncorrelated excitation of one neutron from a bound orbit to continuum states near the threshold. It is rather the motion of two correlated neutrons in the exterior region. To clarify the nature of the correlation, we decomposed the transition densities with respect to the orbital angular momenta of quasineutron orbits contributing to the soft dipole excitation. It is found that the large enhancement in P pp (r) originates from a coherent superposition of twoquasiparticle configurations [l × (l + 1)]L=1 consisting of continuum quasiparticle orbits with high orbital angular momenta l reaching around l ∼ 10 (fig. 2(c)). The coherent contribution of high-l orbits is in accord with the similar high-l contributions to the di-neutron behavior in the twobody correlation density of the ground state (fig. 1(b)): it may be deduced that the large enhancement of neutron pair transition density P pp (r) has the same origin. This observation susggests that the soft dipole excitation is characterized by the motion of a di-neutron in the nuclear exterior against the remaining A−2 subsystem (fig. 2(d)). This work was supported by the Grant-in-Aid for Scientific Research (No. 14540250) from the Japan Society for the Promotion of Science.

References 1. G.F. Bertsch, H. Esbensen, Ann. Phys. (N.Y.) 209, 327 (1991). 2. M.V. Zhukov et al., Phys. Rep. 231, 151 (1993).

M. Matsuo et al.: Di-neutron correlations in medium-mass neutron-rich nuclei near the dripline 3. F. Barranco et al., Eur. Phys. J. A 11, 385 (2001). 4. A. Leistenschneider et al., Phys. Rev. Lett. 86, 5442 (2001). 5. M. Matsuo, K. Mizuyama, Y. Serizawa, preprint nuclth/0408052.

565

6. J. Dobaczewski, H. Flocard, J. Treiner, Nucl. Phys. A 422, 103 (1984); J. Dobaczewski, W. Nazarewicz, M.V. Stoitsov, Eur. Phys. J. A 15, 21 (2002). 7. M. Matsuo, Nucl. Phys. A 696, 371 (2001); Prog. Theor. Phys. Suppl. 146, 110 (2002).

Eur. Phys. J. A 25, s01, 567–568 (2005) DOI: 10.1140/epjad/i2005-06-203-1

EPJ A direct electronic only

Large-scale HFB calculations for deformed nuclei with the exact particle number projection M.V. Stoitsov1,2,3,4,a , J. Dobaczewski1,2,3,5 , W. Nazarewicz1,2,5 , and J. Terasaki6 1 2 3 4 5 6

Department of Physics & Astronomy, University of Tennessee, Knoxville, TN 37996, USA Physics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831, USA Joint Institute for Heavy-Ion Research, Oak Ridge, TN 37831, USA Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria Institute of Theoretical Physics, Warsaw University, ul. Ho˙za 69, PL-00-681 Warsaw, Poland Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3255, USA Received: 12 September 2004 / c Societ` Published online: 9 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Recent theoretical advances in the large-scale HFBTHO calculations of nuclear ground-state properties are presented with the emphasis on the exact particle number projection. The applicability of the widely used Lipkin-Nogami procedure is discussed together with the analysis of the particle number projection after variation. PACS. 21.10.Dr Binding energies and masses – 21.60.Jz Hartree-Fock and random-phase approximations

1 Introduction Modern nuclear structure theory is rapidly expanding from the description of phenomena in stable nuclei toward regions of exotic short-lived nuclei far from stability. Stringent constraints on the microscopic approach to nuclear dynamics, effective nuclear interactions, and nuclear energy density functionals are obtained from studies of the structure and stability of exotic nuclei with extreme isospin values, as well as extended asymmetric nucleonic matter. The Hartree-Fock-Bogoliubov (HFB) method is a reliable tool for a microscopic self-consistent description of nuclei, which can be used in the context of the density functional theory (DFT). We solve the HFB equations by using the Transformed Harmonic-Oscillator (THO) basis [1], which allows for a correct asymptotic behavior of single-quasiparticle wave functions. The method is adopted for performing massive calculations for many axially deformed nuclei including those which are weakly bound [2]. Recently, it has been shown [3] that the total energy in the particle-number–projected (PNP) HFB approach can be expressed as a functional of the unprojected HFB density matrix and pairing tensor. Its variation leads to a set of HFB-like equations with modified Hartree-Fock fields and pairing potentials. The method has been illustrated within schematic models [3], and also implemented a

e-mail: [email protected]

in HFB calculations with the finite-range Gogny force [4]. In the present paper, we adopt it for the Skyrme functionals and zero-range pairing term; in this case the building blocks of the method are the local densities and mean fields. The HFB results using the Lipkin-Nogami (LN) approximation, followed by the particle-number projection after variation (PLN), are compared to the HFB results with projection before variation (PNP).

2 Particle-number–projected Skyrme-HFB method The particle-number–projected HFB state can be written as  2π 1 ˆ dφ eıφ(N −N ) |Φ, (1) |Ψ  ≡ P N |Φ = 2π 0 ˆ is the number operator, N is the particle number, where N and |Φ is the HFB wave function which does not have a well-defined particle number. As shown in ref. [3], the PNP HFB energy ! ˆ Φ|HP N |Φ dφ Φ|Heiφ(N −N ) |Φ N , (2) = E [ρ, ρ¯] =

Φ|P N |Φ dφ Φ|eiφ(Nˆ −N ) |Φ

is an energy functional of the unprojected particle-hole and pairing densities ρ and ρ¯, respectively. In the case of the Skyrme force, the projected energy (2) reads     N ˜ φ) , (3) E [ρ, ρ˜] = dφ y(φ) dr H(r, φ) + H(r,

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The European Physical Journal A

 and Y (φ) = ie−iφ sin φC(φ) − i dφ y(φ )e−iφ sin φ C(φ )   −1 . The gauge-angle– and C(φ) = e2iφ 1 + ρ(e2iφ − 1) ˜ dependent field matrices h(φ) and h(φ) are obtained by simply replacing the particle and pairing local densities in the unprojected fields with their gauge-angle–dependent counterparts.

-218 -220 -222 48

Ca

-224

E - λN (MeV)

LN PLN PNP

24 26 28 30 32 N

| (MeV)

Neutron Pairing

1.5 1.0

pair

6

|En

0.5 4

0.0

pair

|Ep

0.04

PLN rms Differences protons neutrons

Proton Pairing

3

RPLN - RPNP (fm)

| (MeV)

Energy Differences

EPLN/LN - EPNP (MeV)

8

0.02 2

0.00

20

30

40

50

20

30

40

50

NEUTRON NUMBER Fig. 1. The LN and PLN (projection after variation) and PNP HFB (projection before variation) results obtained for the SLy4 force and mixed delta pairing. Arrows in the top panel indicate projection results from the neighboring nuclei.

where 1 e−iφN det(eiφ I)  , 2π det C(φ)

x(φ) , dφ x(φ ) (4) I is the unit matrix, and the gauge-angle–dependent en˜ φ) are derived from the ergy densities H(r, φ) and H(r, unprojected ones by simply replacing particle (pairing) local densities by their gauge-angle–dependent counterparts. The latter ones are defined by the gauge-angle– dependent density matrices. Obviously, the projected energy (3) is a functional of the unprojected density matrices. Its derivatives with respect to ρn n and ρ˜n n lead to the PNP Skyrme-HFB equations  N N     ˜ h h U U N = E , (5) ˜ N −hN V V h x(φ) =

y(φ) =

where 

  dφy(φ) Y (φ)E(φ) + e−2iφ C(φ)h(φ)C(φ)

 ˜ ρ(φ)h(φ)C(φ) + h.c. , (6) − dφy(φ)ie−iφ sin(φ)˜  1 2 1 T ˜ ˜ dφy(φ)e−iφ h(φ)C(φ) + (h(φ)C(φ)) , = 2

hN =

˜N h

3 Results Figure 1 shows the PNP results for the complete chain of the calcium isotopes (from the proton drip to the neutron drip line), calculated with the SLy4 Skyrme functional and mixed delta pairing [1]. Comparison is also made with the LN and PLN results. One can conclude that the PLN approximation works best for open-shell nuclei, where the total energy differences between various variants of calculations are less than 250 keV. For closed-shell nuclei [5], however, the energy differences increase to more than 1 MeV. In such cases, one can improve the PLN results by applying the projection to the LN solutions obtained for the neighboring nuclei [6], as illustrated in the top panel of fig. 1. In summary, the Skyrme HFBTHO PNP framework has been implemented and tested. The particle number corrections maximize for magic nuclei where the static pairing breaks down. It is to be noted that conceptual questions related to the notion of symmetry restoration in DFT still remain; those will be discussed in the following work [7]. This work was supported in part by the U.S. Department of Energy (contract Nos. DE-FG02-96ER40963, DE-AC0500OR22725, and DE-FG05-87ER40361); by the National Nuclear Security Administration under the Stewardship Science Academic Alliances program (contract DE-FG03-03NA00083); by the Polish Committee for Scientific Research (KBN) (contract No. 1 P03B 059 27) and by the Foundation for Polish Science (FNP).

References 1. M.V. Stoitsov, P. Ring, D. Vretenar, G.A. Lalazissis, Phys. Rev. C 58, 2086 (1998); M.V. Stoitsov, W. Nazarewicz, S. Pittel, Phys. Rev. C 58, 2092 (1998); M.V. Stoitsov, J. Dobaczewski, P. Ring, S. Pittel, Phys. Rev. C 61, 034311 (2000); M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, S. Pittel, D.J. Dean, Phys. Rev. C 68, 054312 (2003). 2. Mass tables are available at: http://www.fuw.edu.pl/ ∼dobaczew/thodri/thodri.html. 3. J.A. Sheikh, P. Ring, Nucl. Phys. A 665, 71 (2000). 4. M. Anguiano, J.L. Egido, L.M. Robledo, Nucl. Phys. A 696, 476 (2001). 5. J. Dobaczewski, W. Nazarewicz, Phys. Rev. C 47, 2418 (1993). ´ 6. P. Magierski, S. Cwiok, J. Dobaczewski, W. Nazarewicz, Phys. Rev. C 48, 1686 (1993). 7. J. Dobaczewski, W. Nazarewicz, P.G. Reinhard, M. Stoitsov, in preparation.

Eur. Phys. J. A 25, s01, 569–570 (2005) DOI: 10.1140/epjad/i2005-06-130-1

EPJ A direct electronic only

Collective excitations induced by pairing anti-halo effect M. Yamagamia Heavy Ion Nuclear Physics Laboratory, RIKEN, Hirosawa 2-1, Wako, Saitama 351-0198, Japan Received: 10 December 2004 / Revised version: 7 March 2005 / c Societ` Published online: 24 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We emphasize a special interplay of loosely-bound neutrons with small orbital angular momentum  and self-consistent pairing correlations for low-lying collective vibrational excitations in neutron drip line nuclei. Change of the spatial structure in quasiparticle wave functions by self-consistent pairing correlations leads to the broad localization of two-quasiparticle states with low- neutrons. We show that the broad localization can cause the enhancement of the low-lying collectivity. By performing HFB plus quasiparticle random phase approximation (QRPA) calculation for the first 2 + states in neutron rich Ni isotopes, the unique role of self-consistent pairing correlations is examined. Finally we make a comment on deformation effects for low-lying vibrational excitations in neutron drip line nuclei. PACS. 21.10.Re Collective levels – 21.60.Ev Collective models – 21.60.Jz Hartree-Fock and random-phase approximations

1 Introduction Vibrational excitations are microscopically represented by coherent superposition of two-quasiparticle states (or oneparticle–one-hole (1p-1h) states in closed shell nuclei), and the spatial localization of two-quasiparticle states is one of the important conditions to produce correlations among them. In stable nuclei, because tightly-bound states are mainly involved in the low-lying vibrational excitations, the two-quasiparticle states spatially concentrate around the surface region. In neutron drip line region, by contrast, the contributing single-particle states are loosely-bound states, resonant states and non-resonant continuum states. Because the two-quasiparticle states among them have a rich variety of spatial structures, we may expect qualitatively new aspects of low-lying vibrational excitations in neutron drip line nuclei. In the present study we analyze the spatial structure of the two-quasiparticle states involving loosely-bound and resonant states of low- neutrons. We emphasize the unique role of self-consistent pairing correlations for their induced spatial localization, the broad localization, and the possible enhancement of low-lying collectivity in neutron drip line nuclei.

2 Spatial structure of two-quasiparticle states We examine the spatial structure of the neutron quadrupole two-quasiparticle states in 86 Ni, that is the neutron drip line nucleus within Hartree-Fock (HF) calculation with Skyrme SLy4 force. In this section we solve a

Conference presenter; e-mail: [email protected]

the simplified Hartree-Fock-Bogoliubov (HFB) equation in coordinate space [1, 2]. For the mean field, the spherical Woods-Saxon potential with VWS = −41.4 MeV and RWS = 5.5 fm are used. These parameters simulate the neutron shell structure in 86 Ni. The calculated neutron single-particle states around the Fermi level of 3s1/2 (εh = −0.50 MeV) are 2d5/2 (εh = −1.77 MeV), resonant d3/2 (εp ≈ 0.14 MeV), and resonant g7/2 (εp ≈ 0.98 MeV). The index h (p) represents all necessary quantum numbers to specify the hole (particle) state. The spatial distribution of the particle-hole component of the two-quasiparticle state with a hole part vlj (Elj,n , r) and a particle part ul j  (El j  ,n , r) [1,2] is defined by (L) (r) ≡ {rul j  (El j  ,n , r)}r L {rvlj (Elj,n , r)}/Nuv . (1) Fuv

The normalization factor, Nuv = ul j  ,n vlj,n , is introduced, and the coefficient ul j  ,n (vlj,n ) is the norm of the wave function ul j  (El j  ,n , r) (vlj (Elj,n , r)). L is the multipolarity of the transition, and monopole transitions are taken into account with L = 2. Elj,n is the quasiparticle energy. In our analysis the continuum states are discretized by imposing the box boundary condition with a box radius Rbox = 75 fm. The distribution without pair(L) ing, Fph (r), is similarly defined [1,2]. In fig. 1 the spatial distribution of the low-lying neutron quadrupole 1p-1h excitations without pairing of the configurations; (a) 3s1/2 → resonant d3/2 , (b) 2d5/2 → resonant d3/2 , and (c) 2d5/2 → resonant g7/2 , are shown. They are localized around the surface region, and the correlations among them can cause some collectivity. However the configuration (a) only has the sizable component outside the surface that cannot correlate with the other 1p-1h states. Therefore the first 2+ state, that is a discrete

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6

L=2

4

s1/2

d3/2

2

d5/2 d5/2

d3/2 g7/2

B(E2;0+ 2+) [e2fm4]

No pairing

0

RWS=5.5 fm

-2

0

10

VWS=−41.4 MeV

30

20

r [fm] Fig. 1. The spatial distribution of the neutron quadrupole 1p-1h states with εp − εh < 5 MeV in 86 Ni. 10

HFB pairing

L=2

6

s1/2 s1/2

d3/2 d5/2

4

g7/2 g7/2

d3/2 d5/2

d3/2 d3/2 d3/2 d5/2 d5/2 d5/2

Fuv(r) [fm]

8

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RWS=5.5 fm 0

10

20

s1/2 d5/2 g7/2 s1/2 d3/2 g7/2

40

SLy4

HFB

1000 800 600

Resonant BCS

400 200

HF 52 80

54 82

56 84

58 86

60 88

62 90

A + + Fig. 3. The B(E2, 0+ states 1 → 21 ) values of the first 2 in neutron rich Ni isotopes calculated by HFB plus QRPA, resonant BCS plus QRPA, and RPA with Skyrme SLy4 force.

3 HFB plus QRPA calculations

VWS=−41.4 MeV 30

Ni isotopes

matrix elements, and may cause the enhancement of the low-lying collectivity in neutron drip line nuclei [2].

0 -2

1200

0 50 78

50

40

1400

50

r [fm] Fig. 2. The spatial distribution of the neutron quadrupole twoquasiparticle states among the low-lying resonant s1/2 , d3/2 , d5/2 , and g7/2 states in 86 Ni.

solution in RPA, behaves as a single-particle like excitation with the dominant component of (a) [1,2]. Pairing correlation is one of the important ingredients in low-lying collective vibrational excitations. By taking into account pairing correlation, as known in stable nuclei, not only the particle-hole channel but also the particleparticle and hole-hole channels participate in vibrational excitations, and help to increase the collectivity. In addition, self-consistent pairing correlations have unique effects that change the spatial structure of quasiparticle wave functions in loosely-bound nuclei; namely “the pairing anti-halo effect” in the lower component vlj (r) [3], and “the broadening effect” in the upper component ulj (r) [2]. These effects are more prominent in lower- neutrons. In fig. 2 the spatial distributions of the twoquasiparticle states among the neutron low-lying resonant s1/2 , d3/2 , d5/2 , and g7/2 states are shown. The quasiparticle wave functions at the lowest resonant peak energy are adopted for the plot. The distributions involving the s and d states have sizeable components around the spatially extended region, 10 fm < r < 20 fm, in addition to the surface region where the localization is achieved in stable nuclei. We call such spatially extended but localized distribution “the broad localization”. On the other hand the two-quasiparticle states with the g7/2 state concentrate only around the surface region. The broad localization among low- neutrons can have the large transition

By performing HFB plus QRPA calculation with Skyrme SLy4 force, we investigate the first 2+ states in neutron + rich Ni isotopes. In fig. 3 the B(E2, 0+ 1 → 21 ) values of + 88 the first 2 states up to Ni are shown. These states are discrete solutions below the threshold energies. For comparison the results by resonant BCS plus QRPA and RPA are also shown. As approaching the neutron drip line, the B(E2) values increase in HFB plus QRPA, on the other hand, decrease in resonant BCS plus QRPA, and much smaller in RPA. The broad localization is realized only in HFB, and causes the qualitative difference of the low-lying excitations [1,2].

4 Roles of quadrupole deformation Finally we briefly mention the effects of quadrupole deformation. Because of the breaking of the rotational symmetry and the mixing of isoscalar and isovector modes in deformed neutron drip line nuclei, the low-lying negative parity excitations with K π = 0− , 1− are conjectured to behave like collective soft dipole modes with pear (Y10 + Y30 mixed) or banana (Y11 + Y31 mixed) shape vibration. The possibility of the strong collectivity enhancement by the interplay of self-consistent pairing correlations and loosely-bound low-Ω neutrons, where Ω is the component of one-particle angular momentum along the symmetry axis, is discussed.

References 1. M. Yamagami, in Proceedings of the Fifth Japan-China Joint Nuclear Physics Symposium, edited by Y. Gono, N. Ikeda, K. Ogata (Kyushu University, Fukuoka, 2004) p. 218, preprint nucl-th/0404030. 2. M. Yamagami, submitted to Phys. Rev. C, preprint nuclth/0504059. 3. K. Bennaceur et al., Phys. Lett. B 496, 154 (2000).

Eur. Phys. J. A 25, s01, 571–572 (2005) DOI: 10.1140/epjad/i2005-06-076-2

EPJ A direct electronic only

Continuum effects on the pairing in neutron drip-line nuclei studied with the canonical-basis HFB method N. Tajimaa Department of Applied Physics, Fukui University, 910-8507, Japan Received: 30 November 2004 / Revised version: 11 February 2005 / c Societ` Published online: 12 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The canonical-basis HFB method provides an efficient way to describe pairing correlations involving the continuum part of the single-particle spectrum in coordinate-space representations. It can be applied to super-conducting deformed drip-line nuclei as easily as to stable or spherical nuclei. This method is applied to a simulation of the approach to the neutron drip line. It turns out that the HFB solution has a stronger pairing and a smaller deformation as the Fermi level is raised. However, such changes are smooth and finite. No divergences or discontinuities of the radius or other quantities are found in the limit of zero Fermi energy. The nuclear density continues to be localized even a little beyond the drip line. PACS. 21.10.Pc Single-particle levels and strength functions – 21.30.Fe Forces in hadronic systems and effective interactions – 21.60.Jz Hartree-Fock and random-phase approximations

In nuclei near the neutron drip line, the pairing correlation among the neutrons involves significantly the continuum (positive-energy) part of the Hartree-Fock (HF) single-particle states. In principle, there is no difficulty to treat such nuclei with the Hartree-Fock-Bogoliubov (HFB) method, which is the framework to incorporate the pairing correlation into mean-field approximations. Indeed, there is no practical problem concerning spherical nuclei [1, 2]. However, deformed nuclei are not so easy to treat. The difficulty originates in the huge number of quasiparticle states, most of which are spatially dislocalized continuum-spectrum states. In the quasi-particle formalism, two methods have been used to overcome the difficulty, one using transformed oscillator basis [3] and the other using a coordinate mesh but only for axially symmetric nuclei [4]. Mathematically, HFB ground states can be expressed in the form of the BCS variational function. The singleparticle states in this expression are localized. They are called the HFB canonical basis. This localization makes the level density of the canonical basis by far smaller than that of the quasiparticle states because the former is proportional to the volume of the nucleus while the latter to the volume of the cavity to discretize the positive energy orbitals. The canonical-basis HFB method enables one to obtain the canonical orbitals without knowing anything about the huge number of quasiparticle states. It can be applied to deformed neutron-rich nuclei without difficulties. a

Conference presenter; e-mail: [email protected]

The canonical-basis HFB method was originally introduced for spherical nuclei in ref. [5]. I improved the method and implemented it for deformed nuclei [6,7]. I also found the necessity of momentum dependence for the contact pairing interactions if one employs completely coordinate-space representations (like three-dimensional Cartesian mesh, unlike the radial mesh). In quasiparticle HFB method, the canonical orbitals are obtained from the one-body density matrix and thus people have not noticed the existence of a more direct relation to the Hamiltonian. The canonical-basis formalism discloses this relation. Namely, canonical orbitals above the Fermi level are roughly the bound eigenstates of the pairing Hamiltonian. It is not the HF Hamiltonian which generates them. This finding is helpful to understand the shell structure in the continuum part of the spectrum [7]. Now, let me show a result of a calculation performed with the canonical-basis method. It is a simulation of the approach to the neutron drip line. The system is the N = Z = 14 nucleus. Instead of increasing the difference N − Z, I modify the parameters of the mean-field interaction. Namely, t0 of the Skyrme force is increased (toward zero from below) to raise the Fermi level while t3 (> 0) is decreased so that the saturation density of the symmetric nuclear matter is unchanged. This approach is taken only because the present version of my computer program is designed for N = Z systems. I will examine the adequacy of this approach in future. The interaction in the mean-field channel is the Skyrme SIII force [8] without the spin-orbit term. The coulomb force is also turned off. Owing to the omission of

GAP (MeV)

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5 4

40

3

SINGLE-PARTICLE ENERGY (MEV)

2 1 0

BETA

0.3 0.2 0.1

RMS RADIUS (FM)

0

6

20

0

-20 4 2 0 -12

-10

-8

-4 -6 FERMI LEVEL (MEV)

-2

0

Fig. 1. The average pairing gap (top), the quadrupole deformation parameter β (middle), and the root-mean-square radius (bottom) plotted versus the Fermi level.

these two interactions, the single-particle states are fourfold degenerated. I take into account 70 canonical basis states in each of the four spin-isospin sectors. The parameters of the pairing interaction [7] are vp = −880 MeV fm3 , kc = 2 fm−1 , and ρc = 0.32 fm−3 , and ρ˜c = ∞. A three-dimensional Cartesian mesh representation is employed to express the single-particle wavefunctions without assuming any spatial symmetries. The mesh spacing is 0.8 fm while the edge of the cubic cavity is 40 fm. Figure 1 shows how the HFB ground state changes as the Fermi level (λ) rises. The pairing gap is enhanced almost by a factor of two at the drip line (where λ = 0 MeV) compared with the solution for the original SIII force (λ = −11.7 MeV). The quadrupole deformation β is decreased by the enhanced pairing. The nucleus has a large prolate deformation at λ = −11.7 MeV but becomes spherical for λ > −5.5 MeV. On the other hand, the r.m.s. radius does not change so much. Its increase is only 35% even at the drip line. Dislocalization of the density occurs not at λ = 0 MeV but at higher λ (0.8 MeV). One can see only smooth changes at λ ∼ 0 MeV. Figure 2 shows the energies (expectation value of the HF Hamiltonian) of canonical-basis states. One can see that discrete bound states are obtained for both negative and positive energies. For λ > −5.5 MeV, the nucleus becomes spherical and the levels are degenerated. At λ ∼ −3 MeV, the orbitals are (from the bottom) s, p, s, d, p, f, s, d, g, etc. Here again, there seems to be no violent changes at λ ∼ 0 MeV. Positive-energy localized s orbitals begin to spread over the cavity only for λ > 300 keV. Considering general properties of HFB solutions [1], the true ground state must be a dislocalized state. The reason for the appearance of a localized solution seems to be as follows. The dislocalization of an orbital requires

-40 -12

-10

-8

-4 -6 FERMI LEVEL (MEV)

-2

0

Fig. 2. Expectation value of the HF Hamiltonian for each canonical-basis state plotted versus the Fermi level.

the increase of v 2 toward 1 because otherwise the orbital is confined in the pairing potential, which is usually very deep compared with the size of the kinetic energy term of the pairing Hamiltonian. However, since v 2 = 1 corresponds to weaker pairing correlation and larger total energy, a dislocalized solution is not necessarily reached in the iteration process of the gradient method in certain circumstances like when the Fermi level is positive but low. In contrast, with methods based on the diagonalization of the quasi-particle Hamiltonian, a direct jump to v 2 = 1 can take place and it results in the dislocalization of the corresponding orbital as soon as it becomes energetically favorable. The localized HFB solutions for positive Fermi energies obtained in the canonical-basis formalism may be used as rough approximations to the nuclei just beyond the neutron drip line.

References 1. J. Dobaczewski, H. Flocard, J. Treiner, Nucl. Phys. A 422, 103 (1984). 2. J. Dobaczewski, W. Nazarewicz, T.R. Werner, J.F. Berger, C.R. Chinn, J. Decharg´e, Phys. Rev. C 53, 2809 (1996). 3. M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, S. Pittel, D.J. Dean, Phys. Rev. C 68, 054312 (2003). 4. E. Ter´ an, V.E. Oberacker, A.S. Umar, Phys. Rev. C 67, 064314 (2003). 5. P.G. Reinhard, M. Bender, K. Rutz, J.A. Maruhn, Z. Phys. A 358, 277 (1997). 6. N. Tajima, in Proceedings of the XVII RCNP International Symposium on Innovative Computational Methods in Nuclear Many-Body Problems, Osaka, 1997, edited by H. Horiuchi et al. (World Scientific, Singapore, 1998) p. 343. 7. N. Tajima, Phys. Rev. C 69, 034305 (2004). 8. M. Beiner, H. Flocard, Nguyen van Giai, P. Quentin, Nucl. Phys. A 238, 29 (1975).

Eur. Phys. J. A 25, s01, 573–574 (2005) DOI: 10.1140/epjad/i2005-06-095-y

EPJ A direct electronic only

Pairing effects on the collectivity of quadrupole states around 32 Mg M. Yamagami1,a and Nguyen Van Giai2 1 2

Heavy Ion Nuclear Physics Laboratory, RIKEN, Hirosawa 2-1, Wako, Saitama 351-0198, Japan Institut de Physique Nucl´eaire, IN2P3-CNRS, 91406 Orsay Cedex, France Received: 10 December 2004 / Revised version: 11 January 2005 / c Societ` Published online: 11 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The anomalous E2 properties of the first 2+ states in neutron-rich nuclei 32 Mg and 30 Ne are studied by the Hartree-Fock-Bogoliubov (HFB) plus quasiparticle random phase approximation (QRPA) calculations. The large B(E2) values and the low excitation energies of the first 2 + states are well described by the HFB plus QRPA calculations with spherical symmetry. We conclude that pairing effects account largely for the anomalously large quadrupole collectivity. PACS. 21.10.Ky Electromagnetic moments – 21.10.Re Collective levels – 21.60.Ev Collective models – 21.60.Jz Hartree-Fock and random-phase approximations

1 Introduction

2 Ground-state properties in N = 20 isotones HFB calculations with Skyrme SkM* force are performed for N = 20 isotones from 30 Ne to 40 Ca [7]. The densitya

Conference presenter; e-mail: [email protected]

N=20 isotones

Δn [MeV]

The breaking of the N = 20 shell closure is clearly shown in the observed anomalous E2 properties; the large B(E2) value [1] and the low excitation energy, of the first 2+ state in 32 Mg. Several theoretical studies have shown the importance of the neutron 2p-2h configurations across the N = 20 shell gap to describe the anomalous E2 properties (e.g., [2]). Although the appearance of the 2p-2h configurations imply deformation of the ground state, the microscopic origin is still under great debate. The observed + 32 Mg [3, 4], and this energy ratios E(4+ 1 )/E(21 ) is 2.6 in value is in between the rigid rotor limit 3.3 and the vibrational limit 2.0. The B(E2) value (in single-particle units) is 15.0 ± 2.5 in 32 Mg, and this value is smaller than that in “deformed” Mg isotopes (21.0 ± 5.8 in 24 Mg, 19.2 ± 3.8 in 34 Mg [5]). Moreover, the calculated ground state in 32 Mg have been found to be spherical in mean-field calculations (e.g., [6]). In general, the neutron 2p-2h configurations can originate not only from deformation but also from neutron pairing correlations. In 32 Mg these two effects may coexist and help to make the anomalous E2 properties. In the previous studies it is not clear which effect is more essential to describe the anomalous properties.

1.5

neutron

1

SkM*

0.5

0 8

10

12

14

16

18

20

22

Z Fig. 1. The neutron pairing gaps in N = 20 isotones by HFB calculations with Skyrme SkM* force.

dependent pairing interaction, Vpair (r, r  ) = 12 Vpair (1 − Pσ )[1 − ρ(r)/ρc ]δ(r − r  ),

(1)

is used for the pairing field. The parameters Vpair = −418 MeV · fm−3 and ρc = 0.16 fm−3 with the quasiparticle cut-off energy Ecut = 50 MeV reproduce the experimental neutron pairing gap in 30 Ne. As shown in fig. 1 the calculated neutron pairing gaps change from 1.26 MeV in 30 Ne to almost zero in 36 S, although the size of the N = 20 shell gaps changes slowly as approaching 30 Ne (fig. 2). The mechanism can be understood by the change of the level density in the f p shell. As close to 30 Ne, the single-particle energy (SPE) of the high-l orbit 1f7/2 change almost linearly while the changes of 2p3/2 and 2p1/2 SPEs become very slow. Moreover, the spin-orbit splitting between 2p3/2 and 2p1/2 states becomes smaller. Consequently the level density in the f p shell becomes higher in 32 Mg and 30 Ne.

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-15 -20

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N=20 isotones

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Fig. 2. Neutron single-particle energies in N = 20 isotones by HF calculations with Skyrme SkM* force. Single-particle energies of bound and resonant states are connected by solid lines. The energies of (discretized) non-resonant continuum states are also shown by dashed lines.

8

10

12

14

16

18

20

Z Fig. 4. The excitation energies of the first 2+ states in N = 20 isotones by HFB plus QRPA calculations with Skyrme SkM* force. For comparison the available experimental data [1, 9] and the results of shell model calculations [2] are also shown. 700

700

B(E2;0+ 2+) [e2fm4]

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B(E2;0+ 2+) [e2fm4]

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QRPA (SkM*) Shell Model Exp.

600 500 400

N=20 isotones

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εi [MeV]

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500

N=20 isotones

400 300

100 0

8

10

12

14

16

18

20

Z + Fig. 3. The B(E2, 0+ 1 → 21 ) transition probabilities of the first 2+ states in N = 20 isotones by HFB plus QRPA calculations with Skyrme SkM* force. For comparison the available experimental data [1, 9] and the results of shell model calculations [2] are also shown.

Within HFB calculations with spherical symmetry, the N = 20 shell gap is naturally broken by neutron pairing correlations.

3 Anomalous E2 properties in N = 20 isotones We have performed HFB plus QRPA calculations for the first 2+ states in N = 20 isotones [7]. The QRPA equations are solved in coordinate space by using the Green’s function method [7,8]. To emphasize the role of neutron pairing correlations, spherical symmetry is imposed. The residual interaction is consistently derived from the hamiltonian density of Skyrme force that has an explicit velocity dependence. To reduce the numerical task, the spin-spin parts, the Coulomb parts, and the spin-orbit parts in the resiual interactions are dropped. We impose an approximate self-consistent condition on the residual interaction with a renormalization factor fR , Vres → fR Vres , so as to have the spurious J π = 1− state at zero energy. The typical value is fR ≈ 0.93 in this study. A detailed account of our QRPA calculation can be found in ref. [7]. In figs. 3

Δn =0

200

8

10

12

14

16

18

20

Z + + Fig. 5. The B(E2, 0+ states in 1 → 21 ) values of the first 2 N = 20 isotones with/without neutron pairing. Proton pairing is included in both calculations.

and 4 our QRPA results are compared with the available experimental data [1,9] and the results of shell model calculations [2]. The QRPA calculations have been done with SkM* and the fixed pairing strength. The general properties of the first 2+ states in N = 20 isotones, especially large quadrupole collectivity in 32 Mg and 30 Ne, are well reproduced. In fig. 5 the B(E2) values with/without neutron pairing are shown. Proton pairing is included in both calculations. Without neutron pairing, we cannot explain the anomalous E2 properties. Under these considerations, we can conclude that the neutron pairing correlations account largely for the anomalous E2 properties in 32 Mg and 30 Ne.

References 1. T. Motobayashi et al., Phys. Lett. B 346, 9 (1995). 2. Y. Utsuno, T. Otsuka, T. Mizusaki, M. Honma, Phys. Rev. C 60, 054315 (1999). 3. K. Yoneda et al., Phys. Lett. B 499, 233 (2001). 4. D. Guillemaud-Mueller, Eur. Phys. J. A 13, 63 (2002). 5. H. Iwasaki et al.. Phys. Lett. B 522, 227 (2001). 6. P. -G. Reinhard et al., Phys. Rev. C 60, 014316 (1999). 7. M. Yamagami, Nguyen Van Giai, Phys. Rev. C 69, 034301 (2004). 8. E. Khan et al., Phys. Rev. C 66, 024309 (2002). 9. Y. Yanagisawa et al., Phys. Lett. B 566, 84 (2003).

8 Heavy elements 8.1 Structure and chemistry

Eur. Phys. J. A 25, s01, 577–582 (2005) DOI: 10.1140/epjad/i2005-06-147-4

EPJ A direct electronic only

Beyond darmstadtium —Status and perspectives of superheavy element research D. Ackermanna Gesellschaft f¨ ur Schwerionenforschung GSI, Planckstr. 1, D-64291 Darmstadt, Germany and Johannes Gutenberg-Universit¨ at Mainz, Germany Received: 12 September 2004 / c Societ` Published online: 26 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The search for superheavy elements has yielded exciting results for both the “cold fusion” approach with reactions employing Pb and Bi targets and the “hot fusion” reactions with 48 Ca beams on actinide targets. In recent years the accelerator laboratories in Berkeley, Dubna and Darmstadt have been joined by new players in the game in France with GANIL, Caen, and in Japan with RIKEN, Tokyo. The latter yielding very encouraging results for the reactions on Pb/Bi targets which confirmed the data obtained at GSI. Beyond the successful synthesis, interesting features of the structure of the very heavy nuclei like the hint for a possible K-isomer in 270 Ds or the population of states at a spin of up to 22 in 254 No give a flavor of the exciting physics we can expect in the region at the very extreme upper right of the nuclear chart. To get a hand on it, a considerable increase in sensitivity is demanded from future experimental set-ups. High intensity stable beam accelerators, mass measurement in ion traps and mass spectrometers, as well as the possible employment of unstable neutron-rich projectile species, initially certainly only for systematic studies of reaction mechanism and nuclear structure features for lighter exotic neutron-rich isotopes, are some of the technological challenges which have been taken on. PACS. 24.75.+i General properties of fission – 25.70.Gh Compound nucleus – 25.70.Jj Fusion and fusionfission reactions

1 Introduction The community engaged in the synthesis and investigation of superheavy elements (SHE), traditionally undertaken at the FLNR/JINR in Dubna, Russia at the LBNL in Berkeley, California (USA) and at GSI in Darmstadt, Germany has recently been joined by other laboratories. In particular GANIL in Caen, France and RIKEN in Tokyo, Japan have started substantial experimental programs in this field of nuclear physics. Combined efforts have yielded impressive results in both approaches the hot fusion with actinide target, recently performed successfully using 48 Ca beams at Dubna [1], and the fusion on Pb and Bi targets leading to compound systems of relatively low excitation energy. Whereas the Dubna results still lack confirmation, despite various attempts at LBNL for the reaction 48 Ca + 238 U, the groups at GANIL and, in particular, at RIKEN succeeded in reproducing the GSI results. Here an overview over the recent development at LBNL, GANIL and RIKEN will be given after a more detailed description of the present activities at GSI including the achievements in the synthesis of heavy elements and the investigation of the nuclear structure of heavy isotopes. a

Conference presenter; e-mail: [email protected]

The present sensitivity limit is at a production cross section of ≈ 1 pb. The efforts to push this limit down to even lower values at GSI by various development activities to increase the set-up sensitivity are presented at the end of the paper.

2 Synthesis and identification of superheavy elements at GSI/SHIP The identification of superheavy elements in heavy ion fusion reactions is based on two major ingredients: the separation of the fusion products in flight from the beam particles and the identification of the products via evaporation residue(ER)-α correlations. The velocity filter SHIP at GSI provides separation, using the velocity difference between the faster beam and the slower fusion products in the fashion of a classical Wien-filter, via the comparison of crossed E- and B-fields —in the case of SHIP in a separated field configuration. The particles passing the velocity filter are then implanted into a position sensitive silicon strip detector set-up where position, time and energy of the fusion products and subsequent decays by α emission and spontaneous fission are recorded. The Z and A identification of the starting point of those decay chains is unambiguously provided by the connection to known α emitters

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Fig. 1. Separation, detection and identification of fusion reaction products with the velocity filter SHIP and the ER-α(-α) correlation method. As an example the first decay chain observed in the reaction 70 Zn + 208 Pb → 277 112 + 1n.

at the end of the decay sequence. In fig. 1 the method is illustrated for the example of the first decay chain, observed in the reaction 70 Zn + 208 Pb → 277 112 + 1n in 1996 ref. [2]. The elements with Z = 107–112 have been synthesized and unambiguously identified at SHIP. The elements 107– 111 have already been named and have been entered as bohrium (Bh, Z = 107), hassium (Hs, Z = 108), meitnerium (Mt, Z = 109), darmstadtium (Ds, Z = 110) and roentgenium (Rg, Z = 111) in the periodic table of elements. A summary of these experiments can be found in ref. [3]. The heaviest nucleus synthesized so far at SHIP is the isotope 277 112. In early 1996 the search for element 112 was undertaken using the projectile target combination 70 Zn + 208 Pb. An excitation energy of E ∗ = 10.1 MeV was chosen. One decay chain which could be attributed to 277 112 was observed. The resulting production cross section was σ = (0.37+0.85 −0.31 ) pb. In a recent experiment in May 2000 a second decay chain of 277 112 has been recorded. This latter chain has been observed at an excitation energy of about 2 MeV higher at E ∗ = 12 MeV. During an irradiation time of 19 days a total of 3.5 × 1018 projectiles were sent onto the target. The resulting cross section at this energy is (0.49+1.12 −0.40 ) pb. This value fits well into the cross section systematics for 1n reaction channels shown in fig. 2 upper left panel. The first two α-decays have energies of 11.17 and 11.20 MeV, respectively. They are succeeded by the emission of an α-particle that exhibits with 9.18 MeV a decay energy lower by 2 MeV. Correspondingly, the lifetime increases by about five orders of magnitude between the second and third α-decay. This decay pattern is in agreement with the one observed for the chain in the first experiment and supports the explanation of

a local minimum of the shell correction energy at neutron number N = 162, which is crossed by the α-decay of 273 Ds. The α energy of 9.18 MeV for 269 Hs is within the detector resolution identical to the one observed in the first chain. A new result is the occurrence of fission ending the new chain at 261 Rf, for which fission was not observed so far, but is likely to occur taking into account the high fission probabilities of the neighboring isotopes. For more details see ref. [2]. An experiment performed at GSI in April/May 2001 and designed to investigate the chemical properties of Hs confirmed these findings. Ch.E. D¨ ullmann et al. [4], employing the reaction 26 Mg + 248 Cm, observed in the decay chain of the 5n-evaporation channel which enters our 277 112 decay sequence at 269 Hs both, a fission and an α-decay branch. Finally K. Morita et al. [5] performed the same reaction as employed at SHIP. They observed two decay chains assigned to 277 112 where they observed in both cases fission of 261 Rf, confirming the GSI results. In fig. 2 the cross section systematics for both approaches, fusion on 208 Pb and 209 Bi (“cold fusion”; upper panels) and on actinide targets (“hot fusion”; lower panels) are compared, for 1n-3n and 4n-5n evaporation reaction channels, respectively [6]. Whereas for the “cold fusion” reactions no deviation from the steep decrease of the maximum cross section with increasing Z is observed, the Dubna results for the “hot fusion” show cross-section values which surprisingly remain rather high and constant around and above the 1-pb-level for Z up to 116(118) [1]. Despite a by now relatively vast body of data accumulated and assigned to nuclei in the region of Z = 112–116, the Z and A assignments are still not firm as in those cases the decay chains are not connected to known α emitters, but end in unknown fissioning nuclei.

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Fig. 2. Maximum cross section systematics for reactions with Pb- and Bi-targets (upper panels; 1n-3n reaction channels) and for actinide targets (lower panels; 3n-5n reaction channels) [6].

2.1 Nuclear structure investigations of heavy nuclei at SHIP The detailed understanding of nuclear structure and its development in the vicinity of closed shells, in regions of deformation and towards heavier masses and higher Z is a necessary ingredient for a successful progress in the synthesis of new heavy elements. The possible trends in single particle levels are the most sensitive probe for the formation of low level density, and eventually the appearance of shell gaps and regions of (shell-) stabilized nuclei. Decay spectroscopy of α-emitters stopped after separation is a powerful tool to study their daughter products or isomeric states via α fine structure or α-γ spectroscopy by ER-α or ER-α-γ coincidence measurements. Here the fusion reaction products are after separation implanted into a solid state (“stop”) detector for the residue and α detection which is combined with a high resolving γ-ray (Ge-) detector as shown in fig. 3. This method is very clean as compared to in-beam studies because of the effective shielding from target background due to its spacial separation and the effective cleaning by the ER-α coincidence technique. It is highly efficient because of the favorable close geometry of the α and γ detectors and the very well localized stopped γ-ray source the implantation spot of the ER is forming on the stop detector. The latter has the further advantage of the absence of any γ-ray Doppler shift or broadening which yields, with a moderate crystal size and

a moderate granularity of the Ge-detector, a nevertheless high efficiency . In case of the SHIP set-up we achieve an  of up to ≈ 15%. We have applied the technique of α fine structure and α-(α)-γ spectroscopy to study several radium isotopes (A = 209–212) [7], neutron-deficient nuclei with Z = 86–92 [8] up to the isotopes 252,253 Lr, 255 Rf and 256,257 Db [9]. In fig. 4 as an example the α-γ coincidence spectra for the latter case and the conclusions one can draw in terms of level schemes and single particle level systematics are shown. The nuclear structure of heavy nuclei with Z ≥ 82 is interesting in itself as many interesting features, like e.g. isomers, shape transitions and shape co-existence, are expected and found in this region. One recent example is the hint for a K-isomer in 270 Ds we reported recently [10]. In an experiment in October 2000 we observed in the reaction 64 Ni + 207 Pb eight decay chains of correlated ERα-fission events which we attribute to the decay of the new isotope 270 Ds. Also the daughter and grand daughter products 266 Hs and 262 Sg had not been observed before. Here the production cross section remained surprisingly high as compared to the more neutron rich 271 Ds at 13±5 pb produced in the reaction 64 Ni + 208 Pb. Moreover, from the measured decay data hints for interesting nuclear structure properties could be deduced. The observed eight decay chains could be attributed to two different half-lives, 0.15 ms and 8.6 ms, respectively. Together with the systematics of α-decay energies and a 218 keV γ-ray

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Fig. 3. Schematic view of a decay spectroscopy set-up consisting of a separation stage (SHIP) and a α-γ coincidence detector arrangement. In addition transmission detectors for time of flight and veto purposes are shown. At SHIP reactions like 48 Ca, 40 Ar, 50 Ti, 54 Cr + 206,207,208 Pb, 209 Bi are investigated.

measured in coincidence to one of the emitted α-particles, this was interpreted as the simultaneous population of the ground state and a K-isomer. Support for this interpretation was provided by theoretical calculations which predict spin and parity values of 8+ , 9− or 10− [11]. Recent calculations suggest the occurrence of K-isomers is a general feature in the region of heavy nuclei [12]. 2.2 Reaction mechanism studies Complete fusion reactions appear to be the most successful method for the production of transactinide nuclei. The formation cross section of a specific nuclide in a given reaction, however, is strongly dependent on the excitation energy E ∗ of the compound nucleus, according to the relation E ∗ = Ecm + Q (where Ecm denotes the energy in the center-of-mass system and Q the Qvalue of the reaction), and thus on the bombarding energy Elab = (mp + mt )/mt × Ecm (where mp and mt denote the masses of projectile (p) and target (t), respectively). Since maximum production cross sections are decreasing rapidly with increasing atomic numbers, the choice of the optimum Elab is crucial for the production of the heaviest nuclei. It is, together with the understanding of the nuclear structure of the very heavy nuclei crucial as input knowledge for a successful program to extend the synthesis of new elements to higher Z and eventually to the region of the spherical superheavy nuclei.

3 Synthesis and identification of superheavy elements in other laboratories The recent results for the 48 Ca induced reactions obtained at the FLNR/JINR in Dubna are presented in detail in ref. [1]. I shall here give a brief review on the recent achievements at the LBNL in Berkeley CA, USA, GANIL in Caen, France and RIKEN in Tokyo, Japan. All three laboratories use as at the FLNR and in contrast to GSI

a 100% duty cycle accelerator. At Berkley with the BGS and at RIKEN with GARIS a gas-filled separator is the heart of the SHE-production set-up, whereas at GANIL this part is taken by the velocity filter of LISE. At the BGS in Berkeley both approaches for SHE synthesis, cold and hot fusion are followed [13,14]. They investigated, e.g., the excitation function for the reaction 64 Ni + 208 Pb and compared their results for 271 Ds, the 1n reaction channel, with the ones obtained at GSI and RIKEN. The maxima for the three data sets are shifted by ≈ 2 MeV between each other with the GSI results being the lowest, the RIKEN ones the highest and the LBNL data in between. This observation, however, has to be put in relation to the energy loss in the target of ≈ 2.5 MeV to 6.5 MeV and the uncertainty of the cross section values due to the low statistics. Another interesting result obtained at the BGS is a cross section for 272 Rg of 65 Cu + 208 Pb σ = 1.7+3.9 −1.4 pb observed in the reaction which is within error bars comparable to the one observed at GSI for the same isotope in the reaction 64 Ni + 209 Bi with σ = 3.5+4.4 −2.3 pb. This observation suggests the use of odd-Z projectiles on 208 Pb in other cases like e.g. 55 Mn + 208 Pb where an excitation function has been measured. As far as the hot fusion approach is concerned, an attempt to reproduce the Dubna findings for 48 Ca + 238 U → 283 112 + 3n remained unsuccessful with a cross section limit of σlimit < 1 pb. At GANIL as a first step to enter the field of SHE research the excitation functions for seaborgium and hassium isotopes were measured using the same reactions as in the SHIP experiments, 54 Cr + 208 Pb and 58 Fe + 208 Pb [15]. The obtained results are in good agreement with the GSI data. From the comparison of the yields a relatively low transmission of ≈ 15%–17% of the LISE velocity filter was deduced. In November 2004 the reaction 76 Ge + 208 Pb was employed to search for 283 114. At a beam energy of Ebeam = 5.02 AMeV with an intensity of > 1 particle μA a beam dose of 5 × 1018 76 Ge projectiles was put onto the 420 mg/cm2 thick targets. This corresponds to a sensitivity of 0.6 pb if one event would have been observed. However, no event could be attributed to 283 114. This results in a cross section limit of σlimit = 1.2 pb in the center-of-mass energy range 274.5 MeV–278.5 MeV. Also at the gas-filled separator GARIS of RIKEN the first steps had been made reproducing GSI results of reactions with Pb and Bi targets. The series of successful experiments was started with the observation of 10 decay chains of 265 Hs. For both isotopes 271 Ds and 272 Rg 14 decay chains were produced [16] before Morita and coworkers succeeded in the reproduction of 277 112. They obtained two decay chains, each terminating with the fission of 261 Rf and thus confirming the SHIP results [5]. Finally in two long runs of about 140 days of 70 Zn beam on a 209 Bi target they observed on July 23rd one decay chain for the new isotope 278 113 with the extremely low production cross section of σ = 55+154 −47 fbarn [17]. The observed decay chain ended with α-decay and fission of the known isotopes 266 Bh and 262 Db, respectively.

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Fig. 4. Left panels: α-γ-coincidence spectra for the reactions 50 Ti + 208 Pb (a) and 50 Ti + 207 Pb (b). Right panels: tentative level schemes for 253 No → 249 Fm and 255 Rf → 251 No (a), calculated (b) and measured (c) trend for first excited states for a series of N = 149 isotones [9].

4 Technical development at GSI/SHIP To access a region of lower cross section the number of interactions and, therefore, the number of projectiles has to be increased. The UNILAC at GSI delivers the beam with a duty cycle of about ≤28%. Apart from raising the beam current, the use of an accelerator with 100% duty cycle (DC) would provide a factor of 3.5 higher in beam intensity. Such a CW-linac is presently being studied by the group of Ratzinger et al. at the University of Frankfurt, Germany. As a first step an accelerator upgrade comprising a 28 GHz superconducting ECR ion source together with an adapted RFQ injection accelerator structure is presently being proposed. This configuration will via a substantial increase of charge state and injection beam intensity yield an increase in beam intensity of a factor ≈ 10 as compared to the present UNILAC beam intensities. Figure 5 shows the new ion source combined with the existing 14 GHz normal conducting ERC source. The insert shows a comparison for the performance of both sources in terms of the extracted beam intensity as a function of the charge state for Xe-ions. The higher charge state achievable with the 28 GHz SC-ECRIS source will allow for a UNILAC duty cycle of ≈ 50%. The increased beam current asks for measures to protect the Pb and Bi targets,

both having low melting points at 600.6 K and 544.5 K, respectively. Chemical compounds of Pb or Bi with higher melting temperatures have been successfully tested. The metallic targets have now been replaced by PbS and Bi2 O3 with melting points at 1400 K and 1090 K, respectively. In addition the possibility of an active target cooling has been investigated and will allow for an additional increase of heat power to deposited in the target [18].

5 Open tasks The localization of the region of spherical shell-stabilized superheavy nuclei is still an open task. The results from the FLNR, Dubna seem to have come closer to this region. The non-connected decay chains, however, are at the moment an important and demanding challenge that requires still substantial effort in order to obtain a firm isotopical assignment. At SHIP the investigation of the reaction 48 Ca + 238 U as a first approach to study this region is planned for spring/summer 2005. Additional information like the mass of the reaction products will help for a more reliable positioning of observed decay patterns in A, and possibly Z. Technical development in this direction is presently ongoing at GSI and with SHIPTRAP one promising tool is

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Fig. 5. Upgrade of the UNILAC high charge state injector by a new 28 GHz super-conducting ECR ion source and a new RFQ pre-acceleration structure. Insert: comparison of the new 28 GHz ECR ion source with the present 14 GHz ECR source in intensity (vertical axis) and charge state (horizontal axis).

presently being put into operation [19]. Simultaneously systematic investigations of the structure of very heavy nuclei and the reaction mechanism governing the process of fusion and survival against fission are pursued. Together with the already achieved results this will yield valid input data for the more and more sophisticated models. With an increasing understanding of the properties of the very heavy nuclei one can hope to better localize the region of the spherical superheavy nuclei and to favor the experimental approach to it. High currents of stable beams and radioactive beams are options for the future. The recent experiments were performed together with H.G. Burkhard, F.P. Heßberger, S. Hofmann, B. Kindler, I. Kojouharov, P. Kuusiniemi, R. Mann, G. M¨ unzenberg, B. Lommel, H.-J. Sch¨ ott, J. Steiner, B. Sulignano (GSI Darmstadt), A.N. Andreyev, A.G. Popeko, A.V. Yeremin (FLNR-JINR ˇ Saro, ˇ Dubna), S. Antalic, P. Cagarda, S. B. Streicher (University of Bratislava), J. Uusitalo and M. Leino (University of Jyv¨ askyl¨ a).

3. 4. 5. 6.

7. 8. 9. 10. 11. 12. 13.

14. 15.

References 1. Yu.Ts. Oganessian, V.K. Utyonkov et al., Phys. Rev. C 69, 054607 (2004) and these proceedings. 2. S. Hofmann, G. M¨ unzenberg, Rev. Mod. Phys. 72, 733 (2000).

16. 17. 18. 19.

S. Hofmann, J. Nucl. Rad. Chem. Sci. 4, R1 (2003). Ch.E. D¨ ullmann et al., Nature 418, 859 (2002). K. Morita et al., private communication. S. Hofmann et al., in Proceedings of the VIII International Conference on Nucleus-Nucleus Collisions (NN2003), Moscow, Russia, 17-21 June, 2003, edited by Yu.Ts. Oganessian, R. Kalpakchieva, Nucl. Phys. A 734, 93 (2004). F.P. Heßberger, S. Hofmann, D. Ackermann, Eur. Phys. J. A 16, 365 (2003). F.P. Heßberger et al., Eur. Phys. J. A 3, 521 (2000). F.P. Heßberger et al., Eur. Phys. J. A 12, 57 (2001). S. Hofmann et al., Eur. Phys. J. A 10, 5 (2001). S. Cwiok, W. Nazarewicz, P.H. Heenen, Phys. Rev. Lett. 83, 1108 (1999) and private communication. F.R. Xu et al., Phys. Rev. Lett. 25, 252501 (2004). C.M. Folden, TASCA04 Workshop, August 27th 2004 (GSI, http://www.gsi.de/tasca04) and private communication. C.M. Folden et al., Phys. Rev. Lett. 93, 212702 (2004). Ch. Stodel et al., to be published in Proceedings of the Conference EXON2004, St. Petersburg, Russia, June 2004 (World Scientific, 2005); Ch. Stodel, private communication. K. Morita et al., Nucl. Phys. A 734, 101 (2004). K. Morita et al., J. Phys. Soc. Jpn. 73, 2593 (2004). P. Cagarda, PhD Thesis, University Bratislava (2002). M. Block et al., these proceedings.

Eur. Phys. J. A 25, s01, 583–587 (2005) DOI: 10.1140/epjad/i2005-06-202-2

EPJ A direct electronic only

Chemical properties of transactinides H.W. G¨aggelera Paul Scherrer Institut, 5232 Villigen, Switzerland and University of Bern, Freiestrasse 3, 3012 Bern, Switzerland Received: 10 December 2004 / Revised version: 4 April 2005 / c Societ` Published online: 15 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. First investigations of chemical properties of bohrium (Z = 107) and hassium (Z = 108) showed an expected behaviour as ordinary members of groups 7 and 8 of the periodic table. Two attempts to study element 112 yielded some indication for a behaviour like a very volatile noble metal. However, a very recent experiment to confirm this preliminary observation failed. Two examples are described how chemical studies may help to support element discovery claims from purely physics experiments. The two examples are the discovery claims of the elements 112 and 115, respectively, where the progenies hassium and dubnium were chemically identified.

1 Introduction During the last few decades the discovery of new elements changed from a field of chemistry to a topic in nuclear physics. The last example of a chemical contribution to an element discovery reaches back to the 1960s. A combination of physical and gas chemical experiments was considered sufficiently convincing by the International Union of Pure and Applied Chemistry (IUPAC) to approve the discovery of the first transactinide rutherfordium (Rf). For the elements up to seaborgium (Sg) gas-jet techniques coupled to semiconductor detector systems were applied for their identification. The even heavier elements were discovered using the velocity SHIP at GSI (elements bohrium (Bh) through 112) and a gas-filled magnetic separator at FLNR in Dubna (elements 113–116 and 118) [1,2]. Element 113 has also been discovered independently at RIKEN [3]. However, the heaviest element that has been approved by IUPAC has the atomic number 111 (roentgenium, Rg). In the discovery experiments of the elements Bh through Rg, their α-decay chains had an overlap with already known nuclides. This enabled an unequivocal identification of the new element. In the discovery experiment of element 112 [4,5] a member of the decay chain (261 Rf) revealed a hitherto unknown decay property. Therefore, as yet, IUPAC has not approved the discovery of this element. This holds also for the recent discovery claims of elements 113–116 and 118 of the FLNR in Dubna [2,6]. These elements were produced in complete fusion reactions of 48 Ca beams with actinide targets. The observed decay chains all end in unknown final nuclides, mostly decaying by spontaneous fission (SF). Hence, not only are the primary evaporation residues unknown but also all a

Conference presenter; e-mail: [email protected]

members of the decay chains. For the assignments to a given element purely nuclear physics arguments are used (calculated excitation functions, decay properties of observed nuclei, cross bombardments etc.). For a chemist the mere proof of the existence of a nucleus with a given number of protons is only part of a discovery of a new chemical element. As a member of the periodic table this new member has to find its place in this table, by no means a trivial task! The reasons are relativistic effects that might heavily influence chemical properties. Due to the high Coulomb force between the nucleus and orbiting electrons, energies of the atomic levels can be significantly changed. Symmetrical s and p1/2 orbitals have higher binding energies due to an increased overlap of the wave functions with the nucleus (direct relativistic effect). This causes a shrinking of the orbitals and screens, i.e. destabilizes high angular-momentum levels (p3/2 , d, f ) (indirect relativistic effects). As a consequence, the sequence of electron orbitals may deviate from “classical” expectation which in turn may cause an unexpected chemical behaviour. During the last 5 years two elements have been investigated chemically for the first time: bohrium (Bh) [7, 8] and hassium (Hs) [8,9]. Currently, experiments are in progress to chemically identify element 112 [10,11]. In all these studies continuous gas phase techniques were applied that have proven to be fast and efficient. Bohrium was separated in an isothermal gas chromatography experiment using the On-Line Gas Chemistry Apparatus OLGA [12]. BhO3 Cl was synthesized in a chlorinating gas (HCl/O2 ) which was observed to be volatile in fused silica tubes at about 150 ◦ C. Six detected atoms of the short-lived isotope 266 Bh were sufficient to proof that Bh behaves like a typical member of group 7 of the periodic table [7,8].

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Target

Heavy ion beam

Teflon capillary

Gradient oven

N 2 (liq.) cooling

Recoil chamber

Quartz wool He + O2 Beam stop (graphite)

Quartz column

2 x 36 PIN-Diodes

Fig. 1. IVO set-up applied in the first chemical investigation of hassium (Hs, Z = 108) (for details see text).

This overview summarizes the recent hassium experiment and presents a status on the 112 experiments. In addition, two examples are highlighted how chemistry may help to confirm or refute discovery claims from physics experiments. These are the discovery claims of elements 112 and 115. In the first case it was possible to position the decay chain of 277 112 at atomic number 108 (Hs) and in the second case the decay chain of 288 115 at atomic number 105 (Db) or its possible EC decay product element 104 (Rf), respectively.

2 Chemical investigation of hassium (Hs) If Hs behaves like a normal group-8 member of the periodic table it should form with oxygen a very volatile molecule, HsO4 . For the next homologue of the same group, Os, it is well known that on a single molecule level and at ambient conditions OsO4 behaves like a gas. In macroamounts OsO4 is a liquid. To search for a volatile HsO4 a novel technique was developed, the In situ Volatilization and On-line detection device IVO [13]. From a thin-target recoiling fusion products were thermalized in oxygen containing carrier gas (He) in order to form in situ the volatile tetroxide molecule (fig. 1). In a continuous mode the gas was then flushed through the recoil chamber and fed into an oven kept at about 800 ◦ C in order to retain possible particle-bound contaminants but also to rapidly oxidize Hs oxides from a lower than 8+ oxidation state to HsO4 . The gas was then injected into a channel formed by an array of 36 detector pairs mounted in form of 12 triplets at a distance of 1.5 mm between opposite detectors. The detectors were silicon PIN diodes that enable α and fission fragment spectroscopy. Along the detector pairs a stationary temperature gradient between −20 and −175 ◦ C was established. The chemical information evolved from the determination of the detector pair at which the HsO4 molecules deposited, which in turn defines a deposition temperature on the surface (silicon nitride). The measurement of deposition temperatures of single atoms/molecules along a stationary negative temperature gradient is known as thermochromatography. From measured deposition temperatures adsorption enthalpies may be obtained applying

Fig. 2. Distribution of hassium and osmium tetroxide inside of the detector array. The hassium distribution resembles the behaviour of 7 atoms of 269,270 Hs.

Monte Carlo models. From such enthalpies sublimation enthalpies may be deduced [14]. Figure 2 depicts the results of the first chemical investigation of hassium using the 10 s 269 Hs [9]. This isotope was produced in the 248 Cm(26 Mg; 5n)269 Hs reaction at an energy of 145 MeV in the middle of the 0.55 mg/cm2 thick target. A beam dose of 1 × 1018 particles was accumulated on the target. Seven decay chains were observed that could be assigned to 269 Hs and to the new nuclide 270 Hs. The 7 observed decay chains form a clear deposition peak of HsO4 at −43 ◦ C. Before and after the experiment a 0.8 mg/cm2 thick 152 Gd target was bombarded with the same beam to study the chemical behaviour of osmium via the α-decaying 172 Os under otherwise identical conditions. The deposition peak of OsO4 was found at −82 ◦ C. This indicates a slightly stronger interaction of HsO4 with the detector surface compared to that of OsO4 . Using an empirical correlation established between the adsorption properties of oxides and their volatility [14] a lower volatility of HsO4 compared to OsO4 can be deduced. Theoretical calculations predicted similar volatilities of HsO4 and OsO4 . The errors of the calculations, however, are larger than the observed small difference [15,16]. To conclude, hassium behaves as an oddly normal member of group 8!

3 Chemical investigation of element 112 Element 112 is predicted to exhibit rather exceptional chemical properties: due to relativistic effects on its filled 7s2 6d10 electronic configuration a gaseous behaviour was predicted [17]. Also conventional thermodynamic extrapolations point to a likely behaviour as a very volatile noble metal [18]. More recent calculations corroborate these expectations [14,19]. In a first chemical attempt performed at FLNR Dubna the similarity of element 112 to Hg, its homologue in the periodic table was investigated. The experiment used the 5 min SF isotope 283 112 found in the 48 Ca + 283 U reaction at an energy of 231 MeV using the energy filter VASSILISSA [20]. From a 2 mg/cm2 thick 238 U target

H.W. G¨ aggeler: Chemical properties of transactinides

recoiling products were thermalized in pure helium and then continuously transported along a 25 m long capillary to an array of 8 PIPS detectors covered with a thin layer of Au followed by a gas ionisation chamber (fig. 3). The separation time was up to 20 s. Both detectors were positioned inside an array of 3 He neutron counters to assay prompt neutrons. During the experiment a beam dose of 2.8 × 1018 48 Ca particles was collected at an energy of 233 MeV in the middle of the target. Eight events were detected in the gas ionisation chamber in coincidence with 1 to 3 neutrons [10]. No SF events were detected in the PIPS detectors, where 185 Hg was quantitatively adsorbed that was produced simultaneously by a small admixture of 35 μg/cm2 nat Nd deposited on top of the target. The resulting cross-section of 2 pb agreed reasonably well with published data (4 pb [20]). It was concluded that element 112 exhibits a clearly different behaviour from Hg, obviously interacting weaker with Au. In a subsequent experiment, using the same reaction the thermochemical behaviour of element 112 was investigated applying the IVO device (see fig. 1) but with one side of the detector array consisting of a Au surface (2π counting geometry). The separation time was approximately 25 s. A 1.6 mg/cm2 thick 238 U target covered by 22 μg/cm2 nat Nd was bombarded with 2.8 × 1018 48 Ca particles of 231 MeV (middle of the target). Seven single events with energies larger than 40 MeV were detected at the position of radon, in addition to 4 additional events scattered along the detector array. The background count-rate amounted to ∼ 3 events for the corresponding counting time. The average energies of the 7 events were lower than expected, possibly caused by ice formation on the detector surfaces below approximately −90 ◦ C. Therefore, this result was interpreted as an indication of a gaseous behaviour of element 112 [11]. The ambiguity of this result made a confirmation necessary with an improved set-up that separated volatile products within 2.2 s and operated in a 4π counting mode, to assay SF coincidences. During an additional beam time 1.4 × 1018 48 Ca particles (i.e. 50% of the beam dose of the first experiment) where applied to the same 1.6 mg/cm2 thick 238 U target. No SF coincidences were observed at an expected rate of ∼ 3 events compared to the first experiment [21]. Further investigations are mandatory, especially since additional physics experiments aiming at a confirmation of the long-lived SF-activity failed. At LBNL no evaporation residue formation was observed in the 48 Ca + 238 U reaction at a cross-section limit of about 1 pb using the BGS separator [22]. At FLNR with the gas filled magnetic separator also no indication of a long-lived SF isotope was found but a 4 s α-emitter was discovered with a decay energy of 9.52 MeV followed by a SF-decaying product with T1/2 = 0.18 s. The maximum production cross-section was 2.5 pb at an energy of 234 MeV [23]. The second IVO experiment described above was designed to also detect such decay chains. A preliminary analysis showed that the nonobservation of any 9.5 MeV α-SF correlation yields a crosssection limit of ∼ 2 pb for a 4s-product (95% confidence level) [21]. Hence, presently the situation concerning the

585

Fig. 3. Set-up used for the first chemical attempt to study element 112 (from ref. [10]).

formation of element 112 in the 48 Ca + 238 U reaction and its chemical behaviour remains very controversial.

4 Confirmation of element discoveries by chemical means Chemical procedures enable the separation of a given “atomic number”. This is especially easy in cases where the element to be isolated exhibits exceptional chemical properties. Such an example is hassium. The heavy members of group 8 of the periodic table (osmium and hassium) form very stable and volatile molecules with oxygen. None of the neighbouring elements show such a behaviour. In the chemistry experiment on hassium mentioned above, out of the 7 detected decay chains 3 originated from 269 Hs that decayed after two α-emissions to 261 Rf with unexpected decay properties: 2 atoms of 261 Rf decayed via α-emission with E = 8.50 MeV and lifetimes of 0.9 and 2.4 s, respectively, and one atom of 261 Rf by spontaneous fission after a lifetime of 7.90 s [24]. This decay pattern corroborates the observation made in the discovery experiments of element 112, where 261 Rf as member of the decay chain beginning with 277 112 also showed such an unexpected behaviour [4, 5]. If directly produced in a hot fusion reaction, 261 Rf decays with a α-energy of 8.28 MeV [25] and a lifetime of 113 s [26]. More recently, attempts were made to confirm the decay chains found at FLNR in a 48 Ca bombardment of 243 Am that yielded evidence for the formation of 288 115 [2]. Three decay chains of this isotope were found, ending in a very long-lived SF 268 Db with a half life of 16+19 −6 h, an ideal case for a chemical confirmation! A 1.2 mg/cm2 thick 243 Am target was bombarded with 48 Ca ions at an energy of 247 MeV (middle of target) [27]. Recoiling products were collected in a thick water cooled Cu catcher positioned behind the target at an angle of ±12 degree, to suppress collection of transfer products. Once a day, after having accumulated typically 2–3 × 1017 particles on the target, approximately 10 μm of the front

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Table 1. Measured events in the Db/Rf fraction from the chemical study of the

48

Ca +

243

Am reaction (data from [28]).

Sample

tirr (a) (h)

Beam dose

Ebot + Etop + Nn(b) (MeV) (MeV)

tdetect (c) (h)

tmeas (d) (h)

1

20

2.5 · 1017

120 + 126 + 2

20

429

2

22

3.7 · 1017

– + 86 + 1

74

186

3

22

3.4 · 1017

131 + 124 + 1 116 + 122 + 2

15 72

385

4

22

2.9 · 1017

104 + 120 + 1 97 + 125 + 1 100 + 128 + 1

22 29 51

358

117 108 110 –

2 3 0 2

6 9 15 68

861

5

6

7

8

38

6.7 · 1017

23

3.9 · 1017

22

45

+ + + +

118 107 104 76

+ + + +

120 + 114 + 2

39

933

3.6 · 10

17

–

–

957

7.4 · 10

17

119 + 110 + 2 118 + 105 + 2 65 + 58 + 3

5 93 174

910

(a ) tirr : irradiation time. (b ) Ebot , Etop : measured energies in the bottom and top detectors, respectively. (c ) tdetect : time at which event was registered after start counting. (d ) tmeas : measuring time.

surface was removed mechanically. These Cu chips (100 to 150 mg) were chemically processed for dubnium and rutherfordium, with special efforts to achieve high decontamination factors from actinides [28]. Final samples were deposited on very thin organic foils and assayed for fission fragment energies in a 4π counting geometry using silicon detectors. The counting chambers were positioned inside an array of 3 He counters to detect prompt neutrons. All samples were measured up to 957 hours. In 8 samples, representing a total beam dose of 3.4 × 1018 particles, 15 fission events were observed in coincidence with up to 3 neutrons (table 1). The measured fission fragment energies point to a highly symmetric fissioning nucleus. After corrections of the measured kinetic energies for ionisation defect in the semiconductor detector and energy loss in the sample a total kinetic energy TKE of approximately 235 MeV results. Taking into account a 40% detection efficiency for single neutrons a neutron multiplicity of 4.2 [27] is found. Such a signature (high TKE and ν tot ) yields strong evidence for a heavy nucleus as fissioning source, far beyond, e.g. SF 252 Cf. Therefore, the proposed assignment to 268 Db or 268 Rf from the EC-decay of 268 Db appears very likely. It should be mentioned that formation of transactinides in measurable amounts from the 48 Ca + 243 Am reaction through transfer channels is extremely unlikely. In 48 Ca induced reactions with the actinide target 248 Cm the nucleon flow was observed to occur predominantly from the target to the projectile and not vice versa at energies close to the fusion barrier [29].

References 1. See e.g. S. Hofmann, Properties and synthesis of superheavy elements, in The Chemistry of Superheavy Elements, edited by M. Sch¨ adel (Kluwer Academic Publ., Dordrecht, 2003). 2. Yu.Ts. Oganessian et al., Phys. Rev C. 69, 021601 (2004). 3. K. Morimoto, Workshop on Recoil Separators for Superheavy Element Research, 27 August 2004, GSI Darmstadt, Germany. 4. S. Hofmann et al., Z. Phys. A 354, 229 (1996). 5. S. Hofmann et al., Eur. Phys. J. A 14, 147 (2002). 6. Yu.Ts. Oganessian et al., Phys. Rev C 69, 054607 (2004) and references therein. 7. R. Eichler et al., Nature 407, 63 (2000). 8. H.W. G¨ aggeler, A. T¨ urler, Gas-phase chemistry, in The Chemistry of Superheavy Elements, edited by M. Sch¨ adel (Kluwer Academic Publ., Dordrecht, 2003). 9. Ch.E. D¨ ullmann et al., Nature 418, 859 (2002). 10. A.B. Yakushev et al., Radiochim. Acta 91, 433 (2003). 11. H.W. G¨ aggeler et al., Nucl. Phys. A 734, 208 (2004); S. Soverna, Attempt to chemically characterize element 112, PhD Thesis, Bern University, December 2004. 12. H.W. G¨ aggeler et al., Nucl. Instrum. Methods A 309, 201 (1991). 13. Ch.E. D¨ ullmann et al., Nucl. Instrum. Methods A 479, 631 (2002). 14. B. Eichler and R. Eichler, Gas-phase adsorption chromatographic determination of thermochemical data and empirical methods for their estimation, in The Chemistry of Superheavy Elements, edited by M. Sch¨ adel (Kluwer Academic Publ., Dordrecht, 2003).

H.W. G¨ aggeler: Chemical properties of transactinides 15. 16. 17. 18. 19. 20.

V. Pershina et al., J. Chem. Phys. 115, 792 (2001). Ch.E. D¨ ullmann et al., J. Phys. Chem. B 106, 6679 (2002). K. Pitzer, J. Chem. Phys. 63, 1032 (1975). B. Eichler, Kernenergie 19, 307 (1976). V.G. Pershina, Chem. Rev. 96, 1977 (1999). Yu.Ts. Oganessian et al., Eur. Phys. J. A 19, 3 (2004) and references therein. 21. R. Eichler et al., to be submitted to Radiochim. Acta. 22. W. Loveland et al., Phys. Rev. C. 66, 044617 (2002); K.E. Gregorich, private communication.

23. 24. 25. 26. 27. 28. 29.

587

Yu.Ts. Oganessian et al., Phys. Rev. C 70, 064609 (2004). A. T¨ urler et al., Eur. Phys. J. A 17, 505 (2003). Y. Lazarev et al., Phys. Rev. C 62, 064307 (2000). A. T¨ urler et al., Phys. Rev. C 57, 1648 (1998). S.N. Dmitriev et al., Mendeleev Commun. 15, 1 (2005). D. Schumann et al., submitted to Radiochim. Acta (2005). H. G¨ aggeler et al., J. Less-Common. Metals 122, 433 (1986).

Eur. Phys. J. A 25, s01, 589–594 (2005) DOI: 10.1140/epjad/i2005-06-134-9

EPJ A direct electronic only

New elements from Dubna Yu.Ts. Oganessian1 , V.K. Utyonkov1,a , Yu.V. Lobanov1 , F.Sh. Abdullin1 , A.N. Polyakov1 , I.V. Shirokovsky1 , Yu.S. Tsyganov1 , G.G. Gulbekian1 , S.L. Bogomolov1 , B.N. Gikal1 , A.N. Mezentsev1 , S. Iliev1 , V.G. Subbotin1 , A.M. Sukhov1 , A.A. Voinov1 , G.V. Buklanov1 , K. Subotic1 , V.I. Zagrebaev1 , M.G. Itkis1 , J.B. Patin2 , K.J. Moody2 , J.F. Wild2 , M.A. Stoyer2 , N.J. Stoyer2 , D.A. Shaughnessy2 , J.M. Kenneally2 , P.A. Wilk2 , and R.W. Lougheed2 1 2

Joint Institute for Nuclear Research, 141980 Dubna, Russian Federation University of California, Lawrence Livermore National Laboratory, Livermore, CA 94551, USA Received: 19 October 2004 / c Societ` Published online: 29 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We have studied the dependence of the production cross-sections of the isotopes 282,283 112 and 286–288 114 on the excitation energy of the compound nuclei 286 112 and 290 114. The maximum crosssections of the xn-evaporation channels for the reaction 238 U(48 Ca, xn)286–x 112 were measured to be: +1.6 242 σ3n = 2.5+1.8 Pu(48 Ca, xn)290–x 114: σ2n ∼ 0.5 pb, σ3n = −1.1 pb and σ4n = 0.6−0.5 pb; for the reaction +3.6 233 3.6+3.4 U(48 Ca, 2–4n)277–279 112 we measured an upper cross−1.7 pb and σ4n = 4.5−1.9 pb. In the reaction section limit of σxn ≤ 0.6 pb. An increase of σER in the reactions of actinide targets with 48 Ca can be due to the expected increase of the survivability of the excited compound nucleus upon closer approach to the closed neutron shell N = 184. The observed nuclear decay properties of the nuclides with Z = 104–118 are compared with theoretical nuclear mass calculations and the systematic trends of α-decay properties. As a whole, they give a consistent pattern of decay of the 18 even-Z neutron-rich nuclides with Z = 104–118 and N = 163–177. PACS. 25.70.Gh Compound nucleus – 23.60.+e α decay – 25.85.Ca Spontaneous fission – 27.90.+b 220 ≤ A

1 Introduction According to the nuclear models, the limits of the existence of the heavy nuclei, as well as their decay properties, are completely determined by nuclear shell effects. For the heaviest elements in the vicinity of the hypothetical closed spherical shells Z = 114 and N = 184, the increase of nuclear binding energy results in a considerable increase of stability with respect to various decay modes. We may also speculate that the high fission barriers of the superheavy nuclei in their ground states may persist at low excitation energies, resulting in an increase in their production cross-sections, or to be more precise their survival probability in the process of de-excitation of the compound nucleus. Both the production cross-sections and the stability of superheavy nuclides are expected to increase on closer approach to the closed neutron shell N = 184. Therefore, our first experiments aimed at the synthesis of the heaviest nuclei involved the complete fusion reactions 244 Pu, 248 Cm + 48 Ca that lead to the compound nuclei with the maximum accessible neutron numbers [1]. Following the successful completion of the experiments in which fission in 48 Ca-induced reactions was studied [2] we decided to ina

Conference presenter; e-mail: [email protected]

vestigate the survival probabilities of the compound nuclei by measuring excitation functions for producing evaporation residues (ER). The first such measurements were performed using the reaction 244 Pu(48 Ca, 3–5n)287–289 114 [3]. In the present work, we further develop these investigations with different targets: 233 U, 238 U, 242 Pu and 248 Cm, producing compound nuclei with Z = 112, 114 and 116.

2 Experimental technique The 48 Ca-ion beam was accelerated by the U400 cyclotron at the Flerov Laboratory of Nuclear Reactions. The typical beam intensity at the target was 1.2 pμA. The 32cm2 rotating targets consisted of the enriched isotopes 233 U (99.97%), 238 U (99.3%), 242 Pu (99.98%), and 248 Cm (97.4%) with thicknesses of about 0.44, 0.35, 0.40, and 0.35 mg/cm2 , respectively. The evaporation residues recoiling from the target were separated in flight by the Dubna Gas-filled Recoil Separator [4]. The transmission efficiency of the separator for Z = 112 and 114 nuclei is estimated to be approximately 40% [4]. ERs passed through a time-of-flight system (TOF) and were implanted in a 4 × 12 cm2 semiconductor detector array with 12 vertical position-sensitive

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Table 1. Reaction-specific lab-frame beam energies in the middle of the target layers, corresponding excitation energies [5] and total beam doses for the given reactions.

Reaction 48

Ebeam (MeV)

E ∗ (MeV)

Beam dose

235 238 244 250

30.4–34.7 33.1–37.4 38.0–42.4 43.0–47.2

5.0 × 1018 4.9 × 1018 4.7 × 1018 3.2 × 1018

242

Pu +

238

U + 48 Ca

230 234 240

29.3–33.5 32.9–37.2 37.7–41.9

5.8 × 1018 7.1 × 1018 5.2 × 1018

233

U + 48 Ca

240

32.7–37.1

7.7 × 1018

248

Cm + 48 Ca

247

36.8–41.1

7.0 × 1018

Ca

strips. This detector was surrounded by eight 4×4 cm2 side detectors without position sensitivity, forming a box open to the beam side. The detection efficiency for full-energy α particles emitted from implanted nuclei was 87%. The energy resolution for α particles absorbed in the focal-plane detector was 55–95 keV. The α particles that escaped the focal-plane detector at different angles and which were registered in a side detector had an energy resolution of the summed signals of 140–220 keV. The FWHM position resolutions were 0.9–1.4 mm for ER-α signals and 0.5– 0.9 mm for ER-SF signals. Fission fragments from the decay of 252 No implants produced in the 206 Pb + 48 Ca reaction were used for their energy calibration. The measured fragment energies were not corrected for the pulse-height defect of the detectors, or for energy loss in the detectors’ entrance windows, dead layers, and the pentane gas filling of the detection system. The mean sum energy loss of fission fragments was about 20 MeV. In the experiments we employed a special lowbackground detection scheme for the investigated nuclides [1,3]. The beam was switched off after a recoil signal was detected with parameters of implantation energy and TOF expected for ERs, followed by an α-like signal with an energy expected for an α-particle of the mother nucleus, in the same strip, within a 1.4–1.9 mm wide position window and some preset time interval. The duration of the pause in beam was determined from the observed pattern of out-of-beam α decays and varied from 1 to 12 minutes. Thus, all the expected sequential decays of the daughter nuclides were expected to be observed in the absence of beam-associated background.

3 Experimental results The experimental conditions are summarized in table 1. Excitation energies of the compound nuclei at given ion energies are calculated taking into account the thickness of the targets and the energy spread of the incident cyclotron beam. In the course of the experiments with the 242 Pu target, performed at four bombarding energies, 25 decay chains

Fig. 1. a) α or SF energies and decay times of nuclei produced in the reactions 242 Pu(48 Ca, 3n)287 114 (open symbols) and 238 U(48 Ca, 3n)283 112 (solid symbols). b) The same for even-even isotopes 286 114 and 288 114.

were detected that we assign to the decay of Z = 114 nuclides. The detected energies of events and time intervals between members of decay chains are shown in fig. 1. The decay chains can be sorted into three groups: decay chains of the ER-α-α-SF type lasting for 2–20 s (one special case is an ER-α-α-α-α-SF chain lasting for 6.5 min, see fig. 2) observed at beam energies EL = 235–244 MeV; shorter decays of the ER-α-SF or ER-SF type spanning a typical time of 0.01–0.6 s, observed at higher beam energies EL = 244–250 MeV; and, finally, a single ER-α-SF event, t ≈ 4 s, detected at the lowest beam energy EL = 235 MeV. In the 242 Pu+48 Ca reaction, we detected a total of 33 α-decays in the correlated decay chains. Four α-particles are missing, which is entirely consistent with the α-detection efficiency of the detector array that is approximately 87%. In fig. 1, such events and their daughters are not shown. In the 238 U + 48 Ca experiments, we detected 8 decay sequences that we have assigned to the decay of Z = 112 nuclides. These can be separated into two types: ER-α-SF chains spanning about 0.5–6 s that were observed at beam energies EL = 230–234 MeV; and shorter ER-SF sequences with tSF < 1 ms observed at EL = 240 MeV. Two longer ER-α-α-α-α-SF decay chains observed in the reactions 242 Pu + 48 Ca and 238 U + 48 Ca are shown separately in fig. 2.

Yu.Ts. Oganessian et al.: New elements from Dubna

591

Fig. 2. Time sequences in the average decay chain of 287 114 (left) and in selected decay chains observed in the 242 Pu+ 48 Ca (middle) and 238 U + 48 Ca (right) reactions. Measured energies, time intervals and positions of the observed decay events are shown. Energy uncertainties are shown in parentheses. 1) The energy of this event was detected by side detectors only. 2) The energies of events detected by both the focal-plane and side detectors, respectively, are shown in brackets.

The production cross-sections of the nuclides detected in our experiments as a function of the excitation energies of the compound nuclei 290 114 and 286 112, are shown in fig. 3. In addition, excitation functions of the reactions 244 Pu(48 Ca, 3–5n)287–289 114 that we measured earlier [3] and the available data for the reaction 248 Cm(48 Ca, 3– 4n)292,293 116 are also shown, together with the Bass reaction barrier [6] and the calculated excitation functions [7]. Comparing the decay properties of the observed nuclei and the excitation functions for their production, we can deduce a consistent picture for the masses of the observed nuclides. The decays of the daughter nuclei in the ER-α-αSF chains observed in the reaction 242 Pu + 48 Ca coincides in all the measured parameters (Eα , Tα , TSF , and ESF ) with the decay chain ER-α-SF observed in the 238 U + 48 Ca reaction. The maximum yields of the nuclides that undergo this type of decay correspond to the calculated 3n-evaporation channel in the fusion reactions 242 Pu, 238 U+ 48 Ca. Therefore, the ER-α-α-SF decay chain from the reaction 242 Pu + 48 Ca should be assigned to the decay of 287 114. This conclusion is supported by the data from the reactions 245 Cm, 244 Pu + 48 Ca in which similar decay chains were observed in 2n- and 5n evaporation channels [3], respectively. Accordingly, the ER-α-SF chains observed in the reaction 238 U + 48 Ca are due to the α decay of 283 112 that is terminated by the spontaneous fission of the isotope 279 Ds (TSF = 0.18 s). The excitation functions and the decay properties of the shorter chain members (ER-α-SF) detected in the 242 Pu + 48 Ca reaction, and ER-SF correlations in 238 U + 48 Ca reaction, determine that these originate from

Fig. 3. Excitation functions for the 2–5n evaporation channels from the complete-fusion reactions 233,238 U, 242,244 Pu, 248 Cm + 48 Ca. The Bass barrier [6] is shown by an open arrow in each panel; in the topmost panel it is labeled with BBass . Lines show the results of calculations [7]. Error bars correspond to statistical uncertainties.

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the neighboring even-even isotopes 286 114 and 282 112, respectively. Note that in the decay of 286 114, as observed in all of the experiments, five α decays were observed out of thirteen atoms (bα ≈ 0.4) [3,8]. Finally, a single ER-α-SF event observed in the reaction 242 Pu + 48 Ca at a beam energy EL = 235 MeV agrees well in decay properties with the well-studied nuclide 288 114 (12 events detected) that we previously synthesized in the reaction 244 Pu + 48 Ca [3]. This event should then be assigned to the decay of 288 114 produced via 2n evaporation with a cross-section of about 0.5 pb. We have also studied the reaction 233 U + 48 Ca; despite an accumulated beam dose of about 8 × 1018 ions, we did not observe any decay chains that could be attributed to the decay of isotopes of element 112. We calculate an upper cross-section limit of σ2−4n ≤ 0.6 pb for the reaction 233 U(48 Ca, 2–4n)277–279 112.

4 Discussion In the ER-α-α-SF chains arising in the decay of the isotope 287 114, the energy of the first α-particle is Eα1 = 10.02 ± 0.06 MeV. In all 12 events in which the decay of the mother nuclide has been observed, the measured values of Eα1 agree with the given value within detector resolution, as well as with the value measured for this isotope in [3]. The energy of the second α-particle in 11 cases of 14 is Eα2 = 9.54±0.06 MeV. This value, as we noted above, agrees well with the four measured α-energies of 283 112 (see fig. 1), produced as a fusion-evaporation product in the reaction 238 U(48 Ca, 3n)283 112, and with energies registered for this isotope in previous experiments [3]. However, three of the measured energies of the second alpha, Eα2 = 8.94(7), 9.36(8) and 9.32(6) MeV, are different enough from the average value of Eα2 that they are beyond the experimental uncertainties of measuring αenergies. This means that the observed α-decays of 283 112 correspond to transitions to various excited states in the daughter nucleus 279 110. Given the accuracy with which we measure the α-particle energies and the relatively low statistics, we can evaluate the probability of such transitions as being about 20%. In principle, this kind of decay pattern for an odd nucleus is possible since 279 110 (N = 169) is located in an intermediate region 7 neutrons above the deformed shell closure at N = 162 and 15 neutrons below the spherical shell at N = 184. As a whole, the decay properties of the isotope 283 112 produced in the reactions 238 U + 48 Ca and 242 Pu + 48 Ca do not depend on whether it is observed as a primary nucleus or as an α-decay product of a preceding mother nucleus. At the same time, in one of the 15 decays of 287 114 produced in the reaction 242 Pu + 48 Ca and in one of the 7 decays of 283 112 produced in the reaction 238 U + 48 Ca, we observed lengthy sequential α decays that were terminated by SF with long lifetimes: tSF ≈ 6.3 min and 3.3 h, respectively, see fig. 2. These rare decays result from α/SF competition in the decay of 279 110 (bα ≈ 10%, including three decays observed in [3]) and end in the SF of the relatively neutron-rich isotopes 271 Sg (N = 165) and 267 Rf

Table 2. Decay properties of nuclei produced in this work and [1, 3, 8].

Isotope bα/f (%)

exp. T1/2

Tαcalc.

Eα (MeV)

0.4 ms

11.65 ± 0.06

294

118

α

1.8+75 −1.3

293

116

α

61+57 −20 ms

80 ms

10.54 ± 0.06

292

116

α

18+16 −6 ms

40 ms

10.66 ± 0.07

291

116

α

6.3+11.6 −2.5 ms

20 ms

10.74 ± 0.07

290

116

α

15+26 −6 ms

10 ms

10.85 ± 0.08

289

114

α

2s

9.82 ± 0.05

288

114

α

287

114

α

286

2.6+1.2 −0.7 s 0.80+0.27 −0.16 0.51+0.18 −0.10 0.16+0.07 −0.03

114

α : 40, f : 60

285

112

α

284

112

f

283

112

α, f ≤ 10

282

112

f

281

Ds

f

279

Ds

275

271

267

ms

29+13 −7 s 97+31 −19 ms 4.0+1.3 −0.7 s 0.50+0.33 −0.14

s

0.9 s

9.94 ± 0.06

s

0.5 s

10.02 ± 0.06

s

0.2 s

10.20 ± 0.06

50 s

9.15 ± 0.05

3s

9.54 ± 0.06

≤ 9.67 ≤ 10.67

ms

≤ 8.87

α : 10, f : 90

11.1+5.0 −2.7 s 0.18+0.05 −0.03 s

0.2 s

9.70 ± 0.06

Hs

α

0.15+0.27 −0.06 s

0.8 s

9.30 ± 0.07

Sg

α : 50, f : 50

2.4+4.3 −1.0

min

0.8 min 8.53 ± 0.08

Rf

f

2.3+98 −1.7

h

≤ 8.09

(N = 163). Comparing the two decay chains, one can see that 271 Sg undergoes both α decay (Eα = 8.53 MeV) and SF. Data on the decay properties of 286,287 114, 282,283 112 and their descendant nuclei are summarized in table 2. Included also are the data for heavier isotopes with Z = 110–118 that we produced earlier in the reactions 244 Pu, 245,248 Cm, 249 Cf + 48 Ca [1, 3,8]. The α and SF decay branching ratios, experimental and calculated half-lives and α-particle energies are given. Expected values of Tαcalc were calculated from the measured Qα from the ViolaSeaborg formula [9]. Parameters were fitted to the Tα vs. Qα values of 65 previously known even-even nuclei with Z > 82 and N > 126. The limiting values of Eα for the SF nuclei were estimated in the same way. The measured half-lives closely reproduce the calculated ones for the even-even as well as even-odd isotopes of elements 112– 118 that consequently have rather low hindrance factors, if any, for α decay. For the isotopes of lighter elements, the difference between measured and calculated Tα values increases resulting in hindrance factors of about 10 for 279 Ds. One can suppose that in this region of nuclei, a noticeable transition from spherical to deformed shapes occurs at Z = 100, in agreement with results observed for odd-Z nuclei [10]. Thus, the decay properties of the isotopes of element 114 are generally determined by the spherical shells Z = 114 and N = 184. According to the macroscopic-microscopic (MM) model calculations [11],

Yu.Ts. Oganessian et al.: New elements from Dubna

the nucleus 287 114 is almost spherical (β2 = 0.088). In a succession of sequential α decays, the descendant nuclei move away from the closed N = 184 shell and approach the deformed shell at N = 162. The terminating nucleus, 267 Rf (N = 163), is deformed (β2 ∼ 0.23) [11]. Experimental α-decay energies of the isotopes with Z = 100–118, together with the decay energies of the same nuclides calculated in the MM nuclear model [11, 12], are compared in fig. 4. The experimentally measured values of Qα practically coincide with theoretical predictions for the deformed nuclei in the vicinity of neutron shells N = 152 and N = 162 and becomes somewhat less than the calculated values by ≤ 0.5 MeV for the more neutron-rich nuclides with N ≥ 169. In the decay chain 291 116 → . . . → 267 Rf, we observed a similar variation in α-decay energies as we reported for decay chains starting with 287 115 or 288 115 [10]. The slope of Qα vs. neutron number remains practically the same for elements 112–116 but increases significantly for the nuclides with Z = 111 and 110. Such an effect might be caused by the transition from spherical nuclear shapes to deformed shapes during successive α decays, in agreement with MM calculations [11]. One should note that the predictions of other models within the Skyrme-Hartree-Fock-Bogoliubov [13] and the relativistic mean field [14] methods also compare well with the experimental results. If the theoretical predictions of the existence of closed nuclear shells in the domain of superheavy elements are correct, particularly the stronger influence of the closed neutron shell at N = 184, they should be characterized not only by high stability to various decay modes (longer half-lives) but also by a relatively high probability of production.

Fig. 4. α-decay energy vs. neutron number for isotopes of evenZ elements with Z ≥ 100 (solid circles: even-even isotopes; open circles: even-odd isotopes) [15, 16, 17]. Data at N ≥ 163 that are connected by dashed lines are from [1, 3, 8] and the present work. Solid lines show the theoretical Qα values [11, 12].

593

The production of evaporation residues is determined by the probability of the formation of a compound nucleus and the survival probability in the de-excitation to the ground state by emission of neutrons and γ-rays. From numerous experiments it is known that in the synthesis of heavy nuclei with Z ≥ 102, both in hot and cold fusion reactions, the cross-section σER decreases rapidly with increasing ZCN . Extrapolating the dependence σER (ZCN ) to Z > 110, we would arrive at extremely low cross-sections for the production of isotopes of element 114 (σER ∼ 1–10 fb). However, the experimental values of σER (ZCN = 114) observed in the reactions 242,244 Pu + 48 Ca appeared to be about 3 orders of magnitude higher. In cold fusion reactions, the decrease of σER with increasing ZCN is associated with the dynamic hindrances of the fusion of massive nuclei [7]. Here, extrapolation to superheavy nuclei appears to be justified, as the hindrances should increase with increasing mass and nuclear charge of the projectile. In asymmetric hot fusion reactions, there are practically no fusion limitations. Here, the decrease of σER for higher ZCN is determined by the decreasing survivability of the compound nuclei. The last value strongly depends on the difference between fission barrier Bf and neutron separation energy Bn in the compound nucleus. Since the value of Bf is completely determined by the amplitude of the shell correction (BfLD ≈ 0 for the nuclei with Z ≥ 102), it strongly depends on the neutron number of the compound nucleus. The high fission barriers and correspondingly high cross-sections σER observed in the synthesis of elements with Z = 102–106 are associated with the significant shell effects at N = 152 and at N = 162 (fig. 5). For heavier nuclei with N > 162, Bf values decrease until the next spherical shell at N = 184 starts influencing the fission barrier while Bn values steadily decrease in this region of nuclei. Upon approaching this shell, the fission barriers will increase again. That should result in a substantial increase of σER . As we have shown in fig. 5, the increase of the height of fission barriers due to the influence of the shell closure at N = 184 is expected only for the neutron-rich nuclei with N > 170. For these nuclei, an increase of the neutron number in the compound nucleus results in an increase of the production cross-section observed in the experiments. We consider this to be the major advantage of using the complete-fusion reactions involving the neutronrich transuranic target nuclei and the 48 Ca projectile for the synthesis of superheavy elements. Indeed, the experimental data show that for the nuclei with Z = 112 and 114 and NCN = 174–178 the crosssection of the 4n-evaporation channel (an “open” channel, well above the fusion barrier) systematically increases with increasing neutron number and reaches the maximum value of about 5 pb in the reaction 244 Pu + 48 Ca. The low cross-section for the formation of the isotope 278 112 in the reaction 233 U+ 48 Ca with NCN = 169 has the same explanation. Additionally, in the reaction 248 Cm+48 Ca (ZCN = 116 and NCN = 180), one could expect a higher σ4n cross-section. At present, this experiment is in progress.

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References

Fig. 5. Comparison of cold fusion and hot fusion cross-sections for the production of Z ≥ 102 nuclides using a variety of heavyion beams (top panel). We show the fission barrier heights of corresponding compound nuclei and neutron-evaporation products as a function of neutron number on the bottom panel [18]. The number of neutrons in compound nuclei formed in different reactions are shown by solid symbols.

The cross-section of the reaction 248 Cm(48 Ca, 4n)292 116 at E ∗ = 38.9 MeV (about 3 MeV below the expected maximum cross-section for the 4n-channel) has already reached the value 3.3+2.5 −1.4 pb. In this reaction, six decay chains of the new isotope 292 116 were observed. The decay properties of 292 116 are also included in table 2. This work has been performed with the support of the Russian Ministry of Atomic Energy and grant of RFBR No. 0402-17186. The 233 U and 242 Pu target material were provided by RFNC-VNIIEF, Sarov, Russia. The 248 Cm target material was provided by the U.S. DOE through ORNL. Much of the support for the LLNL authors was provided through the U.S. DOE under Contract No. W-7405-Eng-48. These studies were performed in the framework of the Russian Federation/U.S. Joint Coordinating Committee for Research on Fundamental Properties of Matter.

1. Yu.Ts. Oganessian et al., Phys. Rev. C 62, 041604(R) (2000); Phys. At. Nucl. 63, 1679 (2000); Phys. Rev. C 63, 011301(R) (2001); Phys. At. Nucl. 64, 1349 (2001); Eur. Phys. J. A 15, 201 (2002). 2. M.G. Itkis et al., Proceedings of International Workshop on Fusion Dynamics at the Extremes, Dubna, Russia, 2000, edited by Yu.Ts. Oganessian, V.I. Zagrebaev (World Scientific, Singapore, 2001) p. 93; J. Nucl. Radiochem. Sci. (Jan.) 3, 57 (2002). 3. Yu.Ts. Oganessian et al., Phys. Rev. C 69, 054607 (2004). 4. Yu.Ts. Oganessian et al., Proceedings of the Fourth International Conference on Dynamical Aspects of Nuclear ˘ a-Papierni˘ Fission, Cast´ cka, Slovak Republic, 1998 (World Scientific, Singapore, 2000) p. 334; K. Subotic et al., Nucl. Instrum. Methods Phys. Res. A 481, 71 (2002). 5. W.D. Myers, W.J. Swiatecki, Nucl. Phys. A 601, 141 (1996). 6. R. Bass, Proceedings of the Symposium on Deep Inelastic and Fusion Reactions with Heavy Ions, West Berlin, 1979, edited by W. von Oertzen, Lect. Notes Phys., Vol. 117 (Springer-Verlag, Berlin, 1980) p. 281. 7. V.I. Zagrebaev, M.G. Itkis, Yu.Ts. Oganessian, Phys. At. Nucl. 66, 1033 (2003); V.I. Zagrebaev, Proceedings of the Tours Symposium on Nuclear Physics V, Tours, France, 2003 (AIP, New York, 2004) p. 31. 8. Yu.Ts. Oganessian et al., JINR Communication D7-2002287 (2002); Lawrence Livermore National Laboratory Report, UCRL-ID-151619 (2003). 9. V.E. Viola jr., G.T. Seaborg, J. Inorg. Nucl. Chem. 28, 741 (1966). 10. Yu.Ts. Oganessian et al., Phys. Rev. C 69, 021601(R) (2004). 11. I. Muntian et al., Acta Phys. Pol. B 34, 2073 (2003); Phys. At. Nucl. 66, 1015 (2003). 12. R. Smola´ nczuk, A. Sobiczewski, Proceedings of XV Nuclear Physics Divisional Conference “Low Energy Nuclear Dynamics”, St. Petersburg, Russia, 1995 (World Scientific, Singapore) p. 313; R. Smola´ nczuk, Phys. Rev. C 56, 812 (1997). ´ 13. S. Cwiok, W. Nazarewicz, P.H. Heenen, Phys. Rev. Lett. 83, 1108 (1999); J.F. Berger, D. Hirata, M. Girod, Acta Phys. Pol. B 34, 1909 (2003); S. Typel, B.A. Brown, Phys. Rev. C 67, 034313 (2003). 14. M. Bender, Phys. Rev. C 61, 031302 (2000); P.-G. Reinhard et al., Proceedings of the Tours Symposium on Nuclear Physics IV, Tours, France, 2000 (AIP, New York, 2001) p. 377; Z. Ren, Phys. Rev. C 65, 051304(R) (2002). 15. R.B. Firestone, V.S. Shirley (Editors), Table of Isotopes, 8th ed. (Wiley, New York, 1996). 16. Ch.E. D¨ ullmann et al., Nature 418, 859 (2002). 17. S. Hofmann, G. M¨ unzenberg, Rev. Mod. Phys. 72, 733 (2000); S. Hofmann et al., Eur. Phys. J. A 14, 147 (2002); Z. Phys. A 354, 229 (1996). 18. R. Smola´ nczuk, J. Skalski, A. Sobiczewski, Phys. Rev. C 52, 1871 (1995); I. Muntian, Z. Patyk, A. Sobiczewski, Acta Phys. Pol. B 34, 2141 (2003).

Eur. Phys. J. A 25, s01, 595–597 (2005) DOI: 10.1140/epjad/i2005-06-125-x

EPJ A direct electronic only

Random probability analysis of recent

48

Ca experiments

M.A. Stoyer1,a , J.B. Patin1 , J.M. Kenneally1 , K.J. Moody1 , D.A. Shaughnessy1 , N.J. Stoyer1 , J.F. Wild1 , P.A. Wilk1 , V.K. Utyonkov2 , and Yu.Ts. Oganessian2,b 1 2

Lawrence Livermore National Laboratory, Livermore, CA 94550, USA Joint Institute for Nuclear Research, RU-141980 Dubna, Moscow Region, Russia Received: 25 October 2004 / Revised version: 5 April 2005 / c Societ` Published online: 29 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A Monte Carlo random probability analysis developed at LLNL for heavy element research was performed for recent experiments aimed at the synthesis of nuclides with Z ≥ 112 and N ≥ 170, to estimate the probability that observed decay chains were a result of a random event. Low probabilities (< 10 −4 % for most decay chains) were found. PACS. 27.90.+b 220 ≤ A – 02.50.-r Probability theory, stochastic processes, and statistics – 02.50.Ng Distribution theory and Monte Carlo studies

Since 1998, the Dubna-Livermore collaboration has performed extensive and lengthy experiments at the JINR U400 Cyclotron bombarding various actinide targets (238 U, 242,244 Pu, 243 Am, 245,248 Cm, and 249 Cf) with 48 Ca aimed at producing isotopes of elements 112–118 [1] (see fig. 1). The nuclides of interest, called evaporation residues (EVR) are separated from un-reacted beam, transfer products and other background reactions using the Dubna Gas Filled Separator, and are implanted into a position-sensitive Si detector array. Position-correlated decay events are observed in this detector during the beamon (or beam-off) periods, which thus provides for a variable background counting rate in the detectors during the ∼ month-long experiments. Because of the influence of the closed shells at N = 184 and Z = 114, 120 or 126, the nuclides produced typically alpha-decay one or more times, before the decay sequence is terminated by a spontaneous fission (SF). Because of the low statistics involved in these experiments, often just one or two interesting events per month, and the long duration of the runs requiring stable operation of the accelerator and detection equipment, it is extremely important to understand the probability that the observed decay sequence might be merely due to a random event. Some estimates of these random probabilities [2] rely on average counting rates within the detectors or within position pixels defined by the detector position resolution for example, and thus are not able to consider variable backgrounds or counting rates. a

Conference presenter; e-mail: [email protected] Much of the support for work at LLNL was provided by the U.S. Department of Energy under contract W-7405-Eng-48 and for the work at JINR was through the Russian Federation for Basic Research grant no. 04-02-17186. b

A Monte Carlo method for estimating random probabilities was developed for these kinds of experiments and is discussed more thoroughly in [3]. This method inserts a fission event (could be extended to a random alpha-decay) randomly in time and position into the actual data, and the same search algorithm used to locate decay chains of interest in the experiments searches for correlations with the random event, automatically including fluctuating background effects. The results of the Monte Carlo random probability calculations are shown in table 1. It should be noted that no attempt to eliminate decay chains on the basis of the semi-empirical Geiger-Nuttal relationship has been made in this study. Previously, many assumptions, such as which random number generator was used and nonuniform distributions of random fissions, were tested and found to have negligible effect on the calculated random probabilities [3]. Additionally, for the first element 114 experiment, the random probabilities calculated using this method were compared with other methods and generally found to be higher (thus more conservative). The search algorithm used in this study does not take into account decay chains with missing alpha-decays, decay chains with alpha-events in the side detector only (i.e., no position information), or decay chains that span more than one file or run, which is typically on the order of a few hours. The element 115 SF with a half life of around 30 h was handled differently. Generally, the parameters for the search algorithm were: EVR energy between 7 and 14 MeV, event positions ±2 mm, alpha energies within a 1–2 MeV window around the observed alpha-decay energies, SF energy > 130 MeV, and maximum correlation times variable depending upon the type of correlation

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294

118

D, 11.64 1.8 ms

290

116

D, 10.82 15 ms 287

115

D, 10.58 32 ms

114

286 SF/D 10.19 162 ms 283

113

D, 10.10 100 ms 277

112

282

272

Rg

279

D, 10.82 1.5 ms

267

Ds

269

D 3 Ps 266

Mt

268

D 1.7 ms 264

Hs

D, 10.43 0.08 ms 261

Bh

D, 10.40 12 ms 258

Sg

SF 2.9 ms 255

Db

D, ? 1.6 s

256

Db

D, 9.01 1.6 s

Rf

Rf

254 255 253 SF SF SF D, 8.72 50μs 1.8s 23μs 0.5ms 1.6 s

Rf

252

Lr

D, 9.02 0.36 s 251

No

D, 8.60 0.76 s

253

Lr

D, 8.72 1.5 s 252

No

D, 8.42 2.43 s

254

Lr

D, 8.46 13 s 253

No

D, 8.01 1.6 min

257

Db

D, 8.97 1.5 s 256

Rf

SF D, 8.80 6.5 ms 255

Lr

D, 8.37 22 s 254

No

D, 8.09 47 s

259

Sg

D, 9.62 0.5 s 258

Db

D, 9.17 3.9 s 257

Rf

D, 8.78 4.7 s 256

Lr

D, 8.43 27 s 255

No

D, 8.12 3.1 min

260

Sg

D, 9.77 4 ms 259

Db

D, 9.47 0.5 s 258

Rf

SF 12 ms 257

Lr

D, 8.86 0.65 s 256

No

D, 8.45 2.9 s

262

Bh

264

D, 10.06 0.10 s 261

Sg

D, 9.56 0.23 s 260

Db

D, 9.05 1.5 s 259

Rf

D, 8.77 3.2 s 258

Lr

D, 8.60 4.1 s 257

No

D, 8.22 25 s

265

Hs

D, 10.30 1.7 ms

Sg

SF 6.9 ms 261

Db

D, 8.93 1.8 s 260

Rf

SF 21 ms 259

Lr

D, 8.44 6.2 s 258

No

SF 1.2 ms

263

266

Hs

D, 10.18 2.3 ms

Bh

262

261

Rf

260

Lr

259

No

D, 7.52 58 min

267

Ds

Ds

269

Bh

265

Sg

266

261

Lr

SF 40 min 260

271

Bh

D, ? ?

Sg

272

116

D, 10.66 18 ms

293

116

D, 10.55 61 ms

115

D, 10.44 88 ms 287

114

D, 10.00 510 ms

288

114

D, 9.86 800 ms

289

114

D, 9.77 2.6 s

113

D, 10.03 480 ms 283

112

D, 9.49 4.0 s

284

112

SF 92 ms

285

112

D, 9.15 29 s

Rg

281

Ds

SF 11.1 s

Mt

D, 9.68 730 ms

Hs

Bh

D, 8.99 9.8 s 271

Sg

SF/D 8.51 140 s

D, 8.77 21 s 267

Db

268

Rf

268

SF 2.3 hr

SF ?

267

Rf

Db

SF, H 16 hr

SF 10 m 262

292

D, 9.29 150 ms

SF ~ 73 min

263

276

275

Bh

Db

Rf

Hs

D, 8.83 17 s

263 SF D, 8.35 27 s 262

Mt

116

D, 10.72 6.3 ms

D, 9.73 3.6 s 279 SF/D 9.76 182 ms

D, 9.20 11.2 s 267

280

Ds

273 D, 11.20 D, 9.73 145Ps,118m

D, 10.32 9.7 ms

Hs

D, 8.84 7s

8.28 8.52 SF 65s 4.2s 47ms 2.3s

D, 8.03 3 min

271

D, 10.74 1.1 ms

275

D, 9.88 26 ms 266

Sg

Db

Ds

Mt

D, 9.29 1s

SF D, 9.06 1.0 s

D, 8.45 34 s

270

D, 11.03 100 Ps

Rg

D, 10.30 170 ms

D, 10.24 0.07 s

D, 9.47 0.44 s 262

Ds

D, 11.11 170 Ps

112

SF 0.49 ms

D, 11.45 240 Ps

284

288

291

Rf

Lr

H 3.6 hr

No

SF 110 ms

262

No

SF 5 ms

Fig. 1. Upper end of the Chart of Nuclides showing the isotopes synthesized within the last 6 years and their nuclear properties. Table 1. Calculated probabilities that an observed decay sequence is due to random events for recent heavy element reactions. Note that because the overall decay chain duration is short for many of these isotopes, more random fissions may be required to ensure convergence of the method. These results are for 10–100 million random fissions. In some cases, random probabilities are presented for shorter decay chains than actually observed (i.e., decay chains with fewer alpha-decays), which already results in small probabilities that the observed decay chains are a result of randomness. Additionally, random probabilities for EVR-SF events were also calculated for all cases (not shown).

Initial isotope of decay chain

Production reaction (48 Ca + . . .)

Random probability (%)

294

249

1.0 × 10−5 5.0 × 10−6 2.0 × 10−4 1.5 × 10−4 0.172 8.6 × 10−4 8.5 × 10−5 4.1 × 10−4 6.0 × 10−5

118 116 290 116 288 115 289 114 288 114 287 114 287 114 286 114 291

∗

Cf Cm 245 Cm 243 Am 244 Pu 244 Pu 244 Pu 242 Pu 242 Pu 245

For decay chain with fewer alpha-decays than observed.

∗ ∗ ∗ ∗

Fig. 2. Average time intervals between an implanted EVR and a randomly inserted fission for the 48 Ca + 245 Cm experiment and 1 million random fissions.

(EVR-α, α-α, or α-SF). While counting rates vary depending upon the particular experiment, beam rates, detector positions and target thicknesses, typical counting rates within the ±2 mm position resolution for EVR-like events, for alpha-like events (beam on/beam off), and

M.A. Stoyer et al.: Random probability analysis of recent

SF-like events are ∼ 3 h−1 , (∼ 1.5 h−1 / ∼ 0.7 h−1 ), and ∼ 0.01 h−1 , respectively. For most chains, the probability that the decay chain is due to a random event is in the range of 10−4 –10−5 %, which is in general higher (more conservative) than other methods. The distribution of time differences between a randomly inserted fission event and the nearest preceeding EVR is shown in fig. 2 for the 48 Ca + 245 Cm experiment. Note the location of the actual observed decay chains, much earlier in time than what would be the average of the distribution of random events. The position of the centroid can be estimated from the EVR-like counting rate for the 48 Ca + 245 Cm experiment of ∼ 0.0039 s−1 . The time difference between EVRs in a detector position, averaged over the whole detector, is ∼ 300 s – half this is the average time interval between an EVR and a randomly inserted

48

Ca experiments

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fission, namely ∼ 150 s, which is consistent with the 244 s obtained from the Monte Carlo method properly taking into account all deviations from average.

References 1. Yu.Ts. Oganessian et al., Phys. Rev. Lett. 83, 3154 (1999); Yu.Ts. Oganessian et al., Phys. Rev. C 62, 041604(R) (2000); Yu.Ts. Oganessian et al., Phys. Rev. C 69, 054607 (2004); Yu.Ts. Oganessian et al., Phys. Rev. C 69, 021601 (2004). 2. K.-H. Schmidt et al., Z. Phys. A 316, 19 (1984); Yu.A. Lazarev et al., Phys. Rev. C 54, 620 (1996). 3. N.J. Stoyer et al., Nucl. Instrum. Methods Phys. Res. A 455, 433 (2000).

Eur. Phys. J. A 25, s01, 599–604 (2005) DOI: 10.1140/epjad/i2005-06-026-0

EPJ A direct electronic only

In-beam and decay spectroscopy of transfermium elements P.T. Greenlees1,a , N. Amzal2 , J.E. Bastin2 , E. Bouchez3 , P.A. Butler2,b , A. Chatillon3 , O. Dorvaux4 , S. Eeckhaudt1 , K. Eskola5 , B. Gall4 , J. Gerl6 , T. Grahn1 , A. G¨orgen3 , N.J. Hammond2 , K. Hauschild3,c , R.-D. Herzberg2 , urstel3 , D.G. Jenkins2,d , G.D. Jones2 , P. Jones1 , R. Julin1 , S. Juutinen1 , F.-P. Heßberger6 , R.D. Humphreys2 , A. H¨ 1 1 H. Kankaanp¨ a¨a , A. Keenan , H. Kettunen1 , F. Khalfallah4 , T.L. Khoo7 , W. Korten3 , P. Kuusiniemi1,6 , Y. Le Coz3 , 1 anen1 , M. Muikku1 , P. Nieminen1,e , J. Pakarinen1 , P. Rahkila1 , P. Reiter8,f , M. Rousseau4 , M. Leino , A.-P. Lepp¨ 1 C. Scholey , Ch. Theisen3 , J. Uusitalo1 , J. Wilson3,g , and H.-J. Wollersheim6 1 2 3 4 5 6 7 8

Department of Physics, University of Jyv¨ askyl¨ a, PB 35 (YFL), FIN-40014 University of Jyv¨ askyl¨ a, Finland Department of Physics, University of Liverpool, Oxford Street, Liverpool L69 7ZE, UK DAPNIA/SPhN CEA-Saclay, F-91191 Gif-sur-Yvette, France IReS, 23 Rue du Loess, B.P. 28, F-67037 Strasbourg, France Department of Physical Sciences, University of Helsinki, FIN-00014 University of Helsinki, Finland GSI, D-64291 Darmstadt, Germany Argonne National Laboratory, Argonne, IL 60439, USA Ludwig Maximilians Universit¨ at, D-85748 Garching, Germany Received: 14 January 2004 / Revised version: 3 March 2005 / c Societ` Published online: 22 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Over the past few years a great deal of new spectroscopic data has been obtained for transfermium nuclei. Recoil separators, coupled with modern target position and focal-plane spectrometers, allow detailed studies of the structure and decay properties of transfermium nuclei to be peformed. In-beam studies using the recoil-gating and recoil-decay tagging techniques mainly provide information on yrast states, whilst complementary focal-plane decay studies give access to non-yrast and isomeric structures. In-beam studies of nuclei in this region have largely been performed at ANL and JYFL, and decay experiments at GSI, JYFL, GANIL and ANL. The present contribution is focussed on recent developments and experiments carried out by a number of collaborating institutes at JYFL. PACS. 21.10.-k Properties of nuclei; nuclear energy levels – 23.20.-g Electromagnetic transitions – 29.30.-h Spectrometers and spectroscopic techniques

1 Introduction The coupling of modern arrays of silicon and germanium detectors to recoil separators has in recent years allowed a wealth of new spectroscopic information to be obtained for heavy nuclei. With these devices, it is possible to perform in-beam studies at a production cross-section level much below 100 nb. Detailed focal-plane spectroscopy can still be carried out at a level at least one order of magnitude a

Conference presenter; e-mail: [email protected] Present address: CERN, CH1211 Geneva 23, Switzerland. c Present address: CSNSM, F-91405 Orsay, France. d Present address: Department of Physics, University of York, York YO10 5DD, UK. e Present address: Department of Nuclear Physics, ANU, Canberra, ACT 0200, Australia. f Present address: Institut f¨ ur Kernphysik, Universit¨ at zu K¨ oln, 50937 K¨ oln, Germany. g Present address: IPN Orsay, 91406 Orsay Cedex, France. b

lower. Whilst the heaviest elements are still below the limits for extensive spectroscopy, nuclei in the transfermium region can be produced with cross-sections of up to around 2 μb through reactions of 48 Ca on various targets close to 208 Pb. The nuclei in this region are stabilized by shell effects, which create a barrier against spontaneous fission. The location of the next closed proton and neutron shells above 208 Pb has been a topic of theoretical work for several decades, and the predictions of various theories differ. Most calculations based on the macroscopic-microscopic method using Woods-Saxon or folded Yukawa potentials predict Z = 114 and N = 184 (see, e.g., [1]). The situation with self-consistent mean-field models is not so clear, with different forces and approaches giving different predictions for the shell gaps. Most non-relativistic HartreeFock calculations predict Z = 126 and N = 184, whilst most relativistic mean-field calculations favour Z = 120 and N = 172. A detailed comparison of the predictions of the various forces and mean-field models can be found

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in ref. [2], and overviews of the progress in this area can be found in refs. [3, 4,5] and references therein. Spectroscopic studies of nuclei in the transfermium region may help to shed light on this discussion in an indirect way. In the proton case, single-particle levels originating from the spherical 1h9/2 , 1i13/2 , 2f5/2 and 2f7/2 orbitals in the region of Z = 120 come down in energy with deformation and are close to the Fermi surface in the deformed nuclei close to 254 No. Of particular interest are the 2f5/2 and 2f7/2 spin-orbit partners, as the possible Z = 114 proton shell closure is related to the spin-orbit splitting of these states. The study of even-even nuclei in the region gives information concerning moments of inertia, and allows the extraction of the quadrupole deformation parameter, β2 . Studies of the odd-mass nuclei in the region may allow a determination of the ordering and separation of singleparticle energy levels. If the data obtained in this region can be reproduced theoretically, constraints on the theory may lead to a consensus and more reliable predictions of the properties of superheavy nuclei.

2 Decay spectroscopy

(Recoil−)Alpha−alpha, dT(0−3min,0−15min)

7750

7751

7663.25

Daughter Energy (keV)

The dominant decay mode for many of the nuclei in the region of 254 No is alpha decay. Alpha-decay spectroscopy at the focal plane of recoil separators is by no means a new technique, but advances in ion sources, target design and focal-plane detector technology mean that detailed spectroscopy can be performed on exotic nuclei within a realistic experiment time. The use of alpha-γ and alphaelectron coincidence techniques allows very clean spectra to be obtained, and transition multipolarities can be determined from internal conversion coefficients (provided the relevant detection efficiencies are known). Temporal correlations between different detector groups also allow the lifetimes of isomeric states and/or states populated by the alpha decay to be determined. Long chains of correlated alpha decays are often observed, thus the decay properties of several nuclei are obtained in a single measurement. Many experiments of this type have been carried out using the velocity filter SHIP at GSI, see ref. [6] for an overview. At JYFL, such studies are carried out using the RITU gasfilled recoil separator, which has a transmission efficiency on the order of 40% for the reactions described in this article [7]. A recent addition to the focal plane of RITU has been the GREAT spectrometer, designed by a large group of UK institutions and funded by the UK EPSRC [8]. A schematic of GREAT is shown in fig. 1. The spectrometer consists of a pair of double-sided silicon strip detectors (DSSSDs) placed side-by-side, each with 60 × 40 strips of pitch 1 mm, which act as implantation detectors. Thus, the RITU focal-plane distribution is effectively covered with a detector of 120 × 40 strips in the x- and y-directions, respectively. The DSSSDs measure the energies of implanted ions and their subsequent decays. Immediately behind the DSSSDs is a segmented planar germanium detector (24 × 12 strips of width 5 mm, 15 mm thickness) which is used to detect low-energy gammaand X-rays. Surrounding the DSSSDs on the upstream

Md(2) 7575

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Fig. 1. Upper part: a schematic of the UK Universities GREAT spectrometer, currently installed at the focal plane of the RITU gas-filled recoil separator. Lower part: an alphaalpha correlation plot obtained using an early implementation of GREAT, see text for details.

side is an array of 28 silicon PIN diode detectors in a “box” which can be used to detect escaping alpha particles and conversion electrons. Each PIN diode has dimensions 28 mm × 28 mm and a thickness of 500 μm. A large-volume 16-fold segmented clover germanium detector is mounted above the DSSSDs to detect higher-energy gamma rays. The detector arrangement is completed by a multiwire proportional counter (MWPC) upstream of the DSSSDs. The MWPC is position sensitive, and also measures the energy loss of the recoiling ions. The MWPC can be used in conjunction with the DSSSDs to distinguish recoiling ions and their decay products. A further, major part of the GREAT project was the development

P.T. Greenlees et al.: In-beam and decay spectroscopy of transfermium elements

The SACRED Electron Spectrometer Beam In Cold Finger 25 Element Annular Si Detector To RITU

High Voltage Barrier Carbon He Containment Windows Target Chamber

Counts / 2keV

of a new triggerless Total Data Readout (TDR) data acquisition system [9]. The idea behind the system is to reduce to a minimal level the acquisition dead time. As the name suggests, the data from all detector channels are read out and time-stamped with a 100 MHz clock (10 ns resolution). The data are then collated and merged into a time-ordered stream. Correlations between the various detector groups can then be performed in software and filtering can be performed to reduce the total amount of data prior to storage. An early implementation of GREAT was used in an experiment to study the alpha decay of 255 Lr, produced using the 209 Bi(48 Ca, 2n)255 Lr reaction at a bombarding energy of 221 MeV. Theoretical predictions for 255 Lr suggest that the ground state has a spin and parity I π = 7/2− . The ordering and excitation energies of the low-lying states below 1 MeV differ depending on the model used (see refs. [10,11]), but single-particle states with spins and parities of I π = 1/2− , 9/2+ , 7/2+ and 5/2− are expected. Thus, it is reasonable to assume that the presence of isomeric states is likely. Shown in the lower part of fig. 1 is an alpha-alpha correlation plot produced from the data obtained in the experiment using RITU and GREAT. To create the plot a search is made for correlated chains of the form recoil-mother alpha-daughter alpha in the same pixel of the DSSSDs. An additional constraint is that the mother alpha must be detected within 3 minutes of the recoil implant, and that the daughter alpha must be detected within 15 minutes of the recoil implant. Several clusters of events can be seen in the figure, which are assigned to be correlations of the alpha decay of 255 Lr and its alpha decay daughter 251 Md. Analysis of the decay lifetimes suggests that there are at least two alpha-decaying states in 255 Lr. Two alpha decay lines are also assigned to the decay of 251 Md and analysis suggests that these lines originate from the same state. Alphagamma coincidence data support this interpretation. A similar experiment was carried out by the collaboration using the LISE spectrometer at GANIL. A consistent data set was obtained, with improved alpha-gamma and alphaelectron coincidence data. Analysis of the data from both these experiments is ongoing and will be published in due course [12, 13]. Since these early measurements with GREAT, experiments have also been carried out to study the decay of 253,255 No and also to confirm the presence of an isomeric state in 254 No for which evidence was found both in JYFL and at ANL [14,15]. The isomeric state in 254 No was originally observed by Ghiorso et al. over thirty years ago [16].

601

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Electron Energy (keV) Fig. 2. Upper panel: a schematic of the SACRED conversionelectron spectrometer. Lower panel: recoil-gated singles conversion-electron spectrum from 254 No, see text for details.

up to a spin of at least 14¯h [17]. A later experiment carried out at JYFL using the SARI germanium array and RITU confirmed and extended the ground-state band up to a spin of 16¯h [18]. These (and all subsequent experiments) employed the recoil-gating and recoil-decay tagging (RDT) techniques. As mentioned in sect. 1, the use of such techniques allows the study of nuclei produced with cross-sections much below 100 nb. The following sections describe some of the recent highlights from in-beam conversion-electron and gamma-ray spectroscopic studies.

3 In-beam spectroscopy 3.1 Conversion-electron spectroscopy Over the past few years a number of in-beam experiments have been dedicated to investigation of transfermium nuclei. These experiments began with the observation of the ground-state rotational band in 254 No using GAMMASPHERE and the FMA at Argonne National Laboratory. The results obtained showed that 254 No is deformed, with an estimated quadrupole deformation parameter β2 = 0.27, and that the fission barrier persists

The SACRED electron spectrometer is a unique device for the study of conversion electrons emitted in the decay of heavy nuclei. Operated at JYFL in collaboration with the University of Liverpool, the spectrometer was originally used “stand-alone” in a transverse geometry for electronelectron coincidence measurements. The spectrometer employed a superconducting solenoid magnet, and generally

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used light ion reactions. A detailed description of SACRED in this mode can be found in ref. [19]. In order to use SACRED in recoil-gating and RDT studies, the spectrometer was recently redesigned to operate in a geometry close to collinear with the beam axis. A schematic of SACRED is shown in the upper part of fig. 2. The solenoidal magnetic field ( 0.3 T) is generated by four copper coils, through which a current of 560 A is passed. Electrons produced at the target are transported to a 25 element annular Si detector, allowing electronelectron coincidences to be measured. The intense background of delta electrons is suppressed with the aid of a high voltage barrier, which is normally operated at a voltage of −30 to −45 kV. The He filling of RITU is separated from the high voltage region by a system of carbon foils. Further details and example spectra can be found in ref. [20]. In conjunction with RITU, SACRED has so far been used in experiments to study 250 Fm, 251 Md and 253,254 No [21,22, 23]. One of the highlights from this series of experiments was the observation of evidence for the existence of high-K bands in 254 No (see ref. [23]), in an experiment led by the group from the University of Liverpool. The recoil-gated total singles electron spectrum from the measurement is shown in the lower part of fig. 2. Peaks corresponding to transitions in the ground-state rotational band can clearly be observed, including the 4+ to 2+ transition which had not previously been observed. Also to be noted is the broad distribution of events below the peaks, which is more intense than that normally observed in such measurements. These events have a higher multiplicity than the ground-state band transitions, and are not in prompt coincidence with the ground-state band, indicating that they feed isomeric states. Evidence for such isomeric states has already been observed in focalplane experiments, as mentioned in sect. 2. The conclusion reached is that these events are due to high-K bands in 254 No which decay mainly via highly converted transitions, giving rise to the broad distribution of events seen in fig. 2. A more detailed discussion of the analysis and interpretation can be found in ref. [23]. 3.2 Gamma-ray spectroscopy As mentioned in the introduction to this section, impetus for in-beam studies of transfermium nuclei was gained with the observation of the ground-state band in 254 No at ANL. At ANL, these studies continued with experiments to measure the entry distribution and formation mechanism of 254 No, and a measurement of 253 No [24, 25] in which evidence for two strongly coupled rotational bands was observed. At JYFL, the JUROSPHERE germanium detector array was employed in studies of 250 Fm, 252 No and 255 Lr. A review of the results obtained can be found in ref. [26]. The most recent germanium array to be built at JYFL is JUROGAM, which consists of 43 Compton-suppressed EUROGAM Phase-I type detectors, with a total photopeak efficiency of approximately 4.2% at 1.3 MeV. After the EUROBALL array was dismantled, the EUROBALL owners committee granted the use of thirty

Fig. 3. The JUROGAM array of 43 Compton-suppressed Ge detectors installed at the target position of the RITU gas-filled recoil separator.

Phase-I type detectors for an extended period, with the remainder coming from the UK-France loan pool. A photograph of JUROGAM installed at the target position of RITU is shown in fig. 3. The GREAT project TDR data acquisition system is also used for all in-beam experiments at JYFL, and in the case of JUROGAM the Compton suppression is also performed in software. A new target chamber was recently installed by the IReS Strasbourg group, which allows the use of a rotating target wheel for experiments which require high beam intensities. JUROGAM has been used extensively for studies of neutrondeficient and heavy nuclei, and in the transfermium region experiments for 250 Fm, 251 Md and 254 No have been performed [27, 28,29]. In the 254 No experiment, evidence was found for transitions from non-yrast states for the first time. The results of that measurement are presented in the contribution of Eeckhaudt et al., in these proceedings [29]. A highlight of the JUROGAM experiments has been the study of 251 Md led by the CEA-Saclay group [28]. Gamma-ray spectroscopic studies of high-Z odd-mass nuclei can be strongly affected by the configuration of the odd particle. It can be expected that the decay intensity is strongly fragmented in many rotational bands. In welldeformed nuclei, the signature partners of strongly coupled bands will be linked by low-energy M 1 transitions. The degree to which these interband M 1 transitions compete with the intraband E2 transitions is governed by the magnitude of the gK − gR term, and in the case of

P.T. Greenlees et al.: In-beam and decay spectroscopy of transfermium elements 140

248

5

Fm Fm 251 Md 252 No 254 No

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Count

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603

60 40 20 0

100

200

300

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400

500

600

Fig. 4. Recoil-gated gamma-ray spectra of 251 Md obtained using the JUROGAM Ge array. Upper panel: sum of gammagamma coincidence spectra gated with the marked transitions. Lower panel: total gamma-ray singles spectrum.

K = 1/2 by the decoupling parameter, a, and the related magnetic decoupling factor, b. In 251 Md, theoretical + − calculations predict a [521] 12 ground state, with [633] 72 − and [514] 72 states at low excitation energies (see, e.g., refs. [10, 11]). The K = 1/2 configuration is calculated to have a decoupling parameter of around 0.9, which leads to the expectation that the decay sequence should be domi+ nated by a single band of E2 transitions. The [633] 72 configuration has a calculated gK value of 1.3, resulting in a pair of strongly coupled bands and a decay sequence dom− inated by M 1 transitions. The [514] 72 configuration has a calculated gK value of 0.7, again resulting in strongly coupled bands, but with the decay dominated by E2 transitions. The experiment employed the 205 Tl(48 Ca, 2n)251 Md reaction at a bombarding energy of 218 MeV. Gamma-ray spectra from the measurement are shown in fig. 4. The lower panel shows the total recoil-gated singles gammaray spectrum which was collected with an irradiation time of close to two weeks. The spectrum is dominated by Md X-rays (indicating strong internal conversion) and is somewhat complex. One clear rotational band can however be seen in the spectrum. The assignment of this sequence of peaks into a band is supported by the spectrum shown in the upper panel, which is a sum of gated gamma-gamma coincidence spectra. The gating transitions are marked. In the two spectra, there is no clear indication of a signature partner band, which leads to the tentative conclusion that the band is associated with the K = 1/2 configuration. Further analysis of this data is in progress and will be published in due course [28]. From the data obtained in the various experiments carried out at JYFL and ANL it has been possible to extract the dynamical moment of inertia, J (2) . Figure 5 shows the dynamical moment of inertia for the N = 150 isotones 250 Fm, 251 Md and 252 No along with 248 Fm (one point) and 254 No. The differing behaviour of 252 No and 254 No has been known for some time, and is well reproduced the-

100

80

60 0.05

0.1

0.15 0.2 Rotational Frequency (hω)

0.25

0.3

Fig. 5. Experimental dynamical moments of inertia for several transfermium nuclei.

oretically [11, 30]. For the first time it has been possible to obtain systematic data for the nuclei in this region, and it is of interest to note the similarity in behaviour of the moment of inertia at higher spins in the N = 150 isotones. Obtaining systematic data on the N = 152 isotones may be an even greater experimental challenge, as the production cross-section for 256 Rf is approximately 15 nb, and that for 255 Lr around 300 nb.

4 Future prospects The power of the recoil-gating and RDT techniques in both electron- and gamma-ray spectroscopic studies of very heavy nuclei has been clearly demonstrated. In the near future, the groups from the University of Liverpool, Daresbury Laboratory and JYFL will collaborate to develop a device to simultaneously measure gamma rays and conversion electrons. Based on the JUROGAM and SACRED spectrometers, the device will be known as SAGE. Such a system will allow the measurement of electron-gamma coincidences and will be a powerful tool for the investigation of heavy nuclei. Also under development is a system of digital electronics, which will allow higher detector counting rates to be used. This effectively means that higher beam intensities can be employed, giving greater statistics in a given irradiation time and lowering the spectroscopic limits still further. Even with the

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current combination of JUROGAM and RITU and conventional electronics, it may be possible to attempt the study of 256 Rf. Challenging studies of the odd-mass nuclei 253 No and 255 Lr are also planned for the near future. This work has been supported by the European Union Fifth Framework Programme “Improving Human Potential - Access to Research Infrastructure” Contract No. HPRI-CT-199900044 and by the Academy of Finland under the Finnish Centre of Excellence Programme 2000-2005 (Project No. 44875, Nuclear and Condensed Matter Physics Programme at JYFL).

References ´ 1. S. Cwiok et al., Nucl. Phys. A 611, 211 (1996). 2. M. Bender et al., Phys. Rev. C 60, 034304 (1999). 3. M. Bender, P.-H. Heenen, P.-G. Reinhard, Rev. Mod. Phys. 75, 121 (2003). 4. A.V. Afanasjev et al., Phys. Rev. C 67, 24309 (2003). 5. S. Hofmann, G. M¨ unzenberg, Rev. Mod. Phys. 72, 733 (2000). 6. M. Leino, F.P. Heßberger, Annu. Rev. Nucl. Part. Sci. 54, 175 (2004). 7. M. Leino et al., Nucl. Instrum. Methods B 99, 653 (1995). 8. R.D. Page et al., Nucl. Instrum. Methods B 204, 634 (2003).

9. I.H. Lazarus et al., IEEE Trans. Nucl. Sci. 48, 567 (2001). 10. S. Cwiok, S. Hofmann, W. Nazarewicz, Nucl. Phys. A 573, 356 (1994). 11. M. Bender, P. Bonche, T. Duguet, P.-H. Heenen, Nucl. Phys. A 723, 354 (2003). 12. P.T. Greenlees et al., to be published. 13. Ch. Theisen et al., to be published. 14. P.A. Butler et al., Acta. Phys. Pol. B 34, 2107 (2003). 15. G. Mukherjee et al., to be published in AIP Conf. Proc. 16. A. Ghiorso et al., Phys. Rev. C 7, 2032 (1973). 17. P. Reiter et al., Phys. Rev. Lett. 82, 509 (1999). 18. M. Leino et al., Eur. Phys. J. A 6, 63 (1999). 19. P.A. Butler et al., Nucl. Instrum. Methods A 381, 433 (1996). 20. H. Kankaanp¨ aa ¨ et al., Nucl. Instrum. Methods A 534, 503 (2004). 21. J.E. Bastin et al., to be published in Phys. Rev. C. 22. R.D. Humphreys et al., Phys. Rev. C 69, 064324 (2004). 23. P.A. Butler et al., Phys. Rev. Lett. 89, 202501 (2002). 24. P. Reiter et al., Phys. Rev. Lett. 84, 3542 (2000). 25. T.L. Khoo et al., submitted to Phys. Rev. Lett. 26. R.-D. Herzberg, J. Phys. G 30, R123 (2004). 27. A. Pritchard et al., to be published. 28. A. Chatillon et al., to be published. 29. S. Eeckhaudt et al., these proceedings. 30. T. Duguet, P. Bonche, P.-H. Heenen, Nucl. Phys. A 679, 427 (2001).

Eur. Phys. J. A 25, s01, 605–607 (2005) DOI: 10.1140/epjad/i2005-06-015-3

EPJ A direct electronic only

In-beam gamma-ray spectroscopy of

254

No

S. Eeckhaudt1,a , N. Amzal2,b , J.E. Bastin2 , E. Bouchez3 , P.A. Butler2,4 , A. Chatillon3 , K. Eskola5 , J. Gerl6 , urstel3 , P.J.C. Ikin2 , G.D. Jones2 , T. Grahn1 , A. G¨orgen3 , P.T. Greenlees1 , R.-D. Herzberg2 , F.P. Hessberger6 , A. H¨ 1 1 1 1 7 3 P. Jones , R. Julin , S. Juutinen , H. Kettunen , T.L. Khoo , W. Korten , P. Kuusiniemi6 , Y. Le Coz3 , M. Leino1 , A.-P. Lepp¨ anen1 , P. Nieminen1 , J. Pakarinen1 , J. Perkowski1 , A. Pritchard2 , P. Reiter8 , P. Rahkila1 , C. Scholey1 , Ch. Theisen3 , J. Uusitalo1 , K. Van de Vel1,c , J. Wilson3 , and H.J. Wollersheim6 1 2 3 4 5 6 7 8

Department of Physics, University of Jyv¨ askyl¨ a, Jyv¨ askyl¨ a, Finland Oliver Lodge Laboratory, University of Liverpool, Liverpool, UK DAPNIA/SPhN, CEA-Saclay, Saclay, France CERN-ISOLDE, Geneva, Switzerland Department of Physics, University of Helsinki, Helsinki, Finland GSI, Darmstadt, Germany Argonne National Laboratory, Argonne, IL, USA IKP, University of Cologne, Cologne, Germany Received: 28 October 2004 / c Societ` Published online: 20 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The recoil-tagging technique has been employed to perform an in-beam gamma-ray spectroscopic study of the transfermium nucleus 254 No. The experiment was carried out at the Department of Physics of the University of Jyv¨ askyl¨ a and utilised the JUROGAM array of germanium detectors coupled to the gasfilled recoil separator RITU. The ground-state rotational band was extended and evidence for non-yrast states was observed for the first time. PACS. 21.10.-k Properties of nuclei; nuclear energy levels – 23.20.-g Electromagnetic transitions – 29.30.-h Spectrometers and spectroscopic techniques

1 Introduction

2 Experimental details

Knowledge of the structure of very heavy elements is essential for the testing and development of mean-field theories describing the properties of the heaviest nuclei. Important input comes from the study of transfermium nuclei, the heaviest systems for which high-spin data is experimentally accessible. An important isotope in this region is 254 No, the ground-state band of which has been studied previously [1]. Recent developments in spectrometer and data acquisition techniques at the Accelerator Laboratory of the University of Jyv¨askyl¨a (JYFL) have made the study of these transfermium nuclei possible. A new in-beam gamma-ray spectroscopic study of 254 No has been performed in an attempt to improve upon previously obtained results.

The fusion-evaporation reaction 208 Pb(48 Ca, 2n)254 No was employed. Prompt gamma-rays were detected at the target position with the JUROGAM Ge-array consisting of 43 Compton-suppressed HPGe-detectors. To select the gamma-rays of interest from the high fission background the recoil-tagging technique was employed [2, 3]. Fusion-evaporation residues were separated from primary beam and fission products with the gasfilled recoil separator RITU [4]. They were implanted into the DSSDs (2 × 60 × 40 strips) of the GREAT detector system [5] which has a MWPC placed upstream allowing discrimination between recoils and decay products. Selecting those gamma-rays detected at the target position in coincidence with an implanted recoil led to effective suppression of the fission background. The detector signals were handled by the new TDR (Total Data Readout) dataacquisition system [6]. This is a triggerless system, providing a time-ordered stream of data timestamped with a precision of 10 ns. Event-building is done in software and for both online and offline analysis the software-package Grain [7] was used.

a

Conference presenter; e-mail: [email protected] b Present address: Institute of Physical Research, University of Paisley, UK. c Present address: VITO, IMS, Mol, Belgium.

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200

+

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Fig. 1. Recoil-gated gamma-ray spectrum of 254 No with the rotational ground-state band transitions labeled with spin assignments. The inset shows an enlarged part of the spectrum with the two prominent non-yrast high-energy lines. Table 1. Energies and intensities of ground-state band transitions.

Transition

2 →0 4+ → 2 + 6+ → 4 + 8+ → 6 + 10+ → 8+ 12+ → 10+ +

+

Energy (keV)

44(1) 102(1) 159.5(2) 214.1(1) 267.3(1) 318.1(2)

Transition +

14 16+ 18+ 20+ 22+

→ 12 → 14+ → 16+ → 18+ → 20+ +

Energy (keV)

366.6(2) 412.7(2) 456.0(3) 498(1) 536(1)

Fig. 2. Dynamical moment of inertia of the transfermium nuclei 254 No (diamonds), 250 Fm (triangles), 252 No (squares) and 251 Md (circles). 4000 3500

Level energy [keV]

0

3000 2500 2000 1500 1000 500 0

3 Results and discussion A recoil-gated gamma-ray spectrum is shown in fig. 1. The absence of competing evaporation channels together with the selective recoil-tagging technique allowed the γ-rays of interest to be unambiguously assigned to 254 No. The members of the ground-state rotational band are clearly visible and marked with spin assignments. Studying γγ-coincidences and assuming E2-multipolarity, the band previously established [1] could be confirmed up to spin 20 and extended up to spin 22. Energies of the ground-state band transitions are listed in table 1. The lowest two transitions were not observed, which was attributed to strong internal conversion, but can be extrapolated from a Harris fit to the band. The energy of the 4+ to 2+ transition (101(1) keV) was recently confirmed in a conversion electron spectroscopy measurement [8]. The dynamical moment of inertia for the ground-state band is plotted in fig. 2 and compared with neighbouring nuclei. In contrast to 252 No, the J (2) behaviour of 254 No is very smooth and no upbend is observed. Between the main peaks non-yrast transitions are visible but the lack of statistics prevented placement into the level scheme. More prominent signs of non-yrast structure can be seen at higher energy (see fig. 1 and inset therein) where two relatively intense peaks are observed at 842(1) keV and 943(1) keV. The energy difference of these prominent high-energy lines matches the 4+ to 2+

0

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6

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14

Spin [hbar]

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20

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24

Fig. 3. Yrast plot of ground-state band with suggested positioning of high-energy lines. The assumed feeding pattern of the high-lying low-spin state is shown in dashed lines.

ground-state band transition energy of 101(1) keV. We therefore tentatively place a high-lying low-spin state as in fig. 3, decaying into the ground-state band via the two high-energy transitions mentioned above. This assumption is supported by the absence of clear coincidences with ground-state band transitions. The feeding of this level is assumed to go via highly converted transitions. Similar high-lying low-spin states can be found in neighbouring nuclei. In particular, a level at similar excitation energy (906 keV) is found in the isotone 250 Cf [9] where it is a 3− state and a member of a K = 2 octupole vibrational band. The absence of evidence in the 254 No spectrum of other states belonging to the octupole vibrational band cannot, however, be explained at present. In particular the 2− → 2+ transition is expected to be intense but cannot be distinguished in the spectra of 254 No. The interpretation of the possible high-lying low-spin state in 254 No therefore remains an open question. With the setup used, previous results have been confirmed and some new transitions added. To significantly improve the knowledge of 254 No, a combination of inbeam conversion electron and gamma-ray spectroscopy is required.

S. Eeckhaudt et al.: In-beam gamma-ray spectroscopy of

References 1. 2. 3. 4.

P. Reiter et al., Phys. Rev. Lett. 84, 3542 (2000). R.S. Simon et al., Z. Phys. A 325, 197 (1986). E.S. Paul et al., Phys. Rev. C 51, 78 (1995). M. Leino et al., Nucl. Instrum. Methods B 99, 653 (1995).

254

No

607

5. R.D. Page et al., Nucl. Instrum. Methods B 204, 634 (2003). 6. I.H. Lazarus et al., IEEE Trans. Nucl. Sci. 48, 567 (2001). 7. P. Rahkila et al., to be published in Nucl. Instrum. Methods A. 8. R.D. Humphreys et al., Phys. Rev. C 69, 064324 (2004). 9. M.S. Freedman et al., Phys. Rev. C 15, 760 (1977).

Eur. Phys. J. A 25, s01, 609–610 (2005) DOI: 10.1140/epjad/i2005-06-020-6

EPJ A direct electronic only

Model of binding alpha-particles and applications to superheavy elements K.A. Gridnev1,a , S.Yu. Torilov1,b , D.K. Gridnev1,2 , V.G. Kartavenko3 , W. Greiner2 , and J. Hamilton4 1 2 3 4

Institute of physics, St. Petersburg State University, St. Petersburg 198504, Russia J.W. Goethe University, Frankfurt/Main, D-60054, Germany Joint Institute for Nuclear Research, Dubna, Moscow District, 141980, Russia Vanderbilt University, Nashville, TN 37235, USA Received: 21 October 2004 / c Societ` Published online: 20 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The model of nuclear matter built from alpha-particles is proposed. In this model nuclei possess the molecular-like structure. Analyzing the numbers of bonds one gets the formula for the binding energy of a nucleus. The structure is determined by the minimum of the total potential energy, where interaction between alpha-particles is pairwise and the pair-potential is of Lennard-Jones type. The calculated binding energies show a good agreement with experiment. Calculations predict the stability island for superheavy nuclei around Z = 120. PACS. 21.10.Dr Binding energies and masses – 21.60.Gx Cluster models

1 Introduction We assume that atomic nuclei might be considered as a tight packing of alpha-particles. The basis of the model is assumption that the binding energy can be expressed as a sum of energies coming from interactions between alphaparticles and their self-energies. As a result the nuclear binding energy can be written as Eb = A0 (6Nα + nα ) + C,

(1)

where A0 determines the energy of interaction, Nα is the number of alpha-particles in the nucleus, nα is the number of bonds between alpha-particles (for definition see ref. [1]) and C is the Coulomb energy of the nucleus. Now we can rewrite this formula for alpha-alpha interaction as for potential well. In analogy with molecular physics for the alpha-particle potential we shall take the LennardJones potential.    6  12 σ σ , (2) − Vαα (rij ) = V0 rij rij

where V0 = 19.2 MeV and σ = 2.66 fm. We can calculate positions of alpha-particles from the condition that they bring the total potential energy to its minimum. We do it by calculating the effective one-particle potential by a b

Conference presenter; e-mail: [email protected] e-mail: [email protected]

induction, which is a good approximation. The volume of the nucleus is set on a three-dimensional grid and the first alpha-particle is positioned in the center. Then the potential is calculated in all nodes of the grid and next alpha-particle is positioned into the node with the minimum potential energy. Then we take two particles and calculate their potential and put the third in its minimum. This minimum is achieved on a circle centered in the middle between first two alpha-particles perpendicular to their connection axis. in this way on step i we have the effective potential for the particle i + 1 which comes from i previously located particles  Vαα (ri − rj ). Vi = j
In fig. 1 the separation energy of alpha-particles is plotted as a function of the number of alpha-particles in nuclei. Each peak in this picture corresponds to the nucleus with high binding energy of alpha-particles. Figure 2 shows the set of the simplest configurations. The cases (a), (c) and (d) correspond to “alpha-magic” nuclei and (b) shows that oxygen is a mixture of “classical” and “alpha-magic”. Now we can compare our values of binding energies with the experimental ones. (Experimental binding energies were taken from the website maintained by the Brookhaven National Laboratory [2].) In fig. 3 one finds the plot of the ratio of calculated to experimental binding energies depending on the number of alpha-particles. If we assume that the main trend remains when adding neutrons we obtain in the region Z = 120–122 and A = 300–310

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Fig. 1. Calculated one–alpha-particle separation energy (Q-value) versus the number of alpha-particles.

12

C a)

16

O b)

28

Si c)

52

Fe d)

Fig. 2. The “alpha-magic” numbers. These numbers correspond to geometric figures with the maximal number of bounds per one alpha-particle.

Fig. 4. One–alpha-particle separation energy versus the number of alpha-particles. Stability enhancement is observed at Z = 120 (Nα = 60).

(fermionic) shell structure overlaps with geometric tightly packed structure of atoms. The geometric shell effects still affect the behavior of binding energy in this case. So one might expect the interplay between two effects.

2 Conclusion We have developed a simple model of binding alphaparticles and showed that it predicts very well binding energies in a large range of nuclei, with the accuracy within the range of light and medium heavy nuclei being 1–2%, see fig. 3. For the inter-particle potential we took the one which has the form of the molecular Lennard-Jones potential. With these forces stable configurations have an approximate icosahedral symmetry. Cluster structure of the nuclear system leads to specific shell effects which do not reduce to traditional single-particle ones. Such effects could be important for stability of superheavy nuclei, where shell effects play the key role. Our preliminary calculations show enhancement of binding energy for superheavy nuclei with Z = 120.

Fig. 3. The ratio of calculated to experimental binding energies. The difference is about 1–2%.

there are nuclei having high binding energy per alphaparticle and thus higher lifetime, see fig. 4. One of us, ref. [3] has suggested fullerene nuclei in this region. The shell effects described here have a purely geometrical character. The possibility that they overlap with traditional shell effects based on Fermi-Dirac statistics and spin-orbit force is not excluded but is not considered here. This is in analogy with metal crystals, where the electron

This work was partially supported by Deutsche Forschungsgemeinschaft (grant 436 RUS 113/24/0-4), Russian Foundation for Basic Research (grant 03-02-04021) and the HeisenbergLandau Program (JINR, Dubna) One of us (D.K. Gridnev) appreciates the financial support from the Humboldt Foundation.

References 1. P.D. Norman, Eur. J. Phys. 14, 36 (1993). 2. http://www.nndc.bnl.gov. 3. W. Greiner, Prog. Theor. Phys. Suppl. 146, 84 (2002).

Eur. Phys. J. A 25, s01, 611–612 (2005) DOI: 10.1140/epjad/i2005-06-006-4

EPJ A direct electronic only

Ground-state properties of superheavy elements in macroscopic-microscopic models A. Barana , Z. L  ojewski, and K. Siejab Institute of Physics, Maria Curie-Sklodowska University, ul. Radziszewskiego 10, 20-031 Lublin, Poland Received: 1 October 2004 / c Societ` Published online: 9 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Masses, α-decay and spontaneous fission half-lives of superheavy elements are studied in macroscopic-microscopic approaches with two different macroscopic models and the delta-pairing interaction. Model mass deviations obtained with different formulae are 0.5–0.8 MeV. PACS. 21.10.Dr Binding energies and masses – 21.30.-x Nuclear forces – 25.85.Ca Spontaneous fission – 21.10.Tg Lifetimes

1 Theoretical models In the presented paper we examine masses, α-decay and spontaneous fission half-lives of superheavy elements studied in macroscopic-microscopic (M-M) models. The macroscopic part of the energy is either the LublinStrasbourg Drop (LSD) model introduced in ref. [1], which in addition to the volume, Coulomb and surface terms contains the first-order curvature term, or the traditional formula of Myers and Swiatecki but with an estimate for the congruence energy and parametrs fitted to all presently known masses (dubbed as Refitted Liquid Drop-RLD) [1]. The microscopic part, consisting of the sixth-order Strutinsky shell correction and the pairing correction based on the δ-force, is evaluated with single-particle spectra generated in a Woods-Saxon potential with the universal set of parameters [2]. The pairing energy is calculated in the BCS or Lipkin-Nogami approaches with a blocking effect in case of odd nuclei. The pairing interaction is of the form of the zero-range delta force: 1 − σ 1 · σ2 δ(r1 − r2 ). (1) Vˆ δ (r1 , r2 ) = −V0n|p 4

The coupling strength parameters (V0n , V0p ) are chosen to obtain the best mass formula without any increase of the usual number of parameters of the M-M model. Two fits of the coupling strengths are performed: 1. Constant pairing strengths are found for 258 even-even, odd-even and odd-odd nuclei with Z ≥ 98, the same values for all combinations of the macroscopic and microscopic parts of the energy. The calculations are performed a

e-mail: [email protected] Conference presenter; e-mail: [email protected] b

in a truncated single-particle space containing N levels for neutrons and Z levels for protons. The optimal values, equal for all macroscopic (RLD or LSD)-microscopic (BCS or Lipkin-Nogami) approaches, are V0n = 220 MeV fm3 ,

V0p = 230 MeV fm3 .

2. The δ-pairing strength can be approximated with the following formula [3]: , 1 ¯h2 2 h2 , (2) , kc = 2mc /¯ 2π V0 = π/2a + kc m

where m is the mass of a nucleon, a is the experimental scattering length of the nucleon-nucleon interaction and c is the cutoff energy. In our calculations we have used a renormalized form of V0 given by eq. (2), namely V0n|p = wV0 . The value of w was determined in a fitting procedure to be equal to 0.4 in the case of the WS potential at the cutoff energy c = e(N, Z) − e(1), e being the single-particle energy of the N -th, Z-th or the first level, respectively. In the calculations of spontaneous fission half-lives the potential energy is determined using the LSD formula as it gives higher accuracy for the fission barriers than other models [1] and results in half-lives being closer to experimental data for heavy nuclei than the RLD model [4]. The fission process of a nucleus is described as a tunnelling through the collective potential barrier in the WKB approximation. In order to minimize the action entering the fission probability we have used the dynamic programming method [5]. The potential energy and all the components of the tensor of inertia (evaluated in the adiabatic cranking model) are calculated on a deformation mesh defined as follows β2 = 0(0.05)1.2, β4 = −0.12(0.04)0.32, β6 = −0.12(0.04)0.12. The other degrees of freedom (e.g.,

σrms (MeV) 0.80 0.85 0.89 0.94 0.69 0.67 0.78 0.75

MODEL RLD + BCSC RLD + LNC LSD + BCSC LSD + LNC RLD + BCS RLD + LN LSD + BCS LSD + LN

112

12 (b)

Rf

116

8 6

240

Hs

Q(α) (MeV)

Q(α) (MeV)

12 (a) 10

σmod (MeV) 0.64 0.68 0.75 0.79 0.52 0.51 0.62 0.61

280

260

Sg

Db

Q(α) (MeV)

Q(α) (MeV)

113

10

Lr

8

115 Bh

6

6

240

300

280

260

A

300

240

tal data [6]. The rms deviation for Qα is about 0.5 MeV. Figure 2 shows the spontaneous fission as well as the α-decay half-lives (according to the empirical formula from ref. [8]) of Z = 110–116 isotopes calculated in the LSD + BCS model as well as the recent experimental data measured in Dubna [9].

Rg

12 (d)

10 Md 8

280

260

A

Mt

log (T/s)

114

8

A

12 (c)

20 Z=116 15 10 5 0 -5 -10 -15 -20 250 260 270 280 290 300 310 A

No

240

300

20 Z=114 15 10 5 0 -5 -10 -15 -20 250 260 270 280 290 300 310 A

20 Z=112 15 10 5 0 -5 -10 -15 -20 250 260 270 280 290 300 310 A

Fig. 2. Spontaneous fission and α-decay half-lives of Z = 110–116 elements calculated in LSD + BCS model.

Ds

6

exp

Fm

10

μmod (MeV) −0.18 −0.31 −0.11 −0.26 −0.09 −0.16 −0.03 −0.13

20 Z=110 15 10 5 0 -5 SF -10 α -15 EXP -20 250 260 270 280 290 300 310 A

log (T/s)

Table 1. Standard mass deviations, model mass deviations and model mean errors resulting from M-M calculations. Index “C” means the pairing strengths do not differ from one nucleus to another.

log (T/s)

The European Physical Journal A

log (T/s)

612

280

260

300

A

Fig. 1. α-decay energies calculated in the LSD + BCS model (circles) in comparison to experimental data [6] (crosses) for even-Z (panels (a) and (b)) and odd-Z (panels (c) and (d)) superheavy nuclei.

odd-multipolarity deformations) are not taken into account as they are of a minor importance in this type of calculations for superheavy nuclei.

2 Results In table 1 we list resulting rms deviations for the masses calculated in different M-M models as compared to the experimental measurements and predictions of Audi and Wapstra [6]. Due to the large experimental mass uncertainties (up to 1 MeV for the heaviest nuclei) for a better assessment of the validity of our mass formula we give as well the model standard deviations (σmod ) and model mean errors (μmod ), defined as in [7]. Taking into account only the nuclei with Z ≥ 98 for which the experimental mass was measured we obtain a model mass error of 0.45–0.55 MeV, depending on the M-M approach. In fig. 1 the α-decay energies calculated in the LSD + BCS model are shown in comparison to experimen-

3 Summary The conclusions of our study are the following: i) The M-M mass formulae provide an effective method to describe the binding energies of the heaviest elements. Both liquid drop models, RLD and LSD, give similar rms mass deviations so the curvature terms are of no importance in calculations of equilibrium mass. ii) Using the zero-range pairing force of the δ-type allows to reproduce nuclear masses to a high accuracy by fitting only two coupling strengths for all considered nuclei. iii) The M-M model based on the LSD macroscopic part and the state-dependent δ-pairing correction is an appropriate approach to study simultaneously masses and α and spontaneous fission decays of heaviest nuclei.

References 1. K. Pomorski, J. Dudek, Phys. Rev. C 67, 044316 (2003). ´ 2. S. Cwiok et al., Comput. Phys. Commun. 46, 379 (1987). 3. E. Garrido, P. Sarriguren, E. Moya-de-Guerra, P. Schuck, Phys. Rev. C 60, 064312 (1999); H. Esbensen, G.F. Bertsch, K. Hencken, Phys. Rev. C 56, 3054 (1997). 4. Z. L  ojewski, A. Baran, K. Pomorski, Acta. Phys. Pol. 34, 1801 (2003). 5. A. Baran et al., Nucl. Phys. A 361, 83 (1981). 6. G. Audi, H. Wapstra, C. Thibault, Nucl. Phys. A 729, 337 (2003). 7. P. M¨ oller, J.R. Nix, W.D. Myers, W.J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995). 8. Z. Patyk, A. Sobiczewski, Nucl. Phys. A 533, 132 (1991). 9. Yu.Ts. Oganessian et al., these proceedings.

8 Heavy elements 8.2 Production

Eur. Phys. J. A 25, s01, 615–618 (2005) DOI: 10.1140/epjad/i2005-06-084-2

EPJ A direct electronic only

Fusion hindrance and quasi-fission in

48

Ca induced reactions

Implications for super-heavy element production M. Trotta1,a , A.M. Stefanini1 , S. Beghini2 , B.R. Behera1 , A.Yu. Chizhov3 , L. Corradi1 , S. Courtin4 , E. Fioretto1 , A. Gadea1 , P.R.S. Gomes5 , F. Haas4 , I.M. Itkis3 , M.G. Itkis3 , G.N. Kniajeva3 , N.A. Kondratiev3 , E.M. Kozulin3 , A. Latina1 , G. Montagnoli2 , I.V. Pokrovsky3 , N. Rowley4 , R.N. Sagaidak3 , F. Scarlassara2 , A. Szanto de Toledo6 , S. Szilner1 , V.M. Voskressensky3 , and Y.W. Wu1 1 2 3 4 5 6

INFN Laboratori Nazionali di Legnaro, I-35020 Legnaro, Padova, Italy Dipartimento di Fisica and INFN Sezione di Padova, I-35131 Padova, Italy Flerov Laboratory of Nuclear Reactions, JINR, 141980 Dubna, Russia IReS, IN2P3-CNRS/ULP, F-67037 Strasbourg Cedex 2, France Instituto de Fisica, Universidade Federal Fluminense, Niteroi, R.J. 24210-340, Brazil Departamento de Fisica Nuclear, Universidade de S˜ ao Paulo, C.P. 66318, 5315-970 S˜ ao Paulo, Brazil Received: 13 October 2004 / Revised version: 18 January 2005 / c Societ` Published online: 24 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Recent experimental data on relatively mass-asymmetric collisions show that fusion hindrance can be explained in terms of the onset of quasi-fission reactions. The influence of mass-asymmetry, shell effects and target deformation on such phenomena is presented and possible implications for super-heavy element production are discussed. PACS. 25.70.-z Low and intermediate energy heavy-ion reactions – 25.70.Jj Fusion and fusion-fission reactions – 27.80.+w 190 ≤ A ≤ 219

1 Introduction The search for super-heavy elements (SHE) started in the late sixties as a consequence of the predictions of closed spherical nuclear shells at Z = 114 and N = 184 [1,2]. Nuclei with these “magic” proton and neutron numbers and their neighbours were predicted to be stabilized against spontaneous fission by large shell correction energies. By then many efforts have been devoted to the search for SHE. Experimentally, the SHE production is an extremely challenging issue since many different parameters have to be optimized. Soon, it was realized that in order to favour the formation of very heavy elements from rather mass-symmetric entrance channels, another process had to be minimized besides spontaneous fission. This process, called quasi-fission (QF) [3], competes with complete fusion at near barrier energies and can lead to a large hindrance for fusion, therefore affecting the probability of producing SHE. Namely, the fusion of two massive nuclei leads to superheavies only when the combined system is captured inside the attractive potential pocket, survives quasi-fission and approaches a compact shape; the resulting compound nucleus (CN) has then to survive fission, leading to an evaporation residue (ER) with a finite halfa

Conference presenter; e-mail: [email protected]; Present address: INFN-Sezione di Napoli, Napoli, Italy.

life. The survival to fission can be optimized by minimizing the excitation energy and the angular momentum of the compound nucleus. Therefore, in order to optimize the SHE production rate, the challenge is to understand what are the conditions influencing QF. In the last few years, exciting results have been obtained by both “cold fusion” reactions on Pb and Bi targets and “hot fusion” reactions with 48 Ca beams on actinide targets [4, 5]. However, the very low cross-sections (a few pb) for production of SHE do not allow to make detailed experimental studies on the parameters influencing their formation. Recently, it has been shown that QF reactions may be present even for relatively light combined systems [6,7] and rather mass-asymmetric combinations, where non negligible ER cross-sections are found. Therefore, studies on lighter nuclei can help to understand how entrance channel properties influence the dynamical evolution of the combined system from capture to scission. Many factors may potentially affect ER survival and QF competition. With the purpose of studying the influence of mass-asymmetry, shell effects and target deformation on QF, the following reactions were chosen: – – – –

Er, 12 C + 204 Pb → 216 Ra∗ , Sm, 16 O + 186 W → 202 Pb∗ , 144 Sm → 192 Pb∗ , 154 Sm → 194 Pb∗ .

48

168

48

154

Ca + Ca + 48 Ca + 40 Ca +

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2 The experiments The experiments were carried out at INFN-Laboratori Nazionali di Legnaro, using the stable beams delivered by the XTU-Tandem-Alpi accelerator facility. Highly enriched metallic 154,144 Sm, 168 Er (50–200 μg/cm2 ) and 186 WO3 (50 μg/cm2 ) targets evaporated onto carbon backings (15–20 μg/cm2 ) were used. The experimental setup was a combination of an electrostatic deflector with a time-of-flight (TOF) spectrometer. The electrostatic deflector [8] allowed to separate ER from the incident beam, and residual beam-like particles were further discriminated by an additional Energy-TOF telescope based on a silicon and on a micro-channel plate detector. The doublearm TOF spectrometer CORSET [9], based on positionsensitive micro-channel plates, allowed to detect fission fragments (FF) in coincidence. Position and velocity of FF were used to deduce their mass and total kinetic energy (TKE). Four silicon detectors detected Rutherford yields from the targets, which were used for normalization purposes and for a precise determination of the beam position. Angular distributions for both ER and FF were measured at different energies spanning the Coulomb barrier.

Fig. 1. Capture cross-sections for 48 Ca + 154 Sm (left panel) and 16 O + 186 W (right panel). Experimental data (points) are compared with coupled-channels calculations (lines).

3 Results and discussion It is known that collisions between rather mass symmetric heavy nuclei are characterized by a noticeable contribution of QF events [10]. Recently, the presence of QF was put in evidence even for mass-asymmetric combinations [6]. Three reactions were studied: 12 C + 204 Pb, 19 F + 197 Au and 30 Si + 186 W, all leading to 216 Ra∗ . Different entrance channels leading to the same compound nucleus are expected to give the same reduced ER cross-sections k 2 σER /π at sufficiently high excitation energies, where the transmission coefficients T are approximately 1 for all the low angular momenta leading to ER [6, 7]. However, the comparison of the reduced ER cross-sections for the three above mentioned systems showed a fusion hindrance effect for the 30 Si and 19 F induced reactions in comparison with 12 C + 204 Pb. Such effect was interpreted as due to an unexpected onset of the QF mechanism, as suggested by an increasing width of the FF mass distribution. We extended such studies by populating 216 Ra∗ using a 48 Ca beam on a 168 Er target to move further towards a more symmetric reaction; and we looked for a clear signature of QF events. ER and FF were measured for both 48 Ca + 168 Er and 12 C + 204 Pb. Our data confirm the presence of a large fusion hindrance effect for 48 Ca + 168 Er in comparison with 12 C + 204 Pb [11]. Such fusion hindrance is consistent with a noticeable contribution of asymmetric fission found in the mass-TKE distributions of fission fragments [12]. This contribution was ascribed to the QF process and its mass-asymmetry explained in terms of shell effects manifested in the exit channel [13], favouring the formation of closed shell FF. The large anisotropy observed in the angular distribution of mass-asymmetric FF [13,14] provided a clear signature of QF events.

Fig. 2. Distribution of barrier energies for

48

Ca +

154

Sm.

We then studied the fusion of the magic 48 Ca with the well deformed target 154 Sm. The main purpose of this work was to look for experimental evidence of fusion hindrance in a system where Z1 Z2 is as large as 1240 but the CN is relatively light (202 Pb∗ ), and where deformation is present, so to give us information on the effect of target deformation on QF. To this aim we also extended to higher energies previous measurements on 16 O + 186 W [15,16], also leading to 202 Pb∗ . The 48 Ca + 154 Sm system is on the other hand interesting because it offers the opportunity to study the competition between possible fusion hindrance effects due to QF and fusion enhancement below the barrier due to the strong channel couplings in a reaction between a relatively heavy projectile and a well deformed target [17]. In fig. 1 the total capture (evaporation + fission) crosssections (points) are compared for both systems to the corresponding barrier-passing cross-sections calculated with and without channel couplings. The dashed curves correspond to the no-coupling limit, while the solid curves are coupled-channels (CC) calculations performed using the CCFULL code [18] and including rotational couplings up to the 12+ level, with the indicated β2 and β4 deformation parameters. A good agreement is obtained in the CC approach for the total capture cross-sections of both systems. The experimental distribution of barrier energies for 48 Ca + 154 Sm was extracted from the second energy derivative of the fusion excitation function [19,20] and is shown in fig. 2 (points) together with CC predictions. It can be noticed that such barrier distribution is about

M. Trotta et al.: Fusion hindrance and quasi-fission in

Fig. 3. Experimental ER (triangles), FF (squares) and total capture (circles) cross-sections for both 48 Ca + 154 Sm (left panel) and 16 O + 186 W (right panel) are compared with statistical model calculations (lines).

25 MeV wide and it clearly shows the presence of barriers lower than the average Bass [21] value (vertical line). Collisions between nuclei producing wide barrier distributions lead to enhanced sub-barrier capture cross-sections; therefore, it may be expected that such collisions may favour the production of heavy elements at low energies. Anyway, such qualitative deduction may change somehow when the QF process comes into play and the reaction dynamics leading to the compact CN is considered. Statistical model calculations were performed by means of the HIVAP code [22] to predict both ER and FF cross-sections for 48 Ca + 154 Sm and 16 O + 186 W. Details on similar calculations performed for 48 Ca + 168 Er and 12 C + 204 Pb have been already described [11]. We just mention here that the main parameters of these calculations are the potential barrier fluctuations σ(r0 )/r0 around the average reduced radius, which simulate the deformation effects and can be different for the two systems. The second important parameter is the kf , which is a correction to the liquid drop fission barrier and according to the Bohr hyphothesis should depend only on the compound nucleus. We have determined such kf by making a best-fit to the cross-sections for 16 O + 186 W, where QF is not expected. The overall reproduction of data (fig. 3, right panel) is quite satisfactory. But if we use the same kf parameter for 48 Ca + 154 Sm (fig. 3, left panel), we overestimate the ER cross-sections and underestimate the cross-section for FF which may contain contributions from QF. Although the capture cross-sections are rather well reproduced for both systems, it seems that something (QF?) is missing from the evaporation channel in 48 Ca + 154 Sm, causing an hindrance effect. An alternative and preferable approach to establish if a fusion hindrance effect is really present comes from the comparison of the so-called reduced ER cross-sections [6]. For this purpose, we have to determine which is the threshold CN excitation energy above which the transmission coefficients T are close to unity for all partial waves leading to ER. We performed different calculations [14] and established that for our systems such threshold excitation energy is around 75 MeV, as the saturation of the ER yield in 16 O + 186 W confirms in a model-independent way (see fig. 4).

48

Ca induced reactions

Fig. 4. Reduced ER cross-sections for circles) and 16 O + 186 W (open circles).

617

48

Ca +

154

Sm (solid

The experimental reduced ER cross-sections for Ca + 154 Sm and 16 O + 186 W are shown in fig. 4. We see that fusion is strongly hindered for 48 Ca + 154 Sm in comparison with 16 O + 186 W in the energy range between 75 and 95 MeV, where similar reduced cross-sections are expected. Thus, it is evident that a fusion hindrance effect is present also for a relatively light CN such as 202 Pb∗ if we choose a rather mass-symmetric reaction; and it is confirmed that QF competes with complete fusion even at the low  leading to ER survival. Even more surprising is the fact that going up to excitation energies ≈ 100 MeV this hindrance effect seems to disappear. This could mean that QF at the low  contributing to ER production is no more present and that other processes, such as pre-compound or fast fission, compete with fusion-fission at high  but without affecting the fusion-evaporation mechanism and consequently also the ER cross-sections. It would be interesting if the possible reduction of fusion hindrance effects could be extrapolated to the fusion of very heavy systems. Indeed, if slightly higher excitation energies would really imply a reduction of QF at low , we could hope to gain some factor in the beamtime needed for observing SHE by increasing the excitation energy, finding a reasonable compromise as far as fusion-fission competition is concerned. In the representation of the so-called reduced ER crosssections nothing can be said at low E ∗ , since below a certain threshold energy the approximation T ≈ 1 is no longer valid. Nevertheless, this does not mean that QF is not present at low energies. A complementary information is given by the FF massenergy distributions. The onset of QF for 48 Ca + 154 Sm is indeed confirmed by the presence of an asymmetric component of fission in the FF mass-energy distributions (see fig. 5, right panel). As previously found for 48 Ca + 168 Er, the results for the 48 Ca + 154 Sm reaction confirm that the relative yield of the asymmetric component of fission is increasing with the decreasing excitation energy. Therefore, although at low energies we get an enhanced capture cross-section due to the target deformation, the corresponding elongated configuration at capture leads also (and maybe predominantly) to QF and not only to ER formation, in agreement with results previously found for 16 O + 238 U [23,24]. 48

618

The European Physical Journal A

elements. The results presented here lead us to the following main conclusions: – moving towards a relatively light CN characterized by a low fissility such as 202 Pb∗ , we still have evidence of fusion hindrance effects due to QF even at low  populating ER, if a relatively mass-symmetric system like 48 Ca + 154 Sm is used; – shell effects play a role in the onset of QF (for a complete discussion on shell effects in heavy and superheavy elements, see [13]); – although deformed targets lead to wide barrier distributions, which should favour the production of heavy elements by increasing the sub-barrier capture crosssections, the target deformation favours the onset of QF. Fig. 5. TKE-mass distribution, mass yield and average TKE vs. FF mass for 48 Ca + 144 Sm, 40 Ca + 154 Sm and 48 Ca + 154 Sm at the same excitation energy E ∗ = 50 MeV. QF and fusion-fission events (contours in the upper panels) are distinguishable from deep inelastic and quasi-elastic events (“white wings” on the left and the right, not included in the middle and lower panels). The position of closed shells is indicated by the arrows.

The effect of the target deformation on QF was further investigated by measuring fission fragments in the reactions 48 Ca + 144 Sm and 40 Ca + 154 Sm, to be compared with 48 Ca + 154 Sm. For the two 48 Ca induced reactions, a major difference consists in the use of a spherical or deformed target. However, the influence of shell effects is also different for the two reactions: because of the different number of neutrons in the CN, only the population of the lighter fission fragment is affected in the case of 48 Ca + 144 Sm, instead of both light and heavy fragments as in the case of 48 Ca + 154 Sm. For 48 Ca + 144 Sm and 40 Ca + 154 Sm, leading to near-by CN, shell effects play the same role. Therefore, the main difference between 48 Ca + 144 Sm and 40 Ca + 154 Sm lies in the target deformation. For 48 Ca + 144 Sm we got no evidence of an asymmetric component of fission at any energy [14]. For 40 Ca + 154 Sm very preliminary results from a partial set of data seem to indicate that an asymmetric component of fission is present. In fig. 5 mass-TKE distributions of FF corresponding to the same excitation energy E ∗ = 50 MeV for the three systems are presented. The results indicate that the target deformation favours the onset of QF.

4 Conclusions We studied the influence of mass-asymmetry, shell effects and target deformation on the onset of the QF that competes with complete fusion at near-barrier energies and reduces the probability of producing super-heavy

References 1. S.G. Nilsson et al., Nucl. Phys. A 115, 545 (1968); Phys. Lett. B 29, 458 (1969); Nucl. Phys. A 131, 1 (1969). 2. U. Mosel, W. Greiner, Z. Phys. 217, 256 (1968); 222, 261 (1969). 3. W.J. Swiatecki, Phys. Scr. 24, 113 (1981); S. Bjornholm, W.J. Swiatecki, Nucl. Phys. 391, 471 (1982). 4. S. Hofmann, G. Munzenberg, Rev. Mod. Phys. 72, 733 (2000) and references therein. 5. Yu.Ts. Oganessian et al., Phys. Rev. C 69, 021601(R) (2004) and references therein. 6. A.C. Berriman et al., Nature (London) 413, 144 (2001). 7. D.J. Hinde, M. Dasgupta, A. Mukherjee, Phys. Rev. Lett. 89, 282701 (2002). 8. S. Beghini et al., Nucl. Instrum. Methods A 239, 585 (1985). 9. N.A. Kondratiev et al., Dynamical Aspects of Nuclear Fission, Casta-Papiernicka, Slovak Republic, 1998, edited by Yu.Ts. Oganessian (World Scientific, Singapore, 1999) p. 431. 10. C.-C. Sahm et al., Z. Phys. A 319, 113 (1984). 11. R.N. Sagaidak et al., Phys. Rev. C 68, 014603 (2003). 12. A.Yu. Chizhov et al., Phys. Rev. C 67, 011603 (2003). 13. M.G. Itkis et al., Nucl. Phys. A 734, 136 (2004). 14. M. Trotta et al., Prog. Theor. Phys. Suppl. 154, 37 (2004). 15. J.R. Leigh et al., Phys. Rev. C 52, 3151 (1995). 16. C.E. Beamis et al., ORNL Physics Division Progress Report 6326, 110 (1986). 17. M. Trotta et al., Nucl. Phys. A 734, 245 (2004); A.M. Stefanini et al., Eur. Phys. J. A 23, 473 (2005). 18. K. Hagino, N. Rowley, A.T. Kruppa, Comput. Phys. Commun. 123, 143 (1999). 19. N. Rowley, G.R. Satchler, P.H. Stelson, Phys. Lett. B 254, 25 (1991). 20. M. Dasgupta, D.J. Hinde, N. Rowley, A.M. Stefanini, Annu. Rev. Nucl. Part. Sci. 48, 401 (1998). 21. R. Bass, Nucl. Phys. A 231, 45 (1974). 22. W. Reisdorf et al., Nucl. Phys. A 438, 212 (1985). 23. D.J. Hinde et al., Phys. Rev. Lett. 74, 1295 (1995). 24. D.J. Hinde et al., Phys. Rev. C 53, 1290 (1996).

Eur. Phys. J. A 25, s01, 619–620 (2005) DOI: 10.1140/epjad/i2005-06-106-1

EPJ A direct electronic only

Entrance-channel potentials for hot fusion reactions V.Yu. Denisova Gesellschaft f¨ ur Schwerionenforschung, D-64291 Darmstadt, Germany and Institute for Nuclear Research, 03680 Kiev, Ukraine Received: 26 October 2004 / Revised version: 29 March 2005 / c Societ` Published online: 22 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The semi-microscopic entrance-channel potentials for the reactions 48 Ca + 247,249 Bk → 295,297 117 and 48 Ca + 254 Es → 302 119 are evaluated in the approach of frozen nucleon densities within the framework of the extended Thomas-Fermi approximation. PACS. 25.60.Pj Fusion reactions – 25.70.Jj Fusion and fusion-fission reactions

1 Introduction The hot fusion reactions of superheavy element (SHE) formation are observed in collisions of the spherical projectile 48 Ca with deformed transuranic targets [1]. The population of capture states settled at the capture pocket of the entrance-channel potential depends on detailed behavior of the potential as a function of both the distance R between the nuclei and the orientation of a deformed nucleus. Many quasi-bound states are populated during the collision if the relative kinetic energy is slightly higher then the fusion barrier and the capture pocket is deep and wide. Because of their crucial role at the initial stage of the hot fusion process a precise knowledge of the interaction potentials between the colliding nuclei is needed. In order to determine nucleus-nucleus interaction potentials various methods were suggested in [2,3,4, 5,6, 7,8]. However, the barriers evaluated within these approaches for the same colliding system leading to SHE differ considerably [6,7]. Uncertainty of the interaction potential near the touching point gives rise to a variety of the proposed nuclear-reaction mechanisms. So, it would be nice to decrease this uncertainty. Recently, an accurate and reliable semi-microscopic method for evaluation of the nucleus-nucleus potential has been proposed [6,7,8]. Therefore, we evaluate the entrance-channel semi-microscopic potentials for hot fusion reactions leading to SHE with 117 and 119 protons.

2 Semi-microscopic potentials We evaluate the interaction potential between heavy nuclei within the semi-microscopic frozen-density approximation. The density distribution and the shape of colliding nuclei are perturbed when the nuclear surfaces a

e-mail: [email protected]

are close and nucleons possessed by different nuclei interact strongly enough. In the case of hot fusion reactions the time of passing the distances of strong interaction between nuclei can be approximated as ts ≈ (2μR2 s/(Z1 Z2 e2 ))1/2 ≈ 10−22 s, where Z1 and Z2 are the charges of colliding nuclei, respectively, e is the charge of proton, μ is the reduced mass of colliding nuclei, R is the sum of radii of colliding nuclei, s ≈ 3 fm is the range of strong interaction between nuclear surfaces. The relaxation time of the intrinsic nuclear state arising from nucleon-nucleon interactions, see [9], can be estimated as tr  10−20 s for the case of hot fusion reactions [6]. Since tr  ts the frozen approximation is good for evaluation of the nucleus-nucleus potential near the touching point at collision energies around the barrier height. The nucleus-nucleus potential is obtained with the help of the energy density functional. The extended ThomasFermi (ETF) approximation with 2 corrections is used for evaluation of its kinetic energy part [10]. The Skyrme and Coulomb energy density functionals are employed for the calculation of the potential energy. These functionals depend on the proton and neutron densities. The latter are obtained in the microscopic Hartree-Fock-BCS approximation with SLy4 parametrization of the Skyrme forces [11]. Our approximation is semi-microscopic because we use the microscopic density distributions and the ETF approximation for the calculation of the interaction energy of nuclei. Note that the binding energies of nuclei evaluated in the ETF model with help of the microscopic density distributions are in good agreement with those obtained in the fully microscopic Hartree-FockBCS model [6]. Therefore, our semi-microscopic method for evaluation of the interaction potential between various nuclei is quite accurate. Semi-microscopic potentials (SMP) for the reactions 48 Ca + 247,249 Bk → 295,297 117 and 48 Ca + 254 Es → 302 119 are presented in fig. 1. As seen from fig. 1, the isotopic

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Fig. 1. Entrance-channel SMPs for reactions 48 Ca + 247,249 Bk → 295,297 117 and 48 Ca + 254 Es → 302 119. The ground-state Q-values are indicated by the lowest triangle at the left vertical axis. The other 6 triangles mark, respectively, the thresholds for the emission of 1, 2, 3, 4, 5 and 6 neutrons evaluated by using [12].

composition of berkelium has only a minor influence on the shape of SMP. The SMP barrier heights Bgs evaluated with respect to the ground-state energy of the compound nucleus, slightly increase with growing number of neutrons in berkelium.

The author thanks Profs. W. N¨ orenberg, A.G. Magner and V.K. Utyonkov for useful discussions and gratefully acknowledges support from both GSI and ENAM04 Organizing Committee.

The SMP are shown in fig. 1 for various orientations of the deformed nuclei. For these systems the lowest barriers are obtained for the tip orientation (Θ = 0◦ ). However, the side orientation (Θ ≈ 90◦ ) is relevant to the SHE formation [6, 7]. This conclusion is supported by the experimental analysis of fusion reactions between lighter nuclei [13]. It is shown there that fusion through the tip orientation is strongly suppressed by quasi-fission.

References

Shapes of SMP in fig. 1 are very similar to the ones for hot fusion reactions between 48 Ca and various isotopes of U, Pu, Am, Cm and Cf, see figures in [6, 7] and in the papers cited therein. Moreover, the SMP barrier heights Bgs for side orientation, the neutron separation energies [12] and the fission barriers of compound nuclei are also comparable to the ones for other hot fusion reactions [6,7]. Both the capture properties of reactions 48 Ca + 247,249 Bk → 295,297 117 and 48 Ca + 254 Es → 302 119 and the decay characteristics of compound nuclei 295,297 117 and 302 119 are similar to the ones for other hot fusion reactions. Therefore it is possible to use these reactions for successful synthesis of elements 117 and 119 at collision energies close to 212 MeV and 216 MeV, respectively.

1. Yu.Ts. Oganessian, Nucl. Phys. A 734, 109 (2004). 2. R. Bass, Nuclear Reactions with Heavy Ions (SpringerVerlag, Berlin, 1980). 3. J. Blocki et al., Ann. Phys. (N.Y.) 105, 427 (1977); W.D. Myers, W.J. Swiatecki, Phys. Rev. C 62, 044610 (2000). 4. H.J. Krappe, J.R. Nix, A.J. Sierk, Phys. Rev. C 20, 992 (1979). 5. A. Winther, Nucl. Phys. A 594, 203 (1995). 6. V.Yu. Denisov, W. N¨ orenberg, Eur. Phys. J. A 15, 375 (2002). 7. V.Yu. Denisov, AIP Conf. Proc. 704, 433 (2004). 8. V.Yu. Denisov, Phys. Lett. B 526, 315 (2002). 9. G.F. Bertsch, Z. Phys. A 289, 103 (1978). 10. M. Brack et al., Phys. Rep. 123, 275 (1985). 11. E. Chabanat et al., Nucl. Phys. A 635, 231 (1998). 12. G. Audi et al., Nucl. Phys. A 624, 1 (1997); W.D. Myers, W.J. Swiatecki, Nucl. Phys. A 601, 141 (1996). 13. S. Mitsuoka et al., Phys. Rev. C 62, 054603 (2000); D.J. Hinde et al., Eur. Phys. J. A 13, 149 (2002).

9 Nuclear astrophysics 9.1 Experiment

Eur. Phys. J. A 25, s01, 623–628 (2005) DOI: 10.1140/epjad/i2005-06-103-4

EPJ A direct electronic only

Amazing developments in nuclear astrophysics A.E. Champagnea The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3255, USA, and Triangle Universities Nuclear Laboratory, Durham, NC 27708-0308, USA Received: 12 January 2005 / c Societ` Published online: 2 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The time since ENAM ’01 is short by astrophysical standards, but this period has seen some exciting progress in the area of experimental nuclear astrophysics. New results have been obtained from facilities both large and small, with stable and exotic beams. In the process, we have learned a great deal about stellar structure and evolution. This talk highlights a few of many notable results obtained since ENAM ’01 and will attempt to place them into an astrophysical context. In the process, it may be possible to see where the field is heading and what we might anticipate over the next three years. PACS. 26.20.+f Hydrostatic stellar nucleosynthesis – 26.30.+k Nucleosynthesis in novae, supernovae and other explosive environments – 97.10.Cv Stellar structure, interiors, evolution, nucleosynthesis, ages

1 Introduction Progress in nuclear astrophysics often comes at a measured pace. In many instances a number of nuclear processes may give rise to a particular stellar observable and a systematic approach is needed to gain insight into the underlying astrophysics. On the other hand, there are certainly cases where a single reaction or decay can say a great deal about a particular issue in astrophysics. Two obvious examples of this latter situation are the 7 Be(p,γ)8 B reaction (and the solar neutrino problem), and 12 C(α,γ)16 O (and the evolution of massive stars). Although both reactions have received a great deal of attention in the past 3 years, neither will be featured here. This is not to say that they are unimportant —indeed, they remain as critical challenges for the field. Both will be “solved” by an accumulation of experimental results and it is too early to declare victory on either front. In contrast, the last 3 years have seen striking progress in other areas of nuclear astrophysics, which will be the main focus of attention in this review.

2 14 N(p, γ)15 O and the age of the galaxy One way of estimating the age of the galaxy is by determining the ages of its oldest stellar populations —the globular clusters. Presently, the best understood method for determining the age of a cluster is by locating the “main sequence turnoff” on a color-magnitude plot of the stars in a cluster. This represents the transition point between core a

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hydrogen burning that characterizes the main sequence and shell hydrogen burning on the red giant branch. The turnoff luminosity has a well-defined relationship with the age of the population of stars. The primary uncertainty in this procedure involves determining the distance to the cluster (and hence the absolute luminosity), but there is some confidence that distance determinations will become more reliable. There are also uncertainties involved with the chemical composition of the cluster, model parameters (such as opacity, convection, etc.) and one nuclear reaction, 14 N(p,γ)15 O [1]. This latter source of uncertainty may seem surprising, since the stars of interest are low-mass stars that spend most of their lives generating energy via the pp-chains. However, the core temperature increases during the main sequence stage to the point where the CN-cycle becomes the dominant source of energy near the turnoff point. The power generated by the CN-cycle is governed by the rate of the slowest reaction, namely 14 N(p,γ)15 O. The previously accepted rate for the 14 N(p,γ)15 O reaction is based on measurements by Schr¨oder et al. [2] (hereafter Sch87), which showed that a subthreshold resonance made a significant contribution to the total cross-section. This assertion was questioned in several subsequent studies [3,4,5,6, 7] and recently, two independent experiments have been performed to directly measure the low energy part of the 14 N(p,γ)15 O cross-section. One was carried out at the (underground) LUNA facility at the Gran Sasso Laboratory [8], and the other at the LENA facility, which is part of TUNL [9]. The astrophysical S-factors for the 3 main transitions are shown in fig. 1 and the results of the 2 experiments are in excellent agreement.

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globular clusters to 13.4 Gy. This is still consistent with the WMAP age of the Universe (13.7 Gy [13]), but implies that globular clusters formed soon after the first stars in the Universe.

3 Novae and X-ray bursts As their names suggest, novae and Type I X-ray bursts are observationally quite different, but share a similar underlying mechanism. Both occur in binary systems and are triggered by mass transfer from a main-sequence or giant star onto a companion white dwarf (nova) or neutron star (X-ray burst). Once the accreted mass reaches a critical temperature and density, it ignites under degenerate conditions and a thermonuclear runaway ensues. The conditions governing each class of outburst are quite different. Novae reach peak temperatures of less than 4 × 108 K and densities of 103 –104 g/cm3 whereas X-ray bursts occur at much higher temperatures (> 109 K) and densities (> 105 g/cm3 ). A description of either event must take into account the central role of convection and other uncertain, but critical aspects such as the mass transfer rate. However, since both explosions are driven by nuclear processes, nuclear information can be used to decipher the observational record. 3.1 γ-ray production in novae

Fig. 1. S-factors for the major transitions in 14 N(p,γ)15 O. Here, RC denotes radiative capture. The results of the LUNA [8] and LENA [9] measurements are denoted by the open and solid circles, respectively. The data from Sch87, corrected for summing and with yield data removed [10] are shown as open squares. The solid lines are R-matrix fits to the combined data set [10].

The combined data determine the S-factor at zero energy to about 10% [10] and for temperatures less than about 108 K, the total S-factor (and reaction rate) is approximately 50% of the previously recommended value [11]. This temperature range includes main sequence and red giant stars. In the case of main sequence models, the reduction in the power generated by the CN-cycle produces compensating structural changes in the core. In particular, the core becomes slightly cooler, but larger and more dense. This moves the star to higher effective temperature and luminosity on the color-magnitude diagram. In order to match a turnoff luminosity calculated with the old rate, a calculation with the revised rate requires increasing the age of the star (or reducing its mass), which moves it to lower effective temperature and luminosity. In other words, the ages derived for globular clusters must increase. Detailed calculations show an increase of 0.7–1 Gy [12], which moves the best-fit age (as defined by [1]) of

One nucleus of interest for novae is 18 F. The radioactive decay of 18 F may be an important energy source during the early part of the visible outburst and the ensuing γemission may someday be detected. The net abundance of 18 F is determined by the competition between production and destruction reactions and the major contributor to the latter is the 18 F(p,α)15 O reaction. This reaction has been measured directly [14] down to energies corresponding to a resonance at a center-of-mass energy of Ecm = 330 keV, which is near the upper end of the relevant energy range. For states at lower energies, the proton width would be much less than the alpha and therefore the resonance strength is determined by the proton width. Recently, groups at Louvain la Neuve [15] and at Oak Ridge [16] have used the d(18 F,p)19 F reaction to locate the analogs of potential 18 F + p resonances and to measure their neutron spectroscopic factors. Both studies used the assumption of isospin symmetry to determine the proton spectroscopic factor and thus the proton width for the corresponding state in 19 Ne. The 2 results differ in significant details, particularly in the question of whether there is a resonance at Ecm = 38 keV. However, the respective reaction rates agree within uncertainties (fig. 2). If the rate is actually near the lower end of the allowed range, then the net abundance of 18 F would be 3–5 times previous predictions. Clearly, further work to better define the reaction rate would be valuable. Another target of opportunity for γ-ray astronomy is 22 Na. In novae and X-ray bursts, 22 Na is produced via the

A.E. Champagne: Amazing developments in nuclear astrophysics

Fig. 2. Reaction rate for the 18 F(p,α)15 O reaction. The dark shaded region is the result from the Louvain la Neuve experiment [15] and the lighter band is from the Oak Ridge experiment [16].

sequence 20

Ne(p, γ)21 Na(β + )21 Ne(p, γ)22 Na,

(1)

Ne(p, γ)21 Na(p, γ)22 Mg(β + )22 Na.

(2)

or by

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Fig. 3. The upper panel shows the thick target yield data for the 21 Na(p,γ)22 Mg reaction, obtained with the ISAC facility and DRAGON recoil separator. The solid line is the calculated yield for (gas) target thickness of 4.6 torr. The lower panel is the yield of the 214 keV resonance in the 24 Mg(p,γ)25 Al, which was used for beam energy calibration. All errors are statistical. Reprinted figure with permission from S. Bishop et al., Phys. Rev. Lett. 90, 162501 (2003). Copyright 2003 by the American Physical Society.

3.2 Impedance effects in the rp-process 20

Because of the rather slow β + -decay of 21 Na (T1/2 = 22.5 s), these sets of reactions may occur on quite different time scales and therefore at different phases in the explosion. It is believed that the reaction flow should favor the former sequence if significant amounts of 22 Na are to be produced [17]. However, uncertainties in the rate of the 21 Na(p,γ)22 Mg reaction lead to large uncertainties in the predicted abundance [18] of 22 Na. The rate of the 21 Na(p,γ)22 Mg reaction depends upon the strengths of a relatively small number of isolated, narrow resonances. Determining the properties of these resonances indirectly has proven to be difficult because it has not been possible to make a firm connection to the comparatively well studied analog states in 22 Ne. This situation has changed dramatically with the results of direct (p,γ) measurements using the ISAC facility at TRIUMF [19, 20]. A yield curve for the lowest resonance (at Ecm = 206 keV) is shown in fig. 3. This work determines the reaction rate to an accuracy normally associated with stable beams and targets, and shows that the 21 Na(p,γ) path is favored in ONe novae. The result is that 22 Na is produced earlier in the explosion, when the temperature is higher and when it is more readily destroyed [20]. This reduces the final yield of 22 Na and lowers the predicted γ-ray flux. Unfortunately, the prospects for observing γemission from 22 Na are correspondingly reduced.

In Type I X-ray bursts, nucleosynthesis can proceed via the αp- and rp-processes beyond iron and perhaps to the Sn-Te region [21]. High temperatures and densities ensure that most of these reactions are extremely fast and therefore, their actual rates are relatively unimportant. What is important is knowing where and how the reaction flow is impeded. This affects the energy budget and the light curve, both of which can be observed [22]. One of these waiting points is expected to occur at 68 Se (as shown in fig. 4). Because 69 Br is most likely unbound, the rp-flow must pause until 68 Se either β + decays (with a laboratory half life of 35.5 s) or undergoes a 2p-capture to 70 Kr. The 2p-capture is actually a sequential process: 68 Se(p,γ)69 Br(p)68 Se produces a small equilibrium abundance of 69 Br, which can then undergo a subsequent proton capture. The rate for converting 68 Se into 69 Br depends in part on the mass difference between 68 Se+p and 69 Br, which enters exponentially into the rate equation [23,24]. Recently, the mass of 68 Se was measured to very high precision (1 part in 2854) using the Canadian Penning Trap at Argonne National Laboratory [25]. The stellar half life of 68 Se was then calculated using a theoretical value for the mass of 69 Br [26]. Under typical conditions, the rate for 2p-capture is much slower than that for β + -decay and thus the reaction flow slows considerably. This finding was confirmed by another, independent measurement of the mass of 68 Se [27].

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Fig. 4. The rp-process near

68

Se.

If the rp-process does slow down at 68 Se, then the energy generated at later times in the outburst will be reduced and more power will appear in the peak of the burst [22]. However, nuclear structure may change this picture. New work has shown that a shape isomer exists in a neighboring N = Z nucleus, 72 Kr [28], which is manifested by a 0+ first excited state. If a similar structure exists in 68 Se, then the first excited state could be efficiently populated by thermal excitations, which would lower the Q-value for 2p-capture and increase the phase space term in the β + -decay rate. Either effect would speed the reaction flow through 68 Se. This situation also shows how progress in nuclear structure can become relevant for nucleosynthesis.

4 Presolar grains Presolar grains are pieces of stars that can be brought into the laboratory and analyzed in great detail. Systematic studies reveal contributions from specific types of stars that can be identified based on their unique isotopic signatures (see, e.g. [29] for a recent review). In contrast, stellar spectroscopy is limited with few exceptions to elemental abundances. Although meteoritics is not a new field, the isolation and analysis of presolar grains is a fairly new development that has been driven by constant advances in technology. One challenge has been that most grains are sub-micron in size and thus could not be analyzed individually. However, it is now possible to do just this, which has lead to the discovery of presolar silicates [30]. Silicates are expected from a variety of sites, including young main-sequence stars and in oxygen-rich asymptotic giant branch stars. However, the Solar System itself is rich in silicates and until now it has been impossible to separate out a few presolar silicate grains amongst a comparatively vast number of solar silicates.

Fig. 5. Oxygen isotopic compositions (with 1-σ uncertainties) of presolar silicate grains from the meteorite Acfer 094 compared with those of silicates from various interplanetary dust particles (IDP) and from the ordinary chondrites Semarkona and Bishunpur (14, 15). The mineralogy of the grains is indicated: Clinopyroxene, Cpx; orthopyroxene, Opx; olivine, Ol; pyroxene, Px; forsterite, Fo. Also shown are four different groups of grains defined by the systematics of other oxide grains [31]. Reprinted figure with permission from A.N. Nguyen and E. Zinner, Science 303, 1496 (2004). Copyright (2004) AAAS.

The nine grains that have been isolated thus far have oxygen isotopic ratios that are consistent with origin at some stage on the red giant branch (see fig. 5). One grain also shows the signature of stellar 26 Al (preserved as an anomalous abundance of 26 Mg). In addition to providing information about stars, these grains can be compared with silicates from other sources to provide information about the formation history of meteorites and conditions in the early Solar System.

5 Back to the future with the r-process About half of the elements heavier than iron are formed under conditions of high temperature and neutron density in what is known as the r-process. Observations of very old stars in the halo of our galaxy show an r-process abundance pattern that looks quite similar to what is observed in the Solar System (see for example, the recent review by Truran et al. [32]). However, the abundances of radioactive Th and U are observed to fall below the relative solar abundance, which implies that the ages of these stars lie in the range 14 ± 3 Gy [33,34, 35]. This assumes that the initial r-process abundance pattern can be calculated, despite the fact that it has not been possible to

A.E. Champagne: Amazing developments in nuclear astrophysics

Fig. 6. Abundances of the r-process elements in the Solar System (from the data of ref. [36]).

establish the site of the r-process. So this look into the past points towards one of the frontier areas of the field. Hints about the conditions governing the r-process are contained in the distribution of the r-process elements (shown in fig. 6). For example, the abundance peaks are the remnants of nuclei formed near closed neutron shells and well to the neutron-rich side of stability. A brief (and extremely simplified) picture is that the r-process occurs in supernovae, when the temperature and neutron density are high enough to produce an (n,γ) ↔ (γ,n) equilibrium. This behavior links nuclei along a line of constant neutron separation energy, Sn , initially 10–40 neutrons away from stability. The flow to higher masses is slowed at the neutron magic numbers, where Sn drops and photodisintegration is favored. Steady flow is re-established only after several β-decays and so material accumulates at these waiting points. As the neutron density drops, β-decays move the entire abundance distribution toward higher Sn . Finally, the temperature and density will drop to the point where the β-flow reaches stability. Because the r-process occurs so far from stability, essentially all of the relevant nuclear physics input must be obtained from theory (for now)! The abundance peaks shown in fig. 6 are end products of the waiting points at the closed neutron shells, and their locations and shapes are influenced by a number of factors such as β-decay rates [37, 38], late n-captures [39], β-delayed n-decays, etc. Thus, they are of particular interest as diagnostics of the conditions and physics of the r-process. For example, it has been known for some time that the N = 82 and N = 126 shell splittings must be reduced in order to reproduce the A ≈ 130 and A ≈ 195 abundance peaks in detail [40]. There is experimental evidence for shell quenching in other mass regions, but at present it is possible to produce only a select few r-process nuclei. One of these nuclei is 130 Cd, which is part of the N = 82 waiting point. The decay scheme of 130 Cd reveals several interesting features [41]. For example, the β-decay Q-value is higher than that predicted by mass models that include strong shell splittings. Several models that include shell quenching do a much better job of matching the ex-

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Fig. 7. Comparison of the Solar System r-process abundances in the A ≈ 130 peak region with model predictions. Within the classical “waiting-point” concept, the “longer” half-lives concluded from new nuclear-structure information result in a better reproduction of the rising wing of the solar r-abundance peak. Reprinted figure with permission from I. Dillmann et al., Phys. Rev. Lett. 91, 162503 (2003). Copyright 2003 by the American Physical Society.

perimental value. Also, a significant finding is that the energy of the 2QP, 1+ GT state is substantially higher than expected. In order to reproduce this result using the shell model, the relevant 2-body matrix element for β-decay of 130 Cd must be reduced. If this is a global effect, then the predicted lifetimes of the N = 82 waiting-point nuclei will increase. The manifestation of this change is a broadening of the A ≈ 130 abundance peak to lower masses (fig. 7), which does a much better job of reproducing the observed abundances without invoking any exotic post processing (for example, neutrino interactions).

6 Conclusion This paper has described —in a superficial way— a number of interesting new results that span a range of topics from cosmology to stellar evolution to stellar explosions. The emphasis here was on experiments, and all of these examples pushed against various technological limitations. Progress in the areas of accelerators, detectors and techniques, which are important in other areas of nuclear physics, will continue to have a major impact here as well. It is also clear that in extreme stellar environments, where nucleosynthesis is governed by quasi-equilibria and by the global properties of the gas, the distinction between nuclear structure and nuclear astrophysics is blurred. Thus, the r-process can be approached in the context of astrophysics and/or as a venue for nuclear structure. The general areas described here will continue to be the frontier topics of nuclear astrophysics. Ultimately, nuclear astrophysics derives its motivation from astrophysical observations, whose continuing theme is serendipity. So surprising new results are to be expected.

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This work was supported by the U.S. Department of Energy under contracts DE-AC05-76OR00033 and DE-FG02-97ER41041. I would also like to thank the Boston Red Sox for proving me right (finally).

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

11. 12. 13. 14. 15. 16. 17.

B. Chaboyer et al., Astrophys. J. 494, 96 (1998). U. Schr¨ oder et al., Nucl. Phys. A 467, 240 (1987). E.G. Adelberger et al., Rev. Mod. Phys. 70, 1265 (1998). C. Angulo, P. Descouvemont, Nucl. Phys. A 690, 755 (2001). P.F. Bertone et al., Phys. Rev. Lett. 87, 152501 (2001). A.M. Mukhamedzhanov et al., Phys. Rev. C 67, 065804 (2003). K. Yamada, et al., Phys. Lett. B 579, 265 (2004). A. Formicola et al., Phys. Lett. B 591, 61 (2004). R.C. Runkle et al., Phys. Rev. Lett. 94, 082503 (2005). C. Angulo, A.E. Champagne, H.P. Trautvetter, in Proceedings of Nuclei in the Cosmos 8 (2004), to be published in Nucl. Phys. A. C. Angulo et al., Nucl. Phys. A 656, 3 (1999). G. Imbriani et al., Astron. Astrophys. 420, 625 (2004). D.N. Spergel, et al., Astrophys. J. Suppl. 148, 175 (2003). D. Bardayan et al., Phys. Rev. Lett. 89, 262501 (2002). N. deS´er´eville et al., Phys. Rev. C 67, 052801(R) (2003). R.L. Kozub et al., Phys. Rev. C 71, 032801 (2005). J. Jos´e, A. Coc, M. Hernanz, Astrophys. J. 520, 347 (1999).

18. C. Iliadis et al., Astrophys. J. Suppl. 142, 105 (2002). 19. S. Bishop et al., Phys. Rev. Lett. 90, 162501, 229902(E) (2003). 20. J.M. D’Auria et al., Phys. Rev. C 69, 065803 (2004). 21. H. Schatz et al., Phys. Rev. Lett. 86, 3471, (2001). 22. S.E. Woosley et al., Astrophys. J. Suppl. 151, 75 (2004). 23. J. G¨ orres, M. Wiescher, F.-K. Thielemann, Phys. Rev. C 51, 392 (1995). 24. H. Schatz et al., Phys. Rep. 294, 167 (1998). 25. J.A. Clark et al., Phys. Rev. Lett. 92, 192501, (2004); these proceedings. 26. B.A. Brown et al., Phys. Rev. C 65, 045802 (2002). 27. A. Wohr et al., Nucl. Phys. A 742, 349 (2004). 28. E. Bouchez et al., Phys. Rev. Lett. 90, 082502, (2003). 29. L. Nittler, Earth Planet. Sci. Lett. 209, 259 (2003). 30. A.N. Nguyen, E. Zinner, Science 303, 1496 (2004). 31. L.R. Nittler et al., Astrophys. J. 483, 475 (1997). 32. J.W. Truran et al., Publ. Astron. Soc. Pac. 114, 1293 (2002). 33. J.J. Cowan et al., Astrophys. J. 521, 194 (1999). 34. S. Wanajo et al., Astrophys. J. 577, 853 (2002). 35. K.-L. Kratz et al., New Astron. Rev. 48, 105 (2004). 36. F. K¨ appeler, H. Beer, K. Wisshak, Rep. Prog. Phys. 52, 945 (1989). 37. B.S. Meyer, J.S. Brown, Astrophys. J. Suppl. 112, 199 (1997). 38. J. Engel et al., Phys. Rev. C 60, 014302 (1999). 39. R. Surman, J. Engel, Phys. Rev. C 64, 035801 (2001). 40. K.-L. Kratz et al., Astrophys. J. 403, 216 (1993). 41. I. Dillmann et al., Phys. Rev. Lett 91, 162503 (2003); K.-L. Kratz et al., these proceedings.

Eur. Phys. J. A 25, s01, 629–632 (2005) DOI: 10.1140/epjad/i2005-06-172-3

EPJ A direct electronic only

Investigating the rp-process with the Canadian Penning trap mass spectrometer J.A. Clark1,2,a , R.C. Barber2 , B. Blank1,3 , C. Boudreau1,4 , F. Buchinger4 , J.E. Crawford4 , J.P. Greene1 , S. Gulick4 , J.C. Hardy5 , A.A. Hecht1,6 , A. Heinz1 , J.K.P. Lee4 , A.F. Levand1 , B.F. Lundgren1 , R.B. Moore4 , G. Savard1 , N.D. Scielzo1 , D. Seweryniak1 , K.S. Sharma2 , G.D. Sprouse7 , W. Trimble1 , J. Vaz1,2 , J.C. Wang1,2 , Y. Wang1,2 , B.J. Zabransky1 , and Z. Zhou1 1 2 3 4 5 6 7

Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB R3T 2N2, Canada Centre d’Etudes Nucl´eaires de Bordeaux-Gradignan, F-33175 Gradignan Cedex, France Department of Physics, McGill University, Montreal, QC H3A 2T8, Canada Cyclotron Institute, Texas A&M University, College Station, TX 77843-3366, USA Department of Chemistry, University of Maryland, College Park, MD 20742, USA Physics Department, SUNY, Stony Brook University, Stony Brook, NY 11794, USA Received: 15 January 2005 / c Societ` Published online: 15 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The Canadian Penning trap (CPT) mass spectrometer at the Argonne National Laboratory makes precise mass measurements of nuclides with short half-lives. Since the previous ENAM conference, many significant modifications to the apparatus were implemented to improve both the precision and efficiency of measurement, and now more than 60 radioactive isotopes have been measured with half-lives as short as one second and with a precision (Δm/m) approaching 10−8 . The CPT mass measurement program has concentrated so far on nuclides of importance to astrophysics. In particular, measurements have been obtained of isotopes along the rp-process path, in which energy is released from a series of rapid proton-capture reactions. An X-ray burst is one possible site for the rp-process mechanism which involves the accretion of hydrogen and helium from one star onto the surface of its neutron star binary companion. Mass measurements are required as key inputs to network calculations used to describe the rp-process in terms of the abundances of the nuclides produced, the light-curve profile of the X-ray bursts, and the energy produced. This paper will present the precise mass measurements made along the rp-process path with particular emphasis on the “waiting-point” nuclides 68 Se and 64 Ge. PACS. 21.10.Dr Binding energies and masses – 26.30.+k Nucleosynthesis in novae, supernovae, and other explosive environments – 26.50.+x Nuclear physics aspects of novae, supernovae, and other explosive environments

1 Introduction Since the previous ENAM conference [1], the masses of more than 60 radioactive isotopes have been determined with the Canadian Penning trap (CPT) mass spectrometer at Argonne National Laboratory (ANL) [2, 3,4,5]. Most of the isotopes studied were selected due to their important role in astrophysical processes such as the rpprocess [6] discussed here. A possible site for the rp-process is a binary star system in which hydrogen and helium from a gas giant accrete onto the surface of its neutron star companion. As material accumulates onto the surface, the gravitational presa

Conference presenter; e-mail: [email protected]

sure can become sufficient to ignite nuclear burning of the hydrogen and helium [7]. With accretion rates of ∼ 10−9 solar masses per year, the continuing increase in pressure (and temperature) eventually results in a thermonuclear runaway [8]. At this time, the creation of heavier elements is realized through a series of rapid proton-capture reactions. The resulting energy release is ultimately observed as an X-ray burst [9] with a typical duration of 10–100 seconds. During the thermonuclear runaway, the reaction path is set by thousands of reaction rates, including those of predominant proton-capture, photodisintegration, and β-decay reactions. Nuclides along this path, where the proton-capture reactions are hindered by photodisintegration reactions, are termed “waiting-point” nuclides. At

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these nuclides, the rp-process stalls and cannot continue until the destruction of the waiting-point nuclide, either through its β decay, or through the rapid capture of two protons to bypass the impeding nucleus. The timescale of the rp-process, or equivalently the light-curve profile of X-ray bursts, depends largely upon the contribution of the individual delays at each waiting-point nuclide. Since these delays are dependent upon the reaction rates of the nuclides involved, information about β-decay half-lives and energy levels which can be thermally populated are necessary to assess the delay at each waiting-point nuclide. Furthermore, since the photodisintegration rates are exponentially dependent upon proton separation energies [7], masses of waiting-point nuclides are critical. Even a small uncertainty in the masses yields a large uncertainty in the effective half-lives of, or delays at, the waiting-point nuclides. The potential waiting-point nuclides are the even N = Z nuclei due to the predicted structure of the proton drip-line. Since the delay each waiting-point nuclide contributes to the timescale of the rp-process is at most equal to its β-decay lifetime, the waiting-point nuclides which could have the biggest influence are those at the beginning of the N = Z chain, in particular 64 Ge and 68 Se [7].

2 Measurements Precise mass measurements made with the CPT require sufficient yields of low-energy ions with minimal contamination. Since the objective of the CPT is to make measurements of short-lived, rare isotopes, the injection system must be efficient and quickly prepare the ion samples. As a description of the CPT apparatus has been given previously [10, 11], only a brief description is provided here. Nuclides along the rp-process path were produced from fusion-evaporation reactions between heavy-ion beams from the ATLAS facility at ANL and a rotating target wheel. From there, the high energy nuclides of interest are collected and focussed into a gas cell [12] where they are thermalized with 200 mbar of purified helium gas. Within milliseconds, the nuclides are extracted from the gas catcher, proceed through a differentially pumped ion cooler [13], and enter an isotope separator [14] where contamination is reduced. The ions are then transferred to a linear radio-frequency quadrupole trap (RFQ trap) where they are cooled with helium buffer gas and accumulated. Once the precision Penning trap is ready for more ions, the prepared bunch of pure, low-energy ions in the RFQ are transferred to the precision Penning trap. The efficiency of the entire system, from production to detection, is on the order of 0.1%. Ions can be delivered to the precision Penning trap within 100 milliseconds and with an energy spread of ∼ 1 eV. Ions are confined in the Penning trap with a superposition of a magnetic and electric field [15]. Radial confinement is provided by a 5.9 T homogeneous magnetic field and axial confinement is achieved by a harmonic potential created by applying appropriate voltages on the electrode

structure of the Penning trap. The central, or ring, electrode is divided into quadrants enabling the application of an azimuthally symmetric time-varying quadrupole field. In this manner [16,17], the trapped ions can be driven resonantly at their cyclotron frequency: ωc =

qeB , m

(1)

where the charge of the electron is indicated by e. Since the cyclotron frequency depends only upon the magnetic field strength B, the charge state q, and the mass m of the ion, accurate and precise mass measurements can be made. Furthermore, from eq. (1) and ref. [18], the precision in the mass measurement can be shown to follow the relation

1 m δωc δm √ , ∝ = qeB tRF N ωc m

(2)

with N representing the total number of ions detected and tRF is the duration of the applied quadrupole field. Therefore, under similar operating conditions, higher precision is naturally obtained for lighter masses. The effect of the excitation is determined by a time-offlight (TOF) method [19] in which a multichannel scaler records the time it takes for the ions to reach a microchannel plate detector (MCP) after ejection from the Penning trap. Radial energy gained from the excitation is converted into axial energy by the interaction of the magnetic moment of the ions with the magnetic field gradient outside the Penning trap. If the trapped ions were resonantly excited at their cyclotron frequency, they reach the detector sooner than ions not driven at their cyclotron frequency. This technique is a destructive one; each measurement cycle requires a new ion bunch. To determine the resonant cyclotron frequency, each ion bunch is subjected to a slightly different excitation frequency. After plotting the average arrival time of the ions at the MCP detector as a function of the excitation frequency, the cyclotron frequency is obtained by determining the minimum in the spectrum. Determining the strength of the magnetic field is achieved by periodically measuring the cyclotron frequency of a well-known mass, mref . Assuming this reference mass and the unknown mass are subjected to the same magnetic field, the mass of the unknown nuclide is calculated by    ωc,ref q (mref − qref me ) + qme , (3) m= ωc qref

where me represents the mass of the electron.

3 Results The plotted curve in fig. 1 shows how the effective half-life of 68 Se, t1/2,eff , depends upon the proton-capture Q value, Qp , for typical conditions during an X-ray burst [2]. For small Qp values, the proton-capture rate is small in comparison with the photodisintegration rate of 69 Br, and so

J.A. Clark et al.: Investigating the rp-process with the Canadian Penning trap mass spectrometer

631

600

100

Mass difference (keV)

t1/2, eff (68Se) (s)

400 10

1

200 0 -200 -400

0.1 -2

-1.5

-1

-0.5

0

0.5

1

1.5

Qp (68Se) (MeV) CPT - AME

SPEG - AME

CSS2 - AME

FMA - AME

-600 90Mo 91Mo 90Tc 91Tc 92Tc 93Tc 93Ru 94Ru 94Rh 95Rh

CPT - HF

Pfaff et al.

68

Fig. 1. The effective half-life of Se as a function of the proton-capture Q value for 68 Se. For the data points with a two-name legend entry, the first name indicates the source of the 68 Se mass (SPEG [20], CSS2 [21], or FMA [22]) and the second name represents the source of the 69 Br mass (AME [23] or HF [24]). Also shown is the upper limit for Qp (68 Se) as determined by Pfaff et al. [25]. The curve demonstrates how the effective half-life of 68 Se depends upon the proton-capture Q value and is not a fit to the data. It was calculated under conditions typical for X-ray burst models.

the rp-process is stalled until the β decay of 68 Se occurs. For larger Qp values, the increased likelihood of destruction of 68 Se via proton-capture decreases the effective halflife of 68 Se since the rp-process can continue before the β decay of 68 Se takes place. Along the plotted curve in fig. 1 are data points which represent the Qp values determined by various groups. Since Qp (68 Se) requires both the mass of 68 Se and that of 69 Br, the first name in each legend entry indicates the source of the 68 Se mass, and the second name represents the source of the 69 Br mass. As 69 Br is proton unbound, its short-lived nature prevents a precise measurement of its mass. Instead, its mass is better estimated by HartreeFock (HF) calculations [24]. Now if our mass determination of 68 Se [2] is used in conjunction with HF calculations for the mass of 69 Br, the effective half-life of 68 Se is between 29 and 34 s, and therefore 68 Se provides a significant delay during the rp-process. As 64 Ge has a β-decay half-life of 64 s, its effective halflife could potentially contribute a larger portion to the total timescale of the rp-process. If we combine our mass determination of 64 Ge with the Hartree-Fock calculations for 65 As [24], the effective half-life of 64 Ge is then between 0.7 and 5.7 s. This would indicate 64 Ge is a waiting-point nuclide, but not as significant as 68 Se. The masses of nuclides along the rp-process path, especially in the vicinity of the proton-rich Ru, Rh, and Pd nuclides, have not been measured precisely, if at all. Our analysis to date [26] has resulted in the mass determinations of 10 nuclides in this region. Our preliminary results are shown in fig. 2. Here, the differences between our measurements and the mass values from the 2003 atomic mass evaluation (AME) [23] are shown with

Fig. 2. Mass measurements of proton-rich refractory metals performed by the CPT. Plotted are the differences between the preliminary CPT results and those from AME. The error bars shown represent only the statistical uncertainty from the CPT results (8 keV on average), with the lines indicating the uncertainty in the masses from AME. In two cases, 90 Tc and 91 Tc, it is uncertain as to whether the ground or isomeric state was measured.

the lines indicating the precision of the masses as quoted in AME. Our measurements are plotted with statistical error bars only. Excellent agreement exists between our measurements and those in AME, but our results were obtained with much better precision. For two nuclides, 90 Tc and 91 Tc, our measurements were performed with resolution insufficient to resolve the isomers (with excitation energies of 310(390) keV and 139.3(0.3) keV respectively [23]) from the ground state, and so it is possible our TOF spectra have a mixture of both. We intend to revisit this region to measure more proton-rich nuclides closer to the rp-process path with an increased resolving power to discern the ground and isomeric states. The rp-process path is thought to terminate in the Sb, Sn, and Te region [27]. The Te isotopes are known ground-state alpha emitters, so a cycle is established between the proton capture reactions into the Te isotopes and the subsequent alpha emission of these isotopes. Uncertainties in the masses of the nuclides in this region ultimately affect the resulting nuclide abundances. The preliminary results [26] of our data for 10 nuclides in this region are shown in fig. 3 where again the differences between our measurements and the AME values are plotted. The lines show the uncertainties in the masses from AME. Our measurements, with much better precision, mostly agree with AME. For two cases, 104 In and 106 In, we could not resolve the ground and known isomeric states (with excitation energies 93.48(0.10) keV and 28.6(0.3) keV, respectively [23]). We plan to revisit this region to resolve this issue. Mass measurements are also critical for the study of novae, which are similar to X-ray bursts with the neutron star substituted by a white dwarf. Novae outbursts lead to the production of 22 Na which can be used as an observable of these events [28] by detecting the emission of the 1.275 MeV γ-ray following its β decay. However, one of the main uncertainties in the production of 22 Na is the

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needed the most, namely the proton-rich refractory metals and at the proposed termination of the rp-process path.

Mass difference (keV)

400 300 200 100

This work was supported by the U.S. Department of Energy, Office of Nuclear Physics, under Contract No. W-31-109-ENG38, and by the Natural Sciences and Engineering Research Council of Canada.

0 -100 -200 -300

10 7S b 10 8S b

10 7S n 10 8S n

10 4S n 10 5S n

10 7I n

10 6I n

10 5I n

10 4I n

-400

Fig. 3. Mass measurements of nuclides near the proposed endpoint of the rp-process. Plotted are the differences between the preliminary CPT results and those from AME. The error bars shown represent only the statistical uncertainty from the CPT results (20 keV on average), with the lines indicating the uncertainty in the masses from AME. In two cases, 104 In and 106 In, it is uncertain as to whether the ground or isomeric state was measured. 21

Na(p,γ)22 Mg reaction rate [29] which leads to the importance of the 22 Mg mass as 21 Na is already well known [23]. The current mass evaluation (AME) based the mass of 22 Mg on two measurements published in 1974 [30,31]. However, a recent experiment at ISAC at TRIUMF [32], which directly measured the energy of the resonance into the astrophysically relevant 2+ state, suggested that the mass excess of 22 Mg should shift down by about 6 keV compared to AME assuming the energy of the 2+ state was correct. Since then, the mass excess of one of the initial mass measurements [30] has been lowered by 3 keV to account for the change in the 16 O(p, t)14 O Q value [33] tied to the original measurement [34]. Our precise mass measurement [3], in agreement with a recent measurement conducted by ISOLTRAP [35], only accounts for 3 keV of the 6 keV shift suggested by ref. [32]. The remaining 3 keV discrepancy was removed following a more accurate measurement of the 2+ energy level [36]. All the recent measurements now yield consistent results. With respect to tests of the unitarity of the CKM matrix, our mass of 22 Mg provides for a corrected Ft value of 3081(8) s, with the uncertainty now dominated by the branching ratio.

4 Summary Mass measurements are required to characterize X-ray bursts in terms of the abundance of the elements produced, the energy released, and the timescale of the X-ray burst. The timescale is influenced heavily by the individual delays of the waiting-point nuclides, especially that of 68 Se and 64 Ge. Our mass measurements have shown that the rp-process path is delayed at 64 Ge, and more significantly at 68 Se. To date, the masses of more than 60 nuclides have been measured with the CPT, including nuclides along the rp-process path where mass information is

References 1. J.A. Clark et al., in Exotic Nuclei and Atomic Masses (ENAM2001), H¨ ameenlinna, Finland, 2001, edited by ¨ o, P. Dendooven, A. Jokinen, M. Leino (Springer, J. Ayst¨ Berlin, 2003) p. 39. 2. J.A. Clark et al., Phys. Rev. Lett. 92, 192501 (2004). 3. G. Savard et al., Phys. Rev. C 70, 042501 (2004). 4. J.A. Clark et al., in The r-Process: The Astrophysical Origin of the Heavy Elements and Related Rare Isotope Accelerator Physics, Seattle, Washington, 2004, edited by Y.-Z. Qian, E. Rehm, H. Schatz, F.-K. Thielemann (World Scientific, Singapore, 2004) p. 11. 5. K.S. Sharma et al., these proceedings. 6. R.K. Wallace, S.E. Woosley, Astrophys. J. Suppl. Ser. 45, 389 (1981). 7. H. Schatz et al., Phys. Rep. 294, 167 (1998). 8. M. Wiescher et al., J. Phys. G 25, R133 (1999). 9. T. Strohmayer, L. Bildsten, in Compact Stellar X-Ray Sources, edited by W.H.G. Lewin, M. van der Klis (Cambridge University Press, Cambridge) in press. 10. G. Savard et al., Nucl. Phys. A 626, 353 (1997). 11. J. Clark et al., Nucl. Instrum. Methods Phys. Res. B 204, 487 (2003). 12. G. Savard et al., Nucl. Instrum. Methods Phys. Res. B 204, 582 (2003). 13. C. Boudreau, Master’s thesis, McGill University, 2001. 14. G. Savard et al., Phys. Lett. A 158, 247 (1991). 15. L.S. Brown, G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986). 16. G. Bollen et al., J. Appl. Phys. 68, 4355 (1990). 17. M. K¨ onig et al., Int. J. Mass Spectrom. Ion Processes 142, 95 (1995). 18. G. Bollen, Nucl. Phys. A 693, 3 (2001). 19. G. Gr¨ aff et al., Z. Phys. A 297, 35 (1980). 20. G.F. Lima et al., Phys. Rev. C 65, 044618 (2002). 21. M. Chartier, private communication. 22. A. W¨ ohr et al., Nucl. Phys. A 742, 349 (2004). 23. G. Audi et al., Nucl. Phys. A 729, 337 (2003). 24. B.A. Brown et al., Phys. Rev. C 65, 045802 (2002). 25. R. Pfaff et al., Phys. Rev. C 53, 1753 (1996). 26. J.A. Clark et al., in preparation. 27. H. Schatz et al., Phys. Rev. Lett. 86, 3471 (2001). 28. D.D. Clayton, F. Hoyle, Astrophys. J. 187, L101 (1974). 29. J. Jos´e et al., Astrophys. J. 520, 347 (1999). 30. J.C. Hardy et al., Phys. Rev. C 9, 252 (1974). 31. J.A. Nolen et al., Nucl. Instrum. Methods 115, 189 (1974). 32. S. Bishop et al., Phys. Rev. Lett. 90, 162501 (2003). 33. G. Audi, A.H. Wapstra, Nucl. Phys. A 595, 409 (1995). 34. J.C. Hardy et al., Phys. Rev. Lett. 91, 082501 (2003). 35. M. Mukherjee et al., Phys. Rev. Lett. 93, 150801 (2004). 36. D. Seweryniak et al., Phys. Rev. Lett. 94, 032501 (2005).

Eur. Phys. J. A 25, s01, 633–638 (2005) DOI: 10.1140/epjad/i2005-06-157-2

EPJ A direct electronic only

r-process isotopes in the

132

Sn region

K.-L. Kratz1,2,3,a , B. Pfeiffer1,2 , O. Arndt1 , S. Hennrich1,2 , A. W¨ohr3,4 , and the ISOLDE/IS333, IS378, IS393 Collaborations 1 2 3 4

Institut f¨ ur Kernchemie, Universit¨ at Mainz, D-55128 Mainz, Germany Virtual Institute for Nuclear Structure and Astrophysics, Germany b Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA Joint Institute for Nuclear Astrophysics, USAc Received: 17 January 2005 / c Societ` Published online: 18 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A correct understanding of r-process nucleosynthesis requires the knowledge of nuclear-structure properties far from β-stability and a detailed description of the possible astrophysical environments. With respect to nuclear data, in recent years the main focus at CERN/ISOLDE has been put on the 132 Sn region to explore the role of the N = 82 shell closure and its consequences on the r-process matter flow through the A  130 Solar-System r-abundance peak. PACS. 26.30.+k Nucleosynthesis in novae, supernovae and other explosive environments – 26.50.+x Nuclear physics aspects of novae, supernovae, and other explosive environments – 27.60.+j 90 ≤ A ≤ 149 – 97.60.Bw Supernovae

1 Introduction Nucleosynthesis theory predicts that neutron-capture processes are responsible for the formation of the predominant part of elements heavier than Fe (for historical reviews, see e.g. [1,2,3]). The Solar-System abundance pattern (N ) of heavy nuclei, in particular the splitting of the N peaks (see, e.g., fig. 1 in ref. [1]), reveals evidence for two distinct neutron-capture processes in nature —one at low neutron densities (nn  108 cm−3 ) and the other at high neutron densities (nn ≥ 1020 cm−3 ). Historically, this has led to the definition of the s-process (slow neutron capture) and the r-process (rapid neutron capture) which are identified with different astrophysical environments. Besides this basic understanding, the history of r-process research has been quite diverse in suggested astrophysical scenarios (for reviews, see, e.g., [4,5, 6,7]). In any case, the observation of the three r-process abundance (Nr, ) peaks at A  80, 130 and 195, which are correlated with the neutron shell closures at N = 50, 82 and 126 far from β-stability, suggests that the operation of such a nucleosynthesis process requires conditions that can only be provided by explosive scenarios. Although the question of the exact r-process site(s) is still an open one, type-II supernovae (SNII) and neutron star mergers (NSM; or similar events) are suggested most frequently today. a b c

Conference presenter; e-mail: [email protected] http://www.vistars.de http://www.jina-web.org

2 Nuclear-physics needs for r-process calculations The necessary high neutron-density (nn ) and temperature (T9 = 109 K) environments result in local mass regions with quasi-statistical equilibria (QSE), where the (n,γ  γ,n) equilibrium balance is set by nuclear masses (i.e. the neutron separation energies (Sn )). For a given nn -T9 condition, the r-process then proceeds along a “contour line” of constant Sn to heavier-Z nuclei (see, e.g. fig. 4 in [8]). The weak interactions connecting the elements are the β-decays at the “waiting points”, which act as bottle necks for the r-process matter flow. Thus, when assuming an additional β-flow equilibrium, in principle the knowledge of nuclear masses (Sn values) and β-decay half-lives (T1/2 ) would be sufficient to determine the whole set of the initial (progenitor) r-process abundances prior to the decay back to stability. This then implies approximate equality of progenitor abundance (Nr,prog ) times β-decay rate (λβ = ln 2/T1/2 ). Thus, with Nr,prog (Z)λβ (Z)  const the T1/2 along the r-process flow path would in turn define the Nr,prog , and —when taking into account delayed neutron emission (Pn branching) during freeze-out— also the final Nr, . A verification of the validity of this simple and elegant approximation requires, however, experimental information on far-unstable waiting-point isotopes, for a long time believed to be inaccessible in terrestrial laboratories. However, with the identification of the first two classical neutron-magic waiting-point isotopes, N = 82 130 Cd at

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CERN/ISOLDE [9], and N = 50 80 Zn at OSIRIS [10] and TRISTAN [11], Kratz et al. [9,12,13] could show first evidence for the existence of local steady-flow equilibria. This result immediately presented a stimulating challenge to both theoreticians and experimentalists in the nuclearastrophysics community in the following years. Today, about 35 r-process isotopes have been identified via at least a β-decay half-life determination (see, e.g. [14, 15]). Nevertheless, the vast majority of r-process nuclei is still experimentally not accessible. Therefore, their nuclear properties can only be obtained through theoretical means. Since a number of different quantities are needed in r-process calculations, as outlined above, in the past it was often not possible to derive them all from one source. Taking them from different sources, however, in particular from models with largely different sophistication, may raise the question of consistency. Therefore, since more than a decade our collaboration has performed various rprocess calculations in a unified macroscopic-microscopic approach in which all nuclear properties can be studied in an internally consistent way. This approach is, for example, discussed in detail in [13,16] for the combination of nuclear masses from the Finite Range Droplet Model (FRDM; [17]) and gross β-decay properties (T1/2 and Pn values) from a Quasi-Particle Random Phase Approximation (QRPA) of Gamow-Teller (GT) transitions. In its present version, the model also includes first-forbidden (ff) corrections [18]. Analoguously, when adopting other mass formulae, such as the Extended Thomas-Fermi plus Strutinsky Integral (ETFSI) models (see, e.g., [19]), or the more recent Skyrme Hartree-Fock-Bogolyubov (HFB) models of the Montreal-Brussels group (see, e.g., [20, 21]), we normally use theoretical β-decay quantities deduced from QRPA calculations with masses and deformation parameters given by that particular model. It has been claimed by different authors, that mass models as well as theoretical approaches to calculate βdecay that go beyond the single-particle (SP) ansatz would by virtue of their added microscopic complexity be physically more reliable than gross-theory and macroscopicmicroscopic models, and would provide better predictive power for unknown nuclei. However, recent tests of various HF mean-field and large-scale shell models clearly show that these expectations have so far not been fulfilled (see, e.g. [15, 22,23, 24,25]). As far as nuclear masses are concerned, none of the ETFSI, HF-BCS or the recent HFB model versions of the Montreal-Brussels group exhibit the reliability of the FRDM predictions from 1992 for the recent substantially expanded experimental data base of NUBASE [26]. Moreover, there seem to be fundamental problems with the HFB models. Several parameters are clearly not treated in a “self-consistent” and “fully microsocopic” way [22, 24]. In any case, it is somehow worrying to see the number of parameters to optimize the global mass fits in these approaches increasing from about 10 for the earlier ETFSI models to 20 for HFB-8 when practically no improvement of the quality of fits to known masses is achieved. This is most evident in the mass regions relevant to r-process cal-

culations, in particular the far-unstable regions of the neutron shell closures (see, e.g., [15] for further discussion). In the most recent HFB mass model, HFB-9 [27], where (in contrast to the earlier HFB versions) the nuclear-matter symmetry coefficient has been fixed to J = 30 MeV, the rms deviation of the fit to the data from NUBASE [26] has even increased again from 0.635 to 0.733 MeV. For comparison, the rms deviation of the “old” macroscopicmicroscopic FRDM, which was adjusted to the masses known in 1989, is 0.616 MeV [28]. Over the years, various theoretical approaches have been developed to model β-decay (for a recent review, see, e.g., [25]). As in the case of nuclear masses, these approaches have largely different applicability and sophistication. Some models emphasise global applicability, whereas others seek selfconsistency or the comprehensive inclusion of nuclear correlations. Unfortunately, to date none of these models contains all important aspects in a consistent way. Even the most recent “microscopic” models have strong limitations in that they are restricted either to GT-transitions, to spherical shapes and/or to even-even nuclei (see, e.g., [15,25, 29]), or use a too small SP modelspace [30, 31]. Moreover, the information made available in order to judge the physical reliability of these approaches to calculate gross β-decay properties is often very limited. Therefore, for the time being these models are unsuitable as a basis for global dynamical r-process calculations. As mentioned already above, there is so far only one largely consistent approach with global applicability capable of predicting a variety of nuclear properties, namely the latest FRDM+QRPA version [18]. This model shows an average error in predicting T1/2 far from stability of about 3. Accordingly, the average error for Pn values is 3.5 (see, e.g., figs. 4 and 5 in [18]). Progress in the above approaches certainly asks for more than just the reproduction of known gross β-decay properties, but for a detailed prediction of the full “β-strength distribution”, which has to be deduced from quantities such as the Qβ value, the main GT- and low-lying ff-transitions and their log(f t) values. It is somehow worrying to see that several recent microscopic models succeed to reproduce the measured T1/2 of the N = 82 waiting-point isotope 130 Cd, but either on the basis of an incorrect input of (part of) the above mentioned quantities [30,31], or with the simultaneous result of a stable double-magic 132 Sn nucleus (with T1/2 (exp) = 40 s) just one proton pair above 130 Cd [29]. This implies that in this relativistic PN-RQRPA model the isobaric mass difference between 132 Sn and 132 Sb is too low by at least the known Qβ value of 3.12 MeV [26].

3 Experimental information on r-process nuclei The experimental study of neutron-rich nuclides lying in and near the projected r-process boulevard serves two purposes, i) provision of direct data for use in nucleosynthesis calculations, in particular at magic neutron shells, and ii) testing the theories from which

K.-L. Kratz et al.: r-process isotopes in the

132

Sn region

635

Table 1. Comparison of experimental half-lives (T1/2 ) with a recent update of the empirical Kratz-Herrmann formula (KHF) and different shell-model predictions for pure Gamow-Teller (GT) and GT plus first-forbidden (GT+ff) decays.

Beta-decay half-life, T1/2 (ms) Isotope

Experiment βdn-decay

KHF

[32, 33] 129g

Ag Ag 130 Ag 129g Cd 129m Cd 130 Cd 131 Cd 132 Cd 133 Cd 133 In 134 In 135 In 135 Sn 136 Sn 137 Sn 138 Sn 129m

46(7) [14] 158(60) [14] 35(10 [35] 242(8) [35] 104(6) [35] 162(7) [9, 36] 68(3) [36] 95(10) [36] 57(10) [35] 165(3) [37] 141(5) [37] 92(10) [37] 525(25) [38] 250(30) [38] 185(35) [38] 150(60) [38]

cQRPA (GT) [34]

100

230

29 141

78 385

147 40 38 37 41 35 34 210 143 126 142

488 207 191 157 245 190 251 5337 7041 2442 3106

nuclear properties of far-unstable isotopes are derived when no data are available. As can be inferred from the above discussion, predictions of existing global nuclear models obviously differ considerably when approaching the limits of particle binding. The reason may well be that the model parameters used so far, which were mainly determined to reproduce known properties near β-stability, need not always be proper to be used at the drip-lines. Therefore, experiments very far from stability will be essential to verify possible nuclear-structure changes with isospin, and to motivate improvements in microscopic nuclear theories. It originated, for example, from systematic studies of the evolution of shell structure with increasing distance from stability in the A  100 mass region, that already more than a decade ago Kratz et al. concluded that “the calculated r-abundance “hole” in the A  120 region ... reflects ... the weakening of the shell strength ... below 132 Sn82 .” [13]. This was —in fact— the main motivation for a series of detailed spectroscopic investigations since the late 1980s at CERN/ISOLDE in the 132 Sn region (for a recent review, see, e.g., [14]). These studies have largely benefitted from increasing selectivity in the production, separation and detection of isotopically pure beams by applying combinations of a “neutron converter”, laser ion sources, isobaric mass separation and multi-parameter detection techniques. Presently, experimental masses of only 9 r-process “waiting-point” nuclei —two at A  80 and seven in the A  130 region— are known [26]. The situation concerning the gross β-decay properties, T1/2 and Pn values, is somewhat better, since they have been determined experimentally for about 35 isotopes in the r-process boulevard, the majority of them lying in and just beyond the A  130 Nr, peak [33, 26]. Table 1 summarizes our re-

(GT) [16]

QRPA (GT+ff) [18]

43 1230 28 770 579 290 164 224 297 77 110 84 8207 930 1563 234

42 500 25 515 412 241 112 124 139 62 82 63 1833 543 706 198

Shell Model OXBASH ANTOINE [31] [30]

68 89 63 180 229 180 94 82

35 40

146

162

Fig. 1. Delayed neutron spectrum of 133 Cd with a half-life of T1/2 = 57(10) ms. The longer-lived component is mainly due to the βdn-daughter 132 In with T1/2 = 206(5) ms.

cent T1/2 results obtained at CERN/ISOLDE, in comparison with different model predictions [18,30, 31,32, 33,34]. The measurements were performed by β-neutron coincidence spectroscopy using the high efficiency Mainz neutron longcounter. This 4π detector consists of 64 3 He proportional counters arranged in three concentric rings in a polyethylene matrix. For all these isotopes in the 132 Sn region, the energy position and strength (log(f t) value) of the νg7/2 ⇒ πg9/2 transition dominates the Gamow-Teller (GT) part of the β-decay half-life. For a detailed discussion, see, e.g., [36,38]. As an example for the quality of data that can be obtained for the most exotic nuclei, we show in fig. 1 the β-delayed neutron (βdn) decay curve of the heaviest Cd isotope identified so far, i.e. N = 85 133 Cd with a T1/2 = 57(10) ms [35]. With a Pn value close

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Pb

a-, b-decays fission

ETFSI-Q CS 22892-052

Fig. 2. (Colour on-line) The N = 82 shell gap as a function of Z. Theoretical mass predictions (von Groote, magenta shortdashed line [39]; FRDM, red thick solid line [16]; ETFSI-Q, cyan long-dashed line [19]; HFB-2, green dash-dotted line [20]; HFB-8, blue thin solid line [21]) are compared to experimental values from NUBASE [26]. The data for Z = 47, 48 and 68–70 (open circles) were deduced from combinations of mass derivatives of measured and short-range extrapolated values.

to 100%, 133 Cd mainly decays to (A − 1) 206 ms 132 In and further “down” to stable 132 Xe. It has been mentioned by several speakers at this conference, that one of the recent experimental highlights in nuclear spectroscopy far from stability with clear astrophysical relevance has been the full spectroscopic study of N = 82 130 Cd β-decay [40]. At least for the high-entropy wind scenario of core-collaps SNII explosions —where an r-process starts from a neutron-rich A  90 seed composition beyond N = 50— 130 Cd is probably the most important neutron-magic “waiting-point” isotope. It determines to a large extent the bottle-neck behavior of the r-process matter flow through the respective A  130 Nr, peak. In addition to earlier “surprises” in this mass region, indicating that the shell structure around doublemagic 132 Sn is not yet fully understood [14], also the βdecay of 130 Cd (just lying one proton-pair below 132 Sn) showed several a priori unexpected features. Firstly, although parameter fine-tuned to 132 Sn, none of the recent large-scale shell model calculations [29, 30, 31] was able to correctly predict the rather high energy for the main GTtransition to the νg7/2 ⊗πg9/2 two–quasi-particle 1+ level. Secondly, the experiment clearly indicated that the lowlying ff-strength cannot be neglected. The third and probably most important result of this study with both significant nuclear-structure and astrophysics consequences was the fact that the measured Qβ value of 8.34 MeV (which represents the isobaric mass difference between 130 Cd and

Fig. 3. Upper panel: fit to the isotopic solar r-process abundances (dots; Si = 106 ) obtained from a superposition of sixteen equidistant nn -components. This result also fits the Pband Bi-contributions after summing up the α-decay chains of heavier nuclei. Lower panel: observed neutron-capture elemental abundances in the ultra-metal-poor halo star CS 22892-052 (squares) compared to scaled Nr, -values (dots) and the calculated r-abundance (full line). The arrow at Z = 92 denotes the upper limit of the U abundance.

130

In) was considerably higher than the predictions from most global mass models. As is shown in fig. 3 of [40], only some of the more recent models, which explicitly include a “quenching” of the N = 82 shell gap below 132 Sn, were able to roughly reproduce the correct trend of mass differences relative to the “unquenched” FRDM in the Cd isotopic chain. However, beyond 130 Cd the predictions of even these models diverge drastically. In order to further illustrate the present situation of mass predictions at the N = 82 shell closure, we show here in fig. 2 a comparison of the experimental shell gap (expressed as the energy difference of the two-neutron separation energies (S2n ) at N = 82 and N = 84) as a function of atomic number Z with several mass model predictions. All experimental data were taken from the recent mass evaluation of Audi et al. [26]. It should be noted, however, that the S2n values for Z = 47, 48 and 68–70 are no “true” experimental values, but combinations of mass derivates from two measurements and one short-range extrapolation, each. These data (open circles) therefore have the largest uncertainties. It is immediately evident from this figure that none of the mass models is able to reproduce the overall experimental trend and in particular the reduction of the shell gap on both sides of the double-magic 132 Sn nucleus. The picture also shows that for the N = 82 shell closure (as

K.-L. Kratz et al.: r-process isotopes in the

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Sn region

637

Fig. 4. Possible β-decay properties 110 Zr. The left part shows our QRPA predictions for GT-decay of a strongly deformed Zr-110 Nb system, as expected from the ”unquenched” FRDM with the classical neutron shell gaps [17]. The right part shows the GT-decay when assuming 110 Zr to be a spherical, doubly semi-magic nucleus with “quenched” shells [41]. In the middle part of the figure, the SP-energies for neutrons in a “classical” Nilsson potential (left part) and in a well where the l 2 -term (the parameter μn ) is reduced gradually to one-tenth of the standard value (right part). 110

also for N = 50 and N = 126), there is no improvement of the recent HFB mass model versions of the MontrealBrussels group over earlier global models. With respect to astrophysical calculations of the A  130 Nr, peak, the region from Z = 50 down to Z = 40 is of particular interest. Here, the ETFSI-Q mass formula [19], which —according to a recent statement of its main author [24]— should be replaced by the new Skyrme HFB models, still provides the “best” trend. In any case, the astrophysical consequence is clear: without the experimental masses (and in particular the crucial Qβ measurement of N = 82 130 Cd) together with the corresponding short-range extrapolations of Audi et al. [26], any realistic astrophysical calculation of the 120 ≤ A ≤ 130 r-abundances would yield unreliable results for the r-proces matter flow at the rising wing of the 2nd Nr, peak. It has been shown that this also has considerable consequences for the build-up of the heavier r-elements up to the 3rd peak at A  195 (see, e.g., fig. 8 in [14], or fig. 13 in [7], where the Nr,calc fits for the “unquenched” ETFSI-1 [42] and the “quenched” ETFSI-Q are compared). Moreover, as indicated by the calculated Pb and Bi abundances, the “memory effects” from the N = 82 and N = 126 shell closures will also influence the nucleosynthesis predictions of the Th, U cosmochronometers in ultra-metal-poor halo stars (see, e.g., [7, 43,44]). As an example, fig. 3 displays our fit to the isotopic Nr, yields (upper panel) and their conversion to elemental abundances (lower panel). There is good agreement between observations and our calculations beyond Ba for the so far best studied halo star CS22892-052.

4 Summary and outlook In summary, we have reviewed the present status of experimental and theoretical nuclear data for the astrophysical r-process in the 132 Sn region. On the experimental side, the results of a detailed spectroscopic study of the decay of the neutron-magic waiting-point isotope 130 Cd, as presented in [40], has provided a first direct measure for the reduction of the N = 82 shell gap by about 1 MeV relative to the double-magic 132 Sn. This confirms our earlier predictions of “shell-quenching” in this region, derived from indirect experimental indications (see, e.g., [7,13,14], and references therein). On the theoretical side, apart from further fine-tuning of established macroscopic-microscopic models, large-scale microscopic shell-model and HFB approaches with improved predictive power will have to be extended towards global applicability in nucleosynthesis calculations. With respect to experiments, in particular further data on the quenching of the classical shells far from stability is needed. In this context, detailed spectroscopic studies of r-process “key isotopes” are inevitable for testing the physical reliablity of any theoretical prediction of gross nuclear properties, which often allow only a limited insight into the underlying nuclear structure. When accepting the general occurrance of “shell-quenching” far from stability (see, e.g. fig. 1 in [41], and middle part of fig. 4), new nuclear structure effects may develop which should already be visible for r-process isotopes. As an example, we show on the left and right side

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of fig. 4 possible changes in the decay properties of 110 Zr. According to present model predictions (e.g., the “unquenched” FRDM [17]), this nucleus is strongly deformed in its ground state. Hence, the deformed QRPA [18] predicts GT-decay to a multitude of narrow-spaced 1+ levels in the deformed daughter 110 Nb, with the strongest GTbranch to a level at about 1.67 MeV. This decay pattern results in a T1/2  88 ms and a Pn  8%. When assuming a strongly “quenched” N = 82 shell for Z = 40, 110 Zr will be much less deformed and probably may even become a (near-)spherical, doubly semi-magic nucleus. In this case, the corresponding GT-decay pattern would change drastically, and the resulting gross β-decay properties would be completely dominated by a single allowed transition to a 1+ state at about 1.13 MeV in 110 Nb. The T1/2 would become shorter by about a factor 6, and the Pn value would be smaller by about a factor 10. Such differences in both gross β-decay properties should “easily” be detectable, e.g. by the measurement of β-delayed neutron emission, provided that 110 Zr can be produced at RIB facilitities with sufficient yields, e.g. at GSI or MSU by projectile fragmentation. It should be noted in this context, that our basic ideas about an a priori unexpected groundstate structure of a doubly semi-magic 110 Zr nucleus may find some support from a completely different mean-field shell model approach, i.e. the recent predictions of “large shell gaps for tetrahedral shapes (pyramid-like nuclei with ’rounded edges and corners’)”, among others, also for nucleon numbers Z = N = 40 and Z = N = 70 (see, e.g., [45]). These authors calculate the total energy surfaces for neutron-rich A  110 Zr isotopes with low-lying, coexisting tetrahedral, spherical and quadrupole deformed shapes. If our QRPA predictions for the two possible GTdecay patterns shown in fig. 4 are of any guidance, then also the β-decay of a tetrahedral system should contain strong spherical components. In any case, as far as possible astrophysical consequences are concerned, a doubly semi-magic isotope 110 Zr would replace the classical N = 82 neutron-magic isotope 122 Zr as an r-process waiting point. With this, the r-process would enter the N = 82 shell at somewhat higher Z than predicted by the “unquenched” mass models, thus helping to avoid the unrealistic r-abundance trough prior to the A  130 Nr, peak. In conclusion, given the close and successful interaction between nuclear physics, cosmo-chemistry, astronomy and astrophysical modelling of explosive scenarios, there is hope to finally solve the problem of the “origin of the heavy elements between Fe and Th, U”, which has recently been considered number three of “The Eleven Greatest Unanswered Questions in Physics” [46]. We would like to acknowledge discussions with many colleagues about various aspects of nuclear structure and astrophysics, in particular P. M¨ oller, W.B. Walters, J.J. Cowan, B.A. Brown and J.R. Stone. We also thank H.L. Ravn, V. Fedoseyev and U. K¨ oster for their continuous interest and help in improving the target–ionsource conditions at CERN/ISOLDE. Support for this work was provided DFG (grant KR 806/13-1), GSI (grant MZ/KLK) and the HGF (grant VH-VI-061).

References 1. E.M. Burbidge et al., Rev. Mod. Phys. 29, 547 (1957). 2. A.G.W. Cameron, Atomic Energy of Canada, Ltd., CRL41 (1957). 3. C.D. Coryell, J. Chem. Educ. 38, 67 (1961). 4. W. Hillebrandt, Space Sci. Rev. 21, 639 (1978). 5. J.J. Cowan et al., Phys. Rep. 208, 267 (1991). 6. G. Wallerstein et al., Rev. Mod. Phys. 69, 995 (1997). 7. B. Pfeiffer et al., Nucl. Phys. A 693, 282 (2001). 8. F.-K. Thielemann et al., Nucl. Phys. A 570, 329c (1994). 9. K.-L. Kratz et al., Z. Phys. A 325, 489 (1986). 10. E. Lund et al., Phys. Scr. 34, 614 (1986). 11. R.L. Gill et al., Phys. Rev. Lett. 56, 1874 (1986). 12. K.-L. Kratz, Rev. Mod. Astron. 1, 184 (1988). 13. K.-L. Kratz et al., Ap. J. 402, 216 (1993). 14. K.-L. Kratz et al., Hyperfine Interact. 129, 185 (2000). 15. K.-L. Kratz et al., in Proceedings of the International Conference on Nuclear Data for Science and Technology, ND2004, Santa Fe, New Mexico (USA), 26 September1 October 2004, edited by R.C. Haight et al., AIP Conf. Proc. 769, 1356 (2005). 16. P. M¨ oller et al., At. Data Nucl. Data Tables 66, 131 (1997). 17. P. M¨ oller et al., At. Data Nucl. Data Tables 59, 185 (1995). 18. P. M¨ oller et al., Phys. Rev. C 67, 055802 (2003). 19. J.M. Pearson et al., Phys. Lett. B 387, 455 (1996) and references therein. 20. S. Goriely et al., At. Data Nucl. Data Tables 77, 311 (2001). 21. M. Samyn et al., Phys. Rev. C 70, 044309 (2004), and references therein. 22. D. Lunney et al., Rev. Mod. Phys. 75, 1021 (2003). 23. Y.-Z. Qian et al. (Editors), Proceedings of the 1st RIA Workshop, The r-Process: The Astrophysical Origin of the Heavy Elements, Proceedings from the Institute for Nuclear Theory, Vol. 13 (World Scientific, 2004). 24. J.M. Pearson in [23], p. 43, and references therein. 25. J. Engel in [23], p. 53, and references therein. 26. G. Audi et al., Nucl. Phys. A 729, 3 (2003). 27. S. Goriely et al., Nucl. Phys. A 750, 425 (2005). 28. P. M¨ oller, private communication (2004). 29. T. Nikˇsiˇc et al., Phys. Rev. C 71, 014308 (2005). 30. G. Martinez-Pinedo, Nucl. Phys. A 668, 357c (2000) and references therein. 31. B.A. Brown et al., Nucl. Phys. A 719, 177c (2003) and references therein. 32. K.-L. Kratz, G. Herrmann, Z. Phys. 263, 179 (1974). 33. B. Pfeiffer et al., Prog. Nucl. Energy 41, 39 (2002). 34. I.N. Borzov et al., Phys. Rev. C 62, 035501 (2000). 35. O. Arndt, Diploma Thesis, University of Mainz (2003). 36. M. Hannawald et al., Phys. Rev. C 62, 054301 (2000). 37. I. Dillmann et al., Eur. Phys. J. A 13, 281 (2002). 38. J. Shergur et al., Nucl. Phys. A 682, 493 (2001). 39. H. von Groote et al., At. Data Nucl. Data Tables 17, 418 (1976). 40. I. Dillmann et al., Phys. Rev. Lett. 91, 162503 (2003). 41. B. Pfeiffer et al., Acta Phys. Pol. B 27, 475 (1996). 42. Y. Aboussir et al., At. Data Nucl. Data Tables 61, 127 (1995). 43. K.-L. Kratz et al., New Astr. Rev. 48, 109 (2004). 44. J.J. Cowan et al., Ap. J. 521, 194 (1999). 45. J. Dudek et al., Phys. Rev. Lett. 88, 252502 (2002), and Phys. Rev. C 69, 061305 (2004). 46. E. Haseltine, Discover Mag. 23, No. 2 (2002).

Eur. Phys. J. A 25, s01, 639–642 (2005) DOI: 10.1140/epjad/i2005-06-069-1

EPJ A direct electronic only

The half-life of the doubly-magic r-process nucleus

78

Ni

H. Schatz1,2,3,a , P.T. Hosmer1,2 , A. Aprahamian3,4 , O. Arndt5 , R.R.C. Clement1,2,b , A. Estrade1,2 , K.-L. Kratz5 , S.N. Liddick1,6 , P.F. Mantica1,6 , W.F. Mueller1 , F. Montes1,2 , A.C. Morton1,c , M. Ouellette1,2 , E. Pellegrini1,2 , B. Pfeiffer5 , P. Reeder7 , P. Santi1,d , M. Steiner1 , A. Stolz1 , B.E. Tomlin1,6 , W.B. Walters8 , and A. W¨ohr4 1 2 3 4 5 6 7 8

National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics, USAe Department of Physics, University of Notre Dame, Notre Dame, IN 46556-5670, USA Institut f¨ ur Kernchemie, Universit¨ at Mainz, Fritz-Strassmann Weg 2, D-55128 Mainz, Germany Department of Chemistry, Michigan State University, East Lansing, MI 48824, USA Pacific Northwest National Laboratory, MS P8-50, P.O. Box 999, Richland, WA 99352, USA Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742, USA Received: 28 February 2005 / c Societ` Published online: 12 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Despite a lot of experimental and theoretical progress the question of the r-process site and the origin of the heavy elements in nature remains one of the biggest open questions in nuclear astrophysics. We report first results from experiments with rare isotope beams of r-process nuclei at Michigan State University’s National Superconducting Cyclotron Laboratory. This includes a first measurement of the half-life of the doubly-magic waiting point nucleus 78 Ni, which serves as a major bottle-neck for the synthesis of heavy elements in many r-process models. PACS. 21.10.Tg Lifetimes – 23.40.-s β decay; double β decay; electron and muon capture – 26.50.+x Nuclear physics aspects of novae, supernovae, and other explosive environments

1 Introduction The r-process is one of the major nucleosynthesis processes in the universe producing roughly half of all elements heavier than iron [1, 2]. One of the biggest problems in nuclear astrophysics remains the question of the site of the r-process. The proposed scenarios include the neutrinodriven wind off the newborn neutron star in core-collapse supernovae [3,4], prompt supernova explosions induced by the collapse of a ONeMg core in 8–10 M stars [5], accretion and jets from core-collapse supernovae [6,7], and neutron star mergers [8,9]. Currently none of the proposed models can synthesize self-consistently all r-process nuclides. Observations of r-process elements in very old stars together with Galactic chemical evolution models do provide some constraints. These studies seem to rule out a

Conference presenter; e-mail: [email protected] Present address: Lawrence Livermore National Laboratory, 7000 East Ave. Livermore, CA 94550, USA. c Present address: TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3 Canada. d Present address: Los Alamos National Laboratory, TA 35 Bldg. 2 Room C-160, USA. e http://www.jinaweb.org b

neutron star mergers as a dominant source of r-process nuclei due to their low frequency that cannot explain the observed gradual enrichment of the Galaxy in r-process elements [10]. In the end, observations and experiments will have to solve the problem and address the theoretical ambiguities. In the case of the r-process, the only direct empirical constraint on the process itself and its immediate astrophysical environment are observations of the detailed pattern of the resulting nuclear abundances, together with a thorough understanding of the underlying nuclear physics. Without the latter, observations cannot be connected to r-process models in a quantitative way. On the observational side tremendous progress has been made in recent years. With the availability of detailed and accurate abundance data from r-process enhanced ultra metal poor halo stars, the operation of individual rprocess events in the early galaxy can now be observed. (see Truran et al. [11] for a recent review). For example, for the star CS 22892-052 accurate abundances of 28 neutron capture elements have been obtained [12]. The analysis of the handful of such stars currently known shows a fairly stable r-process abundance pattern from event to event, with some variations for very light r-process elements,

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and possibly also for uranium and thorium [13, 14,15, 16]. This already provides some important new insights into the r-process mechanism. For example, the event to event consistency requires tightly constrained astrophysical conditions. The deficiencies between observed “single” event patterns and the solar r-process abundances for very light r-process elements have been interpreted as a hint for the existence of a second “r-process” producing the missing amount of lighter r-process elements with A < 130 [17, 18]. Facilities and programs are now in place to dramatically increase the available observational data by identifying possibly hundreds of r-process enriched metal poor halo stars in future large scale surveys and their higher resolution follow ups [19]. Similar progress is now needed in experimental nuclear physics. Connecting abundance observations with rprocess models in a quantitative way requires an understanding of the structure of the extremely neutron rich heavy nuclei participating in the r-process [20]. This will not only be important for identifying and understanding the site of the r-process. In the future, once the r-process is on a solid nuclear physics basis, it could be used as a probe for the physics of the extreme astrophysical environments it takes place in.

2 Nuclear physics needs for r-process calculations The nuclear physics needed to model the r-process includes β-decay half-lives, branchings for β-delayed neutron emission, neutron separation energies, fission rates and fragment distributions, and to some extent neutron capture rates [1, 20]. β-decay half-lives are among the most important quantities, especially at neutron shell closures where the r-process path is shifted towards stability and where therefore the slowest β-decay rates are encountered. Slow β-decay rates serve as bottle-necks that control the synthesis of all heavier elements and therefore play a critical role in constraining the astrophysical parameters of the r-process. β-decay rates also determine directly the local abundance pattern with fast decay rates leading to low abundance and slow decay rates leading to high abundance along the r-process path. The mass range of the r-process is delineated by the distribution of seed nuclei at the low mass end, and by the onset of fission at the high mass end, probably around A ≈ 250. The seed distribution depends largely on the particular r-process model. Two classes of models can be distinguished. In scenarios where the seeds are produced by a full α-rich freezeout (standard neutrino driven wind in core collapse supernovae, neutron star mergers, etc.) seed nuclei beyond iron in the A = 90 region are formed. On the other hand, there is a number of scenarios where the r-process sets in at lighter nuclei. These include models of a neutrino driven wind from a relatively massive neutron star where neutron capture starts already in the CNO region [21] and ONeMg core collapse supernovae driven by prompt explosions [5]. In such models with lighter seeds

the first critical bottleneck in the r-process flow is the N = 50 shell closure far from stability. In the initial phase of the r-process the neutron density is high. The r-process runs closer to the neutron drip line, and accelerated by the shorter β-decay half-lives most of the heavy element buildup occurs. Therefore, the half-lives of 79 Cu and 78 Ni set the processing timescale for the synthesis of elements beyond A ≈ 80. As the neutron density drops the r-process path moves closer to stability and the longer-lived 80 Zn becomes an additional r-process waiting point shaping together with 78 Ni and 79 Cu the final A ≈ 80 abundance distribution. While the half-life of 79 Cu has been experimentally determined before to be 188 ms [22], theoretical predictions for the half-life of 78 Ni were ranging from 100 ms to 500 ms (see fig. 2 below) introducing a significant uncertainty in r-process models. We present here a first measurement of the half-life of 78 Ni, which puts these r-process model calculations on a considerably more solid experimental basis.

3 Experiment and results Radioactive beams of r-process nuclei are produced at the NSCL by fragmentation of stable, neutron rich beams at typical energies of 120–140 MeV/u. Important factors for the high exotic beam production capabilities of the facility are high primary beam currents, high beam energy that allows for the use of thicker production targets, and the large momentum acceptance of 5.5% of the A1900 superconducting fragment separator. The A1900 produces a mixed radioactive beam that is transported to various experimental stations and typically contains on the order of a dozen species. Individual nuclei can then be identified event-by-event by measuring their momentum, charge, and velocity. Momenta are measured by tracking particles at the dispersive intermediate image of the A1900, charge numbers are obtained from energy loss measurements in Si PIN diodes, and velocities are determined from the time of flight between two plastic scintillators. For the β-decay experiments the identified nuclei are transported to the NSCL β counting system [23] and continuously implanted into a highly segmented (40 × 40 strips) double-sided silicon strip detector measuring time and location of the implantation. The same detector also registers the electrons emitted in the subsequent β-decay of the short-lived nuclei allowing one to determine the decay time. With this setup decay properties of all species in the radioactive beam can be determined simultaneously. For the experiment reported here the β counting system was surrounded by the neutron detector NERO to measure branchings for β-delayed neutron emission. NERO is a neutron long counter using 3 He and BF3 gas counters embedded in a polyethylene matrix that serves as a neutron moderator. The neutron detection efficiency is 30–40% for neutron energies up to 5 MeV. In a first measurement we succeeded in measuring the half-life of the doubly-magic nucleus 78 Ni [24] —one of the last (besides 48 Ni) and most exotic of the 10 classical doubly-magic nuclei in nature with unknown properties.

H. Schatz et al.: The half-life of the doubly-magic r-process nucleus

Energy Loss [a.u]

550

500 77

Cu

75

450

Ni

78

Ni

400

73

Co

450

500

550

Time of Flight [a.u] Fig. 1. Time of flight versus energy loss in a Si detector for each particle implanted in the double-sides Si strip detector. This information is used for particle identification.

78

Ni

641

by M¨ oller et al. [29] that takes into account first forbidden transitions and enforces zero defomation at shell closures clearly leads to some improvement. However, halflife comparisons can only be a first step in testing theoretical models. For example, deviations in excitation energies, transition strengths, and decay Q-value can in principle compensate each other. More stringent tests, for example through detailed decay spectroscopy as it might become possible at future facilities, are needed to clarify the reliability of the various theoretical models in describing the underlying nuclear structure. The anlaysis of this experiment is still ongoing. Final results will be presented in a forthcoming publication. In addition, due to the mixed nature of the radioactive beam we expect to be able to also determine half-lives for 77 Ni, 73–75 Co, and 80 Cu. Together with data on neutron emission they will be presented in a future publication.

4 Conclusions

Fig. 2. The half-lives of neutron rich N = 50 isotones. Shown is our preliminary result for 78 Ni together with previous experimental data [25] (Experimental) for more stable isotones. In addition, we show theoretical predictions from Engel et al. 1999 [26], Langanke & Martinez-Pinedo 2003 [27] (Shell Model), M¨ oller et al. 1997 [28], and M¨ oller et al. 2003 [29].

Before just 3 78 Ni nuclei had been identified in a pioneering experiment at GSI [30]. We detected a total of 11 78 Ni events in 104 hours of beam time, using the fragmentation of a 15 pnA 140 MeV/u 86 Kr beam and taking advantage of the full momentum acceptance of the A1900. Figure 1 shows the particle identification of a subset of events. Figure 2 shows the experimental half-lives of N = 50 nuclei together with various predictions, including our preliminary result for 78 Ni. Our preliminary result seems to favor a lower half-live for 78 Ni in line, for example, with the predictions by the shell model calculations of Langanke and Martinez-Pinedo [27]. However, r-process calculations require predictions by global models that can be applied to all r-process nuclei in a consistent way. As fig. 2 shows, the overprediction of half-lives by older global models [28, 31] already observed for more stable nuclei persists up to 78 Ni. A more recent revision of the global QRPA model

With a new generation of rare isotope beam facilities such as the new Coupled Cyclotron Facility at Michigan State University there are now new opportunities to carry out experiments deep in the path of the r-process, at least below A ≈ 130. This will put r-process model calculations in this region on a much more solid basis and will allow a quantitative interpretation of observational data. Here we reported on a first experiment determining the halflife of 78 Ni. First r-process model calculations with our new data confirm that indeed the smaller half-life leads to a considerable acceleration of the r-process requiring a significant readjustment of the astrophysical conditions needed for a successful r-process. To extend such measurements in the heavier r-process region, in particular into the region around the N = 126 shell closure will require a next generation facility such as the Rare Isotope Accelerator RIA. With such facilities on the horizon there is now a real prospect to finally determine the nuclear physics of the r-process in the coming decade. Together with expected advances in astronomy we can hope that finally the problem of the origin of the r-process elements in nature will be solved. This work has been supported by NSF grants PHY 01-10253 and PHY 02-16783 (Joint Institute for Nuclear Astrophysics), DFG grant KR 806/13-1, HGF grant VH-VI-061, and the Alfred P. Sloan Foundation.

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The European Physical Journal A J.M. LeBlanc, J.R. Wilson Astrophys. J. 161, 541 (1970). A.G.W. Cameron, Astrophys. J. 562, 456 (2001). J.M. Lattimer et al., Astrophys. J. 213, 225 (1977). S. Rosswog et al., Astron. Astrophys. 341, 499 (1999). D. Argast et al., Astron. Astrophys. 416, 997 (2004). J.W. Truran et al., Publ. Astron. Soc. Pac. 114, 1293 (2002). C. Sneden et al., Astrophys. J. 591, 936 (2003). R. Cayrel et al., Nature 409, 691 (2001). J.J. Cowan et al., Astrophys. J. 572, 861 (2002). H. Schatz et al., Astrophys. J. 579, 626 (2002). S. Goriely, M. Arnould, Astron. Astrophys. 379, 1113 (2001). B. Pfeiffer, U. Ott, K.-L. Kratz, Nucl. Phys. A 688, 575 (2001). C. Travaglio et al., Astrophys. J. 601, 864 (2004). T.C. Beers, P.S. Barklem, N. Christlieb, V. Hill, astroph/0408381

20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.

K.-L. Kratz et al., Astrophys. J. 403, 216 (1993). M. Terasawa et al., Astrophys. J. 562, 470 (2001). K.-L. Kratz et al., Z. Phys. A 340, 419 (1991). J.I. Prisciandaro et al., Nucl. Intrum. Methods A 505, 140 (2003). P. Hosmer et al., Phys. Rev. Lett. 94, 112501 (2005). G. Audi et al., Nucl. Phys. A 729, 3 (2003). J. Engel et al., Phys. Rev. C 60, 014302 (1999). K. Langanke, G. Martinez-Pinedo, Rev. Mod. Phys. 75, 819 (2003). P. M¨ oller, J.R. Nix, K.-L. Kratz, At. Data Nucl. Data Tables 66, 131 (1997). P. M¨ oller, B. Pfeiffer, K.-L. Kratz, Phys. Rev. C 67, 055902 (2003). M. Bernas et al., Phys. Lett. B 415, 111 (1997). I.N. Borzov, S. Goriely, J.M. Pearson, Nucl. Phys. A 621, 307c (1997).

Eur. Phys. J. A 25, s01, 643–644 (2005) DOI: 10.1140/epjad/i2005-06-007-3

EPJ A direct electronic only

New

19

Ne resonance observed using an exotic

18

F beam

D.W. Bardayan1,a , J.C. Blackmon1 , J. G´ omez del Campo1 , R.L. Kozub2 , J.F. Liang1 , Z. Ma3 , D. Shapira1 , 4,5 1 L. Sahin , and M.S. Smith 1 2 3 4 5

Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Physics Department, Tennessee Technological University, Cookeville, TN 38505, USA Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 37599, USA Department of Physics, Dumlupinar University, Kutahya, 43100, Turkey Received: 22 November 2004 / c Societ` Published online: 13 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The rates of the 18 F(p, α)15 O and 18 F(p, γ)19 Ne reactions in astrophysical environments depend on the properties of 19 Ne levels above the 18 F + p threshold. There are at least 8 levels in the mirror nucleus 19 F for which analogs have not been observed in 19 Ne in the excitation energy range Ex = 6.4–7.6 MeV. We have made a search for these levels by measuring the 1 H(18 F, p)18 F excitation function over the energy range Ec.m. = 0.3–1.3 MeV. We have identified and measured the properties of a newly observed level at Ex = 7.420 ± 0.014 MeV, which is most likely the mirror to the J π = 7/2+ 19 F level at 7.56 MeV. This new level is found to increase the calculated 18 F(p, α)15 O reaction rate by 16%, 63%, and 106% at T = 1, 2, and 3 GK, respectively. PACS. 27.20.+n 6 ≤ A ≤ 19 – 25.40.Cm Elastic proton scattering – 25.60.-t Reactions induced by unstable nuclei – 26.30.+k Nucleosynthesis in novae, supernovae, and other explosive environments

The proton-induced reactions on 18 F are of astrophysical interest for a variety of reasons. The amount of the long-lived radioisotope 18 F [1] produced in novae depends directly on the rates of the 18 F(p, α)15 O and 18 F(p, γ)19 Ne reactions [2]. The synthesis of other isotopes (e.g., 16 O, 18 O, and 19 F) also show a dramatic sensitivity to the rates of these reactions [3]. In higher-temperature environments such as X-ray bursts, there may be a transition to heavy element production via the reaction sequence 18 F(p, γ)19 Ne(p, γ)20 Na(p, γ)21 Mg . . . [4]. Whether there is a significant flow through this reaction sequence depends sensitively on the competition between the 18 F(p, γ)19 Ne and 18 F(p, α)15 O reactions, and thus we must know their relative rates in these high-temperature astrophysical environments. To accurately calculate the rates of the 18 F(p, α)15 O and 18 F(p, γ)19 Ne reactions, we must understand the level structure of 19 Ne above the proton threshold at Ex = 6.411 MeV. Despite numerous studies of 19 Ne (see ref. [5] and references therein), there still exist at least 8 levels in the mirror nucleus, 19 F, for which analogs have not been observed in 19 Ne in the excitation energy range Ex = 6.4– 7.6 MeV. These unobserved levels may significantly enhance the 18 F + p reaction rates, and thus their properties must be determined. a

Conference presenter; e-mail: [email protected]

We have searched for these missing levels in 19 Ne by measuring the 1 H(18 F, p)18 F excitation function over the energy range Ec.m.  0.3–1.3 MeV. A 24 MeV 18 F beam was accelerated at the ORNL Holifield Radioactive Ion Beam Facility (HRIBF) and stripped to charge state q = 9+ before the energy-analyzing magnet to reject an unwanted 18 O contamination in the beam. The 18 F beam was then used to bombard a thick 2.8 mg/cm2 polypropylene CH2 target in which the beam was stopped, and scattered protons from the 1 H(18 F, p)18 F reaction were detected at θlab = 8◦ –16◦ by a double-sided silicon-strip detector (DSSD). Because the scattered protons lose relatively little energy in the target, measurements of the proton’s energy and angle of scatter are sufficient to determine the center-of-mass energy at which the reaction occurred [6]. A measurement of the scattered proton energy spectrum at a fixed angle can thus be used to extract the excitation function for the 1 H(18 F, p)18 F reaction over a wide range of center-of-mass energies. Data were collected in event mode for approximately 62 hours. Events identified as protons from their time-offlight and energy [7] were sorted in two-degree angular bins, corrected for energy loss in the target, and are plotted in fig. 1. The number of counts per channel generally fell with increasing Ec.m. , which was simply a manifestation of the Rutherford scattering cross-section. There were, however, significant deviations from Rutherford

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θlab = 8

o

o

θlab = 10

300 200

100

Counts per 10 channels

100 0

θlab = 12

o

0

o

θlab = 14

200

200

100

100 0

o

θlab = 16

400

0 0.4

0.8

1.2

300 200 100 0 0.4

0.8

1.2 Ec.m. (MeV)

Fig. 1. The proton energy spectra from the 1 H(18 F, p)18 F reaction are shown as a function of angle. The solid line shows + the best fit assuming a 72 resonance at Ec.m.  1.01 MeV. The ◦ dashed line in the 8 spectrum shows the excitation function expected using the resonance parameters from ref. [5].

scattering at Ec.m. = 0.665 MeV and 1.01 MeV where the cross-section abruptly rises and falls, respectively. The increase in cross-section at Ec.m. = 665 keV arises from the + previously observed J π = 32 scattering resonance [8]. Since the properties of this resonance are well known, it provided a convenient internal energy calibration. The sharp fall in cross-section near Ec.m. = 1.01 MeV could not be explained using previously known levels and indicated the presence of a newly observed 19 Ne resonance. Excitation functions were calculated with the R-Matrix code MULTI [9]. A good fit to the data was obtained (see fig. 1) using just three resonances: the + J π = 32 resonance at Ec.m. = 0.665 MeV, a newly ob+ + served J π = 72 or 52 resonance near Ec.m. = 1.01 MeV, and a broad s-wave resonance higher in energy. A simultaneous fit of the data sets obtained at each angle was performed by varying the properties of the resonance near Ec.m. = 1.01 MeV, and leaving the properties of the known Ec.m. = 0.665 MeV resonance fixed at the values measured in ref. [8]. The best fit (χ2ν = 1.45) was obtained + for a J π = 72 resonance at Ec.m. = 1.009 ± 0.014 MeV (Ex = 7.420 ± 0.014 MeV) with Γp = 27 ± 4 keV and Γα = 71 ± 11 keV. A fit nearly as good (χ2ν = 1.52) + was obtained for a J π = 52 resonance at the same energy with Γp = 31 ± 4 keV and Γα = 71 ± 11 keV. + A J π = 52 assignment, however, appears to be rather unlikely from a comparison with the mirror nucleus, 19 F. The only known candidates for an analog level + are the J π = 52 19 F state at Ex = 7.54 MeV and the + + J π = 72 19 F state at 7.56 MeV [10]. The 7.54 MeV 52 19 F level is narrow (Γ = 0.16 keV) and is thus not a good candidate for the mirror to our newly observed + level with Γ  98 keV. On the other hand, the 72 19 F level is rather broad (Γ = 85 keV [11]) and has no other

obvious analog in 19 Ne. The newly observed 19 Ne level at Ex = 7.420 ± 0.014 MeV is, therefore, most likely the + mirror to the J π = 72 19 F level at 7.56 MeV. In addition to the best fit calculation, we also show in fig. 1 the calculated excitation function using the 19 Ne resonance parameters from ref. [5]. That calculation includes contributions from 13 resonances, most of which produce only minor perturbations to the excitation function. The one glaring discrepancy is for the expected contribution + from the 52 level at Ec.m. = 1.09 MeV (Ex = 7.500 MeV). This level was observed in ref. [10] to have Γp /Γα  5.25 and a 1σ upper limit of Γ < 32 keV. A width of 16 keV was adopted for this level in ref. [5], but clearly (as seen in fig. 1) the actual width is much smaller. This is not really surprising considering the width of the proposed analog level is only 0.16 keV [12]. Using the ratio of the proton- to the alpha-partial width measured in ref. [10], we can set an upper limit on the proton width of Γp (7.500 MeV) < 2.5 keV at the 90% confidence level. We have made updated calculations of the 18 F + p reaction rates in ref. [7]. We find that the addition of the newly observed 7/2+ resonance increases the calculated 18 F(p, α)15 O rate by 16%, 63%, and 106% at T = 1, 2, and 3 GK, respectively. The calculated 18 F(p, γ)19 Ne reaction rate (using γ widths from ref. [5]) is increased by about ∼ 7% over the 1–3 GK range. At temperatures below this, the rates are dominated by resonances at Ec.m. = 330 and 665 keV [5]. This research was sponsored by the LDRD Program of ORNL, managed by UT-Battelle, LLC, for the U.S. DOE under Contract No. DE-AC05-00OR22725. This work was also supported in part by the U.S. DOE under Contract No. DE-FG0296ER40955 with Tennessee Technological University and Contract No. DE-FG02-97ER41041 with the University of North Carolina at Chapel Hill.

References 1. M. Hernanz, J. G´ omez-Gomar, J. Jos´e, New Astron. Rev. 46, 559 (2002). 2. A. Coc, M. Hernanz, J. Jos´e, J.-P. Thibaud, Astron. Astrophys. 357, 561 (2000). 3. C. Iliadis, A. Champagne, J. Jos´e, S. Starrfield, P. Tupper, Astrophys. J., Suppl. Ser. 142, 105 (2002). 4. A.E. Champagne, M. Wiescher, Annu. Rev. Nucl. Part. Sci. 42, 39 (1992). 5. N.-C. Shu, D.W. Bardayan, J.C. Blackmon, Y.-S. Chen, R.L. Kozub, P.D. Parker, M.S. Smith, Chin. Phys. Lett. 20, 1470 (2003). 6. A. Galindo-Uribarri et al., Nucl. Instrum. Methods Phys. Res. B 172, 647 (2000). 7. D.W. Bardayan et al., Phys. Rev. C 70, 015804 (2004). 8. D.W. Bardayan et al., Phys. Rev. C 63, 065802 (2001). 9. R.O. Nelson, E.G. Bilpuch, G.E. Mitchell, Nucl. Instrum. Methods Phys. Res. A 236, 128 (1985). 10. S. Utku et al., Phys. Rev. C 57 2731 (1998); 58, 1354(E) (1998). 11. T. Mo, H.R. Weller, Nucl. Phys. A 198, 153 (1972). 12. D.R. Tilley, H.R. Weller, C.M. Cheves, R.M. Chasteler, Nucl. Phys. A 595, 1 (1995).

Eur. Phys. J. A 25, s01, 645–646 (2005) DOI: 10.1140/epjad/i2005-06-008-2

EPJ A direct electronic only

12

C+

12

C cross-section measurements at low energies

L. Barr´ on-Palos1,a , E. Ch´ avez L.1 , A. Huerta H.1 , M.E. Ortiz1 , G. Murillo O.2 , E. Aguilera R.2 , E. Mart´ınez Q.2 , 2 E. Moreno , R. Policroniades R.2 , and A. Varela G.2 1 2

Instituto de F´ısica UNAM, Ap. Po. 20-364, Ciudad Universitaria, 01000 Mexico, D.F., Mexico Instituto Nacional de Investigaciones Nucleares, Departamento del Acelerador, Salazar, Edo. Mex., C.P. 52045, Mexico Received: 12 October 2004 / c Societ` Published online: 15 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. In order to study the 12 C + 12 C reaction at low energies, a combination of an intense heavy ion beam on a thick target and the detection of secondary gamma rays on a well-shielded germanium detector has been used. Preliminary cross-section results are reported for Ec.m. = 2.63–3.45 MeV. PACS. 25.70.Jj Fusion and fusion-fission reactions – 26.50.+x Nuclear physics aspects of novae, supernovae, and other explosive environments – 97.10.Cv Stellar structure, interiors, evolution, nucleosynthesis, ages

1 Introduction 4

0.450

2 0

E c.m. (MeV)

The 12 C + 12 C cross-section at low energies (Ec.m. = 1–3 MeV) is needed in order to constrain supernovae events detonated by explosive carbon burning in normal intermediate mass stars [1,2, 3], and binary systems [4, 5,6]. However, the lowest center-of-mass energy at which this cross-section has been measured is only 2.45 MeV [7].

23

16

O+2α

12

Mg+n

12

C+ C

0.440

-2

1.633

23

Na+p

-4 20

-6

Ne+α

-8

-10

2 Secondary gamma rays and thick target

-12 24

For the 12 C + 12 C system, even at low energies, the excitation energy of the compound nucleus 24 Mg is enough to decay by particle emission. Below Ec.m. = 3 MeV, the only open evaporation channels accompanied with a gamma ray are alpha and proton (see fig. 1). Daughter nuclei 23 Na and 20 Ne are formed in states below all particle emission thresholds and the residual excitation energy is emitted as gamma rays. Through the detection of the first to groundstate decay gamma rays, we can work out our way back to the original 12 C(12 C, p 1 )23 Na and 12 C(12 C, α1 )20 Ne crosssections. We have combined this technique with the use of a graphite thick target, whose thickness exceeds the range of the incident particles. This target is strong enough to withstand the intense beam required for very low crosssection measurements. In this way, the cross-section is not just measured at a single energy, instead, the whole energy interval from the beam energy to zero is inspected; in essence, we are measuring the thick target yield. a

Conference presenter; e-mail: [email protected]

Fig. 1.

12

C+

12

Mg

C system and its decay modes.

3 Experimental procedures Measurements were carried out at the IFUNAM 3 MV tandem accelerator. An intense 12 C beam (1 to 15 μA) was directed to a graphite thick target (1 mm thick) placed in the back of our reaction chamber. Gamma rays were detected by a hyper-pure germanium crystal (30% intrinsic efficiency), placed just behind the target. In order to reduce the background radiation, this detector and the reaction chamber were surrounded by lead shielding (9 cm thick). To obtain the total number of carbon ions incident in the target, a thin 197 Au coating (90 × 1015 atoms/cm2 ) was deposited on the front of the target, so that the elastically backscattered particles can be monitored by a solid state detector (PIPS) mounted at 135 degrees,

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Preliminary 23

ELab. = 6.9 MeV

Na Eγ = 0.440 MeV -

20

Ne Eγ = 1.633 MeV

1

40

K Eγ = 1.461 MeV

σp (mb)

Counts

-3

1x10

-4

1x10

-5

10

-6

+

e +e Eγ = 0.511 MeV

100

10

10

IFUNAM Mazarakis et al. 0.0

0.5

1.0

1.5

10

2.0

-7

Energy (MeV) C+

12

C re-

1.5 cm away from the target center. A very small collimator (Ω = 3.42×10−5 sr) was placed in front of the monitor to reduce the intense flux of backscattered particles.

4 Results and discussion Data at six different beam energies from 7 to 5.3 MeV was taken. For every beam energy, we obtained a gammaray spectrum in which the 23 Na and 20 Ne peaks can be distinguished (fig. 2). The deconvolution of thick target yield measurements to obtain the 12 C(12 C, p1 )23 Na and 12 C(12 C, α1 )20 Ne cross-sections was carried out as is described in reference [8]; preliminary results are shown in fig. 3. Our monitor detector for the elastically backscattered 12 C from the 197 Au layer, suffered enough radiation damage to deform the spectrum in a way to turn difficult the desired absolute normalization. We estimate an additional error to the statistical one (shown in fig. 3), from 20% to 50%. A different approach to obtain the required absolute normalization will be used in future experiments. However, since both, the proton and alpha channels are measured simultaneously in the same spectrum, the relative thick target yield can be extracted without necessity of charge integration. The results of such analysis, that could verify the discrepancies observed in fig. 3, will appear in a coming publication.

5 Conclusions The measurement of the thick target yield of secondary gamma emission allowed us to reach reaction crosssections down to very low energies. Although absolute normalization is a matter that needs to be addressed further, our results show some inconsistencies with data found in the literature [7].

10

-3

1x10

-4

1x10

-5

10

-6

1

12

σα (mb)

Fig. 2. Gamma-ray spectrum obtained for the action at indicated laboratory system energy.

Preliminary

IFUNAM Mazarakis et al. 5.0

5.5

6.0

6.5

7.0

ELab. (MeV) Fig. 3. 12 C(12 C, p1 )23 Na and cross-sections.

12

C(12 C, α1 )20 Ne normalized

This work was supported by DGAPA-UNAM project No. IN103999 and by CONACYT project No. 32262. L. Barr´ on-Palos thanks the support given by PAEP-UNAM and CONACYT. The authors want to thank K. L´ opez, F. Jaimes, M. Galindo, M. Veytia, V. Orozco and the IFUNAM’s workshop staff for their valuable collaboration.

References 1. D.W. Arnett, Astrophys. Space Sci. 5, 180 (1969). 2. J. Craig Wheeler, Publ. Korean Astron. Soc. 8, 169 (1993). 3. E. Garc´ıa-Berro, C. Ritossa, I. Iben jr., Astrophys. J. 485, 765 (1997). 4. K. Nomoto, F. Thielemann, K. Yokoi, Astrophys. J. 286, 644 (1984). 5. M. Reinecke, W. Hillebrandt, J.C. Niemeyer, Astron. Astophys. 374, 739 (1999). 6. L. Piersanti, S. Gagliardi, I. Iben jr., A. Tornamb´e, Astrophys. J. 583, 885 (2003). 7. M.G. Mazarakis, W.E. Stephens, Phys. Rev. C 7, 1280 (1973). 8. L. Barr´ on-Palos et al., Rev. Mex. F´ıs. 50, S2, 18 (2004).

Eur. Phys. J. A 25, s01, 647–648 (2005) DOI: 10.1140/epjad/i2005-06-193-x

EPJ A direct electronic only

7

Be breakup on heavy and light targets

N.C. Summersa and F.M. Nunes National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA Received: 19 November 2004 / c Societ` Published online: 15 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We present all-order quantum mechanical calculations of 7 Be breakup on 208 Pb and 12 C targets. We examine the issues concerning the extraction of the astrophysical S-factor from the breakup data, via the methods of asymptotic normalization coefficients and Coulomb dissociation. PACS. 25.70.De Coulomb excitation – 24.10.Eq Coupled-channel and distorted-wave models – 25.60.Gc Breakup and momentum distributions – 27.20.+n 6 ≤ A ≤ 19

1 Introduction

2 Light targets The ANC method requires a peripheral collision and a first-order reaction mechanism. Therefore the contribution to the breakup from the interior and the effect of higherorder couplings have to be examined. In fig. 1 we show the importance of higher-order couplings on the breakup cross section for the 12 C target. The first-order DWBA calculation (dashed line) dramatically overestimates the CDCC cross section (solid line), which includes all couplings to all-orders. To extract astrophysical S-factors from breakup, the reaction has to be a direct a

Conference presenter; e-mail: [email protected]

dσ/dΩ (mb/sr)

The breakup of 7 Be into α + 3 He is of interest to astrophysics for the capture reaction 3 He(α,γ)7 Be. This capture reaction is of importance for the pp chain [1] and big-bang nucleosynthesis [2]. At astrophysical energies, the reaction rates for capture are extremely low and thus rely on extrapolations. The astrophysical quantities can be extracted from the breakup data via Coulomb dissociation on heavy targets [3], and via the asymptotic normalization coefficient (ANC) method [4]. Here we present fully quantum mechanical calculations [5] for two experiments of 7 Be breakup. One at the Cyclotron Lab at Texas A&M, using a 12 C target at 25 MeV/nucleon, and the other at the NSCL, using a 208 Pb target at 100 MeV/nucleon. Calculations were performed within the method of continuum discretized coupled channels (CDCC), reviewed in ref. [6], using the coupled channels code FRESCO [7]. Within CDCC, nuclear and Coulomb are treated on equal footing and the contribution from higher-order couplings can be examined.

3000

CDCC DWBA

2000

1000

0

0

2

4 6 θc.m. (deg)

8

10

Fig. 1. Angular distribution of the cross section for 7 Be breakup on 12 C at 25 MeV/nucleon. The solid line is the full CDCC calculation and the dashed line is a first-order DWBA calculation.

first-order process. It is clear from fig. 1 that higher-order processes have to be reduced via some kinematical selection. Another condition of the ANC method is that the reaction is peripheral. In fig. 2 we show the J-distribution of the cross section. A simple sum of radii for 7 Be + 12 C yields 5.3 fm. Relating the angular momentum to a semiclassical impact parameter, we see that 16% of the total breakup cross section comes from impact parameters less than the sum of the radii (shaded area in fig. 2). Contributions from the interior will have to be considered when extracting the ANC.

3 Heavy targets Breakup reactions on heavy targets can extract astrophysical factors for the inverse reaction, due to the large

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800

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Total Nuclear Coulomb dipole quadrupole

15

4 dσ/dΩ (mb/sr)

600

σJ (mb)

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2

200

1

0

Erel < 1 MeV

400

0

0

20

40 J

60

80

0

1

2

3

θc.m. (deg)

Fig. 2. J-distribution of the cross section for the 12 C target. The top scale relates the angular momentum to the impact parameter via the semi-classical relation J = Kb. The total breakup cross section is shown by the solid line and the shaded area represents impact parameters less than the sum of radii.

Fig. 3. Angular distribution of cross sections for 7 Be elastic breakup on 208 Pb at 100 MeV/nucleon for the lowest 2 energy bins for each j π set. The CDCC (solid) calculation is broken down into nuclear (dotted) and Coulomb (long-dashed) contributions, and also dipole (dot-dashed) and quadrupole (shortdashed) contributions.

Coulomb field of the target [3,8]. Cross sections for these reactions are much larger and thus can provide independent measurements for the extrapolation of capture reactions to low energies. There are three main complications of breakup reactions which are not present in capture reactions: i) nuclear breakup, ii) E2 transitions [9], and iii) multistep effects [10]. Nuclear breakup is traditionally reduced by taking data at forward angles. Assuming semi-classical trajectories this restricts the reaction to large impact parameters outside the range of the nuclear force. But this alone is not enough to neglect the nuclear contribution [5]. By imposing an energy cut on the maximum relative energy between the final fragments the nuclear component can be reduced significantly. We simulate this energy cut in our calculations by including all relative energies in our calculation, but only summing up the cross section to the lowest two energy bins (fig. 3). This gives a maximum relative energy of approximately 1 MeV. In the CDCC method the continuum is discretized into energy bins for each j π of relative motion between the final fragments. The full CDCC calculation for the lowest two energy bins is shown by the solid line, while the nuclear component is shown by the dotted line. The E2 contribution to the breakup cross section was also examined in the CDCC method by including separately only dipole and only quadrupole contributions to breakup. In fig. 3 the dot-dashed line shows the dipole breakup while the quadrupole breakup is represented by the short-dashed line. We see that the E2 component has significant contributions and cannot be neglected. The breakup data on the heavy target can also be used for the extraction of astrophysical factors by the ANC method. As with the breakup data on the light target,

contributions from the interior were significant (28%), but the effect of continuum-continuum couplings was less of a problem [5]. In conclusion, we have presented calculations of 7 Be breakup on two different targets and energies. We discussed the issues concerning the extraction of astrophysical quantities from the data. We have shown that for the lighter target, large contributions from the interior and continuum-continuum couplings will have to be considered when extracting the ANC. For the Coulomb dissociation on the heavy target, significant nuclear and quadrupole contributions at forward angles can be reduced with energy cuts, but not eliminated. This work was supported by the National Superconducting Cyclotron Laboratory, Michigan State University.

References 1. E.G. Adelberger et al., Rev. Mod. Phys. 70, 1265 (1998). 2. R.H. Cyburt, B.D. Fields, K.A. Olive, Phys. Rev. D 69, 123519 (2004). 3. G. Baur, C.A. Bertulani, H. Rebel, Nucl. Phys. A 458, 188 (1986). 4. L. Trache et al., Phys. Rev. Lett. 87, 271102 (2001). 5. N.C. Summers, F.M. Nunes, Phys. Rev. C 70, 011602(R) (2004). 6. Y. Sakuragi, M. Yahiro, M. Kamimura, Prog. Theor. Phys. Suppl. 89, 136 (1986). 7. I.J. Thompson, Comput. Phys. Rep. 7, 167 (1988). 8. T. Motobayashi et al., Phys. Rev. Lett. 73, 2680 (1994). 9. B. Davids et al., Phys. Rev. Lett. 81, 2209 (1998). 10. S.B. Gazes et al., Phys. Rev. Lett. 68, 150 (1992).

Eur. Phys. J. A 25, s01, 649–650 (2005) DOI: 10.1140/epjad/i2005-06-085-1

EPJ A direct electronic only

Quasi-free 6Li(n, α)3H reaction at low energy from 2H break-up A. Tumino1,2,a , C. Spitaleri1,2 , C. Bonomo1,2,b , S. Cherubini2 , P. Figuera1 , M. Gulino1,2 , M. La Cognata1,2 , L. Lamia1,2 , A. Musumarra1,2 , M.G. Pellegriti1,2 , R.G. Pizzone2 , A. Rinollo1,2 , and S. Romano1,2 1 2

Dipartimento di Metodologie Fisiche e Chimiche per l’Ingegneria, Universit` a di Catania, Catania, Italy INFN Laboratori Nazionali del Sud, Catania, Italy Received: 3 November 2004 / c Societ` Published online: 11 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The 6 Li + d reaction was studied in order to investigate the quasi-free 6 Li(n, α)3 H reaction, off the proton in 2 H. A kinematically complete experiment was performed at a beam energy of 14 MeV. Coincidence spectra show the contribution of the quasi-free n+ 6 Li reaction in the relative energy range from 1.5 MeV down to zero. The extracted 6 Li(n, α)3 H quasi-free cross-section was compared with the behavior of direct data throughout the investigated energy range. No penetrability corrections were introduced on the quasi-free data, being the 6 Li(n, α)3 H direct reaction free of Coulomb suppression. PACS. 24.10.-i Nuclear reaction models and methods – 25.40.-h Nucleon-induced reactions

1 Introduction Quasi-free (QF) scattering and reactions have been extensively studied in the past in order to investigate the cluster structure of light nuclei [1, 2,3]. A number of theoretical approaches based on the Impulse Approximation were developed [4, 5], which describe a quasi free A+a → c+C +s reaction (a having a strong x − s cluster structure) by a Pseudo Feynman diagram where only the first term of the Feynman series is retained. A pole of the diagram describes the break-up of the target nucleus a into the clusters x and s, and the other one contains the information on the virtual A + x → c + C two-body process, which leaves the cluster s as spectator (see ref. [6]). Recently the QF mechanism was successfully applied in the framework of the known Trojan Horse Method (THM) [6, 7,8,9] to study charged particle two-body reactions relevant for astrophysics, free of Coulomb suppression and screening effects. The present paper describes an original application of the QF mechanism to the neutron capture 6 Li(n, α)3 H reaction, selected from the 6 Li + d interaction leaving the proton as spectator. Its importance relies on the chance to investigate possible off-energy-shell effects on the QF data in a situation where the Coulomb barrier is absent. This represents an important test for the Trojan Horse Method, also in view of further applications to key astrophysical reactions using deuterons as source of a neutron beam. a

Present address: Laboratori Nazionali del Sud - INFN, Via S. Sofia, 62 - 95123 Catania, Italy; e-mail: [email protected] b Conference presenter; e-mail: [email protected]

2 The experiment The 2 H(6 Li, α3 H)1 H experiment was performed at the Laboratori Nazionali del Sud in Catania. The SMP Tandem Van de Graaf accelerator delivered a 14 MeV 6 Li beam onto a CD2 target of about 150 μg/cm2 . Two silicon ΔE-E telescopes, consisting of 20 μm ΔE- and 1000 μm position-sensitive E-detector, were placed on opposite sides with respect to the beam direction covering the laboratory angles 18◦ to 28◦ and 43◦ to 53◦ . The angular ranges were chosen in order to cover momentum values ps of the undetected proton ranging from about −100 MeV/c to about 100 MeV/c when α and 3 H are detected within 18◦ –28◦ and 43◦ –53◦ , respectively. This assures that the bulk of the QF contributions for the break-up process of interest falls inside the investigated regions, allowing also to cross check the method outside the relevant phase-space regions. The trigger for the event acquisition was given by the coincidences between the two telescopes.

3 Data analysis and results The identification of the α + 3 H + p channel of interest was achieved by selecting α and 3 H loci in the ΔE-E twodimensional plots and the kinematics were reconstructed under the assumption of a proton as third particle. Sequential processes through the ground state of 5 Li or excited states of 4 He or 7 Li can also feed this channel. A way to investigate the reaction mechanism involved and to disentangle QF coincidence events from others, is to examine the shape of the experimental momentum

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Fig. 1. Experimental proton momentum distribution. The dashed line represents the shape of the theoretical Hulth´en function in momentum space.

distribution for the proton. This observable was reconstructed in plane wave impulse approximation (PWIA) by applying the energy sharing method [2] to our coincidence data. The 6 Li-n relative energy was calculated in post collision prescription in the standard way (for details see refs. [6,7, 8,9]) and windows of 100 keV were selected. In PWIA the three-body cross-section is factorized into two terms, corresponding to the two poles mentioned in the introduction:   dσ d3 σ · |Φ(ps )|2 , (1) ∝ KF dΩ dEc dΩc dΩC

where (dσ/dΩ) is the off-energy-shell differential crosssection for the 6 Li(n, α)3 H two-body reaction, KF is a kinematical factor depending on masses, momenta and angles of the outgoing particles refs. [6, 7, 8, 9], and Φ(ps ) is the Fourier transform of the radial wave function for the p-n intercluster motion inside the deuteron, described in terms of a Hulth´en function [9]. Dividing the threebody coincidence yield by KF , we are left with a quantity reflecting the behaviour of the experimental momentum distribution in arbitrary units. Indeed within relative energy ranges of 100 keV, [(dσ/dΩ)A−x ] is about constant. The result is reported in fig. 1. The dashed line superimposed on the data gives the shape of the theoretical Hulth´en function in momentum space, normalized to the experimental maximum. A quite good agreement shows up, making us confident that in the chosen kinematical region, the QF mechanism gives the main contribution to the 6 Li + d reaction and it can be selected without significant interference with contaminant sequential decay processes. The further analysis was performed by considering coincidence events with a neutron momentum ranging between −40 and 40 MeV/c. Following the PWIA approach, a Monte Carlo calculation provided kinematical factors and momentum distribution in the factorization of the cross-section. Then the two-body cross-section was derived dividing the selected three-body coincidence yield by the result of the Monte Carlo calculation. An error

Fig. 2. Comparison between QF data (full dots) and direct cross-section (open triangles) from [11].

calculation for the 6 Li-n relative energy provides a value ranging from 80 to 120 keV, the minimum estimate corresponding to the phase space region where the lens effect is more efficient [10]. The extracted off-energy shell 6 Lin two-body cross-section was then compared with direct data integrated over the same θc.m. = 40◦ –70◦ angular region, θc.m. being the emission angle for the outgoing a particle in the 3 H-α center-of-mass system [6, 7, 8,9]. Since the 6 Li-n direct data are not affected at low energy by Coulomb suppression, the comparison with our indirect cross-section could be performed throughout the investigated energy range without any further correction. The normalization to the direct behaviour was performed at the top of the resonance, around E6 Li-n = 210 keV. The comparison is shown in fig. 2, where full dots represent present data while open triangles are direct data from [11], both sets averaged out at the same energy bin of 120 keV comparable with the uncertainty. The two data sets agree quite well throughout the investigated range, including the resonant region. The good agreement validates the pole approximation for this experiment. Importantly, the present results seem to exclude off-energy shell effects on the QF cross-section other than the lack of the Coulomb suppression at sub-Coulomb energies for reactions involving charged particles.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

Dj. Miljanic et al., Nucl. Phys. A 215, 221 (1973). J. Kasagi et al., Nucl. Phys. A 239, 233 (1975). M. Lattuada et al., Nucl. Phys. A 458, 493 (1986). G.F. Chew, Phys. Rev. 80, 196 (1950). N.S. Chant, P.G. Roos, Phys. Rev. C 15, 57 (1977). C. Spitaleri et al., Phys. Rev. C 69, 055806 (2004). C. Spitaleri et al., Phys. Rev. C 60, 055802 (1999). M. Lattuada et al.., Astrophys. J. 562, 1076 (2001). A. Tumino et al., Phys. Rev. C 67, 065803 (2003). G. Baur et al., Annu. Rev. Nucl. Part. Sci. 46, 321 (1996). J.C. Overley et al., Nucl. Phys. A 221, 573 (1974).

9 Nuclear astrophysics 9.2 Theory

Eur. Phys. J. A 25, s01, 653–657 (2005) DOI: 10.1140/epjad/i2005-06-023-3

EPJ A direct electronic only

Global microscopic models for r-process calculations S. Gorielya Institut d’Astronomie et d’Astrophysique, Universit´e Libre de Bruxelles, CP 226, 1050 Brussels, Belgium Received: 15 October 2004 / c Societ` Published online: 21 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The identification of the astrophysical site and the specific conditions in which r-process nucleosynthesis takes place remain unsolved mysteries of astrophysics. The present paper illustrates the complexity of the r-process nucleosynthesis by describing the nuclear mechanisms taking place during the decompression of neutron star matter, a promising r-process site. Future challenges faced by nuclear physics in this problem are discussed, particularly in the determination of the radiative neutron capture rates by exotic nuclei close to the neutron drip line, as well as the need for improved global microscopic models for a reliable determination of all nuclear properties of relevance. PACS. 97.10.Cv Stellar structure, interiors, evolution, nucleosynthesis, ages – 32.10.Bi Atomic masses, mass spectra, abundances, and isotopes

1 Introduction The rapid neutron-capture process, or r-process, is known to be of fundamental importance for explaining the origin of approximately half of the A > 60 stable nuclei observed in nature. In recent years nuclear astrophysicists have developed more and more sophisticated r-process models, eagerly trying to add new astrophysical or nuclear physics ingredients to explain the solar system composition in a satisfactory way. The r-process remains the most complex nucleosynthetic process to model from the astrophysics as well as nuclear-physics points of view. The site(s) of the r-process is (are) not identified yet, all the proposed scenarios facing serious problems. Complex —and often exotic— sites have been considered in the hope of discovering astrophysical environments in which the production of neutrons is large enough to give rise to a successful rprocess. Progress in the modelling of type-II supernovae and γ-ray bursts has raised a lot of excitement about the so-called neutrino-driven wind model. However, until now no r-process can be simulated ab initio without having to call for an arbitrary modification of the model parameters, leading quite often to physically unrealistic scenarios. On top of the astrophysics uncertainties, the nuclear physics of relevance for the r-process is far from being under control. The nuclear properties of thousands of nuclei located between the valley of β-stability and the neutron drip line are required. These include the (n, γ) and (γ, n) rates, α- and β-decay half-lives, rates of β-delayed single and multiple neutron emission, and the probabilities of neutron-induced, spontaneous, and β-delayed fission. a

Conference presenter; e-mail: [email protected]

When considering more complex astrophysics sites like the neutrino-driven wind, proton-, α-, and neutrino-capture rates need to be estimated, too. New developments of both astrophysics and nuclear physics aspects of the r-process are discussed in this paper. Section 2 describes astrophysics aspects of the r-process nucleosynthesis with a special emphasis on the nucleosynthesis resulting from decompression of initially cold neutron star (NS) matter. It is shown how different the corresponding nuclear mechanisms responsible for the production of r-process elements can be from the more traditional scenarios in core-collapse supernovae. Section 3 is devoted to nuclear physics aspects of the r-process with the description of ground-state and nuclear matter properties within the same framework, and the estimate of the neutron-capture rates by nuclei right at the neutron drip line. Emphasis is made on global microscopic models that have recently been developed to improve the reliability of the extrapolation away from the experimentally known region.

2 Astrophysics aspects of the r-process nucleosynthesis The origin of the r-process nuclei is still a mystery. One of the underlying difficulties is that the astrophysical site (and consequently the astrophysical conditions) in which the r-process takes place has not been identified. Many scenarios have been proposed. The most favoured sites are all linked to core-collapse supernova or gamma-ray burst explosions. Mass ejection in the so-called neutrino-driven

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wind from a nascent NS or in the prompt explosion of a supernova in the case of a small iron core or an O-Ne-Mg core have been shown to give rise to a successful r-process provided the conditions in the ejecta are favorable with respect to high wind entropies, short expansion timescales or low electron number fractions. Although these scenarios remain promising, especially in view of their significant contribution to the galactic enrichment [1], they remain handicapped by large uncertainties associated mainly with the still incompletely understood mechanism that is responsible for the supernova explosion and the persistent difficulties to obtain suitable r-process conditions in selfconsistent dynamical models. In addition, the composition of the ejected matter remains difficult to ascertain due to the remarkable sensitivity of r-process nucleosynthesis to the uncertain properties of the ejecta. Another candidate site has been proposed as possibly contributing to the galactic enrichment in r-nuclei. It concerns the decompression of initially cold NS matter [2,3, 4, 5]. In particular, special attention has been paid to NS mergers due to their large neutron densities and the confirmation by hydrodynamic simulations that a non-negligible amount of matter can be ejected [6,7]. Although recent calculations of the galactic chemical evolution [1] tend to rule out NS mergers as the dominant r-process site, it was shown in [5] that this site, or more generally the ejection of initially cold decompressed NS matter in any possible astrophysical scenario, could be one of the most promising r-process sites. In such a scenario, the nuclear flow towards the production of r-process nuclei is fundamentally different than the one imagined in core-collapse supernovae. The highdensity matter constituting the NS inner crust (at typical densities of ρ  1014 g/cm3 ) is initially at β-equilibrium. The matter composition is characterized by the electron fraction Ye = 0.03 corresponding to a Wigner-Seitz cell made of a Z = 39 protons and N = 157 neutrons immersed in a neutron sea. As discussed in sect. 3, the initial cell characteristics is sensitive to the effective interaction considered in the nuclear matter equation of state. When the matter starts to expand, the density drop leads to a reduction of the number of neutrons enclosed in the cell, but also to some β-transitions as soon as the respective chemical potentials of neutrons, protons and electrons are such that μn −μp −μe > 0 to allow for a neutron to decay into a proton. As the matter reaches the neutron drip line at densities around the drip density of ρdrip  3·1011 g/cm3 , it is composed of drip nuclei distributed over a relatively large range of elements with Z = 40–70 and of free neutrons at a typical density of Nn  1035 cm−3 . The subsequent decompression leads to a nuclear flow which is closer to the “traditional” r-process, i.e. a competition between radiative neutron captures, photodisintegrations, β-decays. In addition, fission processes comes into play as soon as heavy fissioning species are reached. Fission as well as β-decays are also held responsible for a possible increase of the local temperature. As an example, fig. 1 illustrates the final abundance distribution obtained after the decompression of a clump

r-abundances [Si=10 ]

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of material at an initial density ρ = 1014 g/cm3 . The abundance distribution for A > 140 is in relatively good agreement with the solar pattern. In particular the A = 195 peak is found at the right place with the right width. It should be stressed that such an r-abundance distribution results from a sequence of nuclear mechanisms that significantly differ from those traditionally invoked to explain the solar r-abundances, namely the establishment of an (n, γ) − (γ, n) equilibrium followed by the β-decay of the corresponding waiting point. In the present scenario, the neutron density is initially so high that the nuclear flow follows for the first hundreds of ms after reaching the drip density a path touching the neutron drip line. Fission keeps on recycling the material (about 4 times in the example of fig. 1). After a few hundreds of ms, the density has dropped by a few orders of magnitude and the neutron density experiences a dramatic fall-off when neutrons get exhausted by captures. During this period of time, the nuclear flow around the N = 126 region follows the isotonic chain. When the neutron density reaches some Nn = 1020 cm−3 , the timescale of neutron capture for the most abundant N = 126 nuclei becomes larger than a few seconds, and the nuclear flow is dominated by β-decays back to the stability line. In conclusion, the similarity between the predicted and solar abundance patterns as well as the robustness of the prediction against variations of input parameters make this site one of the most promising that deserves further exploration with respect to various aspects such as nucleosynthesis, hydrodynamics and galactic chemical evolution. More details on the decompression of NS matter can be found in [5] and references therein. This site was described here to illustrate how complex the nuclear mechanisms responsible for the solar r-abundance distribution can be, but also how difficult it remains to ascertain the role of nuclear physics for r-process applications without a clear astrophysics hint about the “real” site. From a nuclear physics point of view, the decompression of NS material is indeed extremely challenging. In addition to the usual requirement for nuclear masses and β-decay rates, as in the traditional scenarios, a detailed knowledge of

S. Goriely: Global microscopic models for r-process calculations

the radiative neutron capture rates as well as the neutroninduced, spontaneous and β-delayed fission rates is needed for nuclei up to the neutron drip line. Furthemore, the expansion of the high-density NS material needs a detailed description of the nuclear matter equation of state, including its β-decay transition probabilities. Some of these nuclear ingredients are discussed in the next section.

3 Nuclear physics aspects of the r-process nucleosynthesis Although a great effort has been devoted in recent years to measuring decay half-lives and reaction cross-sections, the r-process involves so many (thousands) unstable exotic nuclei for which so many different properties need to be known that only theoretical predictions can fill the gaps. As illustrated in the previous section, to follow the r-process during the decompression of initially cold NS matter, a detailed knowledge of the various nuclear properties up to and beyond the neutron drip line is required. To fulfill these specific requirements, two major features of nuclear theory must be contemplated, namely its microscopic and universal aspects. A microscopic description by a physically sound model based on first principles ensures a reliable extrapolation away from the experimentally known region. On the other hand, a universal description of all nuclear properties within one unique framework for all nuclei involved ensures a coherent prediction of all unknown data. A special effort has been made recently to derive all the nuclear ingredients of relevance in reaction theory on the basis of global microscopic models [8]. Some of these issues are discussed now.

3.1 Nuclei and nuclear matter properties As detailed in [9], a series of Hartree-Fock-Bogolyubov (HFB) mass formulas have recently been constructed. Such HFB calculations are based on a conventional Skyrme force with a density dependent or independent pairing interaction treated in the full Bogolyubov framework with restoration of broken symmetries. A set of 8 mass tables, referred to as HFB-2 to HFB-9, were designed by adjusting the Skyrme force and pairing parameters (the corresponding forces are labeled BSk2 to BSk9, respectively). All mass tables reproduce the full set of 2149 experimental masses [10] with a high level of accuracy, i.e. with an r.m.s. error of about 0.65 MeV, except in the case of HFB-9, for which the constraint on a high nuclear-matter symmetry coefficient J = 30 MeV raises the r.m.s. value to 0.73 MeV. To test further their predictive power, the HFB calculations were extensively compared to additional observables, namely charge radii and densities, quadrupole moments, giant resonances, nuclear matter properties, (. . . ). As far as the mass extrapolation is concerned, their analysis led to the conclusion that, so far, all these different HFB mass formulas give essentially equivalent predictions, deviations smaller than

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about 5 MeV being found for more than 8000 nuclei with 8 ≤ Z ≤ 110 lying between the two driplines. In the context of the r-process nucleosynthesis, it must be stressed that the latest HFB-9 mass table has been designed in order to enable a consistent modelling of the transition from nuclear matter to nuclei, as required in the description of the decompression of initially cold NS matter. More specifically, to conform with realistic calculations of neutron matter at high densities (e.g., [11]), the latest BSk9 force was constrained [9,12] in such a way that the effective isoscalar nucleon mass M ∗ = 0.8, the incompressibility Kv = 231 MeV and the symmetry coefficient J = 30 MeV. The latter constraint is of particular relevance since it leads to a neutron matter energy per nucleon in excellent agreement with the Friedman and Pandharipande [11] predictions (see [9] for more details). The corresponding Skyrme force is consequently well suited to estimate the initial composition of the NS crust, but also to provide all thermodynamic quantities of relevance during the decompression of the nuclear matter down to densities close to the drip density (below the drip density, the HFB-9 masses provide a consistent description of the nuclear properties). The value adopted for J is of particular importance, especially for a reliable estimate of the initial composition in the NS inner crust. As mentioned above, within the Thomas-Fermi approximation, the β-equilibrated matter at a density of ρ  1014 g/cm3 is composed of Z = 39 and N = 157 cells if use is made of the BSk9 force. However, if we consider instead the BSk8 force which is formally equivalent to BSk9 at the exception of being characterized by J = 28 MeV, the corresponding cells are typically made of Z = 82 protons and N = 475 neutrons. The initial conditions for the r-process nucleosynthesis are consequently strongly affected. Future accurate measurements of the neutron-skin thickness of finite nuclei will hopefully help in further constraining the value of J. More details, can be found in [12]. 3.2 Nuclear level densities Nuclear level densities (NLD) are known to play an essential role in reaction theory. Until recently, only classical analytical models of NLD were used for practical applications. In particular, the back-shifted Fermi gas model (BSFG) —or some variant of it— remains the most popular approach to estimate the spin-dependent NLD, particularly in view of its ability to provide a simple analytical formula. However, none of the important shell, pairing and deformation effects are properly accounted for in any analytical description and therefore large uncertainties are expected, especially when extrapolating to very low (a few MeV) or high energies (U  15 MeV) and/or to nuclei far from the valley of β-stability. Several approximations used to obtain the NLD expressions in an analytical form can be avoided by quantitatively taking into account the discrete structure of the single-particle spectra associated with realistic average potentials. This approach has the advantage of treating in a natural way shell, pairing and deformation effects on

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N Fig. 2. Representation in the (N, Z)-plane of the total number of levels within a 0.25 MeV energy range above the neutron separation energy. The number of levels is estimated with the HFBCS model of [13]. Only nuclei up to the HFBCS-1 neutron drip line [14] are shown.

all the thermodynamic quantities. The computation of the NLD by this technique corresponds to the exact result that the analytical approximation tries to reproduce, and remains by far the most reliable method for estimating NLD (despite inherent problems related to the choice of the single-particle configuration and pairing strength). The NLD estimated within the statistical approach based on a HFBCS ground-state description was shown [13] to reproduce experimental data (neutron resonance spacings) with the same degree of accuracy as the global BSFG formulas. The HFBCS model provides in a consistent way the single-particle level scheme, pairing strength, as well as the deformation parameter and energy. The HFBCS-based NLD significantly differ from those determined within analytical BSFG-type approaches, even at low energies close to the neutron separation energy. NLD are not only a fundamental ingredient for the estimate of reaction cross-sections, but also to define somehow the type of reaction mechanisms that are more likely to dominate. So far, all r-process calculations have made use of neutron capture rates evaluated within the HauserFeshbach statistical model. Such a model makes the fundamental assumption that the capture process takes place through the intermediary formation of a compound nucleus in thermodynamic equilibrium. The formation of a compound nucleus is usually justified if the level density in the compound nucleus at the projectile incident energy is large enough. However, when dealing with exotic neutronrich nuclei, the number of available states in the compound system is relatively small and the validity of the HauserFeshbach model is questionable. In this case, the neutron capture process might be dominated by direct electromagnetic transitions to a bound final state rather than through the formation of a compound nucleus. To estimate the possible contribution of the direct capture mechanism, fig. 2 gives the total number of levels available in the compound nucleus in an energy range of 0.25 MeV above the neutron separation energy. This interval corresponds to the relevant range of interest for low-energy neutron captures at a typical r-process temperature of about 109 K. As seen

in fig. 2, many of the nuclei close to the neutron drip line are predicted to have less than 2 levels in the relevant energy range, so that a resonance capture becomes very unlikely. In these conditions, the direct mechanism may dominate. The direct neutron capture rates have been estimated for exotic neutron-rich nuclei [5, 15, 16] using a modified version of the potential model to avoid the uncertainties affecting the single-particle approach based on the one-neutron particle-hole configuration. Because of the crucial sensitivity of the direct capture cross-section to the spin and parity assignment of the low-energy states in the residual nucleus, only a microscopic combinatorial model of NLD is appropriate. Global calculations within the combinatorial method using the HFB single-particle level scheme and δ-pairing force have now become available [17] and could certainly provide in a near future an accurate and reliable estimate of the intrinsic spin- and paritydependent level density, and in that respect improve the determination of the resonant as well as direct contributions to the neutron capture by exotic neutron-rich nuclei.

4 γ-ray strength function The total photon transmission coefficient from a compound nucleus excited state is one of the key ingredients for statistical cross-section evaluation. The photon transmission coefficient is most frequently described in the framework of the phenomenological generalized Lorentzian model of the giant dipole resonance (GDR) [16, 18]. Until recently, this model has even been the only one used for practical applications, and more specifically when global predictions are requested for large sets of nuclei. The Lorentzian GDR approach suffers, however, from shortcomings of various sorts. On the one hand, it is unable to predict the enhancement of the E1 strength at energies below the neutron separation energy demonstrated by different experiments. On the other hand, even if a Lorentzian function provides a suitable representation of the E1 strength, the location of its maximum and its width remain to be predicted from some underlying model for each nucleus. For astrophysics applications, these properties have often been obtained from a droplet-type model [19]. This approach clearly lacks reliability when dealing with exotic nuclei. In view of this situation, combined with the fact that the GDR properties and low-energy resonances may influence substantially the predictions of radiative capture cross-sections, it is clearly of substantial interest to develop models of the microscopic type which are hoped to provide a reasonable reliability and predictive power for the E1-strength function. Attempts in this direction have been conducted within the Quasi-Particle Random Phase Approximation (QRPA) model based on a realistic Skyrme interaction. The QRPA E1-strength functions obtained within the HFBCS [20] as well as HFB framework [21] have been shown to reproduce satisfactorily the location and width of the GDR and the average resonance capture data at low energies. The aforementioned QRPA

<σv> (HFB) / <σv> (Hybrid)

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calculations have been extended to all the 8 ≤ Z ≤ 110 nuclei lying between the two drip lines. In the neutrondeficient region as well as along the valley of β-stability, the QRPA distributions are very close to a Lorentzian profile. However, significant departures from a Lorentzian are found for neutron-rich nuclei. In particular, QRPA calculations [20, 21] show that the neutron excess affects the spreading of the isovector dipole strength, as well as the centroid of the strength function. The energy shift is found to be larger than predicted by the usual A−1/6 or A−1/3 dependence given by the phenomenological liquid drop approximations [19]. In addition, some extra strength is predicted to be located at sub-GDR energies, and to increase with the neutron excess. Even if it represents only about a few percents of the total E1 strength, as shown in fig. 3, it can be responsible for an increase by up to an order of magnitude of the radiative neutorn capture rate by exotic neutron-rich nuclei with respect to the rate obtained with Lorentz-type formulas (for more details, see [20,21]). It should, however, be kept in mind that for such exotic nuclei, as shown in the previous section, the statistical model might not be valid.

5 Conclusions Most of the problems faced in understanding the origin of r-process elements and observed r-abundances are related to our ignorance of the astrophysical site that is capable of providing the required large neutron flux. In this respect, understanding the r-process nucleosynthesis is essentially an astrophysics issue that will require improved hydrodynamic models to shed light on possible scenarios. Different sites have been proposed, the currently most favoured ones being related to neutrino-driven outflow during su-

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pernova or γ-ray burst explosions, but also to the ejection of initially cold decompressed NS matter. Depending on the astrophysics site, the associated nuclear physics needs can be quite different. At the present time, ignoring the exact r-process site, the only possible strategy is to determine β-decay, neutron-capture, photodisintegration and fission rates for all nuclei which are situated between the valley of β-stability and the neutron drip line. The equation of state of nuclear matter might also play an important role in the determination of the r-process initial conditions. The extrapolation to exotic nuclei constrains the use of nuclear models to the most reliable ones, even if empirical approaches sometime present a better ability to reproduce experimental data. A continued effort is required to improve global microscopic models for a more accurate and reliable description of ground-state properties, nuclear level densities, γ-ray strength functions and optical model potentials (especially for deformed nuclei). This effort is concomitant with new measurements of masses and ground state properties far away from stability, but also reaction cross-sections on stable targets.

References 1. D. Argast, M. Samland, F.-K. Thielemann, Y. Qian, Astron. Astrophys. 416, 997 (2004). 2. J.M. Lattimer, F. Mackie, D.G. Ravenhall, D.N. Schramm, Astrophys. J. 213, 225 (1977). 3. B.S. Meyer, Astrophys. J. 343, 254 (1989). 4. C. Freiburghaus, S. Rosswog, F.-K. Thielemann, Astrophys. J. 525, L121 (1999). 5. S. Goriely, P. Demetriou, H.-J. Janka, J.M. Pearson, M. Samyn, to be published in Nucl. Phys. A (2005). 6. H.-T. Janka, T. Eberl, M. Ruffert, C.L. Fryer, Astrophys. J. 527, L39 (1999). 7. S. Rosswog, R. Speith, G.A. Wynn, Mon. Not. R. Astron. Soc. 351, 1121 (2004). 8. S. Goriely, Nucl. Phys. A 718, 287c (2003). 9. S. Goriely, M. Samyn, J.M. Pearson, E. Khan, these proceedings. 10. G. Audi, A.H. Wapstra, C. Thibault, Nucl. Phys. A 729, 337 (2003). 11. B. Friedman, V.R. Pandharipande, Nucl. Phys. A 361, 502 (1981). 12. S. Goriely, M. Samyn, J.M. Pearson, M. Onsi, Nucl. Phys. A 750, 425 (2005). 13. P. Demetriou, S. Goriely, Nucl. Phys. A 695, 95 (2001). 14. S. Goriely, F. Tondeur, J.M. Pearson, At. Data Nucl. Data Tables 77, 311 (2001). 15. S. Goriely, Astron. Astrophys. 325, 414 (1997). 16. S. Goriely, Phys. Lett. B 436, 10 (1998). 17. S. Hilaire, J.P. Delaroche, M. Girod, Eur. Phys. J. A 12, 169 (2001). 18. J. Kopecky, M. Uhl, Phys. Rev. C 41, 1941 (1990). 19. W.D. Myers, W.J. Swiatecki et al., Phys. Rev. C 15, 2032 (1977). 20. S. Goriely, E. Khan, Nucl. Phys. A 706, 217 (2002). 21. S. Goriely, E. Khan, M. Samyn, Nucl. Phys. A 739, 331 (2004).

Eur. Phys. J. A 25, s01, 659–664 (2005) DOI: 10.1140/epjad/i2005-06-133-x

EPJ A direct electronic only

Shell-model applications in supernova physics G. Mart´ınez-Pinedoa ICREA and Institut d’Estudis Espacials de Catalunya, Universitat Aut` onoma de Barcelona, E-08193 Bellaterra, Spain Received: 16 January 2005 / c Societ` Published online: 29 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. This manuscript reviews recent applications of the nuclear shell-model for the calculation of several quantities relevant for the core-collapse supernova dynamics and nucleosynthesis. These include electron capture rates and neutrino-nucleus cross sections for inelastic scattering. It is shown that electron capture rates on nuclei dominates over capture on free protons during the collapse leading to significant changes in the hydrodynamics of core collapse and bounce. Neutrino-nucleus cross sections at supernova neutrino energies can be determined from precise data on the magnetic dipole strength. The results agree well with large-scale shell-model calculations, validating this model. PACS. 21.60.Cs Shell model – 26.50.+x Nuclear physics aspects of novae, supernovae, and other explosive environments

1 Introduction Stars with masses exceeding roughly 10 M reach a moment in their evolution when their iron core provides no further source of nuclear energy generation. At this time, they collapse and, if not too massive, bounce and explode in spectacular events known as type II or Ib/c supernovae. These explosions mark the formation of a neutron star or black hole at the end of the life of the star and play a preeminent role in the nucleosynthesis and chemical evolution of the galaxy. The evolution in the core is determined by the competition of gravity, that produces the collapse of the core, and the weak interaction, that determines the rate at which electrons are captured and the rate at which neutrinos are trapped during the collapse. The early phases, known as presupernova evolution, follow the late-stage stellar evolution until core densities just below 1010 g cm−3 and temperatures between 5 and 10 GK are reached. Stellar evolution until this time requires the consideration of an extensive nuclear network, but is simplified by the fact that neutrinos need only be treated as a sink of energy and lepton number. This is no longer valid at later stages of the collapse: as the weak interaction rates increase with the increasing density, the neutrino mean free paths become shorter so that the neutrinos eventually proceed through all phases of free streaming, diffusion, and trapping. An adequate handling of the transitions between these transport regimes necessitates a detailed time- and space-dependent bookkeeping of the neutrino distributions in the core. a

Conference presenter; e-mail: [email protected]

Advantageously, the temperature during the collapse and explosion are high enough that the matter composition is given by nuclear statistical equilibrium without the need of reaction networks for the strong and electromagnetic interactions. As the entropy is low during the collapse, the matter composition is dominated by the nuclei with the largest binding energy for a given Ye (defined as the number of electrons per nucleon). In order to correctly determine the evolution of the system a reliable estimate of the different weak interaction rates on the nuclei present is necessary [1]. In the early phases of the collapse (presupernova evolution) the main weak interaction processes are electron/positron capture and β ± decays. Later during the collapse neutrino matter interactions and in particular inelastic processes are also important. Of these neutrinonucleus inelastic scattering is currently not considered in collapse simulations. The calculation of the different rates is a challenging problem in nuclear structure. Moreover, due to the large temperatures and densities present in the astrophysical environment their calculation presents some peculiarities that are discussed in the following sections.

2 Presupernova evolution The main weak interaction processes during the final evolution of a massive star are electron capture and beta decays. Its determination requires the calculation of Fermi and Gamow-Teller (GT) transitions. While the treatment of Fermi transitions (important only for beta decays) is straightforward, a correct description of the GT transitions is a difficult problem in nuclear structure. In the astrophysical environment nuclei are fully ionized,

so electrons are captured from the degenerate electron plasma. The energies of the electrons are high enough to induce transitions to the Gamow-Teller resonance. Shortly after the discovery of this collective excitation Bethe et al. [2] recognized its importance for stellar electron capture. This process is mainly sensitive to the location, fragmentation and total strength of the GamowTeller resonance. The presence of a degenerate electron gas blocks the phase space for the produced electron in beta decay. Then, the decay rate of a given nuclear state is greatly reduced or even completely blocked at high densities. However, due to the finite temperature, excited states in the decaying nucleus can be thermally populated. Some of these states are connected by large GT transitions to low-lying states in the daughter nucleus, which with increased phase space can significantly contribute to the stellar beta decay rates. The importance of these states in the parent nucleus for the beta decay was first recognized by Fuller, Fowler and Newman (FFN) [3,4, 5, 6], who coined the term “backresonances”. Over the years many calculations of weak interaction rates for astrophysical applications have become available [7, 8,9, 10, 11,12,13]. For approximately 15 years, though, the standard in the field were the tabulations of Fuller, Fowler and Newman [3, 4,5,6]. These authors calculated rates for electron capture, positron capture, beta decay and positron emission plus the associated neutrino losses for all the astrophysical relevant nuclei ranging in mass number from 21 to 60. Their calculations were based upon an examination of all available experimental information in the mid 1980s for individual transitions between ground states and low-lying excited states in the nuclei of interest. Recognizing that this only saturated a small part of the Gamow-Teller distribution, they added the collective strength via a single-state representation whose position and strength was parametrized using an independent particle model. Recent experimental data on GT distributions in iron group nuclei [14, 15,16, 17,18,19,20,21], measured in charge exchange reactions [22, 23], show that the GT strength is strongly quenched (reduced), compared with the independent-particle-model value, and fragmented over many states in the daughter nucleus. Both effects are caused by the residual interaction among the valence nucleons. An accurate description of these correlations is essential for a reliable evaluation of the stellar weakinteraction rates due to the large dependence of the available phase-space on the electron energy, particularly for the stellar electron-capture rates [3,24]. The shell model is the only known tool to reliably describe GT distributions in nuclei [25]. Indeed, ref. [26] demonstrated that the shell model reproduces very well all measured GT+ distributions (in this direction a proton is converted to a neutron, as in electron capture) for nuclei in the iron mass range and gives a very reasonable account of the experimentally known GT− distributions (in this direction a neutron is converted to a proton, as in β decay). However, the limited experimental resolution (∼ 1 MeV) achieved by the pioneering (n, p)-type charge-exchange experiments did not

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allow for a detailed determination of the fragmentation of the GT strength in individual states. Very recently, highresolution GT+ distributions measured at KVI, via the (d, 2 He) reaction, have become available for two iron group nuclei, 51 V [27] and 58 Ni [28]. The experimental data for 51 V are compared in fig. 1 with a shell-model calculation using the KB3G interaction [29]. Several years ago, it was pointed out that the interacting shell model is the method of choice for the calculation of stellar weak-interaction rates [13,30, 31,32,33]. Following the work of ref. [25], shell-model rates for all the relevant weak processes for sd-shell nuclei (A = 17–39) were calculated in ref. [34]. This work was then extended to heavier nuclei (A = 45–65) based on shell-model calculations in the complete pf -shell [24,35]. Following the spirit of FFN, the shell model results have been replaced by experimental data (energy positions, transition strengths) wherever available. Reference [24] compares the shell-model–based rates with the ones computed by FFN. The shell-model rates are nearly always smaller than the FFN ones at the relevant temperatures and densities. The differences are caused by a reduction of the Gamow-Teller strength (quenching) compared to the independent-particle-model value and a systematic misplacement of the Gamow-Teller centroid (mean energy value of the Gamow-Teller distribution) in nuclei depending on the pairing structure. In some cases, experimental data that were not available to Fuller, Fowler and Newman, but could be used now, led to significant changes.

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To understand the effect of these differences it is illustrative to investigate the role of the weak-interaction rates in greater detail. The evolution of Ye during the presupernova phase is plotted in fig. 2. Weak processes become particularly important in reducing Ye below 0.5 after oxygen depletion (∼ 107 s and 106 s before core collapse for the 15 M and 25 M stars, respectively) and Ye begins a decline which becomes precipitous during silicon burning. Initially electron capture occurs much more rapidly than beta decay. As the shell-model rates are generally smaller than the FFN electron capture rates, the initial reduction of Ye is smaller in the new models; the temperature in these models is correspondingly larger as less energy is radiated away by neutrino emission. An important feature of the new models is shown in the left panel of fig. 2. For times between 104 and 103 s before core collapse, Ye increases due to the fact that beta decay becomes temporarily competitive with electron capture after silicon depletion in the core and during silicon shell burning. This had been foreseen in ref. [37]. The presence of an important beta decay contribution has two effects. Obviously it counteracts the reduction of Ye in the core, but equally important, beta decays are an additional neutrino source and thus they add to the cooling of the core and a reduction in entropy. This cooling can be quite efficient as often the average neutrino energy in the involved beta decays is larger than for the competing electron captures. As a consequence the new models have significantly lower core temperatures than the WW models after silicon burning. At later stages of the collapse, beta decay becomes unimportant again as an increased electron chemical potential drastically reduces the phase space. We note that the shell model weak interaction rates predict the presupernova evolution to proceed along a temperature-density-Ye trajectory where the weak processes are dominated by nuclei rather close to stability. Thus it will be possible, after next generation radioactive ion-beam facilities become operational, to further con-

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strain the shell-model calculations by measuring relevant GT distributions for unstable nuclei by charge-exchange reaction, where we emphasize that the GT+ distribution is also crucial for stellar β-decays [31]. Figure 2 identifies those nuclei which dominate (defined by the product of abundance times rate) the electron capture during various stages of the final evolution of 15 M and 25 M stars. An exhaustive list of the most important nuclei for both electron capture and beta decay during the final stages of stellar evolution for stars of different masses is given in ref. [38].

3 Electron capture during the collapse Calculations of the reaction rate for electron capture in the collapsing core requires two components: the appropriate electron capture reaction rates and the knowledge of the nuclear composition. The coupling of electron capture rates to energy-dependent neutrino transport adds an additional requirement: information about the spectra of emitted neutrinos. These spectra can be parametrized using the prescription of ref. [39]. During the collapse most of the collapsing matter survives in heavy nuclei as the entropy is rather low [2]. Ye decreases during the collapse due to electron capture, making the matter composition more neutron rich and hence favoring increasingly heavy nuclei. Unlike in stellar evolution and supernova nucleosynthesis simulations, where the nuclear composition is tracked in detail via a reaction network [40, 41], the composition used in supernova simulations is calculated by the equation of state, which assumes nuclear statistical equilibrium (NSE). Typically, the information about the nuclear composition provided by the equation of state is limited to the mass fractions of free neutrons and protons, α particles and the sum of all heavy nuclei, as well as the identity of an average heavy nucleus, calculated either in the liquid drop framework [42] or based on a relativistic mean field model [43,44]. It should be noted that the most abundant nucleus is not necessarily the nucleus which dominate electron capture during the infall phase. For the evaluation of reaction rates on nuclei, due to the dependence on nuclear structure effects, a single nucleus approximation is not sufficient. It must be replaced by an ensemble average. Traditionally, in collapse simulations the treatment of electron capture on nuclei is schematic and rather simplistic. The nuclear structure required to derive the capture rate is then described solely on the basis of an independent-particle model for iron-range nuclei, i.e., considering only Gamow-Teller transitions from f7/2 protons to f5/2 neutrons [2,45,46,47]. In particular, this model predicts that electron capture vanishes for nuclei with neutron number N ≥ 40, arguing that Gamow-Teller transitions are blocked due to the Pauli principle, as all possible final neutron orbitals are already occupied in nuclei with N ≥ 40 [48]. These nuclei dominate the composition for densities larger than a few 1010 g cm3 . As a consequence of the model applied in previous collapse simulations, electron capture on nuclei ceases at these densities and the capture is entirely due to free protons. It has been

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pointed out [49] that this picture is too simple and that the blocking of the Gamow-Teller transitions will be overcome by thermal excitations which either moves protons into the g9/2 orbit or removes neutrons from the pf -shell, in both ways unblocking the GT transitions. According to the work of ref. [49], due to “thermal unblocking” GT transitions dominate again for temperatures of the order of 1.5 MeV. A more important unblocking effect, which is already relevant at lower temperatures is expected from the residual interaction which will mix the g9/2 and higher orbitals with the pf shell [50, 51]. The calculation of electron capture on nuclei during the collapse phase requires a model that is able to describe the correlations and at the same time the high density of levels that can be thermally populated at moderate excitation energies. Direct shell-model diagonalizations are not yet possible due to the large model spaces involved. The calculations can be done using the Shell Model Monte Carlo approach [52] which allows for the calculation of nuclear properties at finite temperature in unprecedentedly large model spaces. This model complemented with Random Phase Approximation calculations for the computation of the transitions necessary for the determination of the electron capture rate has been used recently for the calculation of the relevant rates for nuclei in the mass range A = 65–112 [51]. Figure 3 compares the electron capture rates for free protons and selected nuclei along a stellar trajectory taken from [53]. These nuclei are abundant at different stages of the collapse. For all the nuclei, the rates are dominated by GT transitions at low densities, while forbidden transitions contribute sizably for ρ  1011 g cm−3 . The electron chemical potential μe and the reaction Q value are the two important energy scales of the capture process. For the lowest densities the electron chemical potential (μe ≈ 6 MeV for ρ = 5 × 109 g cm−3 ) is of the same order than the typical nuclear Q-value. Then, the electron capture rates on nuclei are very sensitive to the Q-value and smaller than the rate on protons. For higher densities the chemical potential grows much faster than the Q-value and the rate becomes independent of the heavy nucleus. Due to the much smaller Q-value, the electron capture rate on free protons is larger than the rates on the abundant nuclei during the collapse. However, this is misleading as the low entropy keeps the protons significantly less abundant than heavy nuclei during the collapse. As the commonly used equations of state [42, 43, 44] do not provide any detailed information for the abundances of heavy nuclei, a Saha-like NSE was used for the calculation of the abundances in refs. [51,54]. Once the rate for electron abundances are considered the reaction  capture on heavy nuclei (Rh = i Yi λi , where the sum runs over all the nuclei present and Yi denotes the number abundance of species i) dominates over the one of protons (Rp = Yp λp ) by roughly an order of magnitude throughout the collapse (lower panel, fig. 3) [51,54]. The main consequences of the improved treatment of electron capture rates on nuclei for the collapse have been explored in self-consistent one-dimensional neutrino radi-

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ation hydrodynamics by the Oak Ridge and Garching collaborations [54, 55]. With the improved treatment of electron capture rate on heavy nuclei the total electron capture rate (heavy nuclei plus protons) is larger than previously assumed resulting in a smaller value of Ye . This translates into a smaller size of the homologous core (proportional to Ye2 ) so that the shock wave, which is generated at the edge of the homologous core, has to traverse more material in the new models which appears to make successful explosions more difficult. However, the reduction in capture rates for lighter nuclei (A = 45–65, see sect. 2), which are abundant further out in the core alters the core profile as well and in fact makes the shock wave travel to slightly larger radii in the new supernova models [54]. Nevertheless, the new one-dimensional models do not explode. However, the changes in entropy and lepton gradients may significantly alter the location, extent and strength of the proto-neutron star convection [54, 56]. Figure 4 shows the typical differences between the old supernova simulations (without capture on nuclei) and the new ones for the velocity and Ye core profiles at the moment of shock formation.

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4 Neutrinos in supernova Neutrinos play an important role in core-collapse supernova dynamics and nucleosynthesis. During the collapse the interaction of neutrinos with matter (mainly elastic scattering with nuclei) leads to neutrino trapping. Once the neutrinos are trapped, they achieve thermal equilibrium with matter via inelastic processes. One process so far neglected in simulations but that can be relevant for the thermalization during infall [58] is inelastic neutral-current neutrino-nucleus scattering. Neutrinonucleus cross sections are also important for the r-process nucleosynthesis and in the synthesis of certain elements such as 11 B and 19 F and 138 La by the so-called νprocess [59]. As the ν-process involves both neutralcurrent and charge-current reactions it can provide quite useful constrains for the supernova spectra of νe and νμ , ντ neutrinos [60]. Currently no data for inelastic neutrino-nucleus scattering are available (except for the ground state transition to the T = 1 state at 15.11 MeV in 12 C). A dedicated detector at the Oak Ridge spallation neutron source has been proposed to measure some neutrino-nucleus cross sections relevant for core-collapse supernova (mainly in the iron mass range) [61]. To sharpen the experimental program at this facility and to improve supernova simulations, inelastic neutrino-nucleus cross sections should be incorporated into the supernova models. Based in shellmodel (for the GT transitions) and RPA calculations (for the forbidden transitions) we have recently calculated the required cross sections for around 50 nuclei in the iron mass range [62]. The theoretical calculations can be constrained by precise M 1 data, obtained by inelastic electron scattering, as they supply the required information

Fig. 5. Neutrino-nucleus cross sections calculated from the M 1 data (solid lines) and the shell-model GT0 distributions (dashed). The dot-dashed line shows the cross section once finite temperature effects are included.

about the GT0 distribution which determines the inelastic neutrino-nucleus cross sections for supernova neutrino energies [63]. The reason is that for M 1 transitions the isovector part dominates and the spin part of the isovector M 1 operator is proportional to the spin part of the GT0 operator. Thus, experimental M 1 data provides the needed GT0 information to determine supernova neutrinonucleus cross sections provided that the isoscalar and orbital pieces present in the M 1 operator can be neglected or removed. This can be easily done as the orbital and spin M 1 responses are well separated energetically and moreover the orbital part is strongly related to deformation and suppressed in spherical nuclei, like 50 Ti, 52 Cr and 54 Fe. These nuclei have the additional advantage that M 1 data exist from high-resolution inelastic electron scattering experiments [64]. We have carried out shell-model calculations for the GT0 and various components of the M 1 response in these nuclei. The shell-model calculations reproduce the data rather well [63]. Figure 5 compares the inelastic neutrino-nucleus cross section for 52 Cr (results for the other two nuclei are available on [63]) computed from the M 1 data and the shell-model calculations. This comparison validates the shell-model as a tool for the calculation of the relevant supernova neutrino-nucleus cross sections. This model can then be used for the calculation of the cross sections at the finite temperature in the astrophysical environment. The main effect of finite temperature is an enhancement of cross sections for low energy neutrinos [63,65].

This work is partly supported by the Spanish MEC and the European Union ERDF under contracts AYA2002-04094-C03-02 and AYA2003-06128. It is a pleasure to thank our collaborators D.J. Dean, W.R. Hix, H.Th. Janka, A. Juodagalvis, K. Langanke, M. Liebend¨ orfer, O.E.B. Messer, A. Mezzacappa, P. von Neumann-Cosel, A. Richter, J. Sampaio.

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37. M.B. Aufderheide, I. Fushiki, G.M. Fuller, T.A. Weaver, Astrophys. J. 424, 257 (1994). 38. A. Heger, S.E. Woosley, G. Mart´ınez-Pinedo, K. Langanke, Astrophys. J. 560, 307 (2001). 39. K. Langanke, G. Mart´ınez-Pinedo, J.M. Sampaio, Phys. Rev. C 64, 055801 (2001). 40. S.E. Woosley, in Nucleosynthesis and Chemical Evolution, edited by B. Hauck, A. Maeder, G. Meynet, Vol. 16 of Saas-Fee Advanced Courses (Geneva Observatory, 1986) pp. 1-195. 41. W.R. Hix, F.-K. Thielemann, Astrophys. J. 511, 862 (1999). 42. J.M. Lattimer, F.D. Swesty, Nucl. Phys. A 535, 331 (1991). 43. H. Shen, H. Toki, K. Oyamatsu, K. Sumiyoshi, Nucl. Phys. A 637, 435 (1998). 44. H. Shen, H. Toki, K. Oyamatsu, K. Sumiyoshi, Prog. Theor. Phys. 100, 1013 (1998). 45. S.W. Bruenn, Astrophys. J. Suppl. 58, 771 (1985). 46. A. Mezzacappa, S.W. Bruenn, Astrophys. J. 405, 637 (1993). 47. A. Mezzacappa, S.W. Bruenn, Astrophys. J. 410, 740 (1993). 48. G.M. Fuller, Astrophys. J. 252, 741 (1982). 49. J. Cooperstein, J. Wambach, Nucl. Phys. A 420, 591 (1984). 50. K. Langanke, E. Kolbe, D.J. Dean, Phys. Rev. C 63, 032801 (2001). 51. K. Langanke et al., Phys. Rev. Lett. 90, 241102 (2003). 52. S.E. Koonin, D.J. Dean, K. Langanke, Phys. Rep. 278, 2 (1997). 53. A. Mezzacappa, M. Liebend¨ orfer, O.E. Bronson Messer, W. Raphael Hix, F.-K. Thielemann, S.W. Bruenn, Phys. Rev. Lett. 86, 1935 (2001). 54. W.R. Hix et al., Phys. Rev. Lett. 91, 201102 (2003). 55. M. Rampp, H.-T. Janka, private communication. 56. G. Mart´ınez-Pinedo, M. Liebend¨ orfer, D. Frekers, submitted to Nucl. Phys. A (2004), astro-ph/0412091. 57. A. Heger, K. Langanke, G. Mart´ınez-Pinedo, S.E. Woosley, Phys. Rev. Lett. 86, 1678 (2001). 58. S.W. Bruenn, W.C. Haxton, Astrophys. J. 376, 678 (1991). 59. S.E. Woosley, D.H. Hartmann, R.D. Hoffman, W.C. Haxton, Astrophys. J. 356, 272 (1990). 60. A. Heger, E. Kolbe, W. Haxton, K. Langanke, G. Mart´ınez-Pinedo, S.E. Woosley, Phys. Lett. B 606, 258 (2005). 61. F.T. Avignone, L. Chatterjee, Y.V. Efremenko, M. Strayer (Editors), Neutrino physics at spallation neutron sources, J. Phys. G 29, 2497 (2003). 62. A. Juodagalvis, K. Langanke, G. Mart´ınez-Pinedo, W.R. Hix, D.J. Dean, J.M. Sampaio, Nucl. Phys. A 747, 87 (2005). 63. K. Langanke, G. Mart´ınez-Pinedo, P. von Neumann-Cosel, A. Richter, Phys. Rev. Lett. 93, 202501 (2004). 64. P. von Neumann-Cosel, A. Poves, J. Retamosa, A. Richter, Phys. Lett. B 443, 1 (1998). 65. J.M. Sampaio, K. Langanke, G. Mart´ınez-Pinedo, D.J. Dean, Phys. Lett. B 529, 19 (2002).

Eur. Phys. J. A 25, s01, 665–668 (2005) DOI: 10.1140/epjad/i2005-06-086-0

EPJ A direct electronic only

The Trojan-Horse method for nuclear astrophysics S. Typela Gesellschaft f¨ ur Schwerionenforschung mbH (GSI), Theorie, Planckstraße 1, D-64291 Darmstadt, Germany Received: 1 October 2004 / Revised version: 11 November 2004 / c Societ` Published online: 23 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The Trojan-Horse method is an indirect approach to determine the low-energy astrophysical S-factor of direct nuclear reactions by studying closely related transfer reactions with three particles in the final state under quasi-free scattering conditions. The theoretical foundation and basic features of this approach are presented. General considerations for the application of method and two examples are discussed. PACS. 24.50.+g Direct reactions – 25.70.Hi Transfer reactions

1 Introduction Nuclear reaction rates are a basic ingredient in many astrophysical models that describe primordial nucleosynthesis, stellar evolution, supernovae etc. [1,2,3]. They have to be known with sufficient accuracy, e.g., in the pp chains, CNO cycles, the s-, r-, p-, and rp-processes in order to describe quantitatively the observed abundance pattern of the elements. In principle it is preferable to measure the corresponding cross-sections directly in the laboratory but this is a very difficult task [4]. The cross-sections are often very small and in many reactions unstable nuclei are involved so that the experimental yields in direct experiments are very low. In the following only non-resonant charged-particle reactions are considered. In this case the repulsive Coulomb interaction leads to a strong suppression of the cross-section at small effective energies that are relevant to astrophysics. Usually the cross-section σ(E) is measured at higher energies E and extrapolated to small energies with the help of the astrophysical S-factor S(E) = σ(E)E exp(2πη12 )

(1)

that exhibits only a weak energy dependence. The Sommerfeld parameter η12 = Z1 Z2 e2 /(¯ hv12 ) depends on the charge numbers Z1 and Z2 of the two participating nuclei and their relative velocity v12 in the entrance channel of the reaction. But even if it is possible perform measurements directly at the relevant small energies in the laboratory the experimental cross-section σexp (E) is enhanced as compared to the cross-section σbare (E) of the bare nuclei due to the screening of the Coulomb potential by the electron cloud [5]. Quantitatively the electron screening if well described by σexp (E) = σbare (E) exp(πηUe /E) a

Conference presenter; e-mail: [email protected]

(2)

with the electron screening potential energy Ue . Unfortunately, screening potentials determined in direct experiments tend to be larger than their values expected from theoretical models. This discrepancy seems not to be fully understood and independent information on the screening effect is highly valuable. Additionally, in astrophysical applications the screening in the stellar plasma has to be accounted for. As an alternative to the direct experiments indirect methods have been developed in recent years. They can give complementary information on the cross-sections that are relevant to astrophysics. The indirect approach depends on the particular type of reaction. A general characteristic of the indirect methods is that the astrophysically relevant two-body reaction is replaced by a three-body reaction at high energies. The relation of the cross-sections is established with the help of nuclear reaction theory that has to be well understood to give reliable information. Well-known examples of indirect approaches are the Coulomb dissociation method [6,7] and the method of asymptotic normalization coefficients (ANC) [8, 9] in order to determine the astrophysical S-factor of radiative capture cross-sections a(b, γ)c. In the Coulomb dissociation method the strong electromagnetic field of a highly charged target nucleus X serves as a source of equivalent photons and the photo dissociation cross-section a(γ, c)b, the inverse of the capture reaction, can be extracted from the cross-section of the Coulomb breakup reaction X(a, bc)X. In the ANC method the asymptotic normalization coefficient of the ground state wave function of nucleus c is extracted from transfer reactions. Then the relevant matrix elements for the radiative capture reaction can be calculated numerically. For direct two-body reactions A + x −→ C + c

(3)

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without a photon in the final state the Trojan-Horse (TH) method has been suggested as an alternative approach to determine indirectly the cross-section at low energies [10]. In this case the reaction (3) is replaced by a reaction A + a −→ C + c + b

(4)

with three particles in the final state. The Trojan Horse a = b + x is formed by attaching a spectator b to the nucleus x. The reaction (4) is studied under quasi-free scattering conditions where the momentum transfer to the spectator is small and other reaction mechanisms are suppressed. The relative energy in the system A + a can be above or near the Coulomb barrier so that there are no suppression of the cross-section and no electron screening. Nevertheless, small relative energies in the system A + x are accessible due to the particular kinematical conditions. The validity of the TH method has been tested for various reactions by the Catania group of C. Spitaleri in recent years by comparing direct and indirect results under various kinematical conditions [11,12,13,14,15,16,17, 18, 19]. Basic theoretical considerations of the approach can be found in [20,21]. In the following the theoretical essentials of the method are presented and the application is discussed for two particular examples.

2 Theory of the Trojan-Horse method The relation of the cross-sections for the two-body reaction (3) and the three-body reaction (4) is found by applying standard methods of direct-reaction theory. Denoting the system C + c with B, the triple differential cross-section of reaction (4)

μAa μBb μCc kBb kCc d3 σ = kAa dECc dΩCc dΩBb (2π)5 ¯ h6  1 2 |Tf i | × 2Ji + 1

(5)

is determined by the T -matrix element Tf i that contains all the relevant information. Here, reduced masses and wave numbers of system ij are denoted by μij and kij , respectively. In the post-form distorted-wave Born approximation (DWBA) the T -matrix element is given by Tf i =

(+) χAa ,

(−) χBb

l

assumes a form similar to a scattering amplitude of a twol of the body reaction with the S-matrix elements SAxCc reaction C + c −→ A + x, (8) i.e. the inverse of the astrophysical important reaction (3). For simplification we assumed spinless nuclei in equation (7). The main difference, however, is the appearance (±) of the factors Ul (kBb kCc kAa ) that in general are complicated reduced DWBA matrix elements. Their particular momentum dependence cancels the suppression of the S-matrix element l ∝ exp(−πηAx ) SAxCc

(6)

and bound state wave with distorted waves functions φA , φa , φb as in the case of usual transfer reactions. The wave function φB , however, is a complete scat(−) tering wave function ΨCc that contains the information on the two-body reaction. The potential Vxb is responsible for the binding of the nucleus x and the spectator b in the Trojan Horse a. In the Trojan-Horse approach the full scattering wave (−) function ΨCc is replaced by its asymptotic form for radii r larger than a strong absorption radius R. This so-called

(9)

2 at low energies EAx = ¯h2 kAx /(2μAx ) due to the Coulomb interaction between A and x. In order to find a simple physical interpretation further approximations can be applied that are, however, not necessary in the general approach. They only serve to show the features of the TH method more clearly. Using plane (+) (−) waves for the distorted waves χAa and χBb the crosssection (5) factorizes according to

TH d3 σ 2 dσ = KF |W (QBb )| dΩ dECc dΩCc dΩBb

Mi ,Mf

  (+) ! (−) χBb φB φb Vxb χAa φA φa

surface approximation is the essential approximation of the TH method. It is well justified since there is a strong suppression of the wave functions at smaller radii due to the absorptive part of the optical potentials in the entrance and exit channels of the three-body reaction. As a consequence of the surface approximation, the T -matrix element $ vCc 1 (7) = TfTH i 2ikCc vAx    (+) (−) l × (2l + 1) SAxCc Ul − δ(Ax)(Cc) Ul

(10)

with three contributions similar as in a plane-wave impulse approximation. The kinematic factor KF is proportional −3 at small energies EAx . The momentum amplitude to kAx W (QBb ) is the Fourier transform of Vxb φa with respect to the relative coordination rxb . The argument mb kAa (11) QBb = kBb − mb + m x

corresponds to the momentum transfer to the spectator b. The TH cross-section

dσ dσ TH (12) =P dΩ dΩ contains the usual cross-section dσ/dΩ of the two-body reaction (8) and a penetrability factor 3 P ∝ kAx exp(2πηAx ).

(13)

Collecting the kAx -dependent factors one immediately sees that the product KF dσ TH /dΩ is proportional to the astrophysical S-factor for EAx → 0. It approaches a finite value in this limit. There is no suppression of the crosssection (10) due to the Coulomb barrier in the system Ax.

S. Typel: The Trojan-Horse method for nuclear astrophysics

3 Application

4 Examples In order to check the validity of the Trojan-Horse method several reactions with stable nuclei under various conditions can be studied. E.g., astrophysical S-factors are extracted in the TH method and compared to well-known data from direct experiments. Alternatively, cross-sections from TH experiments are compared with simulated crosssections using information of direct experiments. Here we discuss examples of both approaches. The cross-section of the reaction 2 H(6 Li, α)4 He that is astrophysically relevant for the destruction of 6 Li in the Big Bang has been measured to very low energies in

S factor S(E) [MeV b]

25

→

in the Ax system. This relation is a purely kinematical consequence. The quasi-free energy (14) is much smaller than the relative energy EAa in the initial state of the three-body reaction (4) and easily falls into a range of energies of the two-body reaction (3) that are relevant for nuclear astrophysics. In an actual experiment a cutoff in the momentum transfer QBb is chosen to emphasize the quasifree reaction mechanism corresponding to the peak of the momentum distribution. This cutoff determines the range qf . Depending on the of accessible energies EAx around EAx scattering angle in the two-body reaction (3) the quasifree condition defines a pair of quasi-free angles where the particles C and c are detected in the laboratory. Considering the approximations in the theoretical calculation one cannot expect that the absolute crosssection (10) is well determined quantitatively. However, the energy dependence is expected to be well reproduced. Therefore, the S-factor extracted in the TH method has to be normalized to known direct data at higher energies. In contrast to direct experiments, the main features of the TH method are that there are no electron screening and no suppression of the cross-section at small energies. It remains finite even in the limit EAx → 0.

30

electron screening

20

normalization

15 10 5 0 10

direct data THM data fit to THM data 100 E [keV]

→

In order to apply the Trojan-Horse method to a particular reaction (3) one has to select a Trojan Horse a = b + x with a well-known ground state wave function that is highly clustered so that the momentum amplitude W for the breakup of a into b and c is well determined. Typical examples are the deuteron 2 H = n + p and 6 Li = α + d that allow to study the transfer of nuclei that are the most relevant for nuclear astrophysics. The spectator b is usually not observed in the TH experiment since the complete kinematic information can be deduced from the momenta of the nuclei C and c that are detected in the final state and the known beam energy. The width of the momentum distribution |W |2 is related to the Fermi motion of the transferred particle x and the spectator b inside a with binding energy a > 0. The condition QBb = 0 defines the so-called quasi-free energy   μAa μ2bx qf − a (14) EAx = EAa 1 − μBb m2x

667

1000

Fig. 1. Astrophysical S-factor S(E) for the reaction 2 H(6 Li, α)4 He from a direct experiment [22] (open circles) and from the TH method (filled circles).

a direct experiment with a deuterium gas target and a 6 Li beam [22]. The cross-section is dominated by a nonresonant process with a s wave in the initial state. Extrapolating the experimental data (open circles in Figure 1) at higher energies with a polynomial fit to small energies a S-factor of S(0) = 17.4 MeVb at zero energy has been extracted. From a comparison with the enhanced experimental data at very small energies below 100 keV an electron screening potential of Ue = 330(120) eV was deduced. In a corresponding Trojan-Horse experiment using the reaction 6 Li(6 Li, αα)4 He the nucleus 6 Li has been chosen as the Trojan horse with an α particle as the spectator [17, 18]. With a beam energy of 6 MeV a quasifree energy E qf = 25 keV could be reached for the two-body reaction. Due to the symmetry of the TH reaction both the projectile and the target were used as Trojan Horses. The S-factor was extracted from the experimental data with a cutoff of 35 MeV/c in the momentum distribution. Absolute values were derived by normalizing to the direct data for energies above 600 keV (see fig. 1). A polynomial fit to the indirect data yields a S-factor at zero energy of S(0) = 16.9(0.5) MeVb consistent with the direct experiment. Comparing the S-factor from the TH experiment with the direct data an electron screening potential of Ue = 320(50) eV was determined, supporting the value extracted from the direct experiment alone. Both values are substantially larger than the adiabatic limit of 186 eV expected from theory. Differential cross-sections of the reaction 6 Li(p, α)3 He for a large range of energies were measured in a direct experiment [23]. From them the coefficient Bl in the angular expansion of the cross-section

 dσ = Bl Pl (cos θ) dΩ

(15)

l

with Legendre polynomials Pl were extracted. The coefficients Bl are well described in a R-matrix fit (see fig. 2).

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30 MeV/c in the momentum transfer to the spectator. The drop of the cross-section above 1.5 MeV and 1.0 MeV, respectively, is a consequence of this momentum cutoff. The overall shape of the cross-sections is well reproduced by the simulation, however, small discrepancies remain that have to be investigated in more detail.

20

B0

15 10

Bl [mb/sr]

5 0 8 6 4 2 0 -2 6 4 2 0 -2 -4 0.0

B1 5 Summary and outlook

B2

0.5

1.0

2.0

1.5

2.5

3.0

Ep [MeV] Fig. 2. Coefficients Bl in the expansion (15) as a function of the proton energy Ep for the reaction 6 Li(p, α)3 He in an R-matrix fit to experimental data [23].

3000

cross section [arb. units]

500

ELi = 25 MeV 400

ELi = 13.9 MeV

2500 2000

300

The Trojan-Horse method allows to extract the energydependence of the astrophysical S-factor of a direct twobody reaction from the measurement of a related transfer reaction under quasi-free scattering conditions. The relation of the cross-sections is found by applying a distortedwave Born approximation with the surface approximation that is essential for the method. A characteristic feature of this indirect approach is that the cross-section at low energies is not suppressed due to the Coulomb barrier in the two-body system. Additionally, there is no electron screening and information on the electron screening potential can be extracted by comparing to data of direct measurements. First applications of the method to wellstudied two-body reactions with simple theoretical approximations were quite successful so far, however, further experimental tests are necessary to establish the validity of the method. The full theory has not been applied yet and more elaborate calculations are required. A comparison of different approximations will give additional information on the accuracy and applicability of the method.

1500 200

References

1000 100 0

500 0 0.5 1 1.5 2 2.5

E [MeV]

0

0

0.5

1

1.5

E [MeV]

Fig. 3. Cross-sections of the Trojan-Horse reaction 2 H(6 Li, α3 He)n ([19] and preliminary data) compared with a simulation using S-matrix elements from a R-matrix fit to direct data.

There are both nonresonant s-wave and resonant p-wave contributions. The S-matrix elements derived from the R-matrix fit were then used in the simulation of TrojanHorse experiments. Choosing the deuteron as the Trojan Horse, experiments with the reaction 2 H(6 Li, α3 He)n were performed with the neutron as the spectator [19]. Energies of 13.9 MeV and 25 MeV for the 6 Li beam were selected that correspond to quasi-free energies E qf of −0.24 MeV and 1.35 MeV, respectively. The experimental cross-sections as a function of the relative energy in the 6 Li + p system are compared in fig. 3 with the simulation applying a cutoff of

1. C.E. Rolfs, W.S. Rodney, Cauldrons in the Cosmos (University of Chicago Press, Chicago, 1988). 2. F.K. Thielemann et al., Prog. Part. Nucl. Phys. 46, 1 (2001). 3. C. Rolfs, Prog. Part. Nucl. Phys. 46, 23 (2001). 4. LUNA Collaboration, Nucl. Phys. A 706, 203 (2002). 5. H.J. Assenbaum et al., Z. Phys. A 327, 461 (1987). 6. G. Baur, C.A. Bertulani, H. Rebel, Nucl. Phys. A 459, 188 (1986). 7. G. Baur, K. Hencken, D. Trautmann, Prog. Part. Nucl. Phys. 51, 487 (2003). 8. H.M. Xu et al., Phys. Rev. Lett. 73, 2027 (1994). 9. L. Trache et al., Phys. Rev. Lett. 87, 271102 (2001). 10. G. Baur, Phys. Lett. B 178, 135 (1986). 11. S. Cherubini et al., Astrophys. J. 457, 855 (1996). 12. G. Calvi et al., Nucl. Phys. A 621, 139c (1997). 13. C. Spitaleri et al., Phys. Rev. C 60, 055802 (1999). 14. C. Spitaleri et al., Eur. Phys. J. A 7, 181 (2000). 15. M. Aliotta et al., Eur. Phys. J. A 9, 435 (2000). 16. M. Lattuada et al., Astrophys. J. 562, 1076 (2001). 17. C. Spitaleri et al., Phys. Rev. C 63, 055801 (2001). 18. A. Musumarra et al., Phys. Rev. C 64, 068801 (2001). 19. A. Tumino et al., Phys. Rev. C 67, 065803 (2003). 20. S. Typel, H.H. Wolter, Few-Body Syst. 29, 75 (2000). 21. S. Typel, G. Baur, Ann. Phys. (N.Y.) 305, 228 (2003). 22. S. Engstler et al., Z. Phys. A 342, 471 (1992). 23. J. Elwyn et al., Phys. Rev. C 20, 1084 (1979).

Eur. Phys. J. A 25, s01, 669–672 (2005) DOI: 10.1140/epjad/i2005-06-093-1

EPJ A direct electronic only

Pycnonuclear reactions in dense stellar matter D.G. Yakovlev1,a , K.P. Levenfish1 , and O.Y. Gnedin2 1 2

Ioffe Physical Technical Institute, Politekhnicheskaya 26, St. Petersburg, 194021, Russia Ohio State University, 760 1/2 Park Street, Columbus, OH 43215, USA Received: 23 October 2004 / Revised version: 26 January 2005 / c Societ` Published online: 27 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We discuss pycnonuclear burning of highly exotic atomic nuclei in deep crusts of neutron stars, at densities up to 1013 g cm−3 . As an application, we consider pycnonuclear burning of matter accreted on a neutron star in a soft X-ray transient (SXT, a compact binary containing a neutron star and a lowmass companion). The energy released in this burning, while the matter sinks into the stellar crust under the weight of newly accreted material, is sufficient to warm up the star and initiate neutrino emission in its core. The surface thermal radiation of the star in quiescent states becomes dependent on the poorly known equation of state (EOS) of supranuclear matter in the stellar core, which gives a method to explore this EOS. Four qualitatively different model EOSs are tested against observations of SXTs. They imply different levels of the enhancement of neutrino emission in massive neutron stars by 1) the direct Urca process in nucleon/hyperon matter; 2) pion condensates; 3) kaon condensates; 4) Cooper pairing of neutrons in nucleon matter with the forbidden direct Urca process. A low level of the thermal quiescent emission of two SXTs, SAX J1808.4–3658 and Cen X-4, contradicts model 4). Observations of SXTs test the same physics of dense matter as observations of thermal radiation from cooling isolated neutron stars, but the data on SXTs are currently more conclusive.

PACS. 97.60.Jd Neutron stars – 26.60.+c Nuclear matter aspects of neutron stars

1 Introduction Neutron stars (NSs) are the most compact stars known in the Universe. Their masses are M ∼ 1.4 M (M being the solar mass) while their radii are R ∼ 10 km. They are thought to consist (e.g., ref. [1, 2]) of a massive dense core surrounded by a thin crust (of mass < ∼ 0.01 M and thickness < 1 km). The crust-core interface occurs at the ∼ density ρ ≈ ρ0 /2, where ρ0 = 2.8 × 1014 g cm−3 is the standard density of saturated nuclear matter. The NS crust is composed of neutron-rich atomic nuclei, strongly degenerate electrons and (at ρ > ∼ 4× 1011 g cm−3 ) of free neutrons dripped from nuclei. NS cores contain degenerate matter of supranuclear density (up to 10–15 ρ0 ). Its composition and equation of state (EOS) are model dependent (being determined by still poorly known strong interactions in dense matter). On the other hand, these properties are almost not constrained by observations (e.g., ref. [1]). The NS core is usually subdivided into the outer core (ρ < ∼ 2 ρ0 ) and the inner core (ρ > ∼ 2 ρ0 ). The outer core is available in all NSs, while the inner core is present only in massive, more compact a

Conference presenter; e-mail: [email protected]

NSs. The outer core is thought to be composed of neutrons, with the admixture of protons, electrons (and possibly muons). The composition and EOS of the inner core is still a mystery. It may be the same composition as in the outer core, with a possible addition of hyperons. Alternatively, the inner core may contain pion or kaon condensates, or quark matter, or the mixture of these components. Another complication is introduced by superfluidity of neutrons, protons and other baryons in dense matter. Superfluid gaps are very model dependent (e.g., ref. [3]). It is unlikely that the fundamental problem of the EOS of supranuclear matter can be solved on purely theoretical grounds. However, the solution can be obtained by comparing theoretical models of NSs with observations. We will mention two lines of such studies. The first one is based on theory and observations of cooling isolated NSs (e.g., refs. [4, 5,6, 7]). These studies, carried out over several decades, have constrained the properties of dense matter but have not solved the problem (sect. 4). Here, we focus on an alternative method to test the same physics on another class of objects, transiently accreting NSs in soft X-ray transients (SXTs). This method is based on pycnonuclear burning of accreted matter. The method is new but seems to be currently more restrictive.

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2 Deep crustal heating

3 Thermal states of soft X-ray transients

Nuclear fusion reactions in normal stars proceed in the thermonuclear regime, in which the Coulomb barrier is penetrated owing to the thermal energy of colliding nuclei. Here, we discuss another, pycnonuclear regime where the Coulomb barrier is penetrated due to zero-point vibrations of nuclei arranged, for instance, in a lattice. The thermonuclear regime is realized in a rather low-density and warm plasma, whereas the pycnonuclear regime operates at high densities and not too high temperatures. Pycnonuclear reactions are almost temperature independent and occur even at T = 0. They were suggested by Gamow [8] in 1938. The first calculations of pycnonuclear reaction rates were done by Wildhack [9] upon Gamow’s request. The strict approach for calculating these rates was formulated by Salpeter and van Horn [10] who studied also three other regimes of nuclear burning in dense matter (the thermonuclear regime with strong enhancement due to plasma screening effects; the intermediate thermopycno nuclear regime; and the thermally enhanced pycnonuclear regime). The pycnonuclear regime has been analyzed later in a number of publications (e.g., [11, 12] and references therein). Pycnonuclear reactions are extremely slow at densities ρ typical for normal stars but intensify with increasing ρ. For example, carbon burns rapidly into 10 −3 heavier elements at ρ > ∼ 10 g cm . Pycnonuclear burning can be important in transiently accreting NSs. The heat released due to the infall of matter and thermonuclear reactions in the surface layers is radiated away by photons from the NS surface and cannot warm up the NS interiors. The accreted matter sinks into the NS crust under the weight of newly accreted material. The density gradually increases in a matter element, and the nuclei undergo transformations —beta captures, absorption and emission of neutrons, and pycnonuclear reactions. The nuclei evolve then into highly exotic atomic nuclei which are unstable in laboratory conditions but stable in dense matter. The transformations and associated energy release have been studied by Haensel and 9 −3 Zdunik [13, 14]. At ρ > ∼ 10 g cm the transformations are almost temperature independent but depend on the composition of matter at ρ ∼ 109 g cm−3 . The main energy release occurs at densities from about 1012 to 1013 g cm−3 , several hundred meters under the NS surface, in pycnonuclear reactions. For iron matter at ρ ∼ 109 g cm−3 , these reactions are [13] 34 Ne + 34 Ne → 68 Ca; 36 Ne + 36 Ne → 72 Ca; and 48 Mg + 48 Mg → 96 Cr. The total energy release is then ≈ 1.45 MeV per accreted baryon; the total NS heating power is determined by the mass accretion rate M˙ : Ldh = 1.45 MeV M˙ /mN ≈ 8.74 × 1033 M˙ /(10−10 M yr−1 ) erg s−1 ,

(1)

where mN is the nucleon mass. It produces deep crustal heating of the star. This heat is spread by thermal conductivity over the entire NS and warms it up.

It is possible that the deep crustal heating manifests itself in NSs which enter SXTs, compact binaries with low-mass companions [15]. These objects undergo the periods of outburst activity (days–months, sometimes years) superimposed with the periods of quiescence (months–decades). An active period is thought to be associated with an accretion of matter from a companion through an accretion disk. The accretion energy released at the NS surface is so large that a SXT looks like a bright X-ray source with the luminosity LX ∼ 1036 –1038 erg s−1 . The accretion is switched off or suppressed in quiescent periods when LX drops below 1034 erg s−1 . In many cases, the spectra of quiescent emission contain the thermal component, well described by NS hydrogen atmosphere models with effective surface temperatures from few 105 K to ∼ 106 K. This can be the radiation emergent from warm NSs. The suggestion to interpret the quiescent radiation spectra of SXTs with hydrogen atmosphere models was put forward by Brown et al. [16] who assumed also that NSs in SXTs could be warmed up by the deep crustal heating of accreted matter. It is important that the crustal heat is partly radiated away by neutrinos from the entire NS body. Because the neutrino luminosity depends on the NS structure, the remaining heat, diffused to the surface and radiated away by photons, becomes also dependent on the NS structure. This opens an attractive possibility (see [17,18, 19,20] and references therein) to explore the NS structure by comparing the observed quiescent thermal radiation from SXTs with theoretical predictions. We outline the results of such studies using the theory of thermal states of transiently accreting NSs described in ref. [21]. These stars are thermally inertial, with thermal relaxation times ∼ 104 yr [18]. In the first approximation, a transiently accreting NS is in a (quasi)stationary steady state determined by the mass accretion rate M˙ ≡ M˙  averaged over thermal relaxation time-scales. Typically,

M˙  ranges from 10−14 to 10−9 M yr−1 and does not increase noticeably the NS mass during long periods of NS evolution. Quasistationary states are expected to be rather insensitive to variations of the accretion rate associated with a sequence of active and quiescent states. Thermal states of accreting NSs can be greatly affected by the neutrino emission from NS interiors (mainly from the cores). The neutrino luminosity of the star, Lν , in its turn, can strongly depend on the NS mass (as schematically shown in fig. 1). Low-mass NSs possess nucleon cores with not too high neutrino emission determined mainly by the modified Urca (Murca) and nucleon-nucleon bremsstrahlung (brems) processes. High-mass NSs, in addition to the outer nucleon cores, possess the inner cores whose composition and EOS are unknown (sect. 1). Their neutrino emission can be enhanced with respect to the emission of low-mass NSs. Four qualitatively different enhancement mechanisms are (e.g., ref. [7]): 1) a very powerful direct Urca (Durca) process in the cores of massive NSs containing nucleons (and possibly hyperons); 2) a less powerful direct-Urca-like process in pion-condensed cores; 3) even less powerful similar processes in kaon-condensed

D.G. Yakovlev et al.: Pycnonuclear reactions in dense stellar matter

Fig. 1. A sketch of the NS neutrino luminosity Lν versus NS mass at the internal stellar temperature T = 3 × 108 K for four scenarios of NS structure (from ref. [7]).

or quark NS cores; 4) even weaker enhancement of the neutrino emission owing to mild Cooper pairing of neutrons in the nucleon inner NS cores with forbidden direct Urca process [5,6]. A transition from the slow neutrino emission in low-mass NSs to a fast emission in massive NSs with increasing M occurs in medium-mass NSs; the mass range of medium-mass stars is model dependent. The NS neutrino luminosity is a strong function of the internal stellar temperature. A thermal state of the star is determined by the thermal balance equation (which implies that the crustal heating power is equal to the sum of photon and neutrino luminosities). Solving this equation, one obtains a heating curve, the dependence of the thermal photon luminosity (as detected by a distant observer) on the mean mass ac˙ cretion rate, L∞ γ (M ). Several examples are presented in fig. 2. The upper curve is calculated for a low-mass NS (M = 1.1 M ) whose core is composed of neutrons, protons and electrons. In the core we use a moderately stiff EOS proposed in ref. [22] (the same version as employed in ref. [4]). It is assumed that the core contains strongly superfluid protons. Superfluidity suppresses the modified Urca process, the star has a low neutrino luminosity due to neutronneutron bremsstrahlung and stays relatively warm. The lowest curve in fig. 2 corresponds to the maximum-mass NS (M = 1.977 M ) with the same EOS. This star has a massive inner core where the direct Urca process operates and proton superfluidity dies out. The neutrino luminosity becomes exceptionally high, and the star is very cold. The next two curves above the lowest one are schematic models [21] of high-mass NSs with pion-condensed or kaoncondensed cores. The next curve is calculated for a highmass (M = 2.05 M ) star, where the direct Urca process is forbidden but the neutrino emission is enhanced by mild

671

Fig. 2. Quiescent thermal luminosity of several NSs in SXTs versus mass accretion rate compared with theoretical heating curves. Four ranges of L∞ γ (different hatching types) correspond to four scenarios of neutrino emission (fig. 1).

Cooper pairing of neutrons in the inner core (the same EOS [23] and model for superfluidity as in fig. 1 of ref. [6]). The heating curve of a low-mass NS provides an upper limit of L∞ γ , whereas a heating curve of a high-mass NS gives a lower limit of L∞ γ , for a fixed scenario of neutrino emission. Varying the NS mass from the lower values to the higher we obtain a family of heating curves which fill in the (hatched) space between the upper and lower curves. In fig. 2 we have four hatched (acceptable) regions for four scenarios of neutrino emission in fig. 1.

4 Discussion These results can be compared with observations of SXTs. The observational data are mostly the same as in ref. [21]. We regard L∞ γ as the thermal quiescent luminosity of ˙ NSs, and M as the time-averaged mass accretion rate. The value of M˙ for KS 1731–26 is most probably an upper limit. No quiescent thermal emission has been detected [24] from SAX J1808.4–3658, and we present the upper limit of L∞ γ for this source. The limit was obtained by P. Stykovsky (private communication, 2004) and discussed in the note added in proof of ref. [4]. The NS seems to be cold, but the result should be taken with caution because it is based on one observation (March 24, 2001) with poor statistics. All the data are rather uncertain and are thus plotted by thick dots. According to fig. 2, we can treat NSs in 4U 1608–52 and Aql X-1 as low-mass NSs (the observations of Aql X-1 can be explained [25] assuming the presence of light elements on the NS surface, that increases L∞ γ ). NSs in Cen X-4 and SAX J1808.4–3658 seem to require the enhanced neutrino

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The authors are grateful to P. Haensel, M.E. Gusakov, A.D. Kaminker, A.Y. Potekhin, and Yu.A. Shibanov for discussions, and to M.G. Revnivtsev and P. Stykovsky for reprocessing the observations of SAX J1808.4–3658. DGY is grateful to JINA and the organizers of ENAM2004 for financial support which allowed him to attend the conference. K.P.L. acknowledges the support of the Russian Science Support Foundation. This work was supported in part by the RBRF (grants Nos. 0202-17668 and 03-07-90200) and the RLSS (grant 1115.2003.2).

References

Fig. 3. Effective surface temperatures Ts∞ of several isolated NSs versus their ages compared with theoretical cooling curves (from ref. [7]). Four ranges of Ts∞ (different hatching types) correspond to four scenarios of neutrino emission (fig. 1).

emission and are thus more massive. The status of the NS in KS 1731–26 is less certain [21] because of poorly determined M˙ . Similar conclusions have been made with respect to some of these sources or selected groups (see, e.g., [17,18, 19, 20, 21, 23,24, 25] and references therein) although four scenarios 1)–4) are discussed together for the first time. As seen from fig. 2, the data are still not restrictive. They cannot allow us to discriminate between scenarios 1)–3) (nucleon NS cores with the direct Urca process, pioncondensed or kaon condensed cores). Nevertheless, the observations of Cen X-4 and especially of SAX J1808.4–3658 seem to contradict scenario 4) of nucleon matter with the forbidden direct Urca process (and the data on SAX J1808.4–3658 marginally contradict scenario 3)). The same four scenarios can also be tested by comparing observations of thermal radiation of cooling (isolated) NSs with theoretical cooling curves (the dependence of the effective surface temperatures Ts∞ , redshifted for a distant observer, on the stellar age). These results are presented in fig. 3; the data and curves are taken from ref. [7]. By comparing figs. 2 and 3 we see that the data on isolated NSs, although more numerous, are currently less conclusive and do not discriminate between all scenarios 1)–4) (although a discovery of a not too old isolated NS slightly colder than the Vela pulsar would contradict scenario 4)). Thus, the pycnonuclear burning of highly exotic atomic nuclei in accreting NSs is helpful to solve the longstanding problem of the EOS of supranuclear matter in NS cores. Hopefully, new observations of SXTs and cooling isolated NSs will appear in the near future. Combined together, they will give more stringent constraints on the EOS of dense matter.

1. J.M. Lattimer, M. Prakash, Astrophys. J. 550, 426 (2001). 2. P. Haensel, in Final Stages of Stellar Evolution, edited by C. Motch, J.-M. Hameury, EAS Publ. Ser. (EDP Sciences, 2003) p. 249. 3. U. Lombardo, H.-J. Schulze, in Physics of Neutron Star Interiors, edited by D. Blaschke, N.K. Glendenning, A. Sedrakian (Springer, Berlin, 2001) p. 30. 4. D.G. Yakovlev, C.J. Pethick, Annu. Rev. Astron. Astrophys. 42, 169 (2004). 5. D. Page, J.M. Lattimer, M. Prakash, A.W. Steiner, Astrophys. J. Suppl. Ser. 155, 623 (2004). 6. M.E. Gusakov, A.D. Kaminker, D.G. Yakovlev, O.Y. Gnedin, Astron. Astrophys. 423, 1063 (2004). 7. D.G. Yakovlev, O.Y. Gnedin, M.E. Gusakov, A.D. Kaminker, K.P. Levenfish, A.Y. Potekhin, in Proceedings of the International Nuclear Physics Conference, G¨ oteborg, Sweden, June 27–July 2, 2004, Nucl. Phys. A 752, 590c (2005), astro-ph/0409751. 8. G. Gamow, Phys. Rev. 55, 718 (1939). 9. W.A. Wildhack, Phys. Rev. 57, 81 (1940). 10. E.E. Salpeter, H.M. van Horn, Astrophys. J. 155, 183 (1969). 11. S. Schramm, S.E. Koonin, Astrophys. J. 365, 296 (1990); 377, 343 (1991)(E). 12. H. Kitamura, Astrophys. J. 539, 888 (2000). 13. P. Haensel, J.L. Zdunik, Astron. Astrophys. 227, 431 (1990). 14. P. Haensel, J.L. Zdunik, Astron. Astrophys. 404, L33 (2003). 15. W. Chen, C.R. Shrader, M. Livio, Astrophys. J. 491, 312 (1997). 16. E.F. Brown, L. Bildsten, R.E. Rutledge, Astrophys. J. Lett. 504, L95 (1998). 17. G. Ushomirsky, R.E. Rutledge, Mon. Not. R. Astron. Soc. 325, 1157 (2001). 18. M. Colpi, U. Geppert, D. Page, A. Possenti, Astrophys. J. Lett. 548, L175 (2001). 19. R.E. Rutledge, L. Bildsten, E.F. Brown, G.G. Pavlov, V.E. Zavlin, G. Ushomirsky, Astrophys. J. 580, 413 (2002). 20. E.F. Brown, L. Bildsten, P. Chang, Astrophys. J. 574, 920 (2002). 21. D.G. Yakovlev, K.P. Levenfish, P. Haensel, Astron. Astrophys. 407, 265 (2003). 22. M. Prakash, T.L. Ainsworth, J.M. Lattimer, Phys. Rev. Lett. 61, 2518 (1988). 23. F. Douchin, P. Haensel, Astron. Astrophys. 380, 151 (2001). 24. S. Campana, L. Stella, F. Gastaldello, S. Mereghetti, M. Colpi, G.L. Israel, L. Burderi, T. Di Salvo, R.N. Robba, Astrophys. J. Lett. 575, L15 (2002). 25. D.G. Yakovlev, K.P. Levenfish, A.Y. Potekhin, O.Y. Gnedin, G. Chabrier, Astron. Astrophys. 417, 169 (2004).

Eur. Phys. J. A 25, s01, 673–674 (2005) DOI: 10.1140/epjad/i2005-06-081-5

EPJ A direct electronic only

A statistical spectroscopy approach for calculating nuclear level densities E. Ter´ana and C.W. Johnson Department of Physics, San Diego State University, San Diego, CA 92182-1233, USA Received: 26 October 2004 / c Societ` Published online: 17 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. We compute level densities with a nuclear statistical spectroscopy approach. This model is based on the microscopic physics of the interacting shell model. The level density is constructed by means of a sum of binomial distributions. The partial densities correspond to different configurations of the valence space. The individual binomial parameters fit the exact configuration moments. Calculations of level densities for sd-shell nuclides show the model to work well, when compared to exact calculations with full-diagonalization shell model. PACS. 21.10.-k Properties of nuclei; nuclear energy levels – 21.10.Ma Level density – 26.50.+x Nuclear physics aspects of novae, supernovae, and other explosive environments

1 Introduction The level density —number of excited states per MeV of excitation energy— is an important input to estimate reaction rates in nucleosynthesis. Theoretical prescriptions to calculate nuclear level densities have been developed since Bethe’s formulation [1]. Modifications to this model have been made to include important nuclear properties such as shell effects or neutron resonance spacings [2, 3,4]. On the other hand, full shell model calculations are now possible up to A ≈ 70, although these are often limited by heavy computational loads. We use statistical spectrocopy concepts [5] to model the level density in the shell model using the binomial distribution, first suggested by Zuker [6]. We use the configuration scheme —m-particles distribuited over spherical shell model j-orbits— to compute level densities. The purpose of this work is not to compute “exact” shell model calculations [7], but to use binomial distributions to model the configuration level densities and get the approximate secular behavior of the total level density. We apply the binomial fit to each configuration and sum over all of them to obtain the total level density. The exploration of the model is currently done in sd-shell nuclei. A brief description of the method is presented, and some preliminary results explained.

2 The method Statistical spectroscopy argues that the nuclear properties are defined by the nuclear moments. Following this a

Conference presenter; e-mail: [email protected]

approach we get the configuration moments of the nucleus and construct a binomial fit for each partition of the shell model space. We then get the total level density by adding all the partial densities. The sum of the partitioned binomials (SUPARB) can be compared then, at least for light nuclei in the sd-shell, against full-diagonalization shell model calculations. 2.1 The binomial distribution Every configuration of the valence space contributes with a partial density. Based on the lowest nuclear moments, each partial density is constructed with a binomial fit (1 + λ) =

N 

  N , λ k k

(1)

k=0

where N and λ are obtained from conditions to fit the width and third moment of a given configuration, and k is related to the scaled excitation energy. We make use of analytic formulae to compute the moments [8,9]. The point of using this procedure is to avoid a full shell model calculation to get the configuration moments. Even when the computation of the moments using such formulae is computationally exhaustive for heavier nuclei, it is still a lot more convenient than performing a full shell model calculation. Moreover, the partitioned scheme we use is highly suitable to run on parallel computers and substantially reduce the time to calculate the moments. Once we have the binomial fit for every configuration we get the total level density straightforwardly by

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10

10

ρ (levels/MeV)

21

10

Ne

2

10

α=3

α=1

4

10

1

10

10

Ne

2

10 α=2

20

3

1

4

10

0

20

40

Excitation Energy (MeV)

60

Fig. 1. Calculated level density for 21 Ne. A few individual contributions ρα (broken lines, coloured on line) are shown. The total level density (solid, black line) is the sum over all the configurations. The unscaled Wildenthal interaction was used.

ρ (levels/MeV)

0

10 10

2.2 Performance of the model To test the reliability of the method, we have performed calculations of level densities for several nuclides in the sdshell with the Wildenthal interaction [10] and compared them to exact calculations. To accomplish the comparison we made use of the REDSTICK shell model code [11]. Figure 2 shows the 20 Ne, 34 Ar and 34 Cl level densities computed with the SUPARB method described here, compared against exact shell model calculations. The SUPARB computations shown in fig. 2 reveal an overall good fit of the exact level density in all three cases, although our interest is in the low-energy region (up to 20 MeV), where experimental data is available. We get similar results for other sd-shell nuclei. We plan to extend these calculations to larger spaces, namely, the sdpf and sdpf + g9/2 shells, where exact calculations are very difficult to perform. Besides the level density, computations of locally averaged expectation values of operators and J-dependent level densities with spin cut-off are also possible within this approach. We will explore these possibilites in the short term.

3 Conclusions The SUPARB method to calculate level densities has been described here. The valence space is partitioned and the total level density obtained from the sum of the corresponding partial densities. In our preliminary calculations we have seen evidence that the binomial distribution fits well the level density for sd-shell nuclei, when compared against full-diagonalization shell model calculations. Besides this, the method presented here has also shown to

Ar

2

10

10

adding up the calculated partial densities. To illustrate this, a qualitative plot of the configurations densities is shown in fig. 1. The plots of broken lines in the figure correspond to a selected set of partial densities, labeled by α. In the case of 21 Ne there are only 54 of such configurations. One advantage of this method is that it is mostly analytic, so it will be suitable for nuclei in the sdpf -shell, which have thousands of valence space configurations (i.e. 5 × 105 for 54 Fe up to 3p-3h configurations).

34

3

Exact SUPARB

4

10 10

1

34

Cl

3

2

10

1

0

10 0

20 40 Excitation Energy (MeV)

60

Fig. 2. 20 Ne, 34 Ar and 34 Cl level densities in the sd-shell. The SUPARB calculation (broken line) described here is compared with the “exact” shell model calculations [11] (solid, stair line).

have the advantage of being computationally cheap, since we use analytic formulae and implement the calculation of the moments in parallel computers. We will continue the study of light nuclei, although our ultimate goal is to compute level densities in the pf -shell, namely, V, Mn, Ti, Co isotopes. Also, we are interested in testing different interactions like the Gogny interaction or the surface-delta interaction to see how the results depend on the matrix elements used. Furthermore, we have a particular interest to see how the computed level density with this method compares to available experimental data in the pf -shell. These investigations are currently underway.

References 1. H. Bethe, Rev. Mod. Phys. 9, 69 (1937). 2. T. Ericson, Nucl. Phys. 8, 265 (1958). 3. A. Gilbert, A.G.W. Cameron, Can. J. Phys. 43, 1446 (1965). 4. P. Demetriou, S. Goriely, Nucl. Phys. A 695, 95 (2001). 5. K.K. Mon, J.B. French, Ann. Phys. (N.Y.) 95, 90 (1975). 6. A.P. Zuker, Phys. Rev. C 64, 021303 (2001). 7. V.K.B. Kota, D. Majumdar, Nucl. Phys. A 604, 129 (1996); Z. Phys. 351, 365 (1995). 8. J.B. French, K.F. Ratcliff, Phys. Rev. C 3, 94 (1971). 9. S.S.M. Wong, Nuclear Statistical Spectroscopy (Oxford University Press, New York, 1986). 10. B.H. Wildenthal, Prog. Part. Nucl. Phys. 11, 5 (1984). 11. W.E. Ormand, private communication.

10 Fundamental symmetries

Eur. Phys. J. A 25, s01, 677–683 (2005) DOI: 10.1140/epjad/i2005-06-113-2

EPJ A direct electronic only

Fundamental symmetries and interactions —Some aspects K. Jungmanna Kernfysisch Versneller Instituut, Zernikelaan 25, 9747 AA Groningen, The Netherlands Received: 12 September 2004 / c Societ` Published online: 30 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. In the framework of nuclear physics and at nuclear physics facilities a large number of different experiments can be performed which render the possibility to investigate fundamental symmetries and interactions in nature. In particular, the precise measurements of properties of fundamental fermions, searches for new interactions in β-decays, and violations of discrete symmetries have a robust discovery potential for physics beyond standard theory. Precise measurements of fundamental constants can be carried out as well. Low energy experiments allow probing of New Physics models at mass scales far beyond the reach of present accelerators or such planned for the future in the domain of high energy physics and at which predicted new particles could be produced directly. PACS. 11.30.-j Symmetry and conservation laws – 11.30.Er Charge conjugation, parity, time reversal, and other discrete symmetries – 06.20.Jr Determination of fundamental constants

1 Introduction Symmetries play an important and central role in physics. Whereas global symmetries relate to conservation laws, local symmetries yield forces [1]. Today four fundamental interactions are known in physics: i) Electromagnetism, ii) Weak Interactions, iii) Strong Interactions, and iv) Gravitation. These forces are considered fundamental, because all observed dynamic processes in nature can be traced back to one or a combination of them. Together with fundamental symmetries they from the framework on which all physical descriptions ultimately rest. The Standard Model (SM) is a most remarkable theory. Electromagnetic, Weak and many aspects of Strong Interactions can be described to astounding precision in one single coherent picture. It is a major goal in modern physics to find a unified quantum field theory which includes all the four known fundamental forces. To achieve this, a satisfactory quantum description of gravity remains yet to be found. This is a lively field of actual activity. In this write-up we are concerned with important implications of the SM. In particular, searches for new, yet unobserved interactions play a central role. At present, such are suggested by a variety of speculative models in which extensions to the present standard theory are introduced in order to explain some of the features in the SM, which are not well understood and not well founded, although the corresponding experimental facts are accurately described. Among the intriguing questions in modern physics are the number of fundamental particle gena

e-mail: [email protected]

erations and the hierarchy of the fundamental fermion masses. In addition, the electro-weak SM has a rather large number of some 27 free parameters [2], which all need to be extracted from experiments. It is rather unsatisfactory that the physical origin of the observed breaking of discrete symmetries in weak interactions, e.g. of parity (P ), of time reversal (T ) and of combined charge conjugation and parity (CP ), remains unrevealed, although the experimental findings can be well described within the SM. The speculative models beyond the present standard theory include such which involve left-right symmetry, fundamental fermion compositeness, new particles, leptoquarks, supersymmetry, supergravity and many more. Interesting candidates for an all encompassing quantum field theory are string or membrane (M ) theories which in their low energy limit may include supersymmetry. Without secure future experimental evidence all of these speculative theories will remain without status in physics, independent of the mathematical elegance and partial appeal. Experimental searches for predicted unique features of those models are therefore essential to steer theory towards a better and deeper understanding of fundamental laws in nature. In the field of fundamental interactions there are two important lines of activities: Firstly, there are searches for physics beyond the SM in order to base the description of all physical processes on a conceptually more satisfying foundation, and, secondly, the application of solid knowledge in the SM for extracting fundamental quantities and achieving a description of more complex physical systems,

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such as atomic nuclei. Both these central goals can be achieved at upgraded present and novel, yet to be built facilities. In this connection a high intensity proton driver would serve to allow novel and more precise measurements in a large number of actual and urgent issues [3]. In this article we can only address a few aspects of a rich spectrum of possibilities.

A further rather promising application of such a detector would be a measurement of the neutrino generation mixing angle Θ13 in a reactor experiment with a near and far detector in ≈ few 100 m and ≈ few 100 km distance. For this measurement the importance of directional sensitivity for low energy ν’s is an indispensable requirement.

2.1.2 Neutrino masses

2 Fundamental fermion properties 2.1 Neutrinos The SM knows three charged leptons (e− , μ− , τ − ) and three electrically neutral neutrinos (νe , νμ , ντ ) as well as their respective antiparticles. The members of the lepton families do not participate in strong interactions. Neutrinos eigenstates of mass (ν1 , ν2 , ν3 ) and flavor are different and connected to each other through a mixing matrix analogous to the Cabbibo-Kobayashi-Maskawa mixing in the quark sector (see 2.2). The reported evidence for neutrino oscillations strongly indicate finite ν masses. Among the recent discoveries are the surprisingly large mixing angles Θ12 and Θ23 . The mixing angle Θ13 , the phases for CP violation, the question whether ν’s are Dirac or Majorana particles and a direct measurement of a neutrino mass rank among the top issues in neutrino physics [4].

2.1.1 Novel ideas in the neutrino field Two new and unconventional neutrino detector ideas have come up and gained support in the recent couple of years, which have a potential to contribute significantly towards solving major puzzling questions in physics. The first concept employs the detection of high energetic charged particles originating from neutrino reactions through Cherenkov radiation in the microwave region (or even sound waves), which results, if such particles interact with, e.g., the Antarctic ice or the salt in large salt domes as they can be found also in the middle of Europe [5]. One advantage of such a detector is its larger density as compared to water, the typical detector material used up to date. It remains to be verified whether this concept will also be applicable for high energetic accelerator neutrinos, if narrowband radio detection will be employed. The second concept allows directional sensitivity for low energy anti-neutrinos. The reaction ν + p → e+ + n has a 1.8 eV threshold. The resulting neutron (n) carries directional information in its angular distribution after the event. In typical organic material the neutron has a range rn of a few cm. With a detector consisting of tubes with a diameter of order rn and with, e.g., boronated walls the resulting α-particle from the n + B nuclear reaction can be used to determine on average the direction of incoming anti-neutrinos. Such a detector, if scaled to sufficient mass, can be used to determine the distribution of radionuclides in the interior of the earth (including testing the rather exotic of a nuclear reactor in center of the earth) [6].

The best neutrino mass limits have been extracted from measurements of the tritium β-decay spectrum close to its endpoint. Since neutrinos are very light particles, a mass measurement can best be performed in this region of the spectrum as in other parts the nonlinear dependencies caused by the relativistic nature of the kinematic problem cause a significant loss of accuracy. This by far overwhelms the possible gain in statistics one could hope for. Two groups in Troitzk and Mainz used spectrometers based on Magnetic Adiabatic Collimation combined with an Electrostatic filter (MAC-E technique) and found m(νe ) < 2.2 eV [7, 8]. A new experiment, KATRIN [9], is presently prepared in Karlsruhe, Germany, which is planned to exploit the same technique. It aims for an improvement by about one order of magnitude. The physical dimensions of a MACE device scale inversely with the possible sensitivity to a finite neutrino mass. This may ultimately limit an approach with this principle. The new experiment will be sensitive to the mass range where a finite effective neutrino mass value of between 0.1 and 0.9 eV was extracted from a signal in neutrinoless double β-decay in 76 Ge [10]. The Heidelberg-Moskow collaboration performing this experiment in the Grand Sasso laboratory reports a 4.2 standard deviation effect for the existence of this decay1 . It should be noted that neutrinoless double β-decay is only possible for Majorana neutrinos. A confirmed signal would solve one of the most urgent questions in particle physics. Additional work is needed to obtain more accurate values of the nuclear matrix elements which determine the lifetimes of the possible neutrinoless double β-decay candidates. Only then a positive signal could be converted in a Majorana neutrino mass with small uncertainties [11].

2.2 Quarks —unitarity of Cabbibo-Kobayashi-Maskawa matrix The mass and weak eigenstates of the six quarks (u, d, s, c, b, t) are different and related to each other by a 3 × 3 unitary matrix, the Cabbibo-Kobayashi-Maskawa (CKM) matrix. Non-unitarity of this matrix would be an indication of physics beyond the SM and could be caused by a variety of possibilities, including the existence of more than three quark generations or yet undiscovered muon 1

A number of further experiments is under way using different candidate nuclei to verify this claim. An extensive coverage of this subject is well beyond the scope of this article.

K. Jungmann: Fundamental symmetries and interactions —Some aspects

decay channels. The unitarity of the CKM matrix is therefore a severe check on the validity of the standard theory and sets bounds on speculative extensions to it. The best test of unitarity results from the first row of the CKM matrix through |Vud |2 + |Vus |2 + |Vub |2 = 1 − Δ,

(1)

where the SM predicts Δ to be zero. The size of the known elements determine that with the present uncertainties only the elements Vud and Vus play a role. Vud can be extracted with best accuracy from the ft values of superallowed β-decays. Other possibilities are the neutron decay and the pion β-decay, which both are presently studied. Vus can be extracted from K decays and in principle also from hyperon decays. One of the triumphs of nuclear physics in contributing to a confirmation of the standard theory had remained covered for a long time by a remarkable misjudgment on the side of the Particle Data Group [12]. This expert panel had decided to increase the uncertainty of Vud from nuclear β-decay [13] based on their feelings that nuclei would be too complicated objects to trust theory. Interestingly, their own evaluation of Vus based on Particle Data Group fits of K-decay branching ratios turned out to be not in accordance with recent independent direct measurements. As a result of the earlier too optimistic error estimates in this part a large activity to test the unitarity of the CKM matrix took off, because a between 2 and 3 standard deviation from unitarity had been persistently reported without true basis [14]. Recent careful analysis of the subject has also revealed overlooked inconsistencies in the overall picture [15,16] and at this time new determinations of Vus together with Vud from nuclear β-decay confirm Δ = 0 and the unitarity of the CKM matrix up to presently possible accuracy. Because of the cleanest and therefore most accurate theory pion β-decay offers for future higher precision measurements the best opportunities, in principle. The estimate [17] for accuracy improvement from nuclear βdecays is about a factor 2. The main difficulty for new round rests therefore primarily with finding an experimental technique to obtain sufficient experimental accuracy for pion β-decay.

3 Discrete symmetries 3.1 Parity The observation of neutral currents together with the observation of parity non-conservation in atoms were important to verify the validity of the SM. The fact that physics over 10 orders in momentum transfer —from atoms to highest energy scattering— yields the same electro-weak parameters may be viewed as one of the biggest successes in physics to date. However, at the level of highest precision electro-weak experiments questions arose, which ultimately may call for a refinement. The predicted running of the weak mixing angle sin2 ΘW appears not to be in agreement with

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observations [18, 19,2]. If the value of sin2 ΘW is fixed at the Z0 -pole, deep inelastic neutrino scattering at several GeV appears to yield a considerably higher value. A reported disagreement from atomic parity violation in Cs has disappeared after a revision of atomic theory. A new round of experiments is being started with the Qweak experiment [20] at the Jefferson Laboratory in the USA. For atomic parity violation [21] in principle higher experimental accuracy will be possible from experiments using Fr isotopes [22,23] or single Ba or Ra ions in radiofrequency traps [24]. Although the weak effects are larger in these systems due to their high power dependence on the nuclear charge, this can only be exploited after better atomic wave function calculations will be available, as the observation is always through an interference of weak with electromagnetic effects. 3.2 Time reversal and CP violation The role of a violation of combined charge conjugation (C) and parity (P ) is of particular importance through its possible relation to the observed matter-antimatter asymmetry in the universe. This connection is one of the strong motivations to search for yet unknown sources of CP violation. A. Sakharov [25] has suggested that the observed dominance of matter could be explained via CP violation in the early universe in a state of thermal non-equilibrium and with baryon number violating processes. CP violation as described in the SM is insufficient to satisfy the needs of this elegant model. Permanent Electric Dipole Moments (EDMs) certain correlation observables in β-decays offer excellent opportunities to find new sources of CP violation. 3.2.1 Permanent Electric Dipole Moments (EDMs) An EDM of any fundamental particle violates both parity and time reversal (T ) symmetries. With the assumption of CP T invariance a permanent dipole moment also violates CP . EDMs for all particles are caused by CP violation as it is known from the K systems through higher order loops. These are at least 4 orders of magnitude below the present experimentally established limits. Indeed, a large number of speculative models foresees permanent electric dipole moments which could be as large as the present experimental limits just allow. Historically the non-observation of permanent electric dipole moments has ruled out more speculative models than any other experimental approach in all of particle physics [26]. EDMs have been searched for in various systems with different sensitivities (table 1). In composed systems such as molecules or atoms fundamental particle dipole moments of constituents may be significantly enhanced [27,28]. Particularly in polarizable systems there can exist large internal fields. There is no preferred system to search for an EDM [29]. In fact, many systems need to be examined, because depending on the underlying process different systems have

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Table 1. Actual limits on permanent electric dipole moments.

Particle e μ τ n p Λ νe,μ ντ Hg-atom

Limit/Measurement [e-cm] < 1.6 × 10−27 < 2.8 × 10−19 (−2.2 < dτ < 4.5) × 10−17 < 6.3 × 10−26 (−3.7 ± 6.3) × 10−23 (−3.0 ± 7.4) × 10−17 < 2 × 10−21 < 5.2 × 10−17 < 2.1 × 10−28

Reference [30] [31] [32] [33] [34] [35] [36] [37] [38]

in general quite significantly different susceptibility to acquire an EDM through a particular mechanism. In fact, one needs to investigate different systems. An EDM may be found an “intrinsic property” of an elementary particle as we know them, because the underlying mechanism is not accessible at present. However, it can also arise from CP -odd forces between the constituents under observation, e.g. between nucleons in nuclei or between nuclei and electrons. Such EDMs could be much higher than such expected for elementary particles originating within the popular, usually considered standard theory models. No other constraints are known. This highly active field of research benefited recently from a number of novel developments. One of them concerns the Ra atom, which has rather close lying 7s7p3 P1 and 7s6d3 D2 states. Because they are of opposite parity, a significant enhancement has been predicted for an electron EDM [39], much higher than for any other atomic system. Further more, many Ra isotopes are in a region where (dynamic) octupole deformation occurs for the nuclei, which also may enhance the effect of a nucleon EDM substantially, i.e. by some two orders of magnitude [40]. From a technical point of view the Ra atomic levels of interest for en experiment are well accessible spectroscopically and a variety of isotopes can be produced in nuclear reactions. The advantage of an accelerator based Ra experiment is apparent, because EDMs require isotopes with spin and all Ra isotopes with finite nuclear spin are relatively short-lived [41]. A very novel idea was introduced recently for measuring an EDM of charged particles [42]. The high motional electric field is exploited, which charged particles at relativistic speeds experience in a magnetic storage ring. In such an experiment the Schiff theorem can be circumvented (which had excluded charged particles from experiments due to the Lorentz force acceleration) because of the non-trivial geometry of the problem [27]. With an additional radial electric field in the storage region the spin precession due to the magnetic moment anomaly can be compensated, if the effective magnetic anomaly aeff is small, i.e. aeff  1. The method was first considered for muons. For longitudinally polarized muons injected into the ring an EDM would express itself as a spin rotation out of the orbital plane. This can be observed as a time dependent (to first order linear in time) change of the above/below the plane of orbit counting rate ratio. For

the possible muon beams at the future J-PARC facility in Japan a sensitivity of 10−24 e cm is expected [43, 42]. In such an experiment the possible muon flux is a major limitation. For models with nonlinear mass scaling of EDM’s such an experiment would already be more sensitive to some certain new physics models than the present limit on the electron EDM [44]. An experiment carried out at a more intense muon source could provide a significantly more sensitive probe to CP violation in the second generation of particles without strangeness [45]. The deuteron is the simplest known nucleus. Here an EDM could arise not only from a proton or a neutron EDM, but also from CP -odd nuclear forces [46]. It was shown very recently [47] that the deuteron can be in certain scenarios significantly more sensitive than the neutron. In eq. (2) this situation is evident for the case of quark chromo-EDMs: dD = −4.67 dcd + 5.22 dcu ,

dn = −0.01 dcd + 0.49 dcu . (2)

It should be noted that because of its rather small magnetic anomaly the deuteron is a particularly interesting candidate for a ring EDM experiment and a proposal with a sensitivity of 10−27 e cm exists [48]. In this case scattering off a target will be used to observe a spin precession. As possible sites of an experiment the Brookhaven National Laboratory (BNL), the Indiana University Cyclotron Facility (IUCF) and the Kernfysisch Versneller Instituut (KVI) are considered. 3.2.2 Correlations in β-decays In standard theory the structure of weak interactions is V − A, which means there are vector (V ) and axialvector (A) currents with opposite relative sign causing a left handed structure of the interaction and parity violation [49]. Other possibilities like scalar, pseudo-scalar and tensor type interactions which might be possible would be clear signatures of new physics. So far they have been searched for without positive result. However, the bounds on parameters are not very tight and leave room for various speculative possibilities. The double differential decay probability d2 W/dΩe dΩν for a β-radioactive nucleus is related to the electron and neutrino momenta p and q through

 me p·q d2 W + b 1 − (Zα)2 ∼1+a E E dΩe dΩν

p× q p +B q+D + J · A E E  p q , + Q J + R J  × + σ · G E E

(3)

where me is the β-particle mass, E its energy, σ its spin, and J is the spin of the decaying nucleus. The coefficients D and R are studied in a number of experiments at this time and they are T violating in nature. Here D is of particular interest for further restricting model parameters. It describes the correlation between the neutrino and βparticle momentum vectors for spin polarized nuclei. The

K. Jungmann: Fundamental symmetries and interactions —Some aspects

coefficient R is highly sensitive within a smaller set of speculative models, since in this region there exist some already well established constraints, e.g., from searches for permanent electric dipole moments [49]. From the experimental point of view, an efficient direct measurement of the neutrino momentum is not possible. The recoiling nucleus can be detected instead and the neutrino momentum can be reconstructed using the kinematics of the process. Since the recoil nuclei have typical energies in the few 10 eV range, precise measurements can only be performed, if the decaying isotopes are suspended using extreme shallow potential wells. Such exist, for example, in atom traps formed by laser light, where many atomic species can be stored at temperatures below 1 mK. An overview over actual activities can be found in [50]. Such research is being performed at a number of laboratories worldwide. At KVI a new facility is being set up, in which T violation research will be a central scientific issue [41, 51]. At this new facility the isotopes of primary interest are 20 Na, 21 Na, 18 Ne and 19 Ne. These atoms have suitable spectral lines for optical trapping and the nuclear properties allow to observe rather clean transitions. A recent measurement at Berkeley, USA, the asymmetry parameter a in the β-decay of 21 Na has been measured in optically trapped atoms [52]. The value differs from the present SM value by about 3 standard deviations. Whether this is an indication of new physics reflected in new interactions in β-decay, this depends strongly on the β/(β + γ) decay branching ratio for which some 5 measurements exists which in part disagree significantly [53]. New measurements are needed. The most stringent limit on scalar interactions for β-neutrino correlation measurements comes from an experiment on the pure Fermi decay of 38m K at TRIUMF, where a was extracted to 0.5% accuracy and in good agreement with standard theory [54].

4 Properties of known basic interactions 4.1 Electromagnetism and fundamental constants In the electro-weak part of the SM very high precision can be achieved for calculations, in particular within Quantum Electrodynamics (QED), which is the best tested field theory we know and a key element of the SM. QED allows for extracting accurate values of important fundamental constants from high precision experiments on free particles and light bound systems, where perturbative approaches work very well for their theoretical description. Examples are the fine structure constant α or the Rydberg constant R∞ . The obtained numbers are needed to describe the known interactions precisely. Furthermore, accurate calculations provide a basis to searches for deviations from SM predictions. Such differences would reveal clear and undisputed signs of New Physics and hints for the validity of speculative extensions to the SM. For bound systems containing nuclei with high electric charges QED resembles a field theory with strong coupling and new theoretical methods are needed.

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4.1.1 Muonium The interpretation of measurements in the muonium [55] atom, the bound state of a μ+ and an e− , is free of difficulties arising from the structure of its constituents [56]. Thus QED predictions with two orders of magnitude higher accuracy than for the hydrogen atom are possible. The ground state hyperfine splitting as well as the 1s-2s energy difference have been precisely determined recently. These measurements can be interpreted as QED tests or alternatively —assuming the validity of QED— as independent measurements of α as well as of muon properties (muon mass mμ and muon magnetic moment μμ ). These experiments are statistics limited. Significantly improved values would be possible at new intense muon sources. There is a close connection between muonium spectroscopy and a measurement of the muon magnetic anomaly aμ , the relative deviation of the muon g-factor from the Dirac value 2. Muonium spectroscopy provides precise values for mass, electric charge and magnetic moment of the muon. 4.1.2 Muon magnetic anomaly Precise values of these fundamental constants are indispensable for the evaluation of the experimental results of a muon g-2 measurement series in a magnetic storage ring at BNL [57]. The quantity aμ arises from quantum effects and is mostly due to QED. Further, there is a contribution from strong interactions of 58 ppm which arises from hadronic vacuum polarization. The influence of weak interactions amounts to 1.3 ppm. Whereas QED and weak effects can be calculated from first principles, the hadronic contribution needs to be evaluated through a dispersion relation and experimental input from e+ -e− annihilation into hardrons. Up to now the relevant cross section was determined in the essential energy region in the CMD experiment in Novosibirsk, Russia, or extracted from hadronic τ -decays measured in several setups. Calculations of the hadronic part in aμ depend on the choice of presently available experimental hadronic data and are obtained from an integration over all energies. The results for aμ differ by 3.0 respectively 1.6 standard deviations from the averaged experimental value. Intense theoretical and experimental efforts are needed to solve the hadronic correction puzzle. Evaluations of the hadronic corrections based on available new data on e+ -e− annihilation from the KLOE experiment in Frascati, Italy, appear to confirm earlier values [58], although in small energy intervals significant differences exist in the cross sections from the different experiments. For the muon magnetic anomaly improvements both in theory and experiment are required, before a definite conclusion can be drawn whether a hint of physics beyond standard theory [59] has been seen. A continuation of the g-2 experiment with improved equipment and beams was scientifically approved in 2004.

5 New instrumentation needed Progress in the field of low energy experiments to verify and test the SM and to search for extensions to it would

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benefit in many cases significantly from new instrumentation and a new generation of particle sources. In particular, a high power proton driver would boost a large number of possible experiments which all have a high and robust discovery potential [3]. In [56] two possible scenarios for a 1 GeV and a 30 GeV machine are compared with respect to the physics prospects and the needs of in part novel experimental approaches (see, e.g., [60]). Only a few, but important experiments (like muon g-2) would definitely require the high energy beams. The availability of such a new facility would be desirable for a number of other fields as well, such as neutron scattering, in particular ultra-cold neutron research [61], or a new ISOL facility (e.g. EURISOL) for nuclear physics with nuclei far off the valley of stability. A joint effort of several communities could benefit from synergy effects. Possibilities for such a machine could arise at CERN [60,62], FEMILAB, JPARC and GSI with either a high power linac or a true rapid cycling synchrotron.

6 Conclusions Nuclear physics and nuclear techniques offer a variety of possibilities to investigate fundamental symmetries in physics and to search for physics beyond the SM. Experiments at Nuclear Physics facilities at low and intermediate energies offer in this respect a variety of possibilities which are complementary to approaches in High Energy physics and in some cases exceed those significantly in their potential to steer physical model building. The advantage of high particle fluxes at a Multi-Megawatt facility allow higher sensitivity to rare processes because of higher statistics and because also in part novel experimental approaches are enabled by the combination of particle number and an appropriate time structure of the beam. The field is looking forward to a rich future. The author would like to thank the members of the NuPECC Long Range Plan 2004 Fundamental Interaction working group [3] for numerous fruitful discussions. This work was supported in part by the Dutch Stichting voor Fundamenteel Onderzoek der Materie (FOM) in the framework of the TRIμP programme and by the European Community through the NIPNET RTD project.

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7. V.M. Lobashov et al., Phys. Lett. B 460, 227 (1999); Ch. Kraus et al., hep-ex/0412056 (2004). 8. Ch. Weinheimer, hep-ex/0306057 (2003) and Nucl. Phys. B 118, 279 (2003). 9. A. Osipowicz et al., hep-ex/0109033 (2001). 10. H.V. Klapdor-Kleingrothaus, Phys. Lett. B 586, 198 (2004). 11. For a more detailed review see, e.g., S.R. Elliott, J. Engel, J. Phys. G 30, R183 (2004). 12. Particle Data Group (K. Hagiwara et al.), Phys. Rev. D 66, 010001 (2002); see also S. Eidelmann et al., Phys. Lett. B 592, 1 (2004). 13. I.S. Toner, J.C. Hardy, J. Phys. G 29, 197 (2003). 14. H. Abele et al., Eur. Phys. J. C 33, 1 (2004). 15. A. Czarnecki, W. Marciano, A. Sirlin, hep/ph-0406324 (2004) and references therein. 16. J. Ellis, hep/ph-0409360 (2004). 17. J. Hardy, private communication (2004); see also J. Hardy, these proceedings. 18. A. Czarnecki, W. Marciano, Int. J. Mod. Phys. A 13, 2235 (1998) and references therein. 19. E.W. Hughes, in In Memory of Vernon Willard Hughes, edited by E.W. Hughes, F. Iachello (World Scientific, Singapore, 2004) p. 154. 20. D. Armstrong et al., proposal E02-020 to Jefferson Lab (2002). 21. B.F. Bouchiat, M.A. Bouchiat (Editors), Parity Violation in Atoms and Polarized Electron Scattering (Worls Scientific, Singapore, 1999). 22. S.N. Atutov et al., Hyperfine Interact. 146-147, 83 (2003). 23. E. Gomez et al., physics/0412073 (2004). 24. N. Fortson, in loc. cit. [21], p. 244. 25. A. Sakharov, JETP 5, 32 (1967); M. Trodden, Rev. Mod. Phys. 71, 1463 (1999). 26. N. Ramsey, at Breit Symposium, Yale (1999), (private recording). 27. P.G.H. Sandars, Contemp. Phys. 42, 97 (2001). 28. D. Kawall et al., Phys. Rev. Lett. 92, 13307 (2004). 29. K. Jungmann, physics/0501154 (2005). 30. B.C. Regan et al., Phys. Rev. Lett. 88, 071805 (2002). 31. R. McNabb et al., hep-ex/0407008 (2004). 32. K. Inami et al., Phys. Lett. B 551, 16 (2002). 33. P.G. Harris et al., Phys. Rev. Lett. 82, 904 (1999). 34. D. Cho et al., Phys. Rev. Lett. 63, 2559 (1989). 35. L. Pondrom et al., Phys. Rev. D 23, 814 (1981). 36. F. del Aguila, M. Sher, Phys. Lett. B 252, 116 (1990). 37. R. Escribano, E. Masso, Phys. Lett. B 395, 369 (1997). 38. M. Romalis et al., Phys. Rev. Lett. 86, 2505 (2001). 39. V. Dzuba et al., Phys. Rev. A 63, 062101 (2001). 40. J. Engel, these proceedings; J. Engel et al., Phys. Rev. C 68, 025501 (2003). 41. K. Jungmann, Acta Phys. Pol. 33, 2049 (2002). 42. F.J.M. Farley et al., Phys. Rev. Lett. 93, 052001 (2004). 43. Y. Semertzidis et al., J-PARC Letter of Intent L22 (2003). 44. K.S. Babu, B. Dutta, R. Mohapatra, Phys. Rev. Lett. 85, 5064 (2000); B. Dutta, R. Mohapatra, Phys. Rev. D 68, 113008 (2003). 45. W.-F. Chang, J.N. Ng, hep-ex/0307006 (2004). 46. J. Hisano, hep-ph/0410038 (2004). 47. C.P Liu, R.G.E. Timmermans, nucl-th/0408060 (2004). 48. Y. Semertzidis et al., AIP Conf. Proc. 698, 200 (2004). 49. P. Herczeg, Prog. Part. Nucl. Phys. 46, 413 (2001). 50. J. Behr, these proceedings.

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58. A. Aloisio et al., hep-ex/0407048 (2004). 59. H. Chavez, C.N. Ferreira, hep-ph/0410373 (2004) and references therein. ¨ o et al., hep-ph/0109217 (2001). 60. J. Ayst¨ 61. V.V. Nesvizhevsky et al., Phys. Rev. D 67, 102002 (2003). 62. A. Blondel et al., Physics with a Multi-MW Proton Source, CERN-SPSC-2004-024 (2004).

Eur. Phys. J. A 25, s01, 685–689 (2005) DOI: 10.1140/epjad/i2005-06-097-9

EPJ A direct electronic only

Weak interaction symmetries with atom traps J.A. Behr1,a , A. Gorelov2 , D. Melconian2 , M. Trinczek3 , W.P. Alford4 , D. Ashery5 , P.G. Bricault1 , L. Courneyea6 , uck8 , S. Gryb1 , S. Gu1 , O. H¨ausser2 , J.M. D’Auria3 , J. Deutsch7 , J. Dilling1 , M. Dombsky1 , P. Dub´e2 , F. Gl¨ K.P. Jackson1 , B. Lee1 , A. Mills1 , E. Paradis1 , M. Pearson1 , R. Pitcairn6 , E. Prime6 , D. Roberge6 , and T.B. Swanson3 1 2 3 4 5 6 7 8

TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada Department of Physics, Simon Fraser University, Burnaby, BC, Canada Department of Chemistry, Simon Fraser University, Burnaby, BC, Canada University of Western Ontario, London, ON, Canada School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel University of British Columbia, Vancouver, BC, Canada Universit´e Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium KFKI RMKI, 1525 Budapest, P.O. Box 49, Hungary Received: 3 January 2005 / Revised version: 6 April 2005 / c Societ` Published online: 27 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Neutral atoms trapped with modern laser cooling techniques offer the promise of improving several broad classes of weak interaction experiments with radioactive isotopes. For nuclear β decay, demonstrated trap techniques include neutrino momentum measurements from beta-recoil coincidences, along with methods to produce highly polarized samples. These techniques enable experiments to search for non-Standard Model interactions, test whether parity symmetry is maximally violated, search for 2ndclass tensor and other tensor interactions, and search for new sources of time reversal violation. Ongoing efforts at TRIUMF, Berkeley, and Los Alamos will be highlighted. Trap experiments involving fundamental symmetries in atomic physics, such as time-reversal violating electric dipole moments and neutral current weak interactions, will be briefly mentioned. PACS. 23.40.Bw Weak-interaction and lepton (including neutrino) aspects – 14.60.Pq Neutrino mass and mixing – 32.80.Pj Optical cooling of atoms; trapping

1 Introduction The organizers requested a review of results in fundamental symmetries using radioactive beams since the last ENAM conference in 2001. Personal bias narrows the topic to weak interactions using radioactive species and neutral atom traps, mainly concentrating on β decay work, with a small section on precision experiments with high-Z radioactive atoms. This selection of topic ignores the most interesting symmetries work presented at this conference, limits on 2nd-class currents in A = 8 by T. Sumikama et al. [1] measuring β emission correlations with spin alignment of mirror Gamow-Teller transitions. Ongoing β-ν correlation measurements with a Penning trap (the WITCH recoil spectrometer [2]), the 6 He+ transparent Paul trap [3], and a β-γ Doppler shift measurement in an 14 O Paul trap [4] are slighted here, as are Q-values determined with mass traps [5]. The status of Vud measurements was prea

Conference presenter; e-mail: [email protected]

sented [6], along with an overview of all fundamental symmetries [7]. Neutral atom traps for precision measurements of charge radii [8] were also presented. The workhorse trap in this field is the magneto-optical trap (MOT). A MOT can be treated as a damped harmonic oscillator [9]. The damping is provided by the absorption of laser light a few linewidths lower than an atomic resonance, so that atoms absorb light opposing their motion Doppler-shifted closer to resonance. A force linearly dependent on position is produced by Zeeman shifts from a weak (∼ 10 G/cm) magnetic quadrupole field, which reverses sign at the origin and so selects which handedness of circularly polarized light will be absorbed as a function of position. A normal MOT will have atomic and nuclear polarization close to zero. Because of the nearresonant laser light, MOTs are inherently isotope and isomer selective. One can immediately see several broad classes of experiments that MOTs can assist. Nuclear recoils from β decay freely escape the MOT —they have transmuted to another element so the laser light no longer matters,

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Collection chamber Detection chamber Fig. 1. Prototypical TRIUMF Neutral Atom Trap 2-MOT apparatus. A vapor cell MOT traps radioactives with 0.1% efficiency, and then the atoms are transferred with high efficiency [10] to a second trap with detectors. A uniform electric field collects ion recoils to a microchannel plate, where their position and TOF with respect to the β + is measured.

and the B field is very small. Using an apparatus similar to fig. 1, measurement of the recoil momentum together with the β momentum allows the reconstruction of the ν momentum in a much more direct fashion than possible previously. (Measurement of the β energy is difficult, but there are kinematic regimes —recoil momenta less than Q/c— for which the neutrino momentum is uniquely defined from the other kinematic observables [11].) So the angular distribution of ν’s with respect to the β direction, the β-ν angular correlation, can be measured. A variety of methods exist to polarize laser-cooled neutral atoms and to accurately measure their polarization, and these will be described below. Knowledge of the polarization of the decaying species is a limiting systematic error in many neutron β decay and μ decay experiments. For most experimental tests of maximal parity violation, the polarization must be known with error less than 0.1%. The cold, confined atom cloud also provides a bright source for Doppler-free precision spectroscopy of high-Z radioactive atoms. On the order of 107 photons/s are emitted into 4π for a saturated electric dipole transition. High-Z atoms have larger electron wavefunction overlap with the nucleus, enhancing contact interactions like the weak interaction. E.g., atomic parity violation effects, which measure the strength of the neutral weak interaction, scale with Z 2 N . Tens of thousands of photons must be absorbed to slow atoms from room temperature, so neutral atoms must have reasonably strong cycling transitions to be trapped. Reference [12] reviews MOTs and lists elements that can be trapped in them, to which Ag, Cr, and Yb are recent additions. Radioactive isotopes of most alkali elements (Na, K, Rb, Cs, Fr) have been trapped, along with metastable nobel gas atomic states of He and Kr, and there are plans for alkaline earth elements Ba and Ra. For a more detailed review of the atomic physics and loading of MOTs for radioactive species, see [13], along with a more recent review [14].

2 Beta-neutrino correlations The standard electroweak model unifies electromagnetic and weak interactions, which are mediated by exchange bosons of spin 1, the photon for electromagnetism, and the W + , W − , and Z 0 for the weak interaction. Historically, the β-ν correlation has provided the best evidence that the effective contact interaction was primarily vector and axial vector, which in modern theories is due to exchange of the spin-1 bosons. Berkeley has published the first β-ν correlation using an atom trap [15]. Their abstract quotes the result a = 0.5243 ± 0.0091 for 21 Na, which has a standard model prediction 0.558. They present evidence for a dependence of a on the density of atoms trapped, and if an extrapolation to zero density is done, the value for a is brought into agreement with the standard model. They suggest a possible mechanism, distortions of the recoil momentum produced when the decay originates from a molecular dimer trapped in the weak MOT magnetic field. A Gamow-Teller branch to an excited state is also being remeasured, although to explain the full deviation the branch would have to be 7% rather than the compiled value of 5.0 ± 0.13%. TRIUMF has now submitted a paper with its β-ν correlation result for 38m K, a pure Fermi decay sensitive to scalar interactions [16]. The result is in agreement with the Standard Model with somewhat greater accuracy than the Seattle/Notre Dame/ISOLDE work in β-delayed proton decay of 32 Ar [17], which set the previous best general limits on scalars coupling to the first generation of particles. The TRIUMF work was done with two thousand atoms trapped at a time, at densities less than 0.5% of those in the Berkeley work, avoiding the possibility of trap density distortions. TRIUMF has also published limits on admixtures of MeV-mass neutrinos with the electron neutrino [18]; nonzero admixtures are still allowed by astrophysics and must be constrained experimentally, and the results are listed in PDG2004.

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2.1 Atomic charge state dependence on recoil momentum Berkeley has confronted an additional systematic error common to most recoil momentum measurements, the possibility that the final atomic charge state depends on recoil momentum. This is important to many experiments in this field, so we show some detail here. This effect was first postulated, modelled, and measured in 6 He β − decay work at Oak Ridge [19]. Atomic electrons in the daughter can be treated as suddenly moving with the recoil velocity, and a plane wave expansion of the resulting sudden approximation matrix element produces an effect proportional to the square of the recoil velocity. A recent elegant estimate by Berkeley relates this effect to oscillator strengths and suggests that it could be larger in β + decay [20] because of the difference in atomic binding energies. The recoil energy spectrum to lowest order is distorted by (1 + sErec ). At TRIUMF we can constrain this effect experimentally in two ways. We can fit s and a simultaneously in our TOF[Eβ ] fit for Ar+1,+2,+3 . We fix s = 0 for charge states higher than one, because the model of ref. [20] using semiempirical oscillator strengths [21] suggests that s for the higher charge states is much smaller than for Ar+1 (specifically, s[+2]/s[+1] = 0.11 and s[+3]/s[+1] = 0.05). We find s = 0.008 ± 0.022, which when included changes a by −0.0002 ± 0.0020. We can constrain s and a simultaneously in this method because we fit as a function of Eβ . A fit to the total TOF spectrum summed over all Eβ would be more strongly correlated to the recoil momentum spectrum. We can also simultaneously fit a and s to the fully reconstructed angular distribution, using recoil angle and TOF information. for the Ar+1 data, as shown in fig. 2. Here we can constrain s and a simultaneously because the greatest sensitivity to a is at the null in the angular distribution. The result is s = 0.036 ± 0.027, producing a change in a of −0.0022±0.0017. This is in agreement with our other experimental analysis. Our values of the recoil shakeoff parameter s are in rough agreement with the simple Berkeley estimate [15]. The effect on a is much smaller in our case than they had estimated in 21 Na, because our experimental methods use the full energy and angle information and because in our experimental case a is closer to unity.

3 Polarized β-decay experiments The standard model electroweak bosons also couple only to left-handed neutrinos, and hence the current is called V −A or vector minus axial vector. The leptons and quarks come in weak isospin doublets, which provides cancellations necessary for the theory to be renormalizable; i.e., there are no “2nd-class current” weak-interactions which violate isospin. Polarized experiments in which the polarization can be known atomically can search for the presence of a righthanded ν. Much of the two-parameter space in the sim-

Fig. 2. Constraints from TRIUMF data on the dependence of recoil electron shakeoff on the recoil momentum.

plest “manifest” left-right symmetric models has been excluded by proton-antiproton collider experiments and by superallowed ft values [22, 23]. Indirect limits from the KL KS mass difference also strongly constrain left-right models, although these limits have some model dependence; e.g., reasonable simplifying assumptions must be made about the complicated Higgs sector in left-right models [24, 25]. However, in more complicated non-manifest left-right models direct polarized beta decay measurements are still competitive [25]. The absence of 2nd-class currents can be tested in both polarized and unpolarized observables in isospin-mirror mixed Fermi/GT decays, like 21 Na and 37 K. The Berkeley publication of a also measured weak magnetism in agreement with the standard model [15], i.e. consistent with no 2nd-class currents, although the value achieved is not yet competitive. Los Alamos has demonstrated polarization of t1/2 = 76 s 82 Rb in a TOP trap, which continuously rotates the polarization of the atoms and nuclei, allowing one detector to measure the entire angular distribution [26]. They plan to add a recoil detector, and pursue experiments to test maximal parity violation in the charged current sector and search for tensor interactions [27]. TRIUMF has begun experiments with polarized 37 K by turning off the MOT and optically pumping the expanding cloud. Nuclear vector polarizations of 97 ± 1% have been measured by the vanishing of fluorescence in S1/2 to P1/2 optical pumping as the atoms are polarized.

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The neutrino asymmetry Bν of 37 K has been measured to be 0.989 ± 0.035 of the standard model value [28], the first measurement of a neutrino asymmetry besides that of the neutron. Berkeley has measured precision hyperfine splittings in 21 Na using optical hyperfine pumping and microwave transitions [29]; these techniques are applicable to polarized β-decay experiments. Combining polarization with recoil observables allows a number of unique experiments. The spin asymmetry of slow-going recoils (i.e., back-to-back β-ν emission) vanishes in mixed Fermi/Gamow-Teller decays independent of the size of the Fermi component, and is being measured at TRIUMF. Treiman proposed long ago [30] to measure the spin asymmetry of the nuclear daughters in singles, an observable which is proportional to Aβ + Bν (a reasonable but in reality nontrivial result) and which vanishes for pure Gamow-Teller transitions. Thus the polarization does not have to be as well known. Right-handed currents also cancel, but the observable is sensitive to possible tensor interactions. Possible cases include 80 Rb, 82 Rb, and 47 K, and experiments are actively being pursued at TRIUMF. 3.1 Circularly polarized dipole force trap A trap unique to neutral atoms promises arbitrarily high polarization. The circularly polarized far-off resonant dipole force trap (CFORT) for Rb has now been efficiently loaded and demonstrated at JILA in Boulder [31]. A dipole force trap from a diffraction-limited focussed beam ordinarily traps atoms if it is tuned to the red of resonance, and expels them if tuned to the blue. So if linearly polarized light is tuned just to the blue of the S1/2 → P1/2 (D1) resonance, it repels all the atoms. However, if the atoms are fully polarized, the coupling of circularly polarized light to this transition vanishes. The same coupling coefficients apply as for real absorption, and the atoms already have maximum angular momentum and cannot absorb more. The light is still red-detuned with respect to the D2 transition, so the fully polarized substate, and only that substate, is trapped. The quantization axis is defined by the laser light direction. This trap is not limited by imperfect circular polarization, which merely makes the trap shallower. TRIUMF is developing this trap for 37 K.

4 Weak interaction atomic physics The traps also offer bright sources for Doppler-free spectroscopy, particularly in high-Z atoms where time reversal violating effects are enhanced [32], and where precision measurements could measure the strength of weak neutral nucleon-nucleon and electron-nucleon interactions. Physics with francium atoms has been vigorously pursued at Stony Brook. Several facilities plan work with radioactive atom traps, including plans and efforts at KVI Groningen, Legnaro, and TRIUMF. Explicit atomic parity violation experiments using laser-cooled radioactive atomic beams have been considered in [33].

The enhancement of nuclear Schiff moments by octupole deformation, and their manifestation in timereversal violating electric dipole moments (EDMs) of highZ atoms, was covered at this conference by Engel [34]. There are several experiments underway to take advantage of this effect. Work on a radium atomic beam and Zeeman slower is progressing at Argonne, with a plan to load a MOT and then a dipole force trap based on a CO2 laser [35]. Radium has a convenient forbidden transition at 714 nm with ∼ 10% of an allowed E1 strength. KVI is building a MOT for barium atoms in preparation for a radium trap and EDM experiment [36]. Recent atomic theoretical work has been done [37] to try to confirm some of the interesting radium atomic properties [38]. Work in a radon EDM experiment led by a University of Michigan group has demonstrated 50% transfer of a 120 Xe isotope-separated beam at ISAC/TRIUMF to a mockup of an EDM cell [39], and the Michigan group is proceeding with spin-exchange optical pumping tests to take place at Stony Brook. Measurement of the electron EDM is the goal of a fountain experiment by the group of Gould at LBL, who have measured the scalar dipole polarizability of cesium [40] and are preparing a cesium EDM experiment, with eventual plans for a francium EDM experiment. This group developed the 229 Th source for used for 221 Fr trapping at JILA [41]. The nuclear anapole (“not a pole”) moment is a parityviolating electromagnetic moment induced by the weak interaction between nucleons. Two measurements presently exist, in Cs and Tl isotopes, and the results are neither consistent with each other nor with other parityviolating nuclear experiments [42]. An experiment to measure anapole moments in francium atoms [43] is being actively pursued by a Maryland/Stony Brook collaboration, continuing the long-standing program at Stony Brook in francium atomic lifetimes [44] and precision hyperfine splittings enabling extraction of the hyperfine anomaly and knowledge of the distribution of nuclear magnetism [45]. INFN Legnaro has demonstrated Fr yields [46] and have coupled their Fr ion beam to a MOT. They have pioneered a number of innovative loading techniques [47] in stable Rb and are in the process of applying these to Fr.

5 Conclusion Neutral atom traps provide a suitable environment for precision experiments using radioactive isotopes. The first trap-based measurements in β decay have now been published. Results from francium atomic spectroscopy have long been in evidence, and several labs have plans for electric dipole moment measurements in radium, radon, and francium. This work was supported by NRC through TRIUMF, by NSERC, and by the Canadian Institute for Photonics Innovations.

J.A. Behr et al.: Weak interaction symmetries with atom traps

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

18. 19.

20. 21. 22. 23. 24.

T. Sumikama, these proceedings. M. Beck, these proceedings. D. Rodr´ıguez, these proceedings. N. Scielzo et al., Bull. Am. Phys. Soc., Div. Nucl. Phys., October 2004, JG.009. F. Herfurth, these proceedings. J.C. Hardy, these proceedings. K. Jungmann, these proceedings. P. Mueller, these proceedings. E.L. Raab et al., Phys. Rev. Lett. 59, 2631 (1987). T.B. Swanson et al., J. Opt. Soc. Am. B 15, 2641 (1998). O. Kofoed-Hansen, Dan. Mat. Fys. Medd. 28, 1 (1954). C.S. Adams, E. Riis, Prog. Quantum Electron. 21, 1 (1997). G.D. Sprouse, L.A. Orozco, Annu. Rev. Nucl. Part. Sci. 47, 429 (1997). J.A. Behr, Nucl. Instrum. Methods B 204, 526 (2003). N.D. Scielzo et al., Phys. Rev. Lett. 93, 102501 (2004). A. Gorelov et al., Phys. Rev. Lett. 94, 142501 (2005). E.G. Adelberger et al., Phys. Rev. Lett. 83, 1299 (1999); 83, 3101 (1999)(E). After recent mass measurements a ˜ is being re-evaluated (K. Blaum et al. Phys. Rev. Lett. 91, 260801 (2003) and A. Garcia, Nucl. Phys. A 746, 298c (2004)). M. Trinczek et al., Phys. Rev. Lett 90, 012501 (2003). T.A. Carlson, Frances Pleasonton, C.H. Johnson, Phys. Rev. 129, 2220 (1963); T.A. Carlson et al., Phys. Rev. 169, 27 (1968). N.D. Scielzo et al., Phys. Rev. A 68, 022716 (2003). D.A. Verner et al., Astrophys. J. 465, 487 (1996). S. Abachi et al. Phys. Rev. Lett. 76, 3271 (1996). J.C. Hardy, I.S. Towner, Phys. Rev. Lett. 94, 092502 (2005). P. Herczeg, Prog. Part. Nucl. Phys. 46/2, 413 (2001), and references therein, in particular P. Langacker, S. Uma Sankar, Phys. Rev. D 40, 1569 (1989).

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25. E. Thomas et al. Nucl. Phys. A 694, 559 (2001); N. Severijns et al., to be published in Rev. Mod. Phys. 26. S.G. Crane, et al., Phys. Rev. Lett. 86, 2967 (2001). 27. M. Hausmann et al., Bull. Am. Phys. Soc., Div. Nucl. Phys., October 2003, BG.004. 28. D. Melconian et al., Nucl. Instrum. Methods B 204, 540 (2003); Bull. Am. Phys. Soc., Div. Nucl. Phys., October 2003, BG.003 and to be submitted. 29. M.A. Rowe et al. Phys. Rev. Lett. 59, 1869 (1999). 30. S.B. Treiman, Phys. Rev. 110, 448 (1957). 31. K.W. Miller, S. D¨ urr, C.E. Wieman, Phys. Rev. A 66, 023406 (2002). 32. For an overview, see E.N. Fortson, P. Sandars, S. Barr, Phys. Today 56 (6), 33 (2003). 33. S. Sanguinetti, J. Gu´ena, M. Lintz, Ph. Jacquier, A. Wasan, M.A. Bouchiat, Eur. Phys. J. D 25, 3 (2003). 34. J. Engel, these proceedings. 35. N. Scielzo, Bull. Am. Phys. Soc., April 2004, L14.004, and private communication. 36. H. Wilschut, private communication; J.W. Turkstra et al., Hyperfine Interact. 127, 533 (2000). 37. J. Bieron’ et al., J. Phys. B 37, L305 (2004). 38. V.A. Dzuba, V.V. Flambaum, J.S.M. Ginges, Phys. Rev. A 61, 062509 (2000). 39. S.R. Nuss-Warren et al., Nucl. Instrum. Methods A 533, 275 (2004). 40. J. Amini, H. Gould, Phys. Rev. Lett. 91, 153001 (2003). 41. Z.-T. Lu et al., Phys. Rev. Lett. 79, 994 (1997). 42. W.C. Haxton, C.-P. Liu, M. Ramsey-Musolf, Phys. Rev. C 65, 045502 (2002). 43. D. DeMille, M.G. Kozlov, physics/9801034. 44. J.M. Grossman et al., Phys. Rev. A 62, 062502 (2000) and references therein. 45. J.S. Grossman et al., Phys. Rev. Lett. 83, 935 (1999). 46. S.N. Atutov et al., Hyperfine Interact. 146-147, 83 (2003). 47. S.N. Atutov et al., Phys. Rev. A 67, 053401 (2003).

Eur. Phys. J. A 25, s01, 691–694 (2005) DOI: 10.1140/epjad/i2005-06-017-1

EPJ A direct electronic only

Time-reversal violation in heavy octupole-deformed nuclei J. Engela Department of Physics and Astronomy, CB 3255, University of North Carolina, Chapel Hill, NC 27599-3255, USA Received: 2 December 2004 / c Societ` Published online: 18 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A nonzero atomic electric-dipole moment (EDM) at a level not far from current experimental limits would signify time-reversal violation from outside the Standard Model. EDMs are enhanced in atoms that have octupole-deformed nuclei. We report a careful self-consistent mean-field calculation of the time-reversal-violating nuclear Schiff moment —the quantity that induces an atomic EDM— in the octupole-deformed nucleus 225 Ra. The self-consistent mean field in odd-A nuclei includes important effects of core polarization. The results of the calculation are encouraging for EDM experiments in the light actinides. Accurate calculations of Schiff moments in ordinary spherical and quadrupole-deformed nuclei such as 199 Hg are also important. We describe work in progress on this more general problem. PACS. 11.30.Er General theory of fields and particles: Charge conjugation, parity, time reversal, and other discrete symmetries – 21.60.Jz Nuclear structure: Hartree-Fock and random-phase approximations

1 Introduction Experiments with kaons and B-mesons indicate that timereversal invariance (T ) is violated at a low level. The results of these experiments can be explained by a phase in the Cabibo-Kobayashi-Maskawa (CKM) matrix of the Standard Model. But the absence of antimatter in our universe is evidence that T invariance (or more precisely, CP invariance) was badly violated long ago. The CKM phase is unable to account for so large an effect, and so theorists believe there must be another source of T violation, this one from outside the Standard Model. As we shall see, an atom in its ground state cannot have an electric dipole moment (EDM) without violating T . A number of experiments have searched for atomic EDMs, and the limits are tight. But because CKM T violation shows up in first order only in flavor-changing processes, it should appear in atomic experiments only after the limits are improved by 5 or 6 orders of magnitude. The same constraint does not apply, however, to T violation in extensions to the Standard-Model. The most popular extension, supersymmetry, has many flavor-conserving phases, making EDM experiments ideal for testing it. Already these experiments are putting serious pressure on the theory. Here, after some preliminaries, we argue that experiments on atoms with octupole-deformed nuclei will be more sensitive to T -violation within the nucleus than the current best experiments. The enhancement of T violation in these nuclei is connected with the collective violation of intrinsic parity. This paper discusses work published by a

e-mail: [email protected]

the author together with Jim Friar and Anna Hayes [1] and Michael Bender, Jacek Dobacewski, Joao de Jesus, and Piotr Olbratowski [2], and some work in progress on spherical nuclei with Joao de Jesus.

2 T violation and EDMs 2.1 Why do EDMs require T violation? It is obvious that for the negative-parity (P ) dipole operator to have a non-zero expectation value in a nondegenerate state, P must be violated. But because states with good J, M are not eigenstates of the T operator, the usual argument from “good quantum numbers” does not work for T . Why must it be violated as well? Consider a state |g; J, M  (g stands for “ground”) with no degeneracy besides the 2J + 1 spin multiplicity. Symmetry under rotation by π around the y axis implies that for a vector operator such as d ≡ Σi ei ri ,

g : J, M |d|g : J, M  = − g : J, −M |d|g : J, −M .

(1)

The time reversal operator Tˆ takes |g : J, M  to a real phase times |g : J, −M  (under the usual phase conventions), just like rotation by π. But d does not change under Tˆ, while the rotation flips its sign. So if the system is invariant under T , we also have

g : J, M |d|g : J, M  = + g : J, −M |d|g : J, −M .

(2)

These two equations together imply that d must vanish. If T is violated, the argument fails because Tˆ will take

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|g : J, −M  to a state with J, −M that is not identical to the corresponding member of the ground-state multiplet. In that case, eq. (2) does not hold.

to approach the factor by which EDM limits on the neutron are worse than atomic limits, and the nuclear Schiff moment is more sensitive to neutral pion exchange than the neutron EDM, so atomic experiments are currently competitive in the search for some kinds of T violation.

2.2 How objects get EDMs and why atomic EDMs are suppressed T -violation can work its way up from the most fundamental particles through to atoms. If the symmetry is violated by, e.g. supersymmetry, quarks will develop T -violating couplings, leading to effective T -violating πN N couplings. These in turn lead through pion exchange to an effective two-nucleon interaction of the form " g m2π (σ1 − σ2 ) · (r1 − r2 ) g¯0 τ1 · τ2 HT = − 8πmN

g¯1 − (τ1z + τ2z ) + g¯2 (3τ1z τ2z − τ1 · τ2 ) 2 # g¯1 − (σ1 + σ2 ) · (r1 − r2 ) (τ1z − τ2z ) 2

1 exp(−mπ |r1 − r2 |) , (3) 1 + × mπ |r1 − r2 | mπ |r1 − r2 |2

where g is the normal strong πN N coupling constant and the three g¯’s are dimensionless isoscalar, isovector, and isotensor T -violating πN N couplings. This interaction can cause the nucleus to develop an EDM, which in turn causes an atomic EDM. The goal of the atomic experiments (and this work) is to extract limits on the g¯’s from experimental limits on an atomic EDM, or to determine them if an EDM is observed. Unfortunately, atomic EDMs are suppressed. Any nuclear EDM induced by the interaction in eq. (3) is shielded by the electrons, which rearrange themselves to create an electronic EDM in the opposite direction. Schiff proved [3] that the cancellation is exact in the limit of a point-like nucleus and nonrelativistic electrons1 . Luckily, the nucleus has a finite radius so the shielding is not complete. It turns out, however, that after its effects are accounted for, the nuclear quantity that induces an EDM in the electrons is not the dipole moment D, but rather a kind of weighted dipole moment (with a correction term) called the “Schiff moment”:

5 2 1  2 (4) ep rp − R rp , S= 3 10 p

where R2 is the root-mean-squared nuclear charge-density radius. If, as one would expect, S ≈ 0.1R2 D, then the 2 ) ≈ 10−9 . atomic EDM d is down from D by O(R2 /10RA (RA is the atomic radius.) But the behavior of relativistic Coulomb wave functions near the origin partly offsets this terrible suppression via a factor 10Z 2 ≈ 105 in heavy nuclei, so that the overall suppression of the atomic EDM from shielding is only about 10−4 . This number begins 1

It may be possible to reduce or eliminate shielding in experiments with “naked nuclei” [4, 5].

3 Enhancement by octupole deformation We can make atomic experiments even more attractive by finding the right atom, because some atoms are better places to look for an EDM than others. One reason is that octupole deformation of atomic nuclei enhances the nuclear Schiff moment dramatically. Since the T -violating interaction HT is very weak, it can be treated peturbatively, and the Schiff moment can be written as

S =

 0|S|m m|HT |0 m

E0 − E m

+ c.c.

(5)

Two collective effects associated with octupole deformation make this expression large. The first is the existence of parity doubling. The intrinsic state has a shape that breaks parity symmetry. It contains both positiveand negative-parity components, and when projected onto good parity yields two states of opposite parity very close to one another in energy. In 225 Ra, for example, the J π = 1/2+ ground state (|0 in our notation) has a J π = 1/2− partner |¯ 0 just 55 keV higher. Since HT is pseudoscalar, it connects |0 and |¯ 0, and the single term with |¯0 as the intermediate state dominates the sum in eq. (5). Just like for quadrupole transitions, the transition matrix element

0|S|¯ 0 is proportional to the intrinsic Schiff moment, so that eq. (5) becomes, to good approximation,

S ≈ −2/3

S intr.  HT  . E0 − E¯0

(6)

The second collective enhancement comes from robust intrinsic Schiff moments that often are much larger than R2 times the intrinsic dipole moment. Although the intrinsic dipole moments in octupole-deformed nuclei are collective, they are often quite small. The reason is that they depend on the distribution of charge with respect to the center of mass, and vanish when the neutron and proton densities coincide exactly. Intrinsic Schiff moments are not subject to this kind of cancellation. As a result of this and the parity-doubling, the laboratory Schiff moment in a nucleus like 225 Ra is enhanced, according to collective model estimates [6,7] by two or three orders of magnitude over that of 199 Hg, the atom with the best experimental limit on its EDM [8]. Why is the uncertainty an order of magnitude, a factor large enough to deter experimentalists? The matrix element of HT depends on the nuclear spin distribution, a delicate quantity. In simple collective models (such as the particle-rotor model) a single valence nucleon carries all the spin. In reality, however, the valence nucleon polarizes the core, an effect that can alter the spin distribution

J. Engel: Time-reversal violation in heavy octupole-deformed nuclei

693

Fig. 1. Contours of constant density for a series of even-N radium isotopes. Contour lines are drawn for densities ρ = 0.01, 0.03, 0.07, 0.11, and 0.15 fm−3 .

substantially. Even without core polarization, the matrix element of HT depends sensitively on the wave function of the valence nucleon. To reduce the uncertainty in the Schiff moment to a reasonable level, we need a state-of-the art calculation.

4 Calculation of Schiff moment in

225

Ra

In ref. [2] we used the program HFODD [9] to do a completely self-consistent Skyrme-mean-field calculation of the intrinsic ground state of 225 Ra. The code allows the simultaneous breaking of rotational invariance, P , and T . The first two are needed to obtain octupole deformation, the last to polarize the core (i.e. break Kramers degeneracy). HFODD cannot yet treat pairing when it allows T to be broken, but pairing in T -odd channels is poorly understood. No no existing codes can do more than HFODD in odd-A octupole-deformed nuclei. We used the Skyrme interactions SIII, SkM∗ , SLy4, and SkO , the last our favorite because it was tuned in ref. [10] to treat spin degrees of freedom (particularly isovector spin excitations). Figure 1 shows the shapes produced by SkO in the even Ra isotopes. The nucleus 225 Ra, with N = 137, will clearly have significant amounts of both quadrupole and octupole deformation. Figure 2 shows three parity-violating intrinsic quantities. In the top panel is the ground-state octupole deformation as a function of neutron number. The trend mirrors that in the density profiles shown earlier. The second panel shows the absolute values of intrinsic dipole moments D0 , along with experimental data extracted from E1 transition probabilities [11]. Both the experimental and calculated values change sign between N = 134 and N = 138, illustrating the delicacy of this quantity. None of the forces precisely reproduces the trend through all the isotopes,

. . .

. . .

Fig. 2. The predicted first-order octupole deformations (top), absolute values of the predicted intrinsic dipole moments (middle), and the predicted intrinsic Schiff moments (bottom) for four Skyrme interactions in a series of even-N radium isotopes. The absolute values of the experimental intrinsic dipole moments are also shown.

but the comparison has to be taken with a grain of salt because “data” derive from transitions between excited rotational states. The intrinsic Schiff moment Sz , as noted

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Table 1. Intrinsic-state expectation values of important operators in UT , in the neutron-proton scheme (in 10−3 fm−4 ).

σn · ∇ρn 

σn · ∇ρp 

SIII(0) SkM∗ (0) SLy4(0) SkO (0)

−0.577 −0.619 −0.628 −0.331

−0.491 −0.120 −0.050 −0.013

SkO

−0.320

−0.114

−1.2

−0.8

particle-rotor [7]

x

where ρ0 and ρ1 are the isoscalar and isovector densities and exchange terms are probably negligible. Table 1 shows matrix elements of the most important operators in UT . The zeros following the interaction names mean that the core-polarizing parts of the interactions, which were never fit for the older forces, have been turned off. The differences between the lines labeled SkO (0) and SkO show the effects of core polarization. Our full SkO Schiff moment for 225 Ra, with the finite-range force (though not yet with exchange terms or short-range correlations), is g0 + 6.31g¯ g1 − 3.80 g¯ g2 (e fm3 ).

Sz Ra = −1.90 g¯

(8)

Hg [12] gave

g0 + 0.055 g¯ g1 + 0.009 g¯ g2 (e fm ). (9)

Sz Hg = 0.0004 g¯ 3

Our Schiff moment, though smaller than particle-rotor estimates, is over 100 times larger (and significantly more than that if g¯1 is anomalously small) than that of 199 Hg. Combined with an additional factor-of-three enhancement from atomic physics [13], this result bodes well for upcoming experiments [14] to measure the EDM of 225 Ra.

5 Schiff moment of

199

+ ...

Fig. 3. Leading contributions to the Schiff moment of 199 Hg. The vertical line is the valence neutron, the solid horizontal line a Skyrme interaction, the dashed line HT , the zig-zag line the Schiff operator, and the filled oval an RPA bubble sum.

  · (¯ g0 +2¯ g2 )∇ρ1 (r)−¯ g1 ∇ρ0 (r) +exchange, (7)

199

x Strong

A  g σi τz,i 2m2π mN i=1

A recent calculation for

+

T−odd

above, is more collective and under better control, as the bottom panel of the figure shows. Finally, what about HT ? In the limit of infinite pion mass, eq. (3) reduces to an effective one-body potential ˆT (r) = − U

T−odd

Hg

To be sure of the enhancement factor, and to discern the consequences of existing EDM limits, we need to be more confident of the Schiff moment of 199 Hg. Reference [12] predicts a very weak sensitivity to the isoscalar πN N coupling g¯0 (the first coefficient in eq. (9)). J. de Jesus and the author are calculating the Hg Schiff moment with the same Skyrme interactions we used in Ra. Our approach is to treat 198 Hg as a spherical core in the HFB approximation, and then include polarizing effects of the extra neutron quasiparticle in perturbation theory by allowing it to excite core vibrations, which we treat in QRPA. Figure 3

shows the leading diagrams in the approximation that pairing effects are negligible (we include pairing in the actual calculations). The physics is similar to that included in ref. [12], but our calculation is more self-consistent and our use of several Skyrme interactions gives us a handle on the uncertainty. Our preliminary (still unofficial) result with SkO is = 0.007 g¯ g0 + 0.067 g¯ g1 + 0.009 g¯ g2 (e fm3 ),

Sz prelim. Hg (10) and each of the coefficients changes by factors of 2 or 3 when we change the Skyrme interaction. Our isoscalar coefficient is considerably larger than the one in eq. (9). We will remove the tag “preliminary” as soon as we have explored the uncertainty a little more carefully. Thanks go to collaborators M. Bender, J. Dobaczewski, J. Friar, A.C. Hayes, J. de Jesus, and P. Olbratowski. This work was supported by the U.S. DOE Grant DE-FG02-97ER41019.

References 1. J. Engel, J.L. Friar, A.C. Hayes, Phys. Rev. C 61, 035502 (1999). 2. J. Engel, M. Bender, J. Dobaczewski, J. de Jesus, P. Olbratowski, Phys. Rev. C 68, 025501 (2003). 3. L.I. Schiff, Phys. Rev. 132, 2194 (1963). 4. P.G.H. Sandars, Contemp. Phys. 42, 97 (2001). 5. F.J.M. Farley et al., Phys. Rev. Lett. 93, 052001 (2004). 6. N. Auerbach, V.V. Flambaum, V. Spevak, Phys. Rev. Lett. 76, 4316 (1996). 7. V. Spevak, N. Auerbach, V.V. Flambaum, Phys. Rev. C 56, 1357 (1997). 8. M.V. Romalis, W.C. Griffith, J.P. Jacobs, E.M. Fortson, Phys. Rev. Lett. 86, 2505 (2001). 9. J. Dobaczewski, P. Olbratowski, Comput. Phys. Commun. 158, 158 (2004) and references therein. 10. M. Bender, J. Dobaczewski, J. Engel, W. Nazarewicz, Phys. Rev. C 65, 054322 (2002). 11. P.A. Butler, W. Nazarewicz, Rev. Mod. Phys. 68, 349 (1996). 12. V.F. Dmitriev, R.A. Sen’kov, Phys. At. Nucl. 66, 1940 (2003). 13. V.A. Dzuba, V.V. Flambaum, J.S.M. Ginges, M.G. Kozlov, Phys. Rev. A. 66, 012111 (2002). 14. R. Holt, http://mocha.phys.washington.edu/∼int talk/WorkShops/int 02 3/People/Holt R/ (2002).

Eur. Phys. J. A 25, s01, 695–698 (2005) DOI: 10.1140/epjad/i2005-06-109-x

EPJ A direct electronic only

Superallowed 0+ → 0+ β decay and CKM unitarity: A new overview including more exotic nuclei J.C. Hardya and I.S. Townerb Cyclotron Institute, Texas A&M University, College Station, TX 77843, USA Received: 12 September 2004 / c Societ` Published online: 30 June 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The f t values for superallowed 0+ → 0+ nuclear β transitions are nearly independent of nuclearstructure ambiguities and depend uniquely on the vector part of the weak interaction. They thus provide access to clean tests of some of the fundamental precepts of weak-interaction theory and can even probe physics beyond the standard model. We have just completed a new survey and overview of world data on such transitions, including not just the nine cases considered in the past, but also eleven more from T = 1 parents: even-even Tz = −1 nuclei from 18 Ne to 42 Ti; and odd-odd nuclei from 62 Ga to 74 Rb. These new cases all involve more exotic nuclei and, to yield comparable precision, present real experimental challenges. Nevertheless, three of these new cases are already known well enough to contribute – together with the nine well known transitions – to the setting of limits on fundamental weak-interaction parameters. The remaining eight cases show promise for making important contributions in future. PACS. 23.40.Bw Weak-interaction and lepton (including neutrino) aspects – 12.15.Hh Determination of Kobayashi-Maskawa matrix elements – 12.60.-i Models beyond the standard model

1 Introduction The study of superallowed 0+ → 0+ β decay gives nuclear physicists access to some of the most fundamental properties of the weak interaction. It can be used to test the conservation of the vector current (CVC), set limits on any possible scalar currents, test the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix and probe the existence of right-hand currents. To be interesting, though, these tests demand high precision in the experimental determination of the transition f t values and, until recently, this has limited the study of superallowed decay to parent nuclei very near stability, where decay schemes are less complex and production rates are compatible with high counting statistics. In the past, we have periodically surveyed relevant world data on such superallowed transitions and extracted from them the current best fundamental weak-interaction parameters. However, our most recent complete survey [1], which included eight well measured cases, was published in 1990 and since then, with the rise of radioactive-beam facilities, techniques have been developed that are now bringing even quite exotic nuclei into the realm of precision measurements. With this in mind, we have just a

e-mail: [email protected] Present address: Department of Physics, Queen’s University, Kingston, Ontario K7L 3N6, Canada. b

completed a thorough new overview [2] in which we critically surveyed all relevant measurements, adjusted original data to take account of the most modern calibration standards, obtained statistically rigorous average results for each transition, and used updated and consistent calculations to extract weak-interaction parameters from those results. Although, there are still only eight transitions whose f t values are known to better than 0.1%, four more cases are now known with 0.1–0.4% precision. These four make real contributions to the usefulness of the overall results and several involve quite exotic nuclei. Finally, we identify a further eight transitions that are promising cases for future study.

2 Superallowed β decay All superallowed transitions whose f t values have been measured with high precision are between (J π , T ) = (0+ , 1) analog states. For such transitions, the measured f t-value can be related to the vector coupling constant via an expression that includes several small (∼ 1%) correction terms. It is convenient to combine some of these terms with the f t-value and define a “corrected” Ft-value. Thus, we write [3]  )(1 + δN S − δC ) = Ft ≡ f t(1 + δR

K , 2G2V (1 + ΔVR )

(1)

The European Physical Journal A

3 Weak-interaction tests The data in the bottom panel of fig. 1 can also be analyzed to set a limit on the possible presence of scalar currents, which would affect the calculation of the statisticalrate function, f , via a term in the shape-correction function that is inversely proportional to the positron energy. Since the total superallowed-transition decay energy increases with Z, a scalar contribution would therefore have its greatest effect on the Ft values at low Z, introducing curvature in that region. The curved lines in the figure are the loci of Ft values that would be expected if CS /CV = ±0.002. Obviously, the Ft values do not exhibit any such curvature and, from a least-square fit to the data, we obtain the limit |CS /CV | ≤ 0.0013, as expressed in the conventional notation of Jackson, Treiman and Wyld [4]. The corresponding result for the Fierz interference constant is bF = +0.0001(26). These are, by far,

3140

3130

3120

74

Rb

34

Ar

ft (1+δR’) (s)

where K/(¯ hc)6 = 2π 3 ¯h ln 2/(me c2 )5 = 8120.271(12) × −10 −4 GeV s, GV is the vector coupling constant 10 for semi-leptonic weak interactions, δC is the isospinsymmetry-breaking correction and ΔVR is the transitionindependent part of the radiative correction. The terms  and δN S comprise the transition-dependent part of the δR radiative correction, the former being a function only of the electron’s energy and the Z of the daughter nucleus, while the latter, like δC , depends in its evaluation on the details of nuclear structure. From this equation, it can be seen that each measured transition establishes an individual value for GV and, if the CVC assertion is correct that GV is not renormalized in the nuclear medium, all such values —and all the Ft-values themselves— should be identical within uncertainties, regardless of the specific nuclei involved. The f t-value that characterizes any β-transition depends on three measured quantities: the total transition energy, QEC , the half-life, t1/2 , of the parent state and the branching ratio, R, for the particular transition of interest. The QEC -value is required to determine the statistical rate function, f , while the half-life and branching ratio combine to yield the partial half-life, t. In our treatment [2] of the data, we considered all measurements formally published before November 2004 and those we knew to be in an advanced state of preparation for publication by that date. The final corrected Ft values obtained for the best twelve cases from the survey [2] are plotted in the bottom panel of fig. 1. They cover a broad range of nuclear masses from A = 10 to A = 74. As anticipated by CVC (see eq. (1)) the Ft values are statistically consistant with one another, yielding an average value Ft = 3072.7(8) s, with a corresponding chi-square per degree of freedom of χ2 /ν = 0.42. This expectation of CVC is thus verified at the level of 3 × 10−4 , which is the fractional uncertainty we obtain for Ft. This is a 30% improvement over the best previous value [1] —also obtained from superallowed β decay— and can be attributed to improvements in the experimental data.

3110 22

Mg

3100 34

Cl

10

C

38

K

m 54 46

14

O

Co

V

3090 42 26

Al

m

Sc

50

Mn

3080

3100

t (s)

696

3090

3080

3070

3060 10

20

30

Z of daughter

Fig. 1. In the top panel are plotted the experimental f t-values  corrected only for δR , those radiative effects that are independent of nuclear structure. In the bottom panel, the corresponding Ft values are given; they differ from the top panel simply by inclusion of the nuclear-structure-dependent corrections, δN S and δC . (See eq. (1).) Note that the increased uncertainty for 74 Rb reflects the lack of experimental constraints on the nuclear shell model in this mass region. The horizontal grey band in the bottom panel indicates the average Ft value with its uncertainty. The curved lines represent the approximate loci the Ft values would follow if an induced scalar current existed with CS /CV = ±0.002.

the most stringent limits on |CS /CV | or |bF | ever obtained from nuclear β decay. With a mutually consistent set of Ft values, we can now insert their average value into eq. (1) and determine the vector coupling constant GV using the value ΔVR = 2.40(8)% calculated for the transition-independent radiation correction by Marciano and Sirlin [5]. In doing so, we also make a small adjustment to the value of Ft to account for possible systematic uncertainties in δC by averaging our calculated δC values with those of Ormand and Brown [6] and increasing the assigned uncertainty (see ref. [2]). This leads to Ft = 3073.5(12), the result we carry forward. The derived value of GV itself is of little interest but, when combined with GF , the weak interaction constant for the purely leptonic muon decay, it yields a value for the element Vud of the CKM matrix: Vud = GV /GF . Taking the Particle Data Group (PDG) value [7] of GF /(¯hc)3 = 1.16639(1) × 10−5 GeV−2 , we obtain |Vud | = 0.9738(4). Compared to our previously

J.C. Hardy and I.S. Towner: Superallowed β decay

recommended value [3], this result differs by two units in the last digit quoted and has a reduced uncertainty. Note that, by more than an order of magnitude, Vud is the most precisely determined element of the CKM matrix. The unitarity of the CKM matrix is a fundamental requirement of the standard model and the precise value for Vud obtained from superallowed β decay is a key component of the most demanding test available of that unitarity. Combining our value for Vud with the PDG’s recommended values [7] of Vus = 0.2200(26) and Vub = 0.00367(47), we obtain a unitarity sum for the toprow elements of the CKM matrix of |Vud |2 + |Vus |2 + |Vub |2 = 0.9966 ± 0.0014,

(2)

which fails unitarity by 2.4 standard deviations. A recent + ) branching ratio measurement of the K + → π 0 e+ νe (Ke3 from the Brookhaven E865 experiment [8] obtains Vus = 0.2272 ± 0.0030. If this value alone were adopted for Vus rather than the PDG average of many experiments, the sum in eq. (2) would equal 0.9999(16) and unitarity would be fully satisfied. Depending on what ultimately turns out to be the correct value for Vus , the result for the unitarity sum can be interpreted in terms of the possible presence of right-hand currents. We express the outcome in terms of the left-right and left-left coupling constants, aLR and aLL , defined by Herczeg [9]. If we accept the unitarity test result in eq. (2), then we find ReaLR /aLL = −0.00176(74). Within the context of the manifest left-right symmetric model, this result corresponds to a mixing angle of ζ = 0.00176(74). If, instead, we adopt the E865 value for Vus , the result becomes ReaLR /aLL = −0.00007(84).

4 Sharpening the tests in future The accumulated world data on superallowed 0+ → 0+ β decay comprises the results of over one hundred measurements of comparable precision [2]. Virtually all the important experimental parameters used as input to the f t-value determinations have been measured in at least two, and often four or five, independent experiments. Obviously, just another measurement will not have much impact on the precision of the weak-interaction parameters quoted here. Nevertheless, it is still possible for well selected experiments with existing or currently foreseen techniques to make real improvements. For example, the bottom panel of fig. 1 clearly illustrates the sensitivity of the low-Z cases to the possible presence of scalar currents. Reduced uncertainties, particularly on the decays of 10 C and 14 O, could thus further reduce the scalar-current limit significantly. It is the unitarity test, though, that is attracting the most interest at the moment, with various programs currently underway to improve this test. The appearance of one new measurement of the Ke3 decay, which yielded quite a different result [8] for Vus from the previously accepted average, has stimulated other measurements of the same type. Within a few years, their results should settle

697

the controversy over Vus and may, in themselves, bring eq. (2) into statistical agreement with unity. At the same time, experimentalists and theorists alike are seeking to improve the precision with which Vud is known. Since the biggest contributor to the Vud uncertainty —90% of it, in fact— comes from the calculation of ΔVR , the top priority must be to improve that radiative-correction term, a difficult theoretical problem to which experiment cannot contribute. However, the next most important contributor is the structure-dependent correction terms, δN S and δC . These can actually be tested by experiment, and measurements of 0+ → 0+ β decays have been re-invigorated, now with a focus on the more exotic nuclei which particularly lend themselves to tests of the structure-dependent corrections. The approach is best explained by a comparison of the top and bottom panels in fig. 1. The top panel shows a plot  ), the experimental “raw” f t values corrected of f t(1 + δR only for a structure-independent radiative effect. The corresponding Ft values plotted in the bottom panel differ only by the application of the nuclear-structure-dependent corrections, (δC − δN S ). Obviously, at the current level of precision the structure-dependent corrections act very well to remove the considerable “scatter” that is apparent in the experimental f t values and is effectively absent from the corrected Ft values. It is important to note that the calculations of δN S and δC are based on well-established shell-model wave functions and were further tuned to measured binding energies, charge radii and coefficients of the isobaric multiplet mass equation [10]. Their origins are completely independent of the superallowed decay data. Thus, the consistency of the corrected Ft values shown in fig. 1 is already a powerful validation of the calculated corrections used in their derivation. The comparison in fig. 1 also suggests that the validation of (δC − δN S ) can be further improved if future experiments focus on transitions with large calculated corrections. If the f t values measured for cases with large calculated corrections also turn into corrected Ft values that are consistent with the others, then this must verify the calculation’s reliability for the most precisely measured transitions, which have smaller corrections. The most potentially attractive cases for this purpose are in two series of 0+ nuclei: the even-Z, Tz = −1 nuclei with 18 ≤ A ≤ 42, (18 Ne, 22 Mg, 26 Si, 30 S, 34 Ar, 38 Ca, and 42 Ti) and the odd-Z, Tz = 0 nuclei with A ≥ 62 (62 Ga, 66 As, 70 Br and 74 Rb). In fact, the most recent additions to the twelve transitions shown in fig. 1 —22 Mg, 34 Ar and 74 Rb— were chosen from these series and the latter two have large calculated corrections. Though their precision does not yet equal that of the others, their Ft values do indicate that the corrections so far are living up to expectations. Reducing the uncertainties on these cases and adding new ones, such as 18 Ne, 30 S and 62 Ga, should be considered as high priority goals in improving the precision on Vud and sharpening the unitarity test. Certainly these new series of superallowed emitters present experimental challenges. In each case, both the parent and daughter nuclei are unstable, so each QEC

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60

40

Parts in 104

20

0 18

Ne

22

Mg

26

Si

30

34

S

Ar

38

Ca

42

Ti

TZ = -1 60

TZ = 0

40

Q-value

Half-life

20

Branching ratio

δR’

δC - δNS

0 62

Ga

66

As

70

Br

74

Rb

Parent nucleus

Fig. 2. Summary histogram of the fractional uncertainties attributable to each experimental and theoretical input factor that contributes to the final Ft values for the “new” series of superallowed transitions currently under study. Where the uncertainty is shown as exceeding 60 parts in 104 , no useful experimental measurement has been made.

value requires careful Penning-trap measurements of two masses. With half-lives, particularly of the heavier nuclei, pushing into the 100-ms range, the required ∼ 500-eV precision on these masses is at the very limit of what even Penning traps can achieve, at least in their present on-line configuration. Branching ratios too are stretching experimental limits. The superallowed transitions, dominant (> 99.3%) branches for all but one of the “standard” superallowed cases, are seriously affected and sometimes dwarfed by competing Gamow-Teller branches in the new cases. For the Tz = −1 parents, which populate odd-odd daughters, there are only a few such competing branches in each case but they are strong —strong enough that the superallowed branch must be measured directly to 0.1% precision, a difficult task requiring unprecedented calibration standards in the measurement of β-delayed γ rays. The new Tz = 0 emitters with A ≥ 62 offer a different branching-ratio challenge. Their decays are of higher energy (> 9 MeV) and, although the daughters are eveneven, their level density is high enough that numerous weak Gamow-Teller branches compete with the superallowed branch. Though the total Gamow-Teller strength can be significant, many of the individual branches are unobservably weak [11]. This “Pandemonium” effect (see ref. [12]) can be partially corrected for by careful measure-

ment of weak β-delayed γ rays but ultimately one must rely on calculation to account for those γ rays that remain undetected. Even with work on these new superallowed emitters only in its infancy, the f t values for 22 Mg, 34 Ar and 74 Rb have already been determined with remarkable precision (below ±0.4%). As these cases are improved and new ones added, the test of the nuclear-structure-dependent corrections will become more definitive. Figure 2 shows the present levels of uncertainties on the 11 transitions considered here as new superallowed transitions. Evidently much needs to be done but a very solid beginning has been made.

5 Conclusions Our new survey of superallowed 0+ → 0+ decays has demonstrated the power of these data in probing some fundamental properties of the weak interaction. The CKM unitarity test, which deviates from unity by 2.4 standard deviations, is currently the most provocative outcome and future measurements of QEC -values, half-lives and branching ratios for the decays of some exotic nuclei have been proposed to help clarify this possible discrepancy. The work of JCH was supported by the U.S. Department of Energy under Grant DE-FG03-93ER40773 and by the Robert A. Welch Foundation. IST would like to thank the Cyclotron Institute of Texas A&M University for its hospitality during several two-month visits.

References 1. J.C. Hardy, I.S. Towner, V.T. Koslowsky, E. Hagberg, H. Schmeing, Nucl. Phys. A 509, 429 (1990). 2. J.C. Hardy, I.S. Towner, Phys. Rev. C 71, 055501 (2005). 3. I.S. Towner, J.C. Hardy, J. Phys. G: Nucl. Part. Phys. 29, 197 (2003). 4. J.D. Jackson, S.B. Treiman, H.W. Wyld jr., Phys. Rev. 106, 517 (1957). 5. W.J. Marciano, A. Sirlin, Phys. Rev. Lett. 56, 22 (1986); A. Sirlin, in Precision Tests of the Standard Electroweak Model, edited by P. Langacker (World-Scientific, Singapore, 1994). 6. W.E. Ormand, B.A. Brown, Phys. Rev. C 52, 2455 (1995); Phys. Rev. Lett. 62, 866 (1989); Nucl. Phys. A 440, 274 (1985). 7. S. Eidelman et al., Phys. Lett. B 592, 1 (2004). 8. A. Sher et al., Phys. Rev. Lett. 91, 261802 (2003). 9. P. Herczeg, Phys. Rev. D 34, 3449 (1986); Prog. Part. Nucl. Phys., 46, 413 (2001). 10. I.S. Towner, J.C. Hardy, Phys. Rev. C 66, 035501 (2002). 11. J.C. Hardy, I.S. Towner, Phys. Rev. Lett. 88, 252501 (2002). 12. J.C. Hardy, L.C. Carraz, B. Jonson, P.G. Hansen, Phys. Lett. B 71, 307 (1977).

Eur. Phys. J. A 25, s01, 699–701 (2005) DOI: 10.1140/epjad/i2005-06-104-3

EPJ A direct electronic only

Search for P-odd time reversal noninvariance in nuclear processes T.V. Chuvilskaya1,a , S.D. Kurgalin2 , I.S. Okunev3 , and Yu.M. Tchuvil’sky1,b 1 2 3

Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119992, Moscow, Russia Voronezh State University, 394006, Voronezh, Russia St.-Petersburg Institute of Nuclear Physics RAS, 188350, Gatchina, Russia Received: 30 October 2004 / c Societ` Published online: 24 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The scheme of search for time reversal noninvariance in nuclear processes based on the measurement of linear polarization of gamma radiation of a sample aligned by a preceding nuclear decay or by cryogenic means is presented. PACS. 11.30.Er Charge conjugation, parity, time reversal, and other discrete symmetries

Time reversal noninvariant (T -violating) terms are contained in the standard model. However, twofold suppression of the simultaneous parity and time reversal (P T -) violation effect in all processes besides purely weak ones makes the effect extremely small. Therefore even the detection of a very small P T -violating correlation produced by N N -interaction is a sign of the effect falls beyond the standard model. If one assumes that P T -violation effect reveals itself mainly in nucleon-meson N → N + π vertex than it is possible to estimate upper limits to P T -violating π-meson ΔT (π) determined by the electric dipole moconstants gpt ment (EDM) of neutron measurements [1, 2,3]: ⎧ ⎫ ⎨ 1.4 · 10−11 , ΔT = 0 ⎬ ΔT 1 · 10−10 , ΔT = 1 , gpt (π) ≤ (1) ⎩ 1.4 · 10−11 , ΔT = 2 ⎭ where the value ΔT denotes the isospin change. Thus to set an upper limit on isovector P T -violating amplitude Wpt being of order 10−3 of a measured P odd one would be a vital issue. The P T -violation effect manifesting in nuclear processes possess the isospin structure other than that producing the EDM of neutron. Therefore even a larger value of this limit (10−1.5 –10−2 ) could provide an important information. Moreover the nuclear processes are promising tools for the investigation of 1 (π) is anP T -violation because the isovector constant gpt ticipated to be dominating in this case. In addition there are the mechanisms of enhancement of P T -violation effect in such processes analogous to those of P -violation one. a

e-mail: [email protected] Conference presenter; e-mail: [email protected] b

Performed experiments devoted to attacking the discussed problem are few in number. Up to now the most reliable is the measurement of P T -noninvariant (kγ2 J)(kγ1 [kγ2 × J]) correlation in the γ-cascade of the oriented 180m Hf 1142 keV state (here k is the vector of the direction of the respective linear momentum, J is the vector of the alignment) [4]. The upper limit of the ratio of the discussed amplitude to the value of P -odd one measured before in this transition Wpt /Wp ≤ 1 was obtained. Unfortunately, the most popular subject of discussions namely the σ[k × J] correlation in n + 139 La collision which could result in the upper limit of the ratio Wpt /Wp ≤ 10−4 [5] remains planned experiment only. Thus, new approaches seem to be desirable. In the present work a widespread analysis of approaches of this type is performed. There are many methods of attack. According to our estimates the scheme based on the measurement of the linear polarization of gamma radiation  of a sample aligned by cryogenic means or by a preceding decay seems to be optimal. It should be noted that the linear polarization measurements of the P T -violation effect were already performed ossbauer method in [6] but in the combination with the M¨ of orientation. Let us consider a single γ-transfer in an aligned sample I → J or an αγ-cascade I0 → I → J and characterize the relative directions of the three vectors by the Euler angles θ, φ, and ψ determining the coordinate system x , y  , z  (z  -axis is the direction of the photon emission kγ , x the direction of the vector , and the condition (kγ ⊥ ) takes place) measured from the laboratory one where z-axis is the direction of the alignment (coinciding with the direction of α-emission kα in the second case) J.

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The P T -violating term of interest takes the form [7] Wpt (θψ) = 6−1/2 B2 (I)A22 (pt) sin ψP2 (cos θ), (2)

(2)

where B2 (I) is the alignment i.e. the component of the orientation tensor of the rank 2 characterizing the level I, (2) P2 (cos θ) is the generalized Legendre polynomial. Naturally the term is independent of φ because this angle determines the rotation of the system as a whole. The spin-angular distribution coefficient has the form [7] ⎧ ⎫ ⎨J l I ⎬,  ˆ  1|22) J l I Γγ (pt)/Γγ . (−1)l ˆlˆl IˆJ(l1l A22 (pt) = ⎩ 2 2 0⎭  ll (3) Here Γγ is the amplitude of the respective γ-transition, l, l  are the multipole characteristics of γ-quanta, √ the threeline table is 9j-symbol, and the notation a ˆ ≡ 2a + 1 is used. Expressions of the value B2 (I) for both “cryogenic” and “decay” orientation method can be found in [7]. The choice of optimal angles to observe the correlation is evident from expression (2): θ = π/2, ψ = 3π/4 and π/4. Let us discuss the advantages of the schemes: 1. No beam machine is required. 2. A broad assortment of promising subjects —radionuclides which are rather easily obtainable and contain parity mixing doublets so that the strong “dynamic” enhancement of both P - and P T -violation effects is typical for them. The “structural” enhancement is not a rare case for the discussed nuclides. 3. The linear polarization measurement instead of the γ-γ detection makes the total efficiency of the experiment considerably larger. 4. Values of the spin factor appearing in the expression of P T -violating observable through the amplitude (the  Wpt (θψ) through the Γγ (pt) in the discussed case) turns out to be essentially greater than those in just mentioned coincidence scheme. 5. The cross-shaped four-γ-detector setup enables one to get read of the most part of systematic errors. 6. Both schemes are inexpensive and labor-saving. Comparing two possibilities one can conclude: 1. A polarization of a sample is not wanted in the “decay” version of the scheme unlike in the “cryogenic” one. No refrigerator is required. 2. The “decay” version is the simplest and the cheapest. 3. The cryogenic method of polarization results in higher counting rate because the coincidence scheme is necessary in the opposite case. Evident way of search for P T -violation effect is to investigate an example used before to study P -odd one. The parity violation effect is known for the following example of the αγ-cascade: 241

Am →

237

241

Np (5/2− , 59.5 keV) →

237

Np (g.s.).

Am is reactor produced; the half-life time The isotope is T1/2 = 232 y; the contribution of the necessary αtransition to the total α-width B = 84.5% is large; the doublet splitting ΔE = 59.5 keV is not small but there is

 a great structural enhancement Γirreg /Γreg ∼ 103 . Resulting value of the circular polarization is Pγ = (−1.23 ± 0.25)10−3 [8], i.e. one can expect a strong enhancement of P T -violation effect in the process. The disadvantage of the discussed process is a large contribution of S-wave in the α-decay channel, in other words the angular momentum Lα = 0 which is not capable to produce the alignment is allowed. Because of this the degree of the alignment of 237 Np sample decreases. Another obstacle to high-precision measurement of the discussed effect in this case is the use of low-energy γ-transition resulting in the false effect of γ-eatomic final-state interaction. However, this effect is measurable in independent experiments with a rather high precision. Moreover it is a pure P -even one. Therefore a P T -simulating correlation is generated in the discussed scheme by P -odd amplitudes only. In many cases these two properties make it possible to subtract the false effect from the measured value with an accuracy which is superior to the potentiality of the “decay” scheme. Promising variants of the αγ-cascade are legion. In addition the βγ-cascade can be used for the same purposes. However, first-order forbidden β-transition with ΔJ = 2 is necessary in this case. The “cryogenic” variant of the scheme can be used for the study of the above-mentioned example of the isomeric transition of 180m Hf [4]. Two lines: 180

Hf (8− , 1141.5 keV) →

180

Hf (8− , 1141.5 keV) →

180

180

Hf (8+ , 1083.9 keV) and Hf (6+ , 840.9 keV)

are the subjects of interest. The isomer is reactor produced; the half-life time is T1/2 = 5.5 h; the branching ratios are B1 = 51.0% and B2 = 15.2%, respectively; the doublet splitting and the structural enhancement are ΔE = 57.5 keV and Γirreg /Γreg ∼ 107 , respectively. The P -odd effect is measured and turns out to be extremely large: Pγ = (−2.3 ± 0.6)10−3 for 57 keV γ-line [9] and Aγ = (−1.66 ± 0.18)10−2 for 501 keV γ-line [10], respectively. Estimates demonstrate that there is a possibility to create a setup which offers a way to achieve the upper limit of the ratio Wpt /Wp ≤ 10−3 . The problem of the false effect is in this case a subject of special investigations. There are many isomers and β-sources of delayed γ-transitions promising for using in the “cryogenic” scheme. We consider presented examples as good ones but in our opinion search for processes which are superior to justmentioned should be continued. So presented approach to P T -violation problem looks viable. The work is partially supported by RFBR, grants 02-02-16411 and 04-02-17409.

References 1. P. Herczeg, Hyperfine Interact. 75, 127 (1992). 2. P. Herczeg, Tests of Time Reversal Ivariance, edited by N.R. Robertson, C.R. Gould, J.D. Bowman (World Scientific, Singapore, 1987) p. 24.

T.V. Chuvilskaya et al.: Search for P -odd time reversal noninvariance in nuclear processes 3. I.S. Towner, A.C. Hayes, Phys. Rev. C 49, 2391 (1994). 4. B.T. Murdoch et al., Phys. Lett. B 52, 325 (1974). 5. Y. Masuda, Time Reversal Ivariance and Paruty Violation in Neutron Reactions, edited by C.R. Gould, J.D. Bowman, Yu.P. Popov (World Scientific, Singapore, 1993) p. 126. 6. V.G. Tsinoev et al., Phys. At. Nucl. 61, 1357 (1998).

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7. R.M. Steffen, K. Adler, The Electromagnetic Interaction in Nuclear Spectroscopy, edited by W.D. Hamilton (NorthHolland, Amsterdam, 1975) p. 505. 8. L.V. Inzhenchik et al., Phys. At. Nucl. 51, No. 2, 391 (1990). 9. E.D. Lipson et al., Phys. Lett. B 35, 307 (1971). 10. K.S. Krane et al., Phys. Rev. C 4, 1906 (1971).

Eur. Phys. J. A 25, s01, 703–704 (2005) DOI: 10.1140/epjad/i2005-06-073-5

EPJ A direct electronic only

Parity non-conservation in the γ-decay of polarized 17/2 − isomers in 93Tc B.S. Nara Singh1,a , M. Hass1 , G. Goldring1 , D. Ackermann2,3,b , J. Gerl2 , F.P. Hessberger2 , S. Hofmann2 , I. Kojouharov2 , P. Kuusiniemi2 , H. Schaffner2 , B. Sulignano2,3 , and B.A. Brown4 1 2 3 4

Department of Particle Physics, Weizmann Institute of Science, Rehovot, Israel GSI, Darmstadt, Germany Johannes Gutenberg-Universit¨ at Mainz, Mainz, Germany NSCL, East Lansing, MI, USA Received: 29 October 2004 / c Societ` Published online: 3 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The determination of the 0◦ –180◦ asymmetry (Aγ ), which arises due to the parity violating matrix element, in the 751 keV γ-decay of polarized 17/2− isomers in 93 Tc with respect to the direction of polarization is reported. A combined analysis of the present results together with those of M. Hass et al. (Phys. Lett. B 371, 25 (1996)) yields Aγ = 4.8(2.1) × 10−4 . PACS. 21.10.Ky Electromagnetic moments – 21.10.Pc Single-particle levels and strength functions – 23.40.Hc Relation with nuclear matrix elements and nuclear structure gamma−absorber

1 Introduction Parity non-conservation (PNC) in bound nuclear systems is an interesting probe for the weak interaction part of the nuclear Hamiltonian [1, 2], in particular for the nonleptonic and non-strangeness changing sector and thus it is complementary to the β-decay studies. However, it has been studied in the past in only a few cases, mostly with marginal statistical accuracy, such as 18 F, 19 F, 21 Ne, 93 Tc and 180 Hf [3], and there has been virtually no new experi− 17 + mental information in the last several years. The 17 2 - 2 93 parity doublet with 300 eV proximity in Tc presents a unique possibility among bound nuclei for detecting a non-zero PNC effect through the 751 keV γ-decay, together with meaningful shell model calculations. In a simple model, the high-spin parity doublet has only a twobody component for 93 Tc and hence is different from the cases studied in light nuclei [3].

2 Experimental details In a previous communication [3] we have reported the results of three measurements of the parity violating ma− 17 + 93 Tc. The measurements trix element | 17 2 |Hpnc | 2 | in − isomeric were carried out with tilted foil polarized 17 2 ◦ ◦ nuclei. The 0 –180 anisotropy w.r.t the polarization axis a b

e-mail: [email protected] Conference presenter

Energy degrader P

Primary Beam 52

Cr

l

Seg. Clov L

SHIP 93

Tc

Pr

Collimator

Secondary Beam

Seg Clov

Foil Stack

R

Fig. 1. A schematic of our experimental setup.

was found to be Aγ = 8.4(2.7)×10−4 . We report here on a new measurement carried out at the SHIP facility at GSI with improved detectors and higher count rates in order to improve the statistical significance. For details see ref. [3]. A brief description together with the improvements on this setup (fig. 1) are given here. The secondary beam of 93m Tc isomeric beam was produced at the UNILAC at GSI by the 45 Sc(52 Cr, 2p2n)93 Tc reaction. The primary beam 52 Cr of 900 pA at Elab = 170 MeV on a 45 Sc target of 1 mg/cm2 thickness mounted on a rotating wheel resulted in a high rate for the secondary isomer beam. The − SHIP velocity-filter separated and transfered the 93 Tc 17 2 (T1/2 = 10.2(3) μsec) isomers of Elab = 65 MeV to the focal-plane area where they were polarized using an array of sixteen, 15 + 15 μg/cm2 thick collodin-carbon foils tilted by 70◦ w.r.t the isomer beam direction. The SHIP parameters were optimized for the maximum transmission of 93 Tc isomers by monitoring them in a particle detector at the entrance of the foil stack and by counting the isomer γ-rays. The direction of the polarization was changed every three minutes by rotating the foils by 180◦ . The

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Triple Ratios

Table 1. The triple T R(i) ratios. Column 1: Energy of the γ-ray. Column 2: From ref. [3]. Column 3: From the present work. Column 4: The average of Column 2 and Column 3.

Eγ (keV)

Ref. [3]

Present

1.002

Average

93

629( Tc)

544 ( Ru) 629 (93 Tc) 711 (93 Tc) 751 (93 Tc) 1392 (93 Ru) 1432 (93 Tc)

1.00107 1.00055 0.99989 0.99833 0.99933 0.99977

(73) (53) (38) (54) (84) (39)

0.99912 1.00088 0.99962 1.00028 0.99972 1.00038

(122) (66) (41) (71) (112) (31)

1.00056 1.00068 0.99977 0.99904 0.99947 1.00015

(63) (41) (28) (43) (67) (24)

1.001 93

1432( Tc) 93

711( Tc) TR

93

1 93

544( Ru) 93

1392( Ru)

0.999

93

751( Tc)

93

Tc isomers were subsequently implanted in a Pb stopper of 32.1 mg/cm2 , which preserves the alignment and polarization over the isomer lifetime [4]. The decay γ-rays were detected in two Compton-suppressed GSI clover Ge detectors, (active volume; 2 × 4 HPGe crystals of 7 cm wide and 14 cm long) placed at 0◦ and 180◦ with respect to the induced polarization. The detection efficiency was 4 times higher as compared to ref. [3], essentially due to the increase in the number and size of the HPGe crystals. This arrangement resulted in the geometrical attenuation coefficient of Q = 0.70 and clean γ spectra. Digital signal scan electronic modules were used for signal processing, allowing for high count rates with minimal dead time.

The data analysis was carried out by using the ROOT package based go4 code [5]. Standard double ratios [3] of γ-ray yields defined by $ 3 1 − Aγ W (π) rl ll , (1) = = DR = 1 + Aγ W (0) rr lr

where, e.g., rl refer to the counts in the right detector for the left-polarized isomers, were then derived. This provides a measurement of the 0◦ –180◦ asymmetry (Aγ ) of the 751 keV 17/2− -13/2+ M 2/E3 transition from 93 Tc that is independent of the relative efficiency of the detectors, and of the beam-current fluctuations. However, artifacts due to the interaction of the isomer beam with the foil stack [3] can still arise and can be eliminated by forming the triple ratios, DR(i) , DR(i = 751)

700

900 1100 Energy (keV)

1300

1500

Fig. 2. The triple ratios for isomer lines plotted here are an average of the data from ref. [3] and from the present work.

with similar statistics. After correcting for the differences in Q, an average of T R(i) is given in the last column. The T R(751), which is free of the above-mentioned artifacts, is related to Aγ and the PNC matrix element is obtained from the relations [3]: 1 − T R(751) , 1 + T R(751) % − &  17 |Aγ | 17 +   |H | pnc  = 91(28) pl Q meV,  2 2 Aγ =

3 Results and discussion

T R(i) =

0.998 500

(2)

where i goes over all the isomer lines and the denominator is an average for all the isomer lines excluding 751 keV. For the γ transitions (other than 751 keV) depopulating the 17/2− isomer as well as for γ-rays from 93,94 Ru, and 93,94 Mo PNC asymmetry is not expected and any asymmetry (“null-asymmetry” effect) observed determines the quality of the experiment. Table 1 presents the triple ratios (DR(i = 751) = 0.99601(16)) for the γ-decays of interest from ref. [3] and from a partial set of the present data. Further analysis will include the remaining data

(3)

where pl is the magnitude of polarization. The value of pl was measured under similar conditions in a quadrupole interaction measurement [6]. From a preliminary and partial analysis of the present measurement we have the result Aγ = −1.4(3.6) × 10−4 for the 751 keV γ-decay. The present result differs by ≈ 2 standard deviations (table 1) when compared to our previous result of Aγ = 8.4(2.7) × 10−4 [3]. Figure 2 shows the preliminary results on the triple ratios (T R(i)) when averaged with the data from ref. [3]. This leads to an overall result of all the four measurements of: Aγ = 4.8(2.1) × 10−4 and | Hpnc | = 0.34(14)(25) meV. This is a much reduced (although statistically consistent) anisotropy and a larger relative error. With 2.4 standard deviations the present partial result is at the verge of statistical significance. A full account of the over all and final analysis will be given elsewhere.

References 1. E. Adelberger et al., Annu. Rev. Nucl. Part. Sci. 35, 501 (1985). 2. W.C. Haxton, C.E. Weimann, Annu. Rev. Nucl. Part. Sci. 51, 261 (2001). 3. M. Hass et al., Phys. Lett. B 371, 25 (1996). 4. O. H¨ ausser et al., Nucl. Phys. A 293, 248 (1977). 5. go4 package from www-w2k.gsi.de/go4/. 6. M. Hass et al., Phys. Rev. C 43, 2140 (1991).

Eur. Phys. J. A 25, s01, 705–707 (2005) DOI: 10.1140/epjad/i2005-06-163-4

EPJ A direct electronic only

The LPCTrap for the measurement of the β-ν correlation in 6He D. Rodr´ıgueza , A. M´ery, G. Darius, M. Herbane, G. Ban, P. Delahayeb , D. Durand, X. Fl´echard, M. Labalme, E. Li´enard, F. Mauger, and O. Naviliat-Cuncic LPC-IN2P3-ENSICAEN, 6 Boulevard du Mar´echal Juin, 14050 Caen Cedex, France Received: 1 November 2004 / c Societ` Published online: 4 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The application of traps to precision measurements of the β-ν angular correlation coefficient a in nuclear β-decay is pursued by several laboratories world wide. Various nuclear transitions are addressed and different trap devices are used. At GANIL, a novel transparent Paul trap (LPCTrap) has been built downstream from the SPIRAL source to determine a in the pure Gamow-Teller decay of 6 He. This transition is driven by the axial-vector interaction. The forbidden tensor interaction may be observed through a precise measurement of a. The LPCTrap consists of an RFQ-Buncher, a transparent Paul trap, and the detection system. It is currently the only facility that uses a Paul trap with a novel geometry to perform high-precision nuclear physics experiments. All the elements have been tested and meet the requirements. In this contribution we give a short status report of the project underlining the highlights achieved so far. PACS. 23.40.Bw Weak-interaction and lepton (including neutrino) aspects – 24.80.+y Nuclear tests of fundamental interactions and symmetries – 29.27.Eg Beam handling; beam transport

1 The RFQ-Buncher

a Conference presenter; e-mail: [email protected] b Present address: CERN, Physics Department, 1211 Geneva 23, Switzerland.

Ions per bunch / 105

An RFQ-Buncher is a powerfull tool to improve the quality of radioactive beams required for high-precision experiments [1]. It serves to reduce the emittance and time structure of the radioactive ion beam. At GANIL, the 6 He+ ions will be delivered in continuous mode, with an emittance of about 80 π mm · mrad. The ions are cooled by collisions with buffer-gas atoms or molecules inside the RFQ-Buncher. After an accumulation time varying from one to a few tens of milliseconds depending on the production rate, the ions are extracted as a short ion bunch (ΔtFWHM ∼ 100 ns, ΔEFWHM ∼ 3 eV) with improved emittance ( ≈ 10 π mm · mrad). The device was tested on-line at LIMBE/GANIL using different combinations of ion species and buffer gases [2]. The highlight from these experiments was the cooling and bunching of 4 He+ ions in H2 with an efficiency of 5–10%. This is the lighest ion ever investigated in such a device. Figure 1 shows the accumulation time for a production yield of 4 to 5 × 108 ions/s. This value is close to the expected rate of 3.2 × 108 ions/s of 6 He+ ions from SPIRAL [3]. The coupling between the LPCTrap and SPIRAL was recently tested using 16 O+ ions transferred at 12.7 keV

5 4 4 He+

3 2 1

PH = 8⋅10-3 mbar 2

0

20 40 60 80 Accumulation time / ms

100

Fig. 1. Accumulation of 4 He+ in the RFQ-Buncher.

through a low-energy beam line (LIRAT). The experimental setup is sketched in fig. 2. The buffer gas was helium since the ionization potential for H2 (15.4 eV) is close to the ionization potential for O (13.6 eV). MicroChannel-Plates (MCPs) located at the end of the beam line were used for time-of-flight identification of the extracted ion bunch. The width of the time-of-flight distribution for 16 O+ was ∼ 700 ns after slowing down the beam to about 1 keV. This value is high due to the large number of ions stored in the RFQ. The incident 16 O+

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Trap Chamber

Transfer Region

SPIRAL

3 cm

Ion Bunch

~12.7 keV

MCP ’s detector

Attenuators (1/1000)

E~1 keV

Paul Trap

Fig. 2. Sketch of the LPCTrap setup downstream from SPIRAL. Only the components inside the trap chamber (white square) are shown to scale. The ion optics in front of the trap is used to reduce further the energy of the ion bunch before trapping.

current (Ii ) was 500 pA. The accumulation time in the RFQ-Buncher was about 2 ms. Thus, the number of injected ions per cycle exceeded the space charge limit of the RFQ-Buncher. In addition, other ion species observed in the time-of-flight spectrum were created inside the RFQ by collisions between the 16 O+ ions and the background molecules. The extracted ion bunches were collected in a 90%-attenuator plate located in the transfer region between the RFQ-Buncher and the Paul trap. The plate was attached to a pA-meter to read out the current (Ie ). The ratio Ie /Ii was 0.09. However, we deduced from the timeof-flight spectrum that the extracted oxygen current was approximately Ie /2. Thus, we can conclude that the injection and bunching efficiency measured was about 4.5% in the first test. The next test run with stable ions downstream SPIRAL will be in December 2004. Among other tests aimed at optimizing the efficiency, we also intend to confine the ions in the Paul trap.

2 The transparent Paul trap The transparent Paul trap is a storage device for the confinement of the decaying 6 He+ ions. It is made out of two sets of concentric rings centered on the beam axis (fig. 2). Each set is composed of two rings, inner and outer. The RF voltage (VRF ≈ 120Vpp and νRF ≈ 1.1 MHz for A = 6) is only applied to the inner rings. The outer rings are grounded except during injection and ejection of the ions. In the trapping configuration the RF voltage generates nearly the same potential as that provided by a hyperbolic Paul trap. However, in the present geometry, an electrode-free region allows the detection of the decay products. Figure 3 shows the trap chamber with the detectors placed around the trap. The use of this trap to confine the decaying source has advantages over other techniques. A sample of about 2 × 104 ions (measured value) can be held almost at rest, at energies below 100 meV, in a small volume (1–2 mm3 ) without interaction with matter (Pchamber = 2 × 10−6 mbar).

Fig. 3. Trap chamber with the detectors required for the correlation measurement.

The Paul trap is currently tested off-line using 6 Li+ ions produced in a contamination-free ion source located in front of the RFQ-Buncher. After cooling and bunching, the 6 Li+ ions are slowed down by means of the ion optics located in front of the trap to about 130 eV (ΔEFWHM ≈ 3 eV) and captured in-flight in the trap. The trapping efficiency achieved is 25% (extraction after 500 μs of trapping time). The survival time of the 6 Li+ ions in the trap (time constant) is a bit above 200 ms. The trapping of 6 He+ will be similar to the trapping of 6 Li+ ions.

3 The detection system The coefficient a will be determined by measuring the time of flight of the recoiling ions in coincidence with the β particles. The detection system consists of MCPs with a delay-line anode for position sensitivity (recoil ion detector) and a β-telescope. The detectors will be placed around the trap in a back-to-back geometry as shown in fig. 3. This geometry gives the maximum sensitivity for the detection of tensor-like interaction through the decay of 6 He+ (→ 6 Li++ + β − + ν¯). Systematic investigations have been carried out to charaterize the recoil ion detector [4]. A detection efficiency above 50% has been achieved even for ions in the sub-keV energy range. Furthermore, the value does not depend on the angle of incidence of the ion on the detector. The detector has a temporal and spatial resolution (FWHM) of ≈ 400 ps and ≈ 120 μm, respectively. The β-telescope comprises a Double-Sided-Silicon-Strip Detector (DSSSD) and a plastic scintillator. The DSSSD has a position resolution of about 1 mm and is currently tested. The plastic scintillator together with a light guide and a photomultiplier has been tested using a 22 Na source. The energy resolution is about 10% at 1 MeV. The efficiency of the system shows that, from the statistical point of view, the proposed experiment is feasible. An experiment is planned for March 2005.

D. Rodr´ıguez et al.: The LPCTrap for the measurement of the β-ν correlation in 6 He Part of this work has been supported within the European network NIPNET. We thank F. Varenne for his assistance during the tests performed at LIRAT/GANIL.

707

References 1. 2. 3. 4.

G. Savard, these proceedings. G. Ban et al., Nucl. Instrum. Methods A 518, 712 (2004). A.C.C. Villari et al., Nucl. Phys. A 701, 476 (2002). E. Li´enard, M. Herbane et al., to be published in Nucl. Instrum. Methods A.

Eur. Phys. J. A 25, s01, 709–710 (2005) DOI: 10.1140/epjad/i2005-06-075-3

EPJ A direct electronic only

Alignment correlation term in mass A = 8 system and G-parity irregular term T. Sumikama1,a , T. Iwakoshi1 , T. Nagatomo1 , M. Ogura1 , Y. Nakashima1 , H. Fujiwara1 , K. Matsuta1 , T. Minamisono1 , M. Mihara1 , M. Fukuda1 , K. Minamisono2 , and T. Yamaguchi3 1 2 3

Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, V6T 2A3, Canada Department of Physics, Saitama University, Saitama 338-8570, Japan Received: 8 November 2004 / c Societ` Published online: 3 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The pure nuclear spin alignments of 8 Li and 8 B were produced from the nuclear spin polarization applying the β-NMR method. The alignment correlation terms in the β-ray angular distribution of the mirror pair 8 Li and 8 B were observed to limit the G parity irregular term in the weak nuclear current. The significant deviation due to the forbidden matrix elements between the alignment correlation terms and the β-α correlation terms was observed. The determination of the alignment correlation terms was essential to extract the G-parity violating induced tensor term without the influence of the forbidden term in the vector current. PACS. 11.30.Er Charge conjugation, parity, time reversal, and other discrete symmetries – 23.40.Bw Weak-interaction and lepton (including neutrino) aspects – 27.20.+n 6 ≤ A ≤ 19

1 Introduction The β-α angular correlation terms of the mirror pair 8 Li and 8 B were measured in 1975 and 1980 by Tribble et al. [1] and McKeown et al. [2] to limit the G-parity violating induced tensor term. The results were consistent with non existence of the induced tensor term. While strong interaction induces only the G-parity conserved current into the weak nucleon current, a small but finite G-parity irregular current may be caused by the asymmetry between the up and down quarks such as the mass difference. However, it is difficult to set more accurate limit to the induced tensor term only from the β-α angular correlation terms due to serious contribution from the second-forbidden matrix elements. The other approaches are necessary in the mass A = 8 system. Since some terms of the forbidden matrices contribute in opposite directions to the alignment correlation term, we have a good chance to determine the induced tensor term and these forbidden matrices at the same time.

2 G-parity irregular term In the present study, we observed the alignment correlation terms in the β-ray angular distributions from spin a

Conference presenter; Present address: RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan; e-mail: [email protected]. Thanks for the Special Postdoctoral Researcher Program of RIKEN.

aligned 8 Li and 8 B to extract the induced tensor term gII precisely. The β-ray angular distribution from purely aligned 8 Li and 8 B is given by W (E, θ) ∝ pE(E − E0 )2

B2 (E) P2 (cos θ) , ×B0 (E) 1 + A B0 (E)

(1)

where A is the alignment, E and E0 are the β-ray energy and end-point energy, respectively, p is the β-ray momentum, θ is the β-ray ejection angle and P2 is the Legendre polynomial. The difference δ between the alignment correlation terms B2 /B0 of 8 Li and 8 B is formulated by Holstein [3] as

   B2 (E) B2 (E) − δ= B0 (E) 8 B B0 (E) 8 Li 3 f b dII 2E +√ − =− 3Mn Ac Ac 14 Ac $

3 g E0 − E , + 28 A2 c Mn 

(2)

where b is the weak magnetism, c is the Gamow-Teller term, dII /Ac = gII /gA is the ratio of the induced tensor term to the axial-vector coupling constant, f and g is the second forbidden matrix elements of the vector current, Mn is the nucleon mass and A is the mass number. All

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4

8

B

-2

2 0 -2 -4

8Li

-6

Preliminary

-8

-4

δ (%)

Alignment Correlation Term (%)

6

0

2

4 6 8 10 12 β-Ray Energy (MeV)

-6 -8 -10

14

Fig. 1. The alignment correlation terms. The full circles are from the present result and and the open squares and the crosses are from the β-α correlation terms in refs. [1] and [2], respectively, which are multiplied by −2/3.

the terms have a dependence of the final-state excitationenergy, where the final state is the first excited state of 8 Be, but this dependence is not included in eq. (2) for simplicity. The gII term is given by combining the present alignment correlation term with the weak magnetism [4] and the β-α correlation term [1,2] where the f and g terms contribute in opposite directions to eq. (2). The present experimental procedure and setup were essentially the same as previous one [5]. The 8 Li and 8 B nuclei were produced through the nuclear reactions 7 Li(d, p)8 Li and 6 Li(3 He, n)8 B, respectively. The deuteron and 3 He beams were accelerated by the Van de Graaff accelerator at Osaka University up to 3.5 MeV and 4.7 MeV, and were used to bombard a Li2 O and an enriched metal 6 Li targets, respectively. The recoil angles of the nuclear reaction products were selected to produce the polarized nuclei. The typical polarization was 7.2% for 8 Li and −5.7% for 8 B in the direction of kB × kR , where kB and kR are the momenta of a beam and a recoil nuclei, respectively. 8 Li and 8 B were implanted into Zn and TiO2 single crystals, respectively, which were placed in an external magnetic field B0 to maintain the polarization and to manipulate the spin with the β-NMR technique. The c-axis of the single crystals was set parallel to B0 , which is 60 mT for 8 Li and 230 mT for 8 B. The β-ray asymmetry was observed by two sets of plastic-scintillation-counter telescopes placed above and below the catcher relative to B0 direction. The polarizations were converted into pure positive and negative alignments with ideally zero polarization by applying the β-NMR technique. The alignment was converted back into polarization to check the spin manipulation. The β-ray angular distribution from the pure aligned 8 Li and 8 B was observed as a function of β-ray energy. The alignment correlation terms were preliminarily extracted as shown in fig. 1. The β-α angular correlation terms p∓ (E) in refs. [1,2] are also plotted in the same fig-

Preliminary 0

2

4 6 8 10 12 β-Ray Energy (MeV)

14

Fig. 2. The difference of the alignment correlation terms. The meaning of the marks is same as in fig. 1. The lines show the weak magnetism term b/Ac with ±1σ bands [4].

ure, after multiplied by −2/3 to compare it with the alignment correlation terms. Both of these correlation terms have large E 2 contributions from the second-forbidden matrix elements. There is a significant deviation between the alignment correlation terms and the β-α correlation terms due to the forbidden terms of f and g in the vector current and the one of j2 in the axial-vector current. Among these 3 terms, the contribution of j2 is unique, since the j2 term contributes in same direction to the mirror pair of a same correlation term, while the f and g terms contributes in opposite directions to the mirror pair. Main deviation comes from the j2 term because the alignment correlation terms are lower than β-α correlation terms in the high energy region for both nuclei. The differences δ are shown together with the β-α correlation terms [1,2] and the experimental weak magnetism b/Ac [4] in fig. 2. The dependence of the final-state excitation-energy for b/Ac has been observed experimentally. Small but definite deviation between δ for alignment correlation term and β-α correlation terms was observed. The contribution from f and g was about 8% of b at 10 MeV, while the value extracted from the γ decay width [4] is consistent with zero and the upper limit was half of the present deviation. The induced tensor term was preliminary extracted without  the influence of f and g terms as the limit dII /b < 0.06, where b is the energy average of the weak magnetism [4, 6]. Detailed analysis is in progress.

References 1. 2. 3. 4. 5. 6.

R.E. Tribble et al., Phys. Rev. C 12, 967 (1975). R.D. McKeown, et al., Phys. Rev. C 22, 738 (1980). B.R. Holstein, Rev. Mod. Phys. 46, 789 (1974). L. De Braeckeleer, et al., Phys. Rev. C 51, 2778 (1995). K. Minamisono, et. al., Phys. Rev. C 65, 015501 (2002). K.A. Snover, et al., Proceedings of the International Symposium on NEWS99, Osaka, Japan (World Scientific, 2002) p. 26.

11 Radioactive ion beam production and applications 11.1 Facilities and beams

Eur. Phys. J. A 25, s01, 713–718 (2005) DOI: 10.1140/epjad/i2005-06-206-x

EPJ A direct electronic only

Ion manipulation with cooled and bunched beams G. Savarda Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA and Department of Physics, University of Chicago, Chicago, IL 60637, USA Received: 12 September 2004 / c Societ` Published online: 9 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Ion beam properties are often critical to experiments with rare isotopes. The ability to cool transverse motion and energy spread in a beam or modify its time structure can significantly improve many types of experiments. This ability is now a common feature in existing low-energy facilities and will play a central role in a number of next generation radioactive beam facilities. The basic physics underpinning the operation of these beam cooling devices is introduced below together with the key technical evolutions that have occurred since the previous ENAM conference. Examples of operating devices for various sources of radioactive ions are given, together with the performance presently achieved and improvements expected in the near future. PACS. 29.25.Rm Sources of radioactive nuclei – 41.85.Ja Beam transport – 29.27.Fh Beam characteristics

1 Introduction Ion beam properties determine to a large degree what experiments are possible with rare isotopes. Beam properties are many faceted, including beam intensity and purity, energy spread, size, angular divergence and time structure. And although experimentalists and machine physicists often concentrate on the beam intensity, perhaps because it is the easiest parameter to measure, it is but one of the factors that can affect an experiment. Other properties often also have a significant impact and the ability to cool transverse motion or energy spread, or modify the time structure of a beam, can yield significant improvements in resolution or signal to noise for many types of experiments. This ability has seen significant progress over the last decade, driven to a large degree by technical developments from the field of ion trapping. It is now a common feature in existing low-energy facilities and is expected to play a central role in a number of next generation radioactive beam facilities. The techniques used rely on the efficient injection of the ion beams into large acceptance electromagnetic devices that confine and guide them in two or three dimensions while collisions with a low-pressure high-purity buffer gas reduces the energy (and energy spread) and concentrates the beam at the bottom of the confining potential. These new devices (ion coolers, isobar separators, gas catchers and so on) perform multiple tasks ranging from transverse cooling to bunching and purification of beams and can now even transform recoils from fission, a

e-mail: [email protected]

low-energy nuclear reactions or fragmentation reactions into beams of ISOL-type quality. The basic physics underpinning the operation of these various devices is common and will be introduced in the following, together with the key technical evolutions that have occurred since the previous ENAM conference. The cooling of beams from three common sources of radioactive ions will be treated in some detail, presenting the types of cooling devices required, the performance presently achieved and improvements expected in the near future.

2 Cooling radioactive ion beams Radioactive isotopes are produced typically in hostile environments. They are created in limited quantities and, as a result, extraction techniques must emphasize production rate and not beam quality. This often results in beams with poor ion optical properties. Radioactive isotopes are also often accompanied by contamination from other radioactive isotopes produced simultaneously and much more abundant stable isotopes. Experiments with radioactive beams on the other hand usually benefit from, and in many cases require, high purity beams with good geometrical and timing properties. These requirements can manifest themselves in many forms. A low energy spread is critical for experiments such as collinear laser spectroscopy since the energy spread is directly correlated to the resolution of the measurement. The transverse beam properties, more specifically the transverse emittance of the beams, are critical in determining the transmission and resolution through a mass

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separator or a convoluted beamline. The duty cycle or time structure of a beam also determines our ability to capture this beam in ion traps or accelerate it in pulsed accelerating structures. The majority of experiments become more difficult when significant beam contamination is present, either because of decreased signal to noise or just because the additional count rate can overwhelm the detector system. Essentially, each experiment has optimal beam properties that best suit it. The optimum production method for a given isotope will yield beams with properties that will often be different from the optimum properties required for the given experiment. Ion beam manipulation via cooling, bunching and purifying is the means that allows better experiments to be performed by matching the properties of the produced beam with that of the required beam. 2.1 Ion beam properties The manipulation of beam properties can be performed by very simple means: a simple lens focusing a beam changes both the beam envelope size and its divergence. Similarly, passage through an RF accelerating gap will change both the energy and time structure of the beam. Although individual properties of the beam, such as transverse position or transverse momentum, are modified by such actions, one can define other beam properties that are not affected by them. These properties are the phase-space densities of the beam, determined by the products of conjugate variables such as position and momentum, or energy and time, in the transverse or longitudinal directions. They are essentially equivalent to an excitation temperature for the different degrees of freedom of the beam particles in the frame of the moving beam, expressed usually in term of longitudinal or transverse emittance, and that cannot be reduced or increased unless “heat” is removed from or added to the system. As a result, transverse focusing, time focusing, electrostatic acceleration and many similar types of ion beam manipulation steps are called non-dissipative; they can affect external beam properties but cannot change the intrinsic excitation energy of the beam (this is one form of Liouville’s theorem). On the experimentalist end of things, spectrometers, beamlines and experimental devices have an acceptance that can be expressed in similar terms. The maximum efficiency that can be obtained in transporting the ion beam through a beamline, spectrometer or apparatus can then be determined from the emittance of the produced beam and the acceptance of the device the beam must go through. If the beam emittance is smaller than the acceptance of the device then, in principle, non-dissipative transformations of the beam such as focusing can be applied to match the beam into the device; no “cooling” of the beam is required. Consider a device which has an entrance aperture of 5 mm and can accept a maximum beam particle angle of 10 mrad. Since in a focusing transformation the product of beam diameter and divergence remains constant we find that a beam with a diameter of 20 mm but a maximum beam particle angle of only

2 mrad can be focused to a diameter of 5 mm and a maximum angle of 8 mrad and all particles will be accepted by the device. If, on the other hand, the beam with diameter 20 mm has a maximum beam particle angle of 4 mrad then when focused to 5 mm, it will have a maximum angle of 16 mrad and it is not possible by non-dissipative transformation to obtain full transmission. Similar arguments can be used for the relation between beam pulse duration and energy spread, or for accumulation of DC beams in pulsed devices. If the emittance is larger than the acceptance, then no non-dissipative manipulation can yield the full efficiency and one must resort to dissipative forces to obtain high efficiency, i.e. cooling. A cautionary note must be added here in that the conserved quantities are the phase space densities, such as the product of the transverse position and transverse momentum. The emittance is obtained from the product of transverse position and transverse angle (which is the ratio of the transverse momentum to longitudinal momentum). The emittance is a conserved quantity at a given energy but decreases as the longitudinal momentum is increased by acceleration for example. Multiplying the emittance by the longitudinal momentum yields the proper conserved quantity. This is the principle behind the so-called normalized emittance (emittance times the velocity β) which is a conserved quantity during acceleration and is often used to compare emittance or acceptance at various energies. Finally, ion beams do not have precisely defined boundaries but rather envelopes defined to contain a given fraction of the beam particles. This fact, although important, adds complications to the concept of emittance that are not critical to our discussion and will be neglected here. 2.2 Basic ion cooling principles The action of cooling corresponds to decreasing the phasespace occupied by an ensemble of particles, or, if that ensemble is moving at a common velocity large compared to the relative velocities (i.e. if it forms a beam), to decreasing the emittance of this beam. To perform cooling or bunching, a few basic requirements must be met: – to have a cold thermal bath (cold electrons, buffer gas, laser beam, . . . ); – to have an interaction between your ensemble or ion beam and the cold thermal bath; – to have sufficient acceptance of the bath, interaction time with the bath and thermal capacity of the bath; – to have the ability to extract the ions from the bath without substantial reheating. Numerous thermal baths are available that offer varying advantages depending on the species and properties to be cooled. For the sake of simplicity, the discussion will be limited here to the most frequently used technique that can be applied to essentially any ion species: collisions with a buffer gas in a trapping/guiding structure. In this case the buffer gas provides the thermal bath, collisions are the means of interaction to exchange heat between the ions and the gas, and guiding/trapping structures are

G. Savard: Ion manipulation with cooled and bunched beams

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Fig. 1. Examples of RF structures available for the confinement and manipulation of charged particles. From left to right we find the standard Paul trap configuration, the RF quadrupole, the RF hexapole, and an RF wall. In the Paul trap the RF is applied between the ring and the two endcaps. In the other structures, the RF is applied between adjacent rods.

most often used to provide large interaction time and localization. The conditions to be met here are that there be enough stopping/cooling power to capture the ions in the longitudinal potential within the length of the device, and that it has a large enough guiding/trapping potential and volume to accept the initial transverse emittance and energy spread. These conditions ensure that the ions spend enough time in contact with the gas to be cooled to its temperature.

2.3 Available confinement devices A key issue in cooling ion beams is the choice of a confinement structure that is best suited to the properties of the incoming ions. In general, these are derived from ion traps which are devices aimed at storing ions for extended time. The most versatile confinement devices use RF focusing. The basic operating principle behind RF focusing devices can be understood most easily if we consider only motion in one dimension. In an inhomogeneous RF field, the electric field along the z-axis can be expressed, for small displacements d around a point z0 (z(t) = z0 + d(t)), as   ∂E0 cos ωt . E(z, t) = E0 (z) cos ωt = E0 (z0 ) + d ∂z (1) The motion on an ion of charge e in this oscillating electric field is given by

Fz (t) = m¨ z = eE0 (z) cos ωt

(2)

and for small oscillation amplitude, the position of the ion is given by (3) d(t) = z0 − d0 cos ωt with

eE0 . (4) mω 2 Averaging the force on the ion over a full RF cycle yields   e2 E0 (z) ∂E0 (z) , (5)

−d0 cos2 ωt = −

Fz (t)av = e 2mω 2 ∂z d0 =

or, if we express the force in terms of a pseudo-potential F = −e

∂Vps =⇒ Vps = ∂z

eE02 (z) . 4mω 2

(6)

One can see from eqs. (5) and (6) that in an inhomogeneous RF electric field there is a net force on charged particles pulling them towards the region of lower field amplitude. This force is proportional to the square of the charge so that both positively and negatively charged particles are attracted to the lower field amplitude region. Therefore, all one needs to create confinement is a region with an electric field amplitude minimum. The most simple such structure is the quadrupole trap shown on the left side of fig. 1, the so-called Paul trap [1]. By symmetry the electric field is zero at the center and increases in amplitude in all directions. The Paul trap is a versatile confinement device that has seen much use in various fields of physics. The geometry of the Paul trap is not however most suitable to inject ion beams into, a more elongated structure is required to offer a longer path length through the device. A more extended path length is offered by the second and third structures in fig. 1, the linear quadrupole and sextupole, which confines ions radially along their central axis. Removing energy from ions inside these structure by gas collisions will result in a centering of the ions on the symmetry axis. However, the potential inside these structures scales as r 2 or r3 , so that these devices are limited to a rather small radius by practical considerations. If larger confinement volumes are required, one must look at different structures. In particular, one cannot easily obtain a pseudo-potential that will be effective over the full volume of a larger device. Considering an extension of the quadrupole and hexapole to a very large number of poles, one can see that a small quadrant of that structure would look like a wall of rods as shown on the right of fig. 1. Such a wall, with alternating positive phase and negative phase rods, would have a very strong RF field close to the rods that diminishes rapidly as one moves away from the rods. Essentially it would form an RF wall that repels charged particles. These walls could then be molded in any form such as a box, a sphere or a cone that repels ions approaching it. A combination of such RF walls with proper DC fields could guide ions and possibly confine them over a large volume.

3 Radioactive ion beam cooling applications The requirement for the amount of gas and the strength of the confining structure depend on the properties of the source, or mode of creation, of the radioactive ions. Three

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main cases will be discussed here: cooling and bunching of poor quality ISOL type beams, cooling of fusionevaporation reaction products, and cooling of fragmentation products. Together they give access to essentially all isotope species that have been observed to date.

cooled to cryogenic temperature. Used as a beam accumulator collecting beam continuously and ejecting it in a pulse mode they yield pulses of longitudinal emittance of a few eV-microseconds, ideal for injection into ion traps. 3.2 Fusion-evaporation residues

3.1 Low-energy beams Typically, ISOL type beams have energy in the 30–60 keV range with energy spread of 1–100 eV and transverse emittance of up to about 100 π mm mrad at 60 keV. The best approach for cooling these beams is to decelerate them electrostatically to an energy of a hundred eVs or so, just above the energy spread so that all particles are still moving forward. Electrostatic deceleration is non-dissipative so that taking a typical ISOL beam with emittance of 50 π mm mrad at 60 keV, we obtain after deceleration for a diameter of 6 mm at 100 eV a maximum divergence of roughly 400 mrad. This corresponds to a maximum transverse energy of roughly 15 eV at that point. The deceleration must therefore focus the ions into a guiding structure with a transverse guiding potential of about 20 eV depth. This is large enough to confine radially the ions while they lose their remaining energy by collisions in the gas. The stopping is best done in a light non-reactive noble gas such as helium. This yields optimum ion survival time since helium has a higher ionization potential than any other species. The amount of helium gas required to stop 100 eV heavy ions is typically about 150 mm at 0.1 mbar. The structure used for confining the ions during the final slowing down must therefore be long enough to offer a path length of 15 cm or more in the 0.1 mbar helium pressure before the ion exits the structure. Initial attempts at this task were first performed with a large RFQ trap at ISOLDE [2]. That structure offers a large enough trapping potential but the path length through the device is not sufficient for practical devices. Increasing the pressure in the device would resolve the path length issue but would also result in a reheating of the ions by gas collisions when they are reaccelerated out of the device. A more suitable structure was found to be the linear RF trap [3] (see second panel in fig. 1) which offers an elongated confining volume. The device can be used with only radial confinement in which case it just cools the beam to the gas temperature (typically room temperature) which after reacceleration yields a transverse emittance of roughly π mm mrad at 60 keV, or with an additional longitudinal confining potential which then allows one to bunch a DC beam to better match it to the experiment. Gas coolers of that type are now used in many laboratories to improve beam properties. In DC mode they reach efficiencies of roughly 30–70% when injected with ISOL type beams [4, 5] at 60 or so keV and close to 100% when injected with very low energy beams [6] such as those extracted from a gas catcher (see below). The cooling times in such structure is typically tens of ms, limited by the gas pressure, and the energy spread of the extracted ions is below 1 eV. At low intensity, the transverse emittance and energy spread can be further reduced if the gas is

A second source of radioactive ions is fusion-evaporation reactions. Production by heavy-ion reactions on thin targets results in a radioactive recoil beam with extremely poor ion optical properties, extracted from the target by momentum conservation. The energy of the recoils depends on the kinematics of the reaction and can vary from typically 0.2 to 5 MeV/u. The momentum spread and angular divergence depend on the details of the reaction, in particular the excitation energy of the compound nucleus and the mass and energy of the evaporated particles. Momentum spread of the reaction products is typically 1–15% and angular spread can extend beyond 150 mrad. Although the recoil beam properties are very poor, the fact that the ions are extracted instantly, and that all species can be obtained, make this source still unique for beams of many species. Slowing down such beams, say a 3 MeV/u beam of Sn isotopes, would require 4.6 mg/cm2 of helium. It is however not necessary to lose all the ion energy in the gas. All that is required is that the ions come to rest in the gas, so most of the energy can be lost in a solid and only the final part of the range needs to be in the gas. Since energy loss is a statistical process, not all particles with a given initial energy will have exactly the same range. This variation in range is called the range straggling and for the example given above, it is about 0.2 mg/cm2 . This intrinsic range straggling is further enhanced by the momentum spread in the beam to values up to 1 mg/cm2 . To stop this beam in the gas we therefore only require an amount of gas sufficient to absorb the total range straggling. The approach to be used here is therefore to remove most of the energy before entering the device, use the gas volume to handle the energy spread and range straggling, and finally, use the fact that the thermalized residues are ionized to guide them out selectively from the stopping volume. The transverse emittance of these beams is large enough that a transverse confining potential of hundreds of kilovolts would be required to confine the beams during the slowing down. No practical device can yield such values and the only option remaining is to lose essentially all remaining energy in the gas so that the confining/guiding potential can start affecting the ions. The required amount of gas is however too large for a linear RF structure; the radial size required is 5–10 cm and the required path length in the gas would demand too high a gas pressure and the resulting gas flow would overwhelm any existing pumping system. A larger structure that can be operated at high pressure is required. This cannot easily be achieved with the standard multipole configurations used in linear RF structures and the selected solution is instead based on a cylindrical chamber, typically 20 cm long and 10 cm in diameter, pressurized with 100–200 mbar of helium. A

G. Savard: Ion manipulation with cooled and bunched beams

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Fig. 3. Picture of the RIA gas catcher prototype built and tested at Argonne and now located at GSI for testing at the full RIA energy. The gas catcher is seen from the extraction nozzle end with the RF circuit feeding the cone structure.

Fig. 2. Forces acting on the ions in the gas catcher. The effects of the DC electric field, gas flow, RF electric field and total forces are shown on the four catcher sketches above.

static electric field pushes the ions towards one end of the cylinder where an RF cone (based on the RF wall configuration shown in the right panel of fig. 1), consisting of a large number of plates forming a guiding structure, focuses the ions towards a nozzle where the ions are finally extracted by gas flow. The combination of the static and RF electric fields, together with the gas flow close to the nozzle, yield rapid and efficient extraction of the ions from the stopping volume (see fig. 2). Efficiencies as high as 45% and mean extraction times below 10 ms have been obtained with such a device used to inject the CPT mass spectrometer [7] at Argonne. A RF linear structure of the type mentioned in the previous section removes the ions from the gas extracted from the gas catcher and further cools the ions to yield beams with optimum properties.

3.3 Fragmentation and in-flight fission residues A final source for short-lived isotopes is fragmentation or in-flight fission at a high-energy heavy-ion facility. This approach provides rapid extraction and separation of the isotopes of interest and access to the very neutron-rich isotope region that is not easily accessible by other techniques. The beam properties of the ions extracted from the fragmentation approach are however not suitable for many experiments and a means of cooling these beams would allow breakthrough experiments at lower energy. The gas catcher approach was proposed to fulfill this task and is now a cornerstone of the RIA project.

Cooling fragments extracted from a fragment separator is a daunting task. The recoils have energy of 100–1000 MeV/u and a momentum spread of 1–20% depending on the production mechanism. The transverse emittance of these recoils is too high for any realistic trapping device to handle. The range and range straggling are also enormous, typically 2.2 g/cm2 and 3 mg/cm2 respectively for 250 MeV/u Sn recoils. The effective range straggling that one must deal with is even larger, dominated by the momentum spread of the recoils. For these same 250 MeV/u Sn recoils, the intrinsic (zero momentum spread) range straggling corresponds to 24 cm of helium gas at 500 mbar. The effect of a 0.1% momentum spread of these recoils is to increase this range straggling to 70 cm, a 1% momentum spread would require more than 5 meters of helium gas at 500 mbar. Performing the cooling of these beams must therefore be a multistep approach. The momentum spread of the recoils must first be minimized. This is accomplished by adding a dispersive stage at the end of the fragment separator [8], followed by a wedge that removes more energy from the more energetic particles and less from the less energetic particles so that all particles exit the wedge with essentially the same energy. Much of the energy of the recoils must then be removed in an homogeneous degrader before entering the gas catcher. The helium gas volume in the gas catcher must then handle the remaining energy straggling and angular divergence of the recoils. Once the recoils are thermalized in the gas, one uses the fact that the recoils are ionized to guide them out selectively from the stopping volume. The longitudinal path length required in the gas is of the order of 2–20 mg/cm2 while the lateral dimensions depend critically on the ion optics and achromatization stage but would typically be about 20% of the longitudinal dimension. A device to perform this task was built at Argonne National Laboratory, essentially by scaling up the gas catcher

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developed for the CPT spectrometer system. The device (see fig. 3) consists of a 1.25 meter long, 0.25 meter inner diameter, UHV chamber. Cylindrical electrodes along the body of the chamber establish a DC electric field inside the chamber to push the stopped ions towards the extraction nozzle where an RF cone made of 278 plates with alternating RF phase focuses the ions to the nozzle. The device comprises over 7400 components, with over 4000 prepared to UHV standards. It was tested at low energy with sources and with radioactive beams produced with the ATLAS accelerator [9], and reached efficiencies of up to 30% for ions stopped throughout the volume of the device. It is now at GSI where it will be tested at the full RIA energy behind the FRS fragment separator. A similar approach is being pursued at RIKEN [10].

4 Status and prospects for improvements Cooling of radioactive ions obtained from various sources has been discussed above. The three sources mentioned have specific advantages and as such they are complementary. While the initial beam properties vary significantly between sources, it is possible to find the proper structure to cool each of these beams to essentially room temperature and obtain beam qualities comparable to those obtained with stable beams. Although these applications are fairly new, they are now present in a large number of laboratories where they are used to improve the beam properties for mass separation and better transmission through apparatus, or used to change the time structure of beams for injection in various storage devices. Efficiencies are high and the techniques are essentially universal. A number of issues with this technology are however still present and improvements to the technology are currently trying to address many of them. The emittance of extracted beams could theoretically be even lower if the thermal bath formed by the gas was colder. Linear RF structures at cryogenic temperature are now in the commissioning phase and should soon yield beam of improved emittance for low-intensity cases. The efficiency of current ion coolers is still not optimum. Improved designs for the deceleration section leading into them, stronger radial confinement and a better sequestration and purification of the helium gas will improve the efficiency of these devices further. The delay time in these devices is still fairly large; cooling in a gas cooler takes typically 5–50 ms and the mean extraction time out of a gas catcher can vary from 5 to 200 ms depending on the size and design of the device. For gas cooler the delay time is determined by the gas pressure (and gas type) and reducing this time requires running at higher pressure. This however introduces difficulties with the extraction out of the device that can worsen the emittance obtained if performed in too high a pressure region. The creation of different pressure regions along the cooler, higher pressure in the entrance stopping region and lower pressure at the extraction end, can solve this difficulty at the cost of some additional complications.

In the case of the gas catchers, larger DC guiding fields or the addition of gas circulation throughout the device can be used to speed up extraction. The final and probably most limiting aspects of the devices mention here is the limitations due to space charge. As a beam is essentially stopped for cooling, the ions spend a larger fraction of the time in a small region of space. The resulting higher concentration of charge increases the space charge repulsion they experience which can heat up the ions in the guiding/trapping structure. The problem is more severe in structures where ions are accumulated to bunch the beam. Such buncher gas cooler start observing degradation of the pulse properties at typically around 105 ions per bunch. Gas coolers used as continuous beam coolers can tolerate probably at least 108 ions per second before a similar deterioration occurs but the ion flux at which it occurs depends about the details of the device. This problem is linked to the cooling time in this case since a shorter time in the device results in a lower space charge density for a given number of ions cycling through it per seconds. Attempts are being made to quantify and model the space charge limits more carefully. The space-charge problems are further amplified in the gas catcher systems where because of the large energy loss by each incoming radioactive ions an even larger space charge is created by gas ionization. The space charge limits in these cases depend not only on the geometry but also on the energy loss of the specific radioactive ions and on the measures taken to eliminate the space charge created by the ionization. This is a key issue for many uses of this technology and a vigorous R&D program is ongoing to better determine and push back these limits. This work was supported by the US Department of Energy, Office of Nuclear Physics, under Contract Nos. W-31-109-ENG-38 and DE-FG-06-90ER-41132.

References 1. W. Paul, H.P. Reinhard, U. von Zahn, Z. Phys. 152, 143 (1958). 2. R.B. Moore, G. Rouleau, the ISOLDE Collaboration, J. Mod. Opt. 39, 361 (1992). 3. T. Kim, Buffer gas cooling of ions in a radio frequency quadrupole ion guide, PhD Thesis, McGill University (1997). 4. F. Herfurth et al., Nucl. Instrum. Methods A 469, 254 (2001). 5. A. Nieminen et al., Nucl. Instrum. Methods A 469, 244 (2001). 6. G. Savard et al., Hyperfine Interact. 132, 223 (2001). 7. G. Savard et al., Nucl. Instrum. Methods B 204, 582 (2003). 8. C. Scheidenberger et al., Nucl. Instrum. Methods B 204, 119 (2003). 9. W. Trimble et al., Nucl. Phys. A 746, 415 (2004). 10. M. Wada et al., Nucl. Instrum. Methods B 204, 2003 570.

Eur. Phys. J. A 25, s01, 719–722 (2005) DOI: 10.1140/epjad/i2005-06-170-5

EPJ A direct electronic only

Status of the RISING project at GSI F. Becker1,a , A. Banu1 , T. Beck1 , P. Bednarczyk1,2 , P. Doornenbal1 , H. Geissel1 , J. Gerl1 , M. G´orska1 , H. Grawe1 , J. Grebosz1,2 , M. Hellstr¨om1 , I. Kojouharov1 , N. Kurz1 , R. Lozeva1 , S. Mandal1 , S. Muralithar1 , W. Prokopowicz1 , N. Saito1 , T.R. Saito1 , H. Schaffner1 , H. Weick1 , C. Wheldon1 , M. Winkler1 , H.J. Wollersheim1 , J. Jolie3 , P. Reiter3 , urger4 , H. H¨ ubel4 , J. Simpson5 , M.A. Bentley6 , G. Hammond6 , G. Benzoni7 , A. Bracco7 , F. Camera7 , N. Warr3 , A. B¨ 7 7 n2 , C. Fahlander8 , and D. Rudolph8 B. Million , O. Wieland , M. Kmiecik2 , A. Maj2 , W. Meczynski2 , J. Stycze´ 1 2 3 4 5 6 7 8 9

Gesellschaft f¨ ur Schwerionenforschung, Planckstr. 1, D-64291 Darmstadt, Germany IFJ PAN, ul. Radzikowskiego 152, 31-342 Krakow, Poland Institut f¨ ur Kernphysik, Universit¨ at zu K¨ oln, Z¨ ulpicherstr. 77, D-50937 K¨ oln, Germany Helmholtz-Institut f¨ ur Strahlen- und Kernphysik, Nußallee 14-16, D-53115 Bonn, Germany CCLRC Daresbury Laboratory, Daresbury Warrington, Cheshire WA44AD, UK Department of Physics, Keele University, Keele, Staffordshire ST55BG, UK INFN, Via G. Celoria, 16, I-20133 Milano, Italy IRES, B.P. 28, F-67037 Strasbourg Cedex 2, France Department of Physics, Lund University, Box 118, SE-22100 Lund, Sweden Received: 14 January 2005 / c Societ` Published online: 2 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The FRS-RISING set-up at GSI uses secondary radioactive beams at relativistic energies for nuclear structure studies. At GSI the fragmentation or fission of stable primary beams up to 238 U provide secondary beams with sufficient intensity to perform γ-ray spectroscopy. The RISING set-up is described and results of the first RISING campaign are presented. New experimental methods at relativistic energies are being investigated. Future experiments focus on state-of-the art nuclear structure physics covering exotic nuclei all over the nuclear chart. PACS. 25.70.De Coulomb excitation – 25.70.Mn Projectile and target fragmentation – 29.30.-h Spectrometers and spectroscopic techniques – 29.30.Kv X- and γ-ray spectroscopy

1 Introduction The RISING (Rare ISotope INvestigations at GSI) setup [1] consists of the fragment separator FRS [2] and a highly efficient γ-ray spectrometer. EUROBALL GeCluster detectors [3] together with BaF2 detectors from the HECTOR array [4] form the γ-ray array which is placed at the final focus of the FRS. The SIS/FRS facility [2] provides secondary beams of unstable rare isotopes produced via fragmentation reactions or fission of relativistic heavy ions. These unique radioactive beams have sufficient intensity to perform γ-ray spectroscopy measurements. In the first campaign fast beams in the range of 100 to 400 A · MeV were used for relativistic Coulomb excitation and secondary fragmentation experiments. Coulomb excitation at intermediate energies is a powerful spectroscopic method to study low-spin collective states of exotic nuclei [5]. It takes advantage of the large beam velocities and allows the use of thick secondary targets. Unwanted nuclear contributions to the excitation process are excluded by selecting events with forward scattering angles corresponding to sufficiently large impact parameters. Contrary to Coulomb excitation, fragmentation a

e-mail: [email protected]

and nucleon removal reactions at the secondary target are a universal tool to produce exotic nuclei in rather high spin states [1]. Besides being an excellent tool to investigate radioactive fragments up to higher spin states, fragmentation reactions provide a selective trigger, particularly suppressing the strong background of purely atomic interaction events. For the first fast beam campaign the RISING set-up was optimized to the study of the following subjects of exotic nuclei: the shell structure of nuclei around doubly magic 56 Ni and 100 Sn, the evolution of shell structure towards extreme isospin, the investigation of shapes and shape coexistence in particular around the N = Z line and the mirror symmetry, as well as collective modes and the E1 strength distribution in neutron-rich nuclei (N  Z).

2 Experiments 2.1 Experimental details The SIS facility at GSI provides primary beams of all stable nuclei up to 238 U. For various nuclei a projectile energy up to 1 A · GeV and intensities up to 109 /s are available. Radioactive beams are produced by projectile fragmentation or fission of 238 U. From the exotic fragments

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Fig. 1. Schematic sketch of the FRS-RISING set-up. Two multiwire detectors (MW1 and MW2), an ionization chamber (MUSIC), and two scintillator detectors (SCI1 and SCI2) are the beam diagnostic elements for the FRS. γ-rays produced in the reaction target at the final focus of the FRS are measured with BaF2 -HECTOR and Ge-Cluster detectors. The CATE array identifies the outgoing reaction products by mass and charge.

produced, the nuclei of interest are selected by the FRS using the combined Bρ-ΔE technique [2]. The RISING set-up at the FRS is shown schematically in fig. 1. For the FRS beam diagnostics, scintillator detectors (SCI), an ionization chamber (MUSIC), and multiwire detectors (MW) are employed to identify the produced ions and select the nucleus of interest. The position-sensitive SCI detectors determine the time-of-flight (TOF) and together with the MWs the position of the beam in the FRS. From the TOF and the flight path length, the velocity of the ion is determined. The MUSIC detector measures the energy loss of the ions and gives the atomic number Z. Together with the ion velocity a particle identification in Z and A/Q is achieved. At the final focal plane of the FRS, a reaction target is placed. In all Coulomb excitation experiments this was a gold target, while for the secondary fragmentation experiment a 9 Be target was used. To identify type and track of the particles hitting the secondary target, the two MWs placed upstream were applied. The outgoing particles were identified in charge and mass by the calorimeter telescope CATE [6,7,8], a Si-CsI array. The position-sensitive Si detectors of CATE allow tracking of the outgoing particles required for the scattering angle selection in the Coulomb excitation experiments and for the Doppler correction procedure. In order to perform γ-ray spectroscopy a highly efficient γ-ray array was placed in the view of the reaction target. It consists of EUROBALL Cluster Ge detectors [3] and BaF2 detectors from the HECTOR array [4]. The Cluster detectors benefit from being placed under forward angles between 15 and 36 degrees, since the Lorentz boost increases the γ-ray efficiency from 1.3% measured with a 60 Co source at rest to 2.8% (at 100 A· MeV) for the in-beam studies at relativistic energies. A distance of 70 cm between the Ge detectors and the target is necessary for an energy resolution between 1–3% after Doppler correction. 2.2 Present results In a commissioning experiment a primary 84 Kr beam was used. The aim was to investigate the feasibility of

Coulomb excitation measurements under the present conditions. The 2+ → 0+ transition in 84 Kr was employed to study the impact parameter dependence at relativistic energies. From the γ-array design about 1% energy resolution is expected for a γ-ray emitted from a moving nucleus with β ∼ 0.4 [1]. The commissioning with a primary 84 Kr beam confirms the expected energy resolution of ∼ 1.5% for the Doppler-corrected 2+ → 0+ transition at 884 keV (β ∼ 0.4). Relativistic Coulomb excitation measurements with secondary beams were performed to measure for the first time B(E2) values of first excited 2+ states. Excitation of 54,56,58 Cr was chosen in order to investigate the shell structure of nuclei with extreme isospin. The secondary beam was produced by fragmentation of a primary 84 Kr beam. In another experiment fragmentation of a primary 124 Xe beam produced secondary 108,112 Sn beams. The measurement of the electromagnetic 2+ → 0+ transition probability in the neutron-deficient nucleus 108 Sn gives insight in the nuclear structure towards 100 Sn. It is a sensitive test of E2 correlations related to core polarization. The known B(E2) value in 112 Sn is used for normalization. Secondary fragmentation was used to study the mirror pair 53 Mn/53 Ni. The identification of the so far unknown first excited states in 53 Ni would provide information on isospin symmetry and Coulomb effects at a large proton excess as well as a rigorous test of the shell model. Secondary beams of 55 Ni and 55 Co were produced by fragmentation of a primary 58 Ni beam. The fragmentation of the secondary beams produced many exotic nuclei, among them the nuclei of interest 53 Mn and 53 Ni. Compared to primary beams, secondary beams have a broader momentum distribution. In order to achieve a good energy resolution an accurate vertex reconstruction of incoming and outgoing particles is required. The analysis of the relativistic Coulomb excitation of 54 Cr provides an example [9]. The energy resolution of the 834 keV transition in 54 Cr could be improved from ∼ 4% to ∼ 2% without and with vertex reconstruction for the Doppler correction procedure, respectively. Figure 2 shows the γ-ray spectra of 54,56,58 Cr. The intensities of the clearly visible 2+ → 0+ transitions are a measure of the B(E2) strength which reveals information on the evolution of a possible N = 32 sub-shell closure. A detailed publication on the B(E2) values can be found in references [10,11]. The relativistic Coulomb excitation study of 108 Sn revealed for the first time the B(E2) value for the 2+ → 0+ transition [12]. Concerning the two-step fragmentation of the 55 Ni and 55 Co secondary beams, the ongoing analysis reveals so far the mirror pair 54 Fe and 54 Ni, this is presented in fig. 3. The spectra acquired from ≈ 50% of the data show good statistics and complement previous experiments on 54 Ni obtained in a recent EUROBALL experiment [13] and intermediate-energy Coulomb excitation studies at NSCL [14]. The resolution of the γ-ray lines in fig. 3 is inferior to that of the γ-ray lines shown in fig. 2 due to the different reaction process. The goal to obtain 53 Mn/53 Ni with a factor 50–100 lower cross-section could be reachable

F. Becker et al.: Status of the RISING project at GSI

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with an improved analysis using the full statistics, a refined tracking Doppler correction, and in particular an improved mass determination [15]. The mass resolution in the secondary fragmentation reactions is limited by the accuracy of the momentum distribution determination of the projectile fragments. According to the statistical model derived by Goldhaber [16] the mass resolution of fragments at 100 A · MeV amounts to 2–3% (FWHM) without a momentum or time-of-flight measurement. With the actual CATE set-up we could achieve a mass resolution of the 2–3% for fragmentation and 1–2% for Coulomb excitation reaction channels [8]. From recent experiments we have the following online results. The structure of neutron-rich Mg nuclei is being investigated by lifetime measurements. In the chain of the Mg isotopes strong prolate deformations are expected. B(E2) values of excited states deduced from lifetimes will be a measure of the deformation. The experiment takes advantage of the high abundance of nuclei produced via a two-step fragmentation reaction. According to the expected lifetime a stack of three targets has to be arranged at well defined distances. This allows the extraction of the lifetimes of states in the picosecond range by analysing the specific γ-ray line shapes. The A ≈ 130 region shows strong evidence for the existence of stable triaxial shapes [17]. This is indicated in this transitional region by the observation of chiral doublet structures in the odd-odd N = 75 isotones [18]. N = 74 even-even nuclei 132 Ba, 134 Ce and 136 Nd are good candidates since they are cores of the N = 75 odd-odd nuclei 132 La, 134 Pr and 136 Pm where chiral doublet bands were observed. Relativistic Coulomb excitation of the even-even nuclei are being performed within the RISING campaign. The measurement of the B(E2) values of the transitions + depopulating the 2+ 1 and 22 states will provide a sensitive test for the results of the Monte Carlo shell model. The calculations predict comparable strengths for the B(E2) + + + values of the 4+ 1 → 21 and the 22 → 21 transitions as a fingerprint of the underlying triaxiality [19]. A technical upgrade is a detector behind the reaction target, an additional CATE ΔE Si detector. Compared to the vertex reconstruction achieved with the MW detectors 3 m upstream of the reaction target, the accuracy of the position determination at the target was improved from 1 cm to 3 mm (FWHM). Measuring twice the ΔE, at the target and at CATE, enhanced the measured Z resolution by a factor 1.4.

3 Perspectives

Energy [keV]

Energy [keV]

Fig. 3. Exotic nuclei produced by secondary fragmentation reactions: γ-ray spectra were obtained for 54 Ni (left) and 54 Fe (right) [15].

The differential Doppler shift method applied for the neutron-rich Mg isotopes can also be employed in the light Pb isotopes. The proposed investigation on 185,186,187 Pb would probe the scenario of the predicted triple shape coexistence by the experimental determination of the deformation parameters. The lifetime information on the first excited states could again be extracted from the γ-ray line shapes produced in a secondary fragmentation reaction.

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The investigation of collective modes in nuclei far from the stability line is still in its infancy. In the neutron-rich nuclei the p-n asymmetry could influence the shell structure. Predictions by theory point to changes in the giant dipole resonance (GDR) strength distribution in exotic neutron-rich nuclei like 68–78 Ni. The GDR is supposed to fragment the strength towards lower excitation energy, the so called Pygmy resonances. The RISING set-up provides besides the Ge-Cluster also BaF2 detectors. The latter permit the measurement of γ-rays at relatively high energies making it possible to cover the entire dipole response function. The measurement of the γ-ray decay stemming from GDR is a proposed RISING experiment on 68 Ni. Further it is planned to investigate the structure of neutron-rich nuclei with respect to mixed symmetry [20]. IBM-2 calculations predict mixed-symmetry states in the N = 52 isotones, i.e. non-symmetric states with respect to the p-n degree of freedom. To study the evolution of this structure at N = 52 below Z = 40 suggests an investigation of the neutron-rich nuclei 88 Kr and 90 Sr. Relativistic Coulomb excitation experiments could reveal the B(E2) values for the predicted low-lying first and second excited 2+ states. The 2+ 2 value would be a sensitive test for detailed shell model and IBM-2 calculations and would contribute to understand the evolution of mixed-symmetry configurations [21]. A possible weakening of the spin-orbit splitting resulting in a restoration of the harmonic-oscillator shell closures is predicted by theory for very neutron-rich nuclei [22]. In this scenario the harmonic-oscillator magic numbers would supersede the magic numbers based on the Woods-Saxon potential well known for nuclei close to stability. For the neutron-rich Ni and Sn isotopes the information on the most significant matrix elements, magnetic moments and spectroscopic factors are up to now not available. RISING will contribute revealing these sensitive pieces of nuclear structure information. An investigation of the nuclear structure in the vicinity of 132 Sn is a good testing ground for the evolution of the spin-orbit splitting [23]. For neutron-rich nuclei far from stability this splitting is predicted to decrease or vanish [22]. The RISING set-up offers the opportunity to determine the information on the spin-orbit splitting by the measurement of the spectroscopic factors. It is proposed to measure spectroscopic factors in 131 Sn by a neutron removal reaction of a radioactive 132 Sn beam produced by fission of 238 U. The structure of the unstable neutron-rich isotopes 132,134,136 Te is strongly influenced by the N = 82 shell closure and two protons outside the magic Z = 50 shell [24]. Measurements of g-factors performed within the RISING project would yield the information on the dominant role of protons or neutrons being involved in the configurations of the first excited states. A comparison with predictions by theory would give the information on the specific components induced by neutron and proton orbitals. The proposed measurement of perturbed γ-ray angular correlations for lifetimes in the picosecond range is at present only feasible by the technique of transient magnetic fields

(TF). The future g-factor experiment will employ the relativistic Coulomb excitation of secondary 132,134,136 Te beams in combination with the TF technique. Spectacular is the observation of an anomalous Coulomb energy difference behaviour in the N = Z nucleus 70 Br [25]. Coulomb distortion of the nucleon orbitals is indicated (Thomas-Ehrman shift). This effect should increase as the drip line is approached. The RISING proposal on the supposed proton emitting nucleus 69 Br would allow the investigation of the heaviest mirror pair 69 Br/69 Se at the proton drip line. Moreover 69 Br plays an important role in the rapid-proton capture (rp) process. The odd-Z isotope 69 Br is considered as being a possible termination point in the rp-process when the proton capture lifetime of the 68 Se target is longer than competing decays and the proton flux duration. Previous experiments [26, 27,28] could not attribute clear evidence for the stability of 69 Br due to difficulties of the flight path limit. In the proposed RISING experiment an investigation of the prompt production in a secondary fragmentation reaction would overcome this limitation. At the same time the measurement of the prompt γ-ray decay would give insight into mirror pair properties at the proton drip line.

References 1. H.-J. Wollersheim et al., Nucl. Instrum. Methods A 537, 637 (2005). 2. H. Geissel et al., Nucl. Instrum. Methods B 70, 286 (1992). 3. J. Eberth et al., Nucl. Instrum. Methods A 369, 135 (1996). 4. A. Maj et al., Nucl. Phys. A 571, 185 (1994). 5. T. Motobayashi et al., Phys. Lett. B 346, 9 (1995). 6. R. Lozeva et al., Acta Phys. Pol. B 36, 1245 (2005). 7. R. Lozeva et al., Nucl. Instrum. Methods B 204, 678 (2003). 8. R. Lozeva et al., submitted to J. Phys. G. 9. P. Bednarczyk et al., Acta Phys. Pol. B 36, 1235 (2005). 10. A. B¨ urger et al., Acta Phys. Pol. B 36, 1249 (2005). 11. A. B¨ urger et al., to be published in Phys. Lett. B. 12. A. Banu et al., submitted to Phys. Rev. C. 13. A. Gadea et al., LNL Annu. Rep. 2003, INFN (REP) 202/2004, p. 8. 14. K.L. Yurkewicz et al., Phys. Rev. C 70, 054319 (2004). 15. G. Hammond et al., Acta Phys. Pol. B 36, 1253 (2005). 16. A. Goldhaber et al., Phys. Lett. B 53, 306 (1974). 17. C.M. Petrache et al., Phys. Rev. C 61, 011305(R) (2000). 18. K. Starosta et al., Phys. Rev. Lett. 86, 971 (2001). 19. T. Otsuka, private communication; T. Saito et al., RISING proposal. 20. N. Pietralla et al., Phys. Rev. C 64, 031301(R) (2001). 21. A. Lisetskiy et al., Nucl. Phys. A 677, 100 (2000). 22. J. Dobaczewski et al., Phys. Rev. Lett. 72, 981 (1994). 23. J.P. Schiffer et al., Phys. Rev. Lett. 92, 162501 (2004). 24. D.C. Radford et al., Phys. Rev. Lett. 88, 222501 (2002). 25. G. de Angelis et al., Eur. J. Phys. 12, 51 (2001). 26. M.F. Mohar et al., Phys. Rev. Lett. 66, 1571 (1991). 27. B. Blank et al., Phys. Rev. Lett. 74, 4611 (1995). 28. R. Pfaff et al., Phys. Rev. C 53, 1753 (1996).

Eur. Phys. J. A 25, s01, 723–727 (2005) DOI: 10.1140/epjad/i2005-06-019-y

EPJ A direct electronic only

Recent highlights from ISOLDE@CERN L.M. Frailea For the ISOLDE and REX-ISOLDE Collaborations PH Department, CERN CH-1211 Geneva 23, Switzerland Received: 15 January 2005 / c Societ` Published online: 2 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The ISOLDE online mass separator located at CERN provides a large variety of radioactive ion beams for research on nuclear physics, nuclear astrophysics, fundamental interactions, atomic physics, radiochemistry, nuclear medicine, condensed matter science, life sciences and others. The recently operational REX-ISOLDE post-accelerator is capable of accelerating the isotopes produced at ISOLDE to energies of up to 3.0 MeV/u by using an ion trap and charge breeder and a compact linear accelerator structure. The post-accelerator is complemented by a highly segmented Ge array in conjunction with a compact silicon strip detector at one of the secondary target positions, while a general spectroscopy setup occupies a second station. REX-ISOLDE has opened up the possibility of nuclear spectroscopy studies by means of transfer reactions and Coulomb excitation of exotic nuclei. The facility maintains an extensive physics-driven target and ion source development program, which has helped ISOLDE keep its international status for more than 35 years. Some recent experimental highlights and technical developments are discussed. PACS. 25.40.-h Nucleon-induced reactions – 28.60.+s Isotope separation and enrichment – 29.25.Rm Sources of radioactive nuclei

1 The ISOLDE facility

2 Production of radioactive ion beams

Forty years ago CERN opened a call for proposals to explore the feasibility of nuclear physics experiments at the laboratory. The response was immediate, and already by the end of 1964 a proposition had been presented by a strong international collaboration. In 1967 the ideas of these enterprising scientists had been realized into the ISOLDE facility [1]. It was originally located at the CERN SC, the Synchrocyclotron providing 600 MeV protons. ISOLDE has been producing an extraordinary output in experimental nuclear physics and related fields ever since. Today ISOLDE is located at the CERN PS Booster, which delivers a pulsed beam of 3 × 1013 protons per pulse with an average intensity of 2 μA and energies of 1.0 or 1.4 GeV. The proton beam impinges on a thick target kept at high temperature and produces the radioactive species by fission, fragmentation and spallation reactions. The reaction products diffuse out of the target and are subsequently ionized, mass-separated on line and transported to the different experimental setups in the ISOLDE hall [2]. At present more than 850 radioactive isotopes from more than 65 elements are produced.

The target and ion source development has been the driving force of ISOLDE during decades. The pulsed structure of the driver beam, seen at first as a major concern due to the instantaneous power deposited in the targets, has now become one of the strengths of the facility, as it makes it possible to perform measurements of the release of the exotic isotopes from the target-ion source units. Within this context the TARGISOL project [3], hosted by the European Union, aims at the optimization of the release properties of ISOL targets [4,5]. This involves the development of beams of new elements and more exotic isotopes as well as the improvement of existing beams in terms of intensity, purity and reproducibility. Technical developments have helped ISOLDE keep its competitiveness throughout the years. In particular, the development of the Resonant Ionization Laser Ion Source (RILIS) [6] in collaboration with the Institute of Spectroscopy in Troitsk (Russian Academy of Sciences) set a milestone for selective ionization. The RILIS is used not only to ionize new beams with extraordinary purity, but also to enhance the intensity of existing beams or to probe the properties of nuclear isomers utilizing the hyperfine splitting. Currently the ISOLDE RILIS can ionize 25 different elements and is used in almost 50% of the physics shifts delivered by the facility [7].

a

e-mail: [email protected]; on leave of absence from Universidad Complutense, E-28040 Madrid, Spain.

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The neutron converter target [8] is other development worth mentioning. Instead of hitting directly the target material the protons are focussed into a metal rod parallel to the target, container, the neutron converter, resulting in a shower of neutrons that irradiates the production target made of an actinide. In this way, the fission fragments are enhanced with respect to the spallation and fragmentation products, at the cost of a small decrease of the total production yield. The neutron converter has proven itself invaluable to perform spectroscopy experiments of very neutron rich nuclei [9]. The fact that the proton beam does not directly strike the production target slows down its ageing, but the deterioration of the neutron converter still poses troubles. Recently, radioactive singly-charged ions from ISOLDE have been successfully charge bred with an ECR (Electron Cyclotron Resonance) ion source. In spite of the large stable background contamination, the technique has already been used to purify Ar beams that suffered from multiply-charged heavier noble gas ions coming from the ISOLDE target. This was achieved by tuning the ECR to select a particular mass over charge for the Ar ions, at which the contaminants were strongly reduced. The target and beam research and development program, driven by the physics requests, will continue with further tests on solid state lasers for resonant ionization, the investigation of new carbides for target materials or the implementation of negative ion sources, just to mention a few. A new development of a RFQ (RadioFrequency Quadrupole) cooler and buncher [10] will reduce the transverse and longitudinal emittance and will allow the bunching of the beam delivered to the experiments. This will improve the measurements of nuclear moments and half-life, and open new possibilities for REX-ISOLDE.

3 The ISOLDE Physics programme The ISOLDE facility provides a large variety of radioactive isotopes for many experiments in nuclear physics and related areas like nuclear astrophysics, atomic physics, radiochemistry, physics of the fundamental interactions, nuclear medicine, material science, life sciences and others. The main experimental equipment includes highresolution laser spectroscopy devices, high-precision mass spectrometers, an on-line nuclear polarization setup, spectrometers for emission channelling and angular correlation measurements, a total absorption gamma spectrometer, a HV platform for up to 200 kV post acceleration, ultrahigh-vacuum experimental chambers for surface and interface studies, several general purpose nuclear spectroscopy setups and the REX-ISOLDE post-accelerator (sect. 4). Figure 1 summarizes the variety of experiments performed during the 2001 to 2003 campaigns and the relative distribution of the radioactive beam used. ISOLDE delivers 300 to 350 eight-hour shifts of radioactive beam to some 35 different experiments per year. The experimental programme carried out at ISOLDE is well represented in these proceedings. It is worth mentioning the systematic work carried out in the N ∼ 20 island

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of inversion where investigations by fast timing in βdecay [11], Coulomb excitation at REX-ISOLDE [12] and moment measurements [13, 14] have been performed. An extensive mass measurement programme is carried out at the facility [15,16], together with particle and gamma spectroscopy in β-decay, nuclear astrophysics studies [9], search for physics beyond the standard model by βν correlations (WITCH) and many others.

4 REX-ISOLDE One of the fundamental achievements at ISOLDE has been the realization of the REX-ISOLDE postaccelerator [17], which provides radioactive ion beams accelerated to energies of several MeV. It consists of a highly innovative low-energy section made up of a Penning trap (REX-TRAP) [18] for cooling and bunching the radioactive singly charged species from ISOLDE, and an electron beam ion source (REX-EBIS) [19] where the ions are charge bred. A particular charge state can be selected with a mass separator and then injected into the REX-LINAC. As sketched in fig. 2 the REX-LINAC is a compact lowenergy linear accelerator [20] that consists on a RFQ followed by an interdigital H-type (IH) structure and multigap resonators. The REX-LINAC has recently undergone an upgrade in order to increase the final energy from 2.3 MeV/u to 3.0 MeV/u. For this purpose a new accelerating IH-structure of 0.5 m running at 202.56 MHz, twice the REX frequency, has been installed, commissioned and successfully used for the first experiments during 2004. The post-accelerator is complemented by a highly segmented Ge array, MINIBALL [21], in conjunction with a compact silicon strip detector, located at a dedicated secondary target position. A second beam line allows performing experiments with tailored detection setups. A very significant fraction of the isotopes produced at ISOLDE are already available for experiments at REXISOLDE. Virtually all the isotopes produced can be accelerated through REX provided the charge breeding of heavy masses to higher charge states in REX-EBIS can

L.M. Fraile: Recent highlights from ISOLDE@CERN

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2.6 2.9 2.5 2.1–2.2 2.7 2.8 2.8 2.9 2.9 2.9 2.8 2.8 2.8 2.8 0.3

n pick-up (d, p) (Be, 2α) Scattering (Pb) (p, α) reaction Fusion (Si) Coulomb Excitation (Ni) Coulomb Excitation (Ag) Coulomb Excitation (Pd) Coulomb Excitation (Pd) Coulomb Excitation (Pd) Coulomb Excitation (Pd) Coulomb Excitation (Ni) Coulomb Excitation (Ni) Coulomb Excitation (Ni) Coulomb Excitation (Ni) Implantation (SiC) for DLTS

Gas cooling with Ne and Ar. Foil stripping Test beam Beam development: molecular sideband & foil stripping Test beam Previously at 2.3 MeV/u Previously at 2.3 MeV/u Beam development: molecular sideband [22] Previously at 2.3 MeV/u Previously at 2.3 MeV/u New beam New beam New beam New beam New beam Test beam at 300 keV/u (RFQ)

Li(a) Li 17 F 28 Mg 30 Mg [12] 32 Mg [12] 70 Se 74 Zn [7] 76 Zn [7] 78 Zn [7] 110 Sn 122 Cd 124 Cd 126 Cd 148 Pm 11

(a )

See text for a brief discussion.

be achieved in a reasonable time. This is attainable by an improvement on the current density of the EBIS electron beam. Longer breeding times up to 200 ms, longer accumulation times and storage of a larger amount of ions in the trap have to be investigated as well. The high vacuum of the breeding system assures that the resulting beam of highly charged ions is of high purity. The main beam contaminants result then from the buffer gas used in REXTRAP and from residual gases coming from the REX mass separator sector, and also from the isobaric contaminants originated at the ISOLDE target that end up with the same A/q ratio as the beam of interest. A summary of the accelerated beams during 2004 can be found in table 1. An extensive physics program is carried out at REXISOLDE. The beam purity and general applicability are crucial to allow for investigation of bound and unbound light nuclei at the drip line, heavy fission fragments and nuclei at the N = Z line. The main reactions employed are Coulomb excitation, transfer and fusion-evaporation. The disappearance of the neutron shell closures for neutronrich nuclei (N = 20, N = 28) is investigated by means of Coulomb excitation around the barrier by determining the energy of the 2+ 1 state and the reduced transition

probability for excitation to that state. Recent Coulomb excitation experiments with the MINIBALL setup have succeeded to extract the deformation of neutron rich Mg, Zn and Cd isotopes [7, 12] for nuclei as heavy as 126 Cd. The results show the versatility of REX-ISOLDE for this type of studies aiming at the investigation of the structure of exotic nuclei. First tests with fusion evaporation reactions have also started. They will enable the investigation of neutron rich compound nuclei and the study of the enhancement of sub-barrier fusion by neutron transfer. Reactions of astrophysical interest, like the study of the inelastic branch of the 14 O(α, p)17 F [23] reaction, have been proposed too. Other experiments concerning the structure of nuclei along the N = Z line, proton radioactivity, etc. are foreseen in the near future. REX-ISOLDE is an excellent tool for the investigation of unbound light nuclei by means of transfer reactions and elastic resonance scattering. As an example, the first excited state of the nucleus 10 Li, unbound subsystem of the halo nucleus 11 Li, can be characterized by using neutron pick-up 9 Li(d, p)10 Li and 9 Li(9 Li, 2α)10 Li reactions, which favour s-wave or p-wave pick-up, respectively. In a recent experiment by Jeppesen et al. [24] the incident 9 Li beam

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from REX-ISOLDE with 105 particles/s intensity was sent to a C3 D6 deuterium target surrounded by a compact array of position sensitive Si detectors. Most of the reaction channels, with exception of those leading to three-body or five-body final states, were identified, which shows the great applicability of the method. In particular, the (d, p) transfer leading to 10 Li was studied, and the excitation energy of the unbound 10 Li system was reconstructed, as shown in fig. 3. The only peak at positive energy can be described by a R-matrix calculation assuming a p-wave resonance at 350 keV above the 9 Li + n threshold with a FWHM amplitude of ∼ 300 keV [24,25]. The one neutron transfer differential cross-section for 10 Li can be then determined by selecting the events on the 350 keV peak (inset of fig. 3). There are negative-energy structures that cannot derive from the 9 Li + d reaction. They can be explained as originating from the elastically scattered protons from the H contamination of the C3 D6 target and from the contribution of the compound reaction of the 9 Li beam on the 12 C of the C3 D6 target.

5 Outlook The breadth of the science achievable with radioactive ion beams has brought a large interest and fresh ideas to the field in recent times. Several projects are underway in Europe, being the Facility for Antiproton and Ion Research (FAIR) in Germany the most advanced at this stage. ISOLDE plays a central role in the European Union design study for the third-generation radioactive ion beam ISOL facility, EURISOL [26]. The plans for this new installation include a post-accelerator for up to 100 MeV/u radioactive ions, storage rings, recoil mass separators and large multi-segmented detectors. Such a high-intensity facility is the natural successor of ISOLDE and CERN would be an ideal site for it, with the required proton driver of several MW assuring exceptional synergies with other areas of research. Within this context, the future of ISOLDE and REXISOLDE is strongly influenced by the proposed upgrades

of the injector accelerators at CERN to deliver a driver proton beam of much higher intensity. An ongoing study is analyzing the feasibility of a superconducting proton LINAC (SPL) [27] on the CERN site and its impact on a later upgrade of the LHC and on new physics. In a possible staged approach to the SPL, the present 50 MeV proton LINAC of the CERN PS complex would be replaced by a high-performance H− low-energy LINAC structure at room temperature which will later inject into a superconducting section. This will be already advantageous for ISOLDE, as it will allow increasing the PS Booster intensity up to a factor 2, on the wayt to the maximum 10 μA driver beam intensity that this facility can handle prior to the construction of a new target area. Tests are under consideration to reduce the cycling of the PS Booster from 1.2 s to 900 ms, providing an increase of the driver intensity of more than 30%. In addition, plans are underway for a further energy upgrade of REXISOLDE to ∼ 5.0 MeV/u, which will allow overcoming the Coulomb barrier limit of the projectiles that can be used to induce nuclear reactions. Furthermore, CERN is undertaking a major consolidation of the ISOLDE facility itself including a new radioactive laboratory for target manipulation that will be ready for the 2005 campaign. The extension of the ISOLDE experimental hall is also in progress and will be completed for 2005. It will house the next REX upgrade and joint experimental equipment, and a new solid state physics laboratory.

6 Conclusions The ISOLDE facility enjoys a lively programme of a high scientific quality. This is possible not only due to the collaboration of many European physics institutes but also to the infrastructure and manpower provided by CERN, that makes it possible to run a large facility delivering beam to many users. ISOLDE is integrated in the European research structure through the EURONS (EUROpean Nuclear Structure) infrastructure initiative, and plays a key role in the design study of the future European thirdgeneration ISOL radioactive ion beam facility, EURISOL.

References 1. http://www.cern.ch/ISOLDE. 2. E. Kugler, Hyperfine Interact. 129, 23 (2000). 3. http://www.targisol.csic.es, EU RTD project TARGISOL, HPRI-CT-2001-50033. 4. M. Turri´ on et al., Nucl. Phys. A 746, 441 (2004). 5. U. K¨ oster et al., these proceedings. 6. V. Fedosseev et al., Nucl. Instrum. Methods B 204, 353 (2003). 7. P. Van Duppen, these proceedings. 8. J. Nolen et al., AIP Conf. Proc. 473, 477 (1999). 9. K.-L. Kratz et al., these proceedings. 10. I. Podadera et al., these proceedings. 11. H. Mach, these proceedings. 12. H. Scheit, these proceedings.

L.M. Fraile: Recent highlights from ISOLDE@CERN 13. 14. 15. 16. 17. 18. 19. 20. 21.

G. Neyens, these proceedings. M. Kowalska, these proceedings. D. Lunney, these proceedings. F. Herfurth, these proceedings. O. Kester et al., Nucl. Instrum. Methods B 204, 20 (2003). F. Ames et al., Hyperfine Interact. 132, 469 (2001). F. Wenander et al., Nucl. Phys. A 701, 528c (2002). T. Sieber et al., Nucl. Phys. A 701, 656c (2002). J. Eberth et al., Prog. Part. Nucl. Phys. 46, 389 (2001).

22. 23. 24. 25. 26.

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P. Delahaye, these proceedings. P.J. Woods et al., CERN-INTC-2003-026. H. Jeppesen et al., Nucl. Phys. A 748, 374 (2005). H. Jeppesen, PhD Thesis, Aarhus University. http://www.ganil.fr/eurisol, EU RTD project EURISOL, HPRI-CT-2001-500001 & http://www.eurisolds.lnl.infn.it/. 27. M. Vretenar (Editor), Conceptual and Desing of The SPL (Yellow report, CERN 2000-012).

Eur. Phys. J. A 25, s01, 729–731 (2005) DOI: 10.1140/epjad/i2005-06-199-4

EPJ A direct electronic only

ISOL beams of neutron-rich oxygen isotopes U. K¨oster1,a , O. Arndt2 , U.C. Bergmann1 , R. Catherall1 , J. Cederk¨all1 , I. Dillmann2 , M. Dubois3 , F. Durantel3 , L. Fraile1 , S. Franchoo1 , G. Gaubert3 , L. Gaudefroy4 , O. Hallmann2 , C. Huet-Equilbec3 , B. Jacquot3 , P. Jardin3 , K.L. Kratz2 , N. Lecesne3 , R. Leroy3 , A. Lopez3 , L. Maunoury3 , J.Y. Pacquet3 , B. Pfeiffer2 , M.G. Saint-Laurent3 , C. Stodel3 , A.C.C. Villari3,5 , and L. Weissman6 1 2 3 4 5 6

ISOLDE, CERN, CH-1211 Gen`eve 23, Switzerland Institut f¨ ur Kernchemie, Universit¨ at Mainz, D-55128 Mainz, Germany GANIL, IN2P3-CNRS/DSM-CEA, B.P. 55027, F-14076 Caen Cedex 5, France Institut de Physique Nucl´eaire d’Orsay, F-91406 Orsay Cedex, France Physics Division, Argonne National Laboratory, IL 60439, USA NSCL, Michigan State University, East Lansing, MI 48824, USA Received: 15 January 2005 / c Societ` Published online: 9 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. ISOL beams of 19–22 O were produced at ISOLDE and GANIL. At ISOLDE the neutron-rich oxygen isotopes are produced by 1.4 GeV proton-induced reactions in a UC x /graphite target. The target is connected via a water-cooled transfer line (to retain all non-volatile isobars) to an ISOLDE type FEBIAD ion source where the released CO is dominantly ionized as CO+ . 19–22 O beams were also produced at SPIRAL (GANIL). A 77.5 MeV/nucleon 36 S beam was fragmented in a thick graphite target, coupled by a cold transfer tube to an ECR ion source which ionizes the released CO dominantly as O + and CO+ . PACS. 28.60.+s Isotope separation and enrichment – 29.25.Ni Ion sources: positive and negative – 29.25.Rm Sources of radioactive nuclei

1 Introduction Radioactive ion beams are mainly produced by two different methods: either by in-flight separation of fast reaction products created in projectile fragmentation, fusionevaporation or fission reactions or by the isotope separation on-line (ISOL) method. In the latter the reaction products are first stopped in a thick target. From the target, which is typically heated to high temperatures, the reaction products can diffuse and effuse out towards an attached ion source where they are ionized, extracted, accelerated to tens of keV and mass-separated. ISOL beams have normally the advantage of higher beam intensity (since thicker targets can be used) and higher beam quality (smaller emittance, small energy spread), but not all elements are easily released from the thick target. This leads to significant decay losses for short-lived isotopes. Oxygen is a more “difficult” element for ISOL facilities due to its high chemical reactivity. Atomic oxygen would easily react at each surface collision in the target and ion source unit, thus getting retained for too long time. To favor a rapid release, the oxygen radicals have to be bound as soon as possible in a volatile, but less reactive molecule. A suitable molecule is CO which is readily formed by rea

Conference presenter; e-mail: [email protected]

action of oxygen radicals with hot carbon. Thus targets made from pure graphite or graphite mixed with other materials are expected to be favorable for the fast release of radioactive oxygen isotopes. Beams of the neutron-deficient oxygen isotopes 14,15 O have been produced at several ISOL facilities, see ref. [1] for a review. In the present article we discuss recent results and future prospects of the production of ISOL beams of neutron-rich oxygen isotopes at ISOLDE and SPIRAL.

2 Neutron-rich oxygen beams at ISOLDE At ISOLDE neutron-rich oxygen isotopes are produced by high-energy proton-induced reactions of heavy target materials. Previously beams of 19–22 O12 C+ [2] had been obtained from a mixed 26.8 g/cm2 Pt/graphite powder target bombarded with 0.6 GeV protons and connected to a special ISOLDE-type FEBIAD ion source with tungsten cathode and graphite plasma chamber. Recently such beams were also produced by 1.4 GeV proton bombardment of a 44 g/cm2 standard ISOLDE UCx /graphite target. The 2000 ◦ C hot target is connected via a watercooled transfer line (to retain all non-volatile isobars) to an ISOLDE MK7-type FEBIAD ion source [3] where the

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-1

10

8

10

7

10

6

10

5

10

4

10

3

10

2

10

Beam intensity (ions/s)

-2

Efficiency

10 -3

10 -4

10 -5

10 -6

GANIL NANOGAN-3

10

CO+2

O+2

+

NO

+

CO

+

H2O

HO+

8+

O

7+

O

6+

O

5+

O

4+

O

3+

O

O+

10

O2+

ISOLDE FEBIAD MK7

-7

Ion species

Fig. 1. Measured relative (ISOLDE FEBIAD MK7) and absolute (GANIL NANOGAN-3) ionization efficiencies for different oxygen containing ion species.

released CO is dominantly ionized as CO+ . Figure 1 shows the relative population of atomic oxygen ions and molecular sidebands as measured with stable and radioactive oxygen tracers. Since abundant amounts of stable CO are already released from the hot target and ion source unit it is difficult to measure the absolute ion source efficiency by injecting CO with natural isotopic composition through a calibrated leak. Thus, the displayed absolute ionization efficiency for CO+ of 3.7% was obtained by scaling measured efficiencies of the noble gases He, Ne, Ar, Kr and Xe with the known electron impact ionization cross-sections [4,5, 6] and an A−1/2 mass dependence which represents the transit time through the plasma chamber. However, the overall efficiency for release and ionization of radioactive oxygen isotopes is indeed much lower, due to strong getter losses at the 1900 ◦ C hot tantalum cathode and tantalum target enclosure. Comparing the measured 19 O12 C+ beam intensity (see fig. 2) with the 0.29(8) mb production crosssection measured in inverse kinematics (1 GeV/nucleon 238 U on 1 H) at GSI [7, 8] gives an overall efficiency of only 0.03%. In fact, the cross-sections for production of light isotopes in proton-induced reactions on heavy targets rise typically by a factor two or more when increasing the proton energy from 1.0 GeV to 1.4 GeV [1]. Hence, the real overall efficiency is probably even lower, indicating that > 99% of the produced 19 O gets trapped somewhere and is never released. The yields from the UCx /graphite target are 50% to 300% higher than those formerly measured with the Pt/graphite target and a short test run with a 22 O12 C+ beam already gave new nuclear structure information [9]. The only observable contamination of the x O12 C+ beams stems from x−1 O13 C+ which is of the order of few percent (1.1% abundance of 13 C times the yield ratio for x−1 O/x O).

3 Neutron-rich oxygen beams at SPIRAL At GANIL neutron-rich oxygen isotopes were produced by fragmenting a 77.5 MeV/nucleon 36 S beam in the SPIRAL

ISOLDE 2 μA p on Pt/gr., FEBIAD ISOLDE 2 μA p on UCx/gr., FEBIAD ISOLDE 2 μA p on UCx/gr., 1+ ECRIS 36 SPIRAL 1.5 kW S beam 22 36 SPIRAL 6 kW Ne or S beam 19

20

21

22

Isotope

Fig. 2. Measured (full symbols) and extrapolated (open symbols) beam intensities for neutron-rich oxygen isotopes.

graphite target [10]. Oxygen is again forming CO which reaches via a cold transfer tube the NANOGAN3 ECR ion source. The latter (plasma chamber at room temperature) is optimized for the production of multiply charged ions, but delivers also singly charged atoms and ions. The ionization efficiencies of the different ion species have been measured with a 13 C16 O tracer [11] and are displayed for comparison in fig. 1. Compared to the FEBIAD ion source a much higher fraction of multiply charged oxygen ions is present as well as a considerable amount of HO+ and H2 O+ . These, stemming from water vapor, are significantly suppressed by the hot plasma chamber of the FEBIAD. The beam intensities measured in two different test runs (with 0.8 kW to 1.4 kW primary beam power) were scaled to 1.5 kW of primary beam power and displayed in fig. 2. If ions other than singly charged atomic oxygen had been measured, the beam intensity was scaled to O+ with the relative ionization efficiencies from fig. 1. The shown intensities are fully consistent with those previously measured at the SHyPIE set-up [12] when taking into account the lower beam power and a roughly twice lower ionization efficiency.

4 Conclusion and outlook Although the obtained beam intensities are already sufficient to perform certain experiments, there is clear room for improvement: 1. Replacing at ISOLDE the FEBIAD by a 1+ ECR ion source without hot Ta parts and lining the entire Ta target container with graphite would strongly reduce the gettering losses and may result in a gain of up to three orders of magnitude in yield. 2. The GANIL yields of 19,20 O could by enhanced by about a factor five (calculated with EPAX V2.1 [13]) by replacing the primary 36 S beam with a 22 Ne beam of the same beam power. A straightforward gain of a factor of four is expected from the THI upgrade to 6 kW primary beam intensity [14].

U. K¨ oster et al.: ISOL beams of neutron-rich oxygen isotopes

3. An extension towards 23,24 O is more difficult, not only due to the lower production cross-section and the very short half-life (increasing the decay losses), but mainly due to the background situation. Atomic 23 O+ beams suffer from very intense 23 Ne+ background and molecular 12 C23 O+ beams have strong background from 35 Ar+ and at ISOLDE moreover from the abundantly produced fission product 140 Xe4+ . However, this background could be removed, by: – A gas-filled beam manipulation device (Penning trap or RFQ cooler) which resets the multiply charged background to the 1+ charge state, followed by a A/q separation to suppress it. – Molecular beams could be separated from atomic background by breaking the molecules (via stripping or charge-breeding) and subsequent second mass separation.

Supported by the EU-RTD project TARGISOL (contract HPRI-CT-2001-50033). A.C.C.V. acknowledges his partial support by the U.S. Department of Energy, Office of Nuclear Physics (contract W31-109-ENG-38).

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References 1. U. K¨ oster, Eur. Phys. J. A 15, 255 (2002). 2. ISOLDE SC yield database, http://www.cern.ch/ ISOLDE/normal/isoprodsc.html. 3. S. Sundell, H. Ravn, the ISOLDE Collaboration, Nucl. Instrum. Methods B 70, 160 (1992). 4. H.C. Straub, B.G. Lindsay, K.A. Smith, R.F. Stebbings, J. Chem. Phys. 105, 4015 (1996). 5. M.A. Mangan, B.G. Lindsay, R.F. Stebbings, J. Phys. B 33, 3225 (2000). 6. R. Rejoub, B.G. Lindsay, R.F. Stebbings, Phys. Rev. A 65, 042713 (2002). 7. P. Armbruster et al., Phys. Rev. Lett. 93, 212701 (2004). 8. Maria-Valentina Ricciardi, High-resolution measurements of light nuclides produced in 1 A GeV 238 U-induced reactions in hydrogen and in titanium, PhD Thesis, Universidad de Santiago de Compostela (2005). 9. L. Weissman et al., J. Phys. G 31, 553 (2005). 10. J.C. Putaux et al., Nucl. Instrum. Methods B 126, 113 (1997). 11. S. Gibouin et al., Nucl. Instrum. Methods B 204, 240 (2003). 12. Nathalie Lecesne, Etude de la production d’ions radioactifs multicharg´ es en ligne, PhD Thesis, Universit´e de Caen (1997). 13. K. S¨ ummerer, B. Blank, Phys. Rev. C 61, 034607 (2000). 14. E. Baron et al., in Proceedings of the 15th International Conference Cyclotrons and Their Applications, 14-19 June 1998, Caen, France, edited by E. Baron, M. Lieuvin (IOP, 1999) pp. 385-388.

Eur. Phys. J. A 25, s01, 733–736 (2005) DOI: 10.1140/epjad/i2005-06-043-y

EPJ A direct electronic only

Radioactive Ion beams in Brazil (RIBRAS) R. Lichtenth¨ aler1,a , A. L´epine-Szily1 , V. Guimar˜ aes1 , C. Perego1 , V. Placco1 , O. Camargo jr.1 , R. Denke1 , 1 1 1 P.N. de Faria , E.A. Benjamim , N. Added , G.F. Lima1 , M.S. Hussein1 , J. Kolata2 , and A. Arazi3 1 2 3

Departamento de F´ısica Nuclear, Instituto de F´ısica da Universidade de S˜ ao Paulo, CP 66318, 05315-970 S˜ ao Paulo SP, Brazil Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA Laboratorio Tandar CNEA, Av. del Libertador 8250, 1429, Buenos Aires, Argentina Received: 4 November 2004 / c Societ` Published online: 3 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A double superconducting solenoid system is being installed at the Pelletron Laboratory of the University of S˜ ao Paulo, Brazil. This system allows the production of secondary beams of light exotic nuclei like 8 Li, 6 He and others. The first results using this facility are presented. PACS. 28.52.Lf Components and instrumentation – 41.85.Lc Beam focusing and bending magnets, wiggler magnets, and quadrupoles – 29.27.-a Beams in particle accelerators – 25.60.-t Reactions induced by unstable nuclei

1 Introduction The Pelletron Laboratory of the University of S˜ ao Paulo installed the first South America Radioactive Ion beams device (RIBRAS) [1,2]. This facility extends the capabilities of the original 8 MV Pelletron accelerator by producing secondary beams of unstable nuclei. The most important components in this system are the two new superconducting solenoids. The solenoids have 6.5 T maximum central field (5 T · m axial field integral) and a 30 cm clear warm bore, which corresponds to an angular acceptance in the range of 2 ≤ θ ≤ 15 degrees in the laboratory system. The solenoids were built by Cryomagnetics INC [3] and were designed to operate in connection with the Linac post-accelerator, presently under construction. With the Linac, the energy of the primary beam will be about 2–3 times larger than the maximum energy of the present Pelletron Tandem of 3–5 MeV · A. The presence of two magnets is very important to produce pure secondary beams [4,5]. The first solenoid makes an in-flight selection of the reaction products emerging from the primary target in the forward angle region. As the first magnet transmits all ions with the same magnetic rigidity mE/Q2 the radioactive secondary beam can be rather contaminated. With two solenoids, it is possible to use differential energy loss in an energy degrader foil, located at the crossover point between the magnets. This degrader foil will allow the second solenoid to select the ion of interest by moving 

Aux´ılio Pesquisa FAPESP No. 97/9956-5, Tem´ atico FAPESP No. 2001/06676-9. a Conference presenter; e-mail: [email protected]

Projeto

the contaminant ions out of its bandpass. An additional future possibility of the two solenoid system is the production of tertiary beams using a secondary target in the middle scattering chamber. The second solenoid can be tuned to select a different magnetic rigidity producing lowintensity (1–100 /s) tertiary beams like 9 Li, 8 He. [6] This is in principle possible with secondary beams of 107 /s and assuming a typical conversion efficiency of 10−5 for the production reaction.

2 Recent developments The RIBRAS beam line is presently mounted in the experimental room of the Pelletron accelerator Laboratory (fig. 1). The production system consists of a gas cell, mounted in a ISO chamber followed by a tungsten Faraday cup which suppress the primary beam and measures its current. The gas cell was mounted with a 2.2 μm Havar entrance window and a 9 Be vacuum tight exit window 12 μm thick which plays the role of the primary target and the window of the gas cell at the same time. The gas inside the cell has the purpose of cooling the Berilium foil heated by the primary beam and can also be used as production target. In case we want to use a gas target to produce secondary beams, the berilium foil can be replaced by another Havar foil and the pressure inside the cell can be increased up to several bars. In table 1 we present some typical production rates and reactions used at Notre Dame [5] and ao Paulo. at RIBRAS, S˜

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Fig. 1. RIBRAS facility installed in the 45B Pelletron beam line.

Table 1. (*) Production reactions measured at RIBRAS using only 1 solenoid.

Production reaction 9

7

8

(∗)

Be( Li, Li) Be(7 Li, 6 He)(∗) 3 He(7 Li, 7 Be)(∗) 3 He(6 Li, n)8 B 12 C(17 O, 18m F) 9

Secondary beam (part/s/μAe)

106 105 105 105 103

fig. 3 show the telescope spectra with the solenoid 1 tuned to select 8 Li and 6 He ions, respectively. The production rates measured at RIBRAS for these two exotic ions were about 105 p/s and 106 p/s, respectively, per microampere of primary 7 Li beam. The second solenoid is mounted and in place waiting for the secondary scattering chamber to complete the system.

3 Scientific program with RIBRAS The first radioactive beams produced by this system were delivered during the XIII J.A. Swieca Summer School on Experimental Nuclear Physics on February/2004 using only the first solenoid. The 8 Li and 6 He particles produced by the reaction of the 7 Li primary beam on the 9 Be primary target were focused by the first solenoid in the scattering chamber located at the crossover point between the two solenoids. The secondary-beam profile (x-y) was measured by a Paralell Plate Avalanche Counter (PPAC) placed in the crossover point. A triple ΔE(20 μm) − E1(150 μm) − E2(150 μm) silicon telescope placed at zero degrees and 5 cm after the PPAC allowed the identification of the atomic number, mass and the energy of the secondary-beam particles. The secondary-beam spot measured at the PPAC position was of about 7 mm in diameter which is consistent with a primary-beam spot size of 4–5 mm multiplied by a magnifying factor of 1.5 of the first solenoid. Figure 2 and

The proposals of experiments for RIBRAS approved in the last PAC of the S˜ ao Paulo Pelletron Laboratory for the year of 2005 consist basically of elastic scattering studies with exotic projectiles on several targets. Measurements of elastic scattering angular distributions using projetiles like 6 He, 8 Li and 7 Be are in progress with RIBRAS. Three systems are being studied at the moment, 6 He + 27 Al, 6 He + 208 Pb and 7 Be + 120 Sn at energies around the Coulomb barriers. The main interests are in the effect of nuclear and Coulomb breakup on the elastic scattering and the threshold anomaly behaviour in systems with weakly bound projectiles. Elastic scattering measurements with these radioactive ion beams are feasible with the present intensities of the Pelletron primary 7 Li beam which are in the range of 100–300 ηAe. In a second stage, with the new ionizer for our SNICS ion source, we expect to have primary intensities above 1 μAe. This will permit the measurement of transfer reactions. The

R. Lichtenth¨ aler et al.: Radioactive Ion beams in Brazil (RIBRAS)

Fig. 2. ΔE-E spectrum for the 9 Be(7 Li, 8 Li) reaction.

Fig. 3. ΔE-E spectrum for the 9 Be(7 Li, 6 He) reaction.

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study of transfer and capture reactions of astrophysical interest will be possible to be performed in the near future with both solenoids.

4 Conclusions In conclusion, a double superconducting 6.5 T facility is installed at the Pelletron Laboratory of the University of S˜ ao Paulo to produce secondary beams of radioactive nuclei. The two solenoids are mounted and tested on the 45B beam line of the Pelletron experimental area. The system began its operation with only the first solenoid and using the 7 Li primary beam delivered by the 8 MV Pelletron Tandem. Secondary beams of 8 Li and 6 He were produced. Experiments using these secondary beams are in progress.

References 1. R. Lichtenth¨ aler, A. L´epine-Szily, V. Guimar˜ aes, G.F. Lima, M.S. Hussein, Nucl. Instrum. Methods Phys. Res. A 505, 612 (2003). 2. R. Lichtenth¨ aler, A. L´epine-Szily, V. Guimar˜ aes, G.F. Lima, M.S. Hussein, Braz. J. Phys. 33, 294 (2003). 3. Cryomagnetics, Inc. 1006 Alvin Weinberg Drive Oak Ridge, TN 37830, USA. 4. M.Y. Lee, F.D. Bechetti, T.W. O’Donnell, D.A. Roberts, J.A. Zimmerman, J.J. Kolata, V. Guimar˜ aes, D. Peterson, P. Santi, P.A. DeYoung, G.F. Peaslee, J.D. Hinnefeld, Nucl. Instrum. Methods Phys. Res. A 422, 536 (1999). 5. F.D. Bechetti, M.Y. Lee, T.W. O’Donnell, D.A. Roberts, J.J. Kolata, L.O. Lamm, G. Rogachev, V. Guimar˜ aes, P.A. DeYoung, S. Vincent, Nucl. Instrum. Methods Phys. Res. A 505, 377 (2003). 6. F.D. Bechetti, M.Y. Lee, T.W. O’Donnell, D.A. Roberts, J.A. Zimmerman, J.J. Kolata, V. Guimar˜ aes, D. Peterson, P. Santi, Nucl. Instrum. Methods Phys. Res. A 422, 505 (1999).

Eur. Phys. J. A 25, s01, 737–738 (2005) DOI: 10.1140/epjad/i2005-06-137-6

EPJ A direct electronic only

GANIL and the SPIRAL2 project W. Mittiga and A.C.C. Villari For the SPIRAL2 APD group GANIL (DSM/CEA, IN2P3/CNRS), BP 55027, 14076 Caen Cedex 5, France Received: 15 January 2005 / c Societ` Published online: 4 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Based on a multibeam high intensity driver (5 mA of deuterons, 1 mA of heavy ions) a detailed project study for Spiral2 was started in November 2002 in a large collaboration. Fission rates of up to 10 13 /s will be possible with standard density UC (2.3 g/cm3 ), and up to 1014 /s with high density (11 g/cm3 ) UC. Fission may be induced either by neutrons from a converter, or with direct beams. The multibeam driver will allow other high intensity beams, with energies up to 14 MeV/nucleon for A/Q = 3. The radioactive ions will be accelerated by the existing CIME cyclotron, with energies of 1.7–25 MeV/nucleon. PACS. 29.17.+w Electrostatic, collective, and linear accelerators – 29.25.-t Particle sources and targets

Based on the LINAG (LINear Accelerator at GANIL) Phase 1 conceptual design [1,2] and the European RTD (Research for Technical Development) program [3], a two years detailed design study of a facility for the production of high intensity secondary beams, mainly by the ISOL method, named SPIRAL2, was started in November 2002 in a large collaboration. The multibeam driver will allow various production modes to reach various regions of the nuclear chart (see fig. 1). Radioactive isotope beams can be produced via the fission process, with the aim of 1013 fissions/s, induced in a UCx target by fast neutrons from a C converter [4] using a 5 mA deuteron beam of 40 MeV. With the use of high density UCx (11 g/cm3 ) the fission rate can reach 1014 /s. In this case the fission products are coming from 239 U at an excitation energy of about 25 MeV, that is optimal for the production of neutronrich nuclei in the main fission bumps (region 1 of fig. 1). Higher excitation energy fission products that populate a much broader range, including region 4 on the chart can be obtained by direct bombardment of a fissile target with a heavier beam, such as He, Li, C, . . . . The driver is made of the following main elements: the primary beam is produced in high-performance ECR sources, and accelerated by a RFQ cavity and independent phase superconducting resonators. Energies up to 14.5 MeV/nucleon and intensities of 1 mA will be possible for A/Q = 3, with present technologies up to Ar-Ca. Further upgrade will be possible. The recently commissioned cyclotron CIME will perform the post acceleration in the SPIRAL2 project. It allows acceleration of heavy ions in the energy range of 1.7 MeV/nucleon up to 25 MeV/nucleon, depending on a

e-mail: [email protected]

Fig. 1. The different domains on the nuclear chart covered by the SPIRAL2 project (see text).

the A/Q. For fission fragments and with present performances of an ECR charge booster, optimal energies would be of the order of 8 MeV/nucleon. Yield calculations of fission fragments (see, e.g., [5] and references cited) with the Monte Carlo codes (LAHET + MCNP + CINDER, see references in [5]) for a 5 mA deuteron beam of 40 MeV energy in a carbon converter, followed by a UCx target have been performed. The expected radioactive beam intensities (after diffusion, effusion, ionisation and acceleration) are for some examples: 78 Zn, 8 · 106 /s; 91 Kr, 8 · 1010 /s; 94 Sr, 1010 /s; 123 Cd, 109 /s; 132 Sn, 3·109 /s; 140 Xe, 8·1010 /s. The in target production yields are those calculated using the 11 g/cm3 UC2 . The Arrhenius coefficients used in

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Fig. 4. Scheme of the plug system for the converter and the TIS (Target Ion Source) for fission products. Fig. 2. General layout of the SPIRAL2-project. Ions coming either from a deuteron ion source, or a high performance heavy ion source are first bunched and accelerated up to 0.75 MeV/nucleon in a room temperature RFQ. The superconducting Linac accelerates up to 40 MeV for deuterons, or 14 MeV/nucleon for A/Q = 3. The beams may be used directly, or in a RIB-ISOL production station. After selection, the ISOL beams can be used at TIS-energy and, simultaneously, can be re-accelerated by the existing CIME cyclotron.

region N = Z (region 6 on fig. 1) will be accessible via the fusion-evaporation process, using the high intensity heavy ion beams of the LINAG. Light radioactive nuclei (region 7) can be produced using either neutron induced reactions or appropriate light heavy ion induced reactions. It was estimated that 1013 /s of 6 He can be produced. Regions 2, 3 and 5 will come in reach using fusion evaporation reactions induced by secondary beams. The general scheme of the project is shown on fig. 2. The target ion-source system must be carefully optimized to achieve the highest possible production rates for the secondary beams, together with a long lifetime for all components in the highly radioactive environment. The scheme of the converter and the target is shown on fig. 3. The high radioactivity that will result from the neutrons from the converter and the fission products, needs a very careful design for handling all parts in a safe way, acceptable with present safety rules. A design similar to the plug system at TRIUMF-ISAC was adopted. It is shown schematically on fig. 4. The green light for the construction is expected by mid-2005 from French funding agencies.

References

Fig. 3. Scheme for the deuteron-to-neutron converter and the fission product target. In the upper part a general view of the system is shown, in the lower part a front and side view of the UCx container is shown, with dimensions in mm.

this calculation were supposed to be the same as for C and Ta, both tabulated in the literature. The assumed 1+ and 1+/N+ ionisation efficiencies are adopted as 90% (1+) and 12% (1+/N+) for Kr and Xe, 30% (1+) and 4% (1+/N+) for Zn, Sr, Sn, I and Cd. The assumed acceleration efficiency in the CIME cyclotron is 50%. The

1. G. Auger, W. Mittig, M.H. Moscatello, A.C.C. Villari, High Intensity Beams at GANIL and Future Opportunities: LINAG, GANIL, September 2001, report GANIL R 01 02. 2. LINAG Phase I, a technical report, version 1.3, GANIL, June 27, 2002, GANIL R 02 08. 3. M.G. Saint Laurent et al., SPIRAL Phase II European RTD report, GANIL R 01-03 2001. 4. J. Nolen, A target concept for intense radioactive beams in the 132 Sn region, in Proceedings of the Third International Conference on Radioactive Nuclear Beams, East Lansing, MI, May 24-27, 1993, edited by D.J. Morrissey (Editions Fronti`eres, Gif-sur-Yvette, 1993). 5. D. Ridikas, W. Mittig, A.C.C. Villari, Nucl. Phys. A 701, 343c (2002).

Eur. Phys. J. A 25, s01, 739–741 (2005) DOI: 10.1140/epjad/i2005-06-150-9

EPJ A direct electronic only

Recent developments of the radioactive beam preparation at REX-ISOLDE P. Delahaye1,a , F. Ames2 , I. Podadera3 , R. Savreux1 , and F. Wenander3 1 2 3

ISOLDE, PH-IS division, CERN, Geneva, Switzerland TRIUMF, Vancouver, B.C., Canada ISOLDE, AB division, Geneva, Switzerland Received: 16 November 2004 / c Societ` Published online: 11 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. This year, three main topics of research and development have been pursued at the REXISOLDE facility low-energy stage, complementary to the energy upgrade of the postaccelerator. These concern the ion cooling method tests, the charge exchange process study in the buffer gas of the Penning trap REXTRAP, and the molecular beam injection into the trap and REXEBIS ion source. We report here on some progress in these different investigations. PACS. 29.27.-a Beams in particle accelerators – 41.75.-i Charged-particle beams – 52.55.-s Magnetic confinement and equilibrium – 34.70.+e Charge transfer – 29.25.Rm Sources of radioactive nuclei

1 Introduction The low-energy stage of REX-ISOLDE [1] consists of a Penning trap (REXTRAP) for radioactive ions bunching and cooling, and an electron beam ion source (REXEBIS) for the charge breeding. It allows an efficient acceleration of the radioactive beams produced at ISOLDE in a compact LINAC. Complementary to the last energy upgrade [2], research and development are pursued to improve the beam preparation.

2 Buffer gas cooling tests The charge breeding efficiency within REXEBIS depends strongly on the quality of the incoming cooled beam, i.e. longitudinal and transversal emittances from the trap. For high intensities, the space charge of the trapped ion cloud prevents an efficient cooling in REXTRAP with the presently adopted method, the so-called sideband cooling [3]. Eventually this results in a decreased efficiency of the trapping process. A new cooling method has been introduced and was first tested 2 years ago, the so-called rotating wall cooling. It is inspired by an existing technique used to compress the cloud of a non-neutral plasma along the axis of Penning traps, see e.g. [4]. It uses a combination of a rotating multipole excitation in the transverse plane of the trap with a buffer gas damping the ions motion [5]. During the latest tests this method was directly compared to sideband cooling. Both quadrupolar and a

Conference presenter; e-mail: [email protected]

Fig. 1. Cooling efficiencies. See comments in the text.

dipolar excitations were applied at the (2,1) plasma mode eigenfrequency [5]. The measured efficiencies of the different cooling methods for 39 K+ ion numbers above 107 are showed in fig. 1. The experimental conditions were identical to those described in [5] except the excitation amplitude Vpp = 30 V. The excitation frequency was optimized for each measurement as it is slightly varying according to the number of injected ions. Clearly the rotating wall dipolar excitation and sideband cooling excitation efficiencies show a quite similar behaviour. The rotating wall quadrupolar excitation is slightly less efficient. A saturation effect appears for every method above 109 ions per bunch.

The European Physical Journal A

number of ions (arb. units)

740

1.5

Kr

+

1

+

Ne

0.5 0

0

250

500

750

1000

cooling time (ms)

Fig. 2. Evolution of 78 Kr+ and 20 Ne+ ion numbers as a function of the cooling time. These were recorded and identified by time of flight on a MCP detector. See comments in the text. Fig. 3. Ions time-of-flight spectra after REXTRAP.

3 Charge exchange study In REXTRAP, Ne is commonly used as a buffer gas with a pressure of about 10−4 mbar in the trapping area. For noble gas beams charge exchange losses have been observed. Cooled He+ ions are neutralized in less than 1 ms. In the case of Ar+ Kr+ and Xe+ ions, the direct charge exchange process with the buffer gas atoms is a closed channel, i.e. a channel for which the Q value is negative. Ion survival times of and above 120 ms were measured [6]. Time-offlight spectra were recorded at the exit of the trap on a MCP detector after variable cooling times. Since the typical cooling time applied at REXTRAP is well below 100 ms it does not usually affect the overall REX efficiency. However a careful study has been undertaken as such a process might occur in a more critical manner in other buffer gas cooling devices presently in development. Numerical calculations are currently in progress to give a theoretical estimate of the contribution of the direct charge transfer. The main competitive processes are charge exchange with impurities in the buffer gas or charge exchange with the atoms of the gas mediated by a third neutral partner. In the case of Kr+ ions, no evidence for impurities were observed in the time-of-flight spectra. The Ne+ and Kr+ ion number evolution is shown in fig. 2. Due to the absence of any cooling excitation at the right frequency, the magnetron motion of the Ne+ ions increases with time and the ions are eventually lost on the wall of the trap. Dashed lines are fit to the spectra, assuming that Kr+ ions are only lost by charge transfer with the Ne atoms of the buffer gas. The adjusted exponential decay constants give survival times for Kr+ and Ne+ ions of 118 ms and 413 ms, respectively.

4 Molecular beam injection According to their chemical properties, the radioactive elements can combine themselves with the impurities present in the ISOLDE target. To avoid isobaric contaminants from the ISOLDE separator it has been demonstrated this year that molecules rather than atomic ions can be efficiently injected and broken up in the low-energy stage of REX-ISOLDE [7].

During off-line tests, SeCO+ molecules were injected into the trap. By varying the trap potentials it was possible either to cool or to break them and subsequently cool the Se+ ions. Figure 3 shows the timeof-flight spectra corresponding to the different trapping schemes. In the latter one, the collision induced dissociation SeCO+ → Se+ + CO was obviously less probable than SeCO+ → Se + CO+ , even with optimized parameters. Due to the different trapping and ejecting voltages the size and location of ion peaks are different in both spectra. More than 50% efficiency was obtained for molecule cooling, and about 8% for molecule breakup and Se+ cooling. Molecule cooling and subsequent injection and breakup into the EBIS was first demonstrated during the radioactive beam time devoted to the Coulomb excitation of 70 Se. Preliminary analysis gives a charge breeding efficiency between 2 and 10% for 70 Se17+ with a breeding time of 33 ms.

5 Summary The presented investigations address important issues for the radioactive beam developments in light of the EURISOL and RIA projects. The cooling method tests aim at an efficiency improvement for the acceleration of high intensity radioactive beams At the present stage the rotating wall cooling shows similar efficiencies as the sideband cooling. More systematic and stringent tests will be undertaken by injecting the cold beams into the EBIS. The charge exchange process study at thermal energies is of primary interest for the ongoing developments, in several different European or overseas nuclear laboratories, of buffer gas cooling cells for fission fragments —the socalled ion catchers. Lastly an efficient chemically selective method has been successfully tested this year to improve the radioactive beam purity. This work was supported by the European Commission within the NIPNET RTD network under contract No. HPRI-CT2001-50034.

P. Delahaye et al.: Recent developments of the radioactive beam preparation at REX-ISOLDE

References 1. D. Habs et al., Hyperfine Interact. 129, 43 (2000). 2. T. Sieber et al., Proceedings of the LINAC 2004 Conference, L¨ ubeck, 2004, Germany. 3. G. Savard et al., Phys. Lett. A 158, 247 (1991).

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4. E.M. Hollmann et al., Phys. Plasmas 7, 2776 (2000). 5. F. Ames et al., Nucl. Instrum. Methods Phys. Res. A 538, 17 (2005). 6. P. Delahaye et al., Nucl. Phys. A 746, 604 (2004). 7. P. Delahaye, F. Wenander, in preparation.

Eur. Phys. J. A 25, s01, 743–744 (2005) DOI: 10.1140/epjad/i2005-06-063-7

EPJ A direct electronic only

Preparation of cooled and bunched ion beams at ISOLDE-CERN I. Podadera1,2,a , T. Fritioff1 , A. Jokinen1,3,5 , J.F. Kepinski4 , M. Lindroos1 , D. Lunney4 , and F. Wenander1 1 2 3 4 5

CERN, AB department, CH-1211 Geneva 23, Switzerland Universitat Polit`ecnica de Catalunya, Barcelona, Spain Department of Physics, FIN-40014 University of Jyv¨ askyl¨ a, Jyv¨ askyl¨ a, Finland CSNSM-IN2P3-CNRS, F-91405 Orsay-Campus, France Helsinki Institute of Physics, FIN-00014 University of Helsinki, Helsinki, Finland Received: 12 December 2004 / Revised version: 26 January 2005 / c Societ` Published online: 10 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. At ISOLDE a new RadioFrequency Quadrupole ion Cooler and Buncher (RFQCB) is being constructed to improve ion optical properties of low-energy RIBs. The new features of the mechanical design and the status of the test bench, which will serve to test the device, will be presented in this contribution. PACS. 41.85.-p Beam optics

1 Introduction The new Radio Frequency Quadrupole ion Cooler and Buncher (RFQCB) for ISOLDE [1], called ISCOOL (ISolde COOLer) will be able to cool most ion beams delivered by the High-Resolution Separator (HRS) (see [2,3]). Therefore, ISCOOL will be completely integrated at ISOLDE and will be able to deliver most of different ion beams coming out from HRS to the experiments working with this separator. Unlike others existing similar devices [4,5] with more specific working conditions, ISCOOL is defined as a general purpose ion trap for the preparation of cooled and bunched radioactive ion beams. This sets special requirements for flexibility and reliability of the device. One of the main points to assure the flexibility of the system is to design a robust and simple mechanical structure. Some of the highlights of the design are presented in the following section. In addition, the reliability and performance of the system have to be tested. A new test bench has been constructed with this objective and the first results will be reported in the last section.

2 Mechanical construction of the cooler The mechanical design of the RFQCB provides some unique features in comparison with the devices constructed before. The main points to be underlined are: the axial electrodes (see fig. 1), which allow a simplified electronics system separating the RF and DC components; a a

Conference presenter; e-mail: [email protected]

Fig. 1. Picture of axial electrodes of different lengths (left) and axial view showing the four-wedges shape (right).

mechanical structure of variable-depth, stacked axial electrodes forming a cavity which encloses the buffer gas volume and accommodates (separate) RF-rods, providing a flexible system for the optimization of the axial electric field of the cooler (see [6] for further information). Once all the parts are received from the workshops, mechanical compatibility will be verified in a full assembly of the apparatus.

3 Test bench Before installation on-line at ISOLDE, the RFQCB will be tested in a new test bench constructed at ISOLDE off-line laboratory [7] for this purpose. Before and after ISCOOL, diagnostics will be placed for the characterization of the ion beam. In fig. 2, the layout of the test bench is shown. The ion beam will be produced by an ion source (see next

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Fig. 2. Layout of the test bench for the RFQCB verification and optimization.

Fig. 4. Example of emittance plots from ion source of the test bench: horizontal phase spaces coordinates (x-x ) (left) and vertical (y-y  ) (right).

Fig. 5. As fig. 4 for a beam better focused (note difference scales). Fig. 3. Picture of the test bench for the ion source measurements.

paragraph), and directly transported to the RFQCB. Up and downstream the RFQCB diagnostic devices will be placed to characterize the main parameters of the machine. For example, transmission tests depending on buffer gas pressure, RF frequency or RF voltage amplitude. The ion source installed in the test bench is a plasma ion source from the MISTRAL experiment [8]. It is able to provide ion beams either of alkali elements (mainly potassium) acting as a surface ionization source or gas elements as a plasma ion source. The maximum beam energy is 80 keV with 60 keV used for normal operation. Downstream the ion source, four pairs of steering plates (two for the longitudinal steering and two for the vertical) allow to displace the beam before it enters the quadrupole triplet placed just afterwards for focusing of the beam (injection into the RFQCB). In parallel to the construction of the RFQCB, the ion source and an emittance meter have been coupled: firstly, to verify the correct operation of the source either in surface and gas mode; secondly, to produce figures for the emittance in both phase space planes (x, x ) and (y, y  ) for the transmission tests of ISCOOL; finally, to find out the proper settings to assure that the shape of the phase space in the emittance meter is the same that would be in the location of the ISOLDE beam line where the RFQCB will be installed [2]. Figure 3 shows a picture of the line for the optics optimization of the beam from the ion source.

Figure 4 illustrates original emittances from an ion source in (x, x ) and (y, y  ) planes. After tuning the beam with the quadrupole triplet, emittances in both planes were better focused, as shown in fig. 5. All emittance plots were measured for an alkali beam at 60 keV. The mean value obtained for the measurements of the transverse geometrical emittance enclosing 90% of the beam (90% 60 keV ) is around 6.5 π mm · mrad in (x, x ) and (y, y  ). We acknowledge the collaboration of LMU and University of Mainz in the construction of the RFQCB. One of us (A.J.) acknowledges the support from the Academy of Finland.

References 1. E. Kugler, Hyperfine Interact. 129, 23 (2000). 2. A. Jokinen et al., Nucl. Instrum. Methods Phys. Res. B 204, 86 (2003). 3. I. Podadera, CERN-AB-NOTE-2004-062 (2004). 4. A. Nieminen et al., Nucl. Instrum. Methods Phys. Res. A 469, 244 (2001). 5. F. Herfurth et al., Nucl. Instrum. Methods Phys. Res. A 469, 254 (2001). 6. I. Podadera et al., Nucl. Phys. A 746 C, 647 (2004). 7. www.cern.ch/isolde-offline. 8. M.D. Lunney et al., Hyperfine Interact. 99, 105 (1996).

Eur. Phys. J. A 25, s01, 745–747 (2005) DOI: 10.1140/epjad/i2005-06-141-x

EPJ A direct electronic only

Performance of IGISOL 3 H. Penttil¨a1,a , J. Billowes2 , P. Campbell2 , P. Dendooven1,3 , V.-V. Elomaa1 , T. Eronen1 , U. Hager1 , J. Hakala1 , J. Huikari1,b , A. Jokinen1 , A. Kankainen1 , P. Karvonen1 , S. Kopecky1,c , B. Marsh2 , I. Moore1 , A. Nieminen1,2 , ¨ o1 A. Popov1,d , S. Rinta-Antila1 , Y. Wang1,e , and J. Ayst¨ 1 2 3

Department of Physics, P.O. Box 35 YFL, FIN-40014 University of Jyv¨ askyl¨ a, Finland Nuclear Physics Group, Schuster Laboratory, University of Manchester, Brunswick Street, Manchester, M13 9PL, UK KVI, Zernikelaan 25, 9747 AA Groningen, The Netherlands Received: 5 January 2005 / c Societ` Published online: 4 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The main goal of the upgrade project of the IGISOL was to increase the yields of the massseparated reaction products. The first tests showed that the goal was met. Typically, the yields normalized to the primary beam intensity are at least three times higher than before the upgrade. In addition, we have started a project to selectively laser ionize neutral atoms in the gas jet emerging from the ion guide and guide the photo-ions with a radiofrequency ion trap to the acceleration stage of the isotope separator. PACS. 29.25.Rm Sources of radioactive nuclei – 07.75.+h Mass spectrometers – 32.80.Fb Photoionization of atoms and ions

1 Introduction The ion guide technique was developed in Jyv¨askyl¨a during the 1980’s. In the ion guide the primary ions from a nuclear reaction are thermalized in very pure noble gas where they stay as ions due to the high ionization potential of the stopping gas. Ions are flushed out of the ion guide to a differential pumping section where they are skimmed from the neutral gas with electric fields [1,2]. The success of the method has had a major impact on planned concepts of future radioactive beam facilities, such as the radioactive ion acceleration project at Texas A&M University [3], EURISOL [4] and the Rare Isotope Accelerator RIA [5]. The IGISOL upgrade project was launched after it had become clear that the new ion beam handling techniques such as the radiofrequency quadrupole ion cooler [6] and the mass purification Penning trap [7] would soon make the front end of the IGISOL mass separator the weakest link of the facility. Also, the a

Conference presenter; e-mail: [email protected] b Present address: 1 Cyclotron Laboratory, East Lansing, MI 48824, USA. c Present address: IKS, University of Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. d Present address: PNPI, 188300 Gatchina, St. Petersburg, Russia. e Present address: Department of Nuclear Physics, China Institute of Atomic Energy, P.O. Box 275(46), Beijing 102413, PRC.

Table 1. Yield of mass-separated radioactive ions after IGISOL dipole magnet for some light-ion–induced reactions.

Ion 12

B Na 31 Si 46 V 58 Cu 20

62

Ga Ga 100 Tc 209 Pb 66

Reaction

(d, p) (p, αn) (d, p) (p, n) (p, n) (3 He, p2n) (p, 3n) (p, n) (p, n) (d, p)

Beam MeV μA

10 40 19 20 18 50 48 22 10 13

11 5 4 5 1 3.3 35 1 6 1.5

Yield /μC

Old yield

Gain

900 100 400 800 1500 320 20 17000 2300 3000

500(a)

1.8

150

2.7

350

4.3

10 2500 300(b)

2.0 6.8 7.6

(a ) Using 6 MeV protons. (b ) Using 12 MeV protons.

need of selective ionization techniques such as laser ionization was recognized and technical requirements for such a system were taken into account in the new front end design.

2 Upgrade to IGISOL 3 Proton beams with intensities higher than 50 μA are used for medical isotope production from the K-130 cyclotron [8]. Beam intensities of this order could not have

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previously been delivered to the IGISOL as the radiation level in the experimental area next to the IGISOL cave exceeded 1 μSv/h. In the upgrade the shielding thickness in the primary beam direction was increased by 1.0 meter to 2.5 m of concrete. This has decreased the radiation level behind the shielding below the measurement threshhold even with the highest beam intensities used thus far (see table 1). In particular the fission application of the ion guide technique has been handicapped by the limitations in the pumping speed. Stopping of energetic recoils in helium gas requires high pressure in the stopping cell, which leads to a higher gas load in the differential pumping stage and consequently requires more efficient pumping. In IGISOL 3 the vacuum chamber housing the ion guide is larger than before. In particular more space is available towards the separator, providing wider pumping channels between the ion guide and the skimmer electrode. Also, the extraction region is evacuated by a more effective diffusion pump (8000 l/s vs. 2000 l/s) through wider pumping channels than before. A larger chamber also allows alternate ways of coupling the ion guide to the separator, such as use of a radio frequency multipole instead of a skimmer. The enlargement of the target chamber towards the cyclotron gives more space for a heavy ion fusion reaction type ion guide. The higher beam intensities also lead to higher activation of the front end of the mass separator. To minimize the working time in the high radiation area, all valves and electrodes in this area were switched from manual to remote control. The whole separator vacuum system is now computer controlled. The ion guide mounting system was modified so that ion guides can now be changed as complete units. The first on-line tests were performed with light-ion– induced fusion reactions. Yield data for some recently used reactions at the IGISOL 3 are given in table 1. Whenever a comparison to “IGISOL 2” is possible, the yields per μC are between 2 and 8 times higher. However, many of these yields have been tested only with low primary beam intensities. Although the ion yield has been shown to scale linearly with primary beam at the IGISOL [9], ambitious extrapolations should still be avoided. In the first proton-induced fission experiments after the upgrade in June 2004 the size and shape of the ion guide, except the new mounting, were exactly the same as in the last fission run before the upgrade in February 2003. Any improvements in the fission product yields can thus be attributed to the changes in the extraction and skimmer region. With 10 μA primary beam intensity the cumulative yields of 112 Rh were 18000 and 47000 ions/s in February 2003 and in June 2004, respectively. With 25 μA primary beam intensity this yield reached the 105 ions/s level in June. The primary reason for the improvement in efficiency appears to be due to a better transmission through the extraction electrode. The increased pumping efficiency allows the use of a 7 mm aperture in the extractor instead of a 4 mm one that had in fact been collimating the ion

beam. This could be deduced from the surprisingly good emittance of 12 π mm mrad of the old IGISOL. The emittance of IGISOL 3 has not yet been measured. However, a lower than before mass resolving power (MRP) achieved immediately after the upgrade gives reason to believe that the emittance has increased. After replacing the old dipole magnet with an ISOL magnet from GSI a MRP of 350 could be reached with 400 V skimmer voltage and 300 mbar helium pressure inside the ion guide. This is sufficient to focus the IGISOL beam properly to the deceleration stage of the RF cooler. For A = 112 fission fragments a 69 ± 3% transmission through the cooler was measured in June 2004.

3 The FURIOS project Despite the fact that IGISOL is a fast and universal method, it lacks in both efficiency and selectivity. To address these important issues, the development and construction of a laser ion source, coupled to the existing facility began in early 2004. The Fast Universal Resonant laser IOn Source, FURIOS, will provide singly charged ions using a combination of solid state Ti-Sapphire lasers and dye lasers. This twin laser facility will provide a good coverage of ionization schemes throughout the periodic table, and the ability to perform optical spectroscopy within the ion guide. Two forms of laser ion source development will be undertaken. These will study both the well-developed intra-source ionization of elements and the high selectivity production achievable with a LIST (Laser Ion Source Trap) [10]. Unlike a conventional laser ion source, ion production in LIST is achieved outside the recoil stopping and thermalization region. The proposed JYFL LIST uses an RF-hexapole trap placed immediately after the ion guide in the gas expansion region. Counter-propagating lasers directed through the mass separator selectively ionize the fast neutral atoms as they exit the ion guide within the effective volume of the RF-hexapole. If successful, this new project will allow future experiments at the IGISOL facility to proceed with elementally pure beams produced at greatly improved absolute efficiency. This research was supported by the Academy of Finland under the Finnish Centre of Excellence Programme 2000-2005 (Project No. 44875, Nuclear and Condensed Matter Physics Programme at JYFL) and through a European Community Marie Curie Fellowship.

References 1. 2. 3. 4. 5. 6.

P. Dendooven, Nucl. Instrum. Methods B 126, 182 (1997). ¨ o, Nucl. Phys. A 693, 477 (2001). J. Ayst¨ R.E. Tribble, Nucl. Phys. A 746, 27c (2004). http://www.ganil.fr/eurisol/. http://www.orau.org/ria/. ¨ o, P. CampA. Nieminen, J. Huikari, A. Jokinen, J. Ayst¨ bell, E. Cochrane and the EXOTRAPS Collaboration, Nucl. Instrum. Methods A 469, 244 (2001).

H. Penttil¨ a et al.: Performance of IGISOL 3 7. V. Kolhinen, T. Eronen, U. Hager, J. Hakala, A. Jokinen, ¨ o, Nucl. S. Kopecky, S. Rinta-Antila, J. Szerypo, J. Ayst¨ Instrum. Methods A 528, 776 (2004). 8. http : / /www.phys.jyu.fi/research/accelerator/ionsources.

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9. J. Huikari, P. Dendooven, A. Jokinen, A. Nieminen, H. ¨ o, Penttil¨ a, K. Per¨ aj¨ arvi, A. Popov, S. Rinta-Antila, J. Ayst¨ Nucl. Instrum. Methods B 222, 632 (2004). 10. K. Blaum, C. Geppert, H.-J. Kluge, M. Mukherjee, S. Schwarz, K. Wendt, Nucl. Instrum. Methods B 204, 331 (2003).

Eur. Phys. J. A 25, s01, 749–750 (2005) DOI: 10.1140/epjad/i2005-06-060-x

EPJ A direct electronic only

Production of beams of neutron-rich nuclei between Ca and Ni using the ion-guide technique K. Per¨aj¨ arvi1,a , J. Cerny1 , U. Hager2 , J. Hakala2 , J. Huikari2 , A. Jokinen2 , P. Karvonen2 , J. Kurpeta3 , D. Lee1 , ¨ o2 a2 , A. Popov4 , and J. Ayst¨ I. Moore2 , H. Penttil¨ 1 2 3 4

Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Department of Physics, P.O. Box 35, FIN-40014 University of Jyv¨ askyl¨ a, Jyv¨ askyl¨ a, Finland University of Warsaw, PL-00681 Warsaw, Poland St. Petersburg Nuclear Physics Institute, Gatchina, 188350, Russia Received: 22 October 2004 / c Societ` Published online: 11 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. It was shown for the first time that quasi- and deep-inelastic reactions can be successfully incorporated into the conventional Ion-Guide Isotope Separator On-Line (IGISOL) technique. Yields of radioactive projectile-like species such as 62,63 Co are about 0.8 ions/s/pnA corresponding to a total IGISOL efficiency of about 0.06%. PACS. 28.60.+s Isotope separation and enrichment – 29.25.Rm Sources of radioactive nuclei

1 Introduction Since several elements between Z = 20–28 are refractory by their nature, their neutron-rich isotopes are rarely available as low-energy Radioactive Ion Beams (RIB) in ordinary Isotope Separator On-Line facilities [1,2, 3, 4]. These low-energy RIBs would be especially interesting to have available under conditions which allow high-resolution beta-decay spectroscopy, ion-trapping and laser-spectroscopy. As an example, availability of these beams would open a way for research which could produce interesting and important data on neutron-rich nuclei in the vicinity of the doubly magic 78 Ni. One way to overcome the intrinsic difficulty of producing these beams is to rely on the chemically unselective Ion-Guide Isotope Separator On-Line (IGISOL) technique [5]. Quasi- and deep-inelastic reactions, such as 197 Au(65 Cu, X)Y , could be used to produce these nuclei in existing IGISOL facilities, but before they can be successfully incorporated into the IGISOL concept their kinematics must be well understood. Therefore the reaction kinematics part of this study was first performed at the Lawrence Berkeley National Laboratory using its 88-Inch cyclotron and, based on those results, a specialized target chamber was built, see fig. 1 [6]. This chamber was then moved to the Jyv¨askyl¨a IGISOL facility for on- and off-line tests. In addition to the spectroscopy station, the Jyv¨askyl¨a IGISOL facility is coupled to a double Penning trap (m/Δm = 107 –108 ) and a laser spectroscopy instala

Conference presenter; e-mail: [email protected]

Fig. 1. Target chamber designed for use with quasi- and deepinelastic reactions. The parts of the chamber are: 1) Havarwindows (1.8 mg/cm2 ), 2) Au-target (3.0 mg/cm2 , diameter = 7 mm), 3) conical Ni-window (9.0 mg/cm2 , angular acceptance from 40 to 70 degrees), 4) He-inlet, 5) stopping volume, 6) exithole (d = 1.2 mm), 7) connecting channel (d = 1 mm), 8) second exit-hole (d = 0.3 mm), 9) skimmer electrode, α) see text.

lation. We wish to report here the first results from the studies done at Jyv¨ askyl¨a.

2 Experimental The 197 Au(65 Cu, X)Y reaction was used in the on-line experiment at Jyv¨askyl¨a. The Au target used had a thickness of about 3 mg/cm2 and the maximum beam intensity of the 443 MeV 65 Cu15+ beam is typically about 20 pnA

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at Jyv¨ askyl¨a. A small fraction of the projectile-like reaction products recoiling out from the Au target could be converted to a low-energy +1 ion beam using the target chamber shown in fig. 1 (see also next section). The +1 ion beam was separated from the neutral gas, accelerated up to 40 keV kinetic energy, mass-separated and transported into the experimental area using the existing IGISOL installations [7]. Mass-separated RIBs were implanted into a movable tape viewed by a coaxial HPGe detector (70% relative efficiency) and two ion implanted Si-detectors (thickness 500 μm). The master trigger of the VME based data acquisition system was a logical OR of all the detectors. In addition to the above on-line setup, for off-line tests a 223 Ra alpha-recoil source (collected onto the tip of a needle) was placed at position α in fig. 1 between the He-inlet channel and the stopping volume (at the opposite side of the stopping volume compared to the exit hole). Emitted 219 Rn alpha-recoils were then used for transport efficiency studies. The resulting mass-separated 40 keV 219 Rn ion beam was implanted into a thin C-foil viewed by a single ion implanted Si-detector (thickness 500 μm). The data generated by this Si-detector was collected using a separate multi-channel analyzer system.

Fig. 2. Part of the beta-gated gamma spectrum of A = 63.

4 Conclusions 3 Results The yields of mass-separated radioactive projectile-like species such as 62,63 Co are about 0.8 ions/s/pnA, corresponding to about 0.06% of the total IGISOL efficiency for the products that hit the Ni-window, see fig. 1. (These yields were measured using a 65 Cu beam intensity of about 4 pnA.) For the efficiency calculation see [6]. This total IGISOL efficiency is a product of two coupled loss factors, namely inadequate thermalization and the intrinsic IGISOL efficiency. In our now tested chamber, about 9% of the Co recoils are thermalized in the flowing He gas (pHe = 300 mbar) and about 0.7% of them are converted into the mass-separated ion beams. This intrinsic IGISOL efficiency is comparable to the one reported in [8] for the Heavy Ion-Guide Isotope Separator On-Line system (0.5%). Figure 2 shows a part of the beta-gated gamma spectrum of A = 63. The 87 keV gamma-transition belonging to the beta-decay of 63 Co is clearly seen. The calibrated 223 Ra alpha-recoil source was used to further investigate the intrinsic IGISOL efficiency. Absolute intrinsic efficiencies of about 1.3% for the 219 Rn alpha-recoils from the source position through the whole system (without the cyclotron beam) were measured (pHe = 200 mbar). These efficiencies are comparable to the ones published in [9] for a long cylindrically symmetric gas cell which suggests that there must be a relatively “direct” and fast flow channel between the source position and the exit hole. This claim was verified with Heflow simulations [6]. These simulations also suggest a relatively smooth overall evacuation of the chamber. When the 2.7 pnA 65 Cu beam was switched on, the transport efficiency dropped by a factor of five.

It has been shown for the first time that quasi- and deepinelastic reactions can be successfully incorporated into the conventional IGISOL technique. In the future, both of the discussed physical/chemical loss mechanisms (thermalization and intrinsic IGISOL efficiency) can be suppressed by introducing Ar as a buffer gas and by relying on selective laser re-ionization. This combination will produce isobarically pure beams and it will increase the existing yields by about a factor of 100, making this overall approach to the study of neutron-rich nuclei really attractive. See also [10] for an operational gas catcher laser ion source. This work was supported by the Director, Office of Science, Nuclear Physics, U.S. Department of Energy under Contract No. DE-AC03-76SF00098. We also thank the Academy of Finland for financial support and the European Union for experimental access via its Large Scale Facilities programme.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

E. Runte et al., Nucl. Phys. A 399, 163 (1983). E. Runte et al., Nucl. Phys. A 441, 237 (1985). U. Bosch et al., Nucl. Phys. A 477, 89 (1988). M. Hannawald et al., Phys. Rev. Lett. 82, 1391 (1999). ¨ o, Nucl. Phys. A 693, 477 (2001). J. Ayst¨ K. Per¨ aj¨ arvi et al., Nucl. Instrum. Methods Phys. Res. A (in press). H. Penttil¨ a et al., these proceedings. P. Dendooven et al., Nucl. Instrum. Methods Phys. Res. A 408, 530 (1998). K. Per¨ aj¨ arvi et al., Nucl. Phys. A 701, 570 (2002). Y. Kudryavtsev et al., Nucl. Instrum. Methods Phys. Res. B 204, 336 (2003).

Eur. Phys. J. A 25, s01, 751–752 (2005) DOI: 10.1140/epjad/i2005-06-079-y

EPJ A direct electronic only

LISE++ development: Application to projectile fission at relativistic energies O.B. Tarasova National Superconducting Cyclotron Laboratory, MSU, East Lansing, MI 48824-1321, USA and Flerov Laboratory of Nuclear Reactions, JINR, Dubna, Moscow region, 141980, Russia Received: 11 October 2004 / Revised version: 1 December 2004 / c Societ` Published online: 11 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. A new model of fast analytical calculation of fission fragment transmissions through a fragment separator has been developed in the framework of the code LISE++. In the development of this new reaction mechanism in the LISE++ framework it is possible to distinguish the following principal directions: kinematics of reaction products, production cross-section of fragments, spectrometer tuning to the fragment of interest to produce maximal rate (or purification). PACS. 25.70.De Coulomb excitation – 25.85.-w Fission reactions – 07.05.Tp Computer modeling and simulation – 29.30.-h Spectrometers and spectroscopic techniques

1 Introduction The program LISE++ [1, 2] calculates the transmission and yields of fragments produced and collected in a fragment separator at medium- and high-energy facilities (fragment- and recoil-separators with electrostatic and/or magnetic selections). The projectile fragmentation and fusion-evaporation [3], assumed in this program for the production reaction mechanisms, allows one to simulate experiments at beam energies above the Coulomb barrier. The LISE++ code operates under the MS Windows environment and provides a highly userfriendly interface. It can be freely downloaded from the following internet addresses: www.nscl.msu.edu/lise or http://dnr080.jinr.ru/lise. Further development of the program is directed towards high energies, and involves other types of reactions. High-energy secondary-beam facilities such as GSI, RIA, and RIBF provide the technical equipment for a new kind of fission experiments. The advantage of inverse kinematics for the electromagnetic excitation mechanism and for the detection of the short-lived fission fragments has been demonstrated in several experiments with relativistic 238 U primary projectiles at GSI [4]. Therefore a new model of fast analytical calculation of fission fragment transmission through a fragment separator, a fast algorithm for calculating fission fragment production cross-sections have been developed in the framework of the code LISE++.

a

e-mail: [email protected]

Fig. 1. Calculated energy distributions of 128 Te in the fission of 238 U(1 GeV/u) on a lead target (1 mm). Angular acceptances: H = ±12 and V = ±15 mrad, beam angular emittances: H = ±3 and V = ±3 mrad. Calculated transmissions by DistrMethod and MCmethod are equal to 32.6% and 33.9%, respectively.

2 Fission fragment kinematics at intermediate and high energies The kinematics of the fission process is characterized by the fact that the velocity vectors of the fission residues populate a narrow shell of a sphere in the frame of the fissioning nucleus. The radius of this sphere is defined by the Coulomb repulsion between both fission fragments. In the case of reactions induced by relativistic heavy ions, the transformation into the laboratory frame leads to an ellipsoidal distribution which will characterize the angular distribution of fission residues [5]. Only forward and

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Fig. 2. The differential cross-section of electromagnetic excitation in 238 U on a lead target at 920 MeV/u (solid curve). De-excitation channels for excited 238 U nuclei as a function of excitation energy are denoted by letters in the figure.

backward cups of the sphere, defined by the angular acceptance of the fragment separator, are transmitted, and the longitudinal projections of their velocity distributions are shaping the two peaks (see fig. 1). Two different methods for fission fragment kinematics are available in LISE++: – MCmethod (Monte Carlo) has been developed for a qualitative analysis of fission fragment kinematics and utilized in the Kinematics calculator. – DistrMethod is the fast analytical method applied to calculate the fragment transmission through all optical blocks of the spectrometer. In order to calculate the kinematics of the final fission fragment, the code looks for the most probable excited fragment for a given final fragment. For more detail information about LISE’s fission fragment kinematics models use the LISE code sites. Calculated energy distributions for both models of 128 Te in the fission of 238 U(1 GeV/u) on a lead target are shown in fig. 1.

3 Coulomb fission fragment production cross-sections

Fig. 3. Calculated mean number of evaporated nucleons as a function of the excited fission-fragment number of neutrons in the fission of the excited nucleus 238 U with excitation energy equal to 30 MeV.

using the semi-empirical model [7] based on a version of the abrasion-ablation model. This model describes the formation of excited prefragment due to the nuclear collisions and their consecutive decay. The model has some similarities with previously published approaches [8, 9], but in contrast to those, Benlliure’s model describes the fission properties of a large number of fissioning nuclei are a wide range of excitation energies. The macroscopic part of the potential energy at the fission barrier as a function of the mass-asymmetry degree of freedom has been taken from experiment [9]. Post-scission nucleon emission is the final stage. The code calculates five final cross-section matrices using the initial matrix. Use of the LisFus method [3] to define the number of post-scission nucleons is a big advantage of the LISE++ code which allows one to observe shell effects in the TKE distribution, and enables the user to estimate qualitatively the final fission fragment faster. All three stages together take no more than 5 seconds in the case of low-energy fission. The LISE calculation package of fission fragment cross-sections can be used for higher excitation energy. For example, calculated mean number of evaporated nucleons, as a function of the excited fission-fragment number of neutrons in the fission of the excited nucleus 238 U with excitation energy equal to 30 MeV, is shown in fig. 3.

References Calculations of fission fragment cross-sections consist of three sequential steps. The average electromagnetic excitation and the total fission cross-section are calculated at the first stage. The electromagnetic excitation cross-section calculation (see fig. 2) is based on work of C.A. Bertulani [6] and the LisFus evaporation model [3] assuming that the reaction takes place in the middle of the target. Statistical parameters (mean value E ∗ , and area σ f ) of the de-excitation fission function dσ f /d(E ∗ ) are used in the next stage to calculate an initial fission cross-section matrix of production cross-sections excited fragments

1. D. Bazin et al., Nucl. Instrum. Methods A 482, 314 (2002). 2. O. Tarasov et al., Nucl. Phys. A 701, 661 (2002). 3. O. Tarasov, D. Bazin, Nucl. Instrum. Methods B 204, 174 (2003). 4. K.-H. Schmidt et al., Nucl. Phys. A 693, 169 (2001). 5. P. Armbruster et al., Z. Phys. A 355, 191 (1996). 6. C.A. Bertulani, G. Baur, Phys. Rep. 163, 299 (1988). 7. J. Benlliure et al., Nucl. Phys. A 628, 458 (1998). 8. M.G. Itkis et al., Yad. Fiz. 43, 1125 (1986). 9. M.G. Itkis et al., Fiz. Elem. Chastits At. Yadra 19, 701 (1988).

Eur. Phys. J. A 25, s01, 753–754 (2005) DOI: 10.1140/epjad/i2005-06-101-6

EPJ A direct electronic only

Exotic nuclei within the INFN-PI32 network A. Bonaccorsoa INFN, Sezione di Pisa and Dipartimento di Fisica, Universit` a di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy Received: 28 December 2004 / c Societ` Published online: 17 May 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. The INFN (Italian National Institute for Nuclear Physics) has approved a national theoretical network on “Structure and Reactions with Exotic Nuclei”. The project involves the INFN branches of Laboratorio Nazionale del Sud, Padova and Pisa. The aim of the project is to coordinate and homogenize the research already performed in Italy in this field and to strengthen and improve the Italian contribution on the international scenario. Furthermore it aims at creating a solid theoretical structure to support future experimental facilities at the INFN national laboratories such as SPES at LNL and EXCYT at LNS. A review of present and future activities is presented. PACS. 25.60.-t Reactions induced by unstable nuclei – 21.60.-n Nuclear structure models and methods

1 Introduction Since a few years an increasing number of Italian theoreticians has concentrated his research on the study of exotic nuclei. Such activities have so far been carried out within pre-existing national projects related to a wide spectrum of themes of nuclear dynamics, structure and reactions using many body techniques, shell model, collective modes and semiclassical or fully quantum-mechanical approaches to peripheral and central reactions such as transfer and breakup, fusion, elastic scattering via microscopic optical potentials, multifragmentation. The goal of our project is to start coordinating and homogenizing such efforts, to improve our mutual understanding and to strengthen the Italian contribution on the international scenario. Furthermore, our efforts will help creating a solid theoretical structure to support future experimental activities at the INFN national laboratories. In fact, in the last two decades, the use of radioactive beams of rare isotopes in several laboratories around the world has provided new research directions and an increasing number of researchers all over the world is converging on such subject. The INFN in Italy is also getting involved in this field. The facility EXCYT and the large acceptance spectrometer called MAGNEX are being completed at Laboratorio Nazionale del Sud. On the other hand the first step of the SPES project at the Laboratorio Nazionale di Legnaro has been approved in the form of a proton driver. Furthermore the INFN is promoting the new Eua In collaboration with G. Blanchon and A. Garcia-Camacho, INFN Sezione di Pisa; M. Colonna, M. Di Toro, Cao Li Gang, U. Lombardo, J. Rizzo, INFN-LNS; S. Lenzi, P. Lotti, A. Vitturi, INFN Sezione di Padova; e-mail: [email protected]

ropean Radioactive Beam Facility (EURISOL). Members of our collaboration are actively participating in NuPECC working groups, in particular in the preparation of “The Physics Case” for EURISOL [1], and in general of the NuPECC Long Range Plan. The proposed research activity will deal with the following aspects: reaction mechanisms and structure information extraction for nuclei close to the driplines, single particle and collective degrees of freedom, dynamical symmetries at the phase transitions, dynamics of heavy nuclei with anomalus N/Z ratios and isospin degrees of freedom, equation of state. The partecipants have complementary competences in the fields of structure and reaction theory. We have common national (LNS,LNL) and international collaborations (i.e.: IPN, Orsay; GANIL, Caen; France, MSU; USA, etc.). Our present abilities and activities in the above research fields are described in the following.

2 Reaction mechanisms at Pisa and Padova In recent years we have concentrated on a consistent treatment of nuclear and Coulomb breakup and recoil effects treated to all orders and including interference effects. We have developed a formalism which allows the calculations of energy, momentum and angular distributions for the core and halo particle and absolute cross-sections. The dependence on the final-state interaction used has been clarified. An extension of the method to proton breakup has been recently presented. A microscopic model for the calculation of the optical potential in the breakup channel has been developed for both light and heavy targets including recoil effects. We are also studying nuclei unbound against neutron emission, such as 10 Li and 13 Be.

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The study of their low-lying resonance states is of fundamental importance for the understanding of two neutron halo nuclei and of the core-neutron interaction. We are at present discussing the differences between the technique of projectile fragmentation and of transfer to the continuum in order to understand whether they would convey the same structure information [2,3,4,5]. The Padova group has similar and complementary lines of research as the Pisa group as far as reaction mechanisms are concerned. However, it has a special interest for a somehow lowerenergy domain where fusion and the coupling to breakup channels are particularly important [6,7, 8].

3 Structure of rare isotopes at Padova In Padova we are also studying structure problems such as: the pairing correlations in low-density nuclear systems, as in the external part of halo nuclei; microscopic estimate of inelastic excitation to the low-lying continuum dipole strength via continuum RPA calculations; isospin symmetry in low- and high-spin states in medium-mass N = Z nuclei up to 100 Sn; study of the interplay of T = 0 and T = 1 pairing; nuclear structure with algebraic models. This line of research is associated with the use of algebraic models, as the Interacting Boson Model or its variations, to describe different aspects of nuclear spectra. Our traditional approach is based on the use of the concept of boson intrinsic state. In this framework we will study the new symmetries E(5) and X(5) associated with phase transitions and individuate mass regions far from stability where such critical points may occur.

4 Isospin dynamics at LNS Our main motivation is to extract physics information on the isovector channel of the nuclear interaction in the medium, from dissipative collisions in this energy range using the already available stable exotic ions and in perspective the new radioactive facilties. We have developed very reliable microscopic transport models, in an extended mean-field frame, for the simulations of the reaction dynamics in order to check the connection between the tested effective interactions and the experiments, in particular for the isospin degree of freedom [9,10,11,12,13,14]. This work is of interest for the understanding of the physics behind the reaction mechanisms and for the selection of observables most sensitive to different features of the nuclear interaction. Moreoever we have a more general theoretical activity on the isospin dynamics in nuclear liquid-gas phase transitions. New instabilities have been evidenced with a different “concentration” between the gas and cluster phases, leading to the Isospin Distillation effects recently observed in experiments. A quantitative analysis can give direct information on the density dependence of the symmetry term for dilute asymmetric matter, i.e. around and below saturation.

5 Finite nuclear systems in Brueckner theory at LNS The second team at LNS is interested in relating nuclear properties to elementary interactions between nucleons and to build up an energy density functional starting from a more fundamental level than the present phenomenological energy functionals of non-relativistic mean field or RMF [15]. It has been shown that the inclusion of 3-body forces in the Brueckner theory is necessary for obtaining the correct saturation point of nuclear matter and going away from the so-called Coester line. From the results of infinite matter we will construct an energy density functional which can give the same results in nuclear matter and also can be used in finite nuclei. This nuclear energy functional should be trustable away from the stability region since no adjustment will be made to reproduce the properties of stable nuclei, contrarily to phenomenological energy functionals whose extrapolations can be questionable. The proposed method is a simpler alternative than direct Brueckner calculations of finite systems. It also allows for studies of excitations of nuclei, within RPA-type of calculations built on top of the mean-field ground state. This is again in the same spirit as the time-dependent LDA (TDLDA) method which has proved very successful in atomic cluster physics. The main objectives of the project are: BHF calculations of asymmetric and polarized matter. Construction of the energy functional. Ground states of finite nuclei. Excitations of finite nuclei. Neutron star crust.

References 1. http://www.ganil.fr/eurisol/. 2. J. Margueron, A. Bonaccorso, D.M. Brink, Nucl. Phys. A 720, 337 (2003), nucl-th/0303022. 3. A. Bonaccorso, D.M. Brink, C.A. Bertulani, Phys. Rev. C 69, 024615 (2004), nucl-th/0302001. 4. G. Blanchon, A. Bonaccorso, N. Vinh Mau, Nucl. Phys. A 739, 259 (2004), nucl-th/0402050. 5. A.A. Ibraheem, A. Bonaccorso, Nucl. Phys. A 748, 414 (2005), nucl-th/0411091. 6. L. Fortunato, A. Vitturi, J. Phys. G 30, 627 (2004). 7. A. Jungclaus, S.M. Lenzi et al., Eur. Phys. J. A 20, 55 (2004). 8. C. Beck, S.M. Lenzi et al., Nucl. Phys. A 734, 453 (2004). 9. V. Baran, M. Colonna, M. Di Toro, Nucl. Phys. A 730, 329 (2004). 10. T.X. Liu, X.D. Liu, M.J. van Goethem, W.G. Lynch, M. Colonna, M. Di Toro et al., Phys. Rev. C 69, 014603 (2004). 11. J. Rizzo, M. Colonna, M. Di Toro, V. Greco, Nucl. Phys. A 732, 202 (2004). 12. M. Di Toro, V. Baran, M. Colonna, T. Gaitanos, J. Rizzo, H. H. Wolter, Prog. Part. Nucl. Phys. 53, 81 (2004). 13. E. Geraci, M. Di Toro et al., Nucl. Phys. A 732, 173 (2004). 14. P. Sapienza, R. Coniglione, M. Colonna et al., Nucl. Phys. A 734, 601 (2004). 15. C.W. Shen, U. Lombardo, N. Van Giai, W. Zuo, Phys. Rev. C 68, 055802 (2003); Nucl. Phys. A 722, 532 (2003).

11 Radioactive ion beam production and applications 11.2 Applications

Eur. Phys. J. A 25, s01, 757–762 (2005) DOI: 10.1140/epjad/i2005-06-148-3

EPJ A direct electronic only

Spallation reactions for nuclear waste transmutation and production of radioactive nuclear beams J. Benlliurea Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain Received: 12 January 2005 / Revised version: 12 April 2005 / c Societ` Published online: 14 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. Spallation reactions are considered an optimum neutron source for nuclear waste transmutation in accelerator-driven systems (ADS). They are also used to produce intense radioactive nuclear beams in ISOL facilities. A difficulty in both applications is the characterisation of these reactions in terms of residual nuclei production. In this paper we review the GSI experimental program for the investigation of spallation reactions and their implications both in radioactive nuclear beams production and basic nuclear structure research. PACS. 25.40.Sc Spallation reactions – 21.10.-k Properties of nuclei; nuclear energy levels

1 Introduction Spallation reactions have been proposed as an optimum neutron source to feed subcritical reactors in accelerator driven systems (ADS) used to burn long-lived nuclear waste [1] or produce energy [2]. These reactions are also considered for the production of intense radioactive nuclear beams using the ISOL technique [3,4]. A common issue in both applications is the design of the spallation targets, which requires making a complete inventory of residual nuclides produced in these reactions. Until now, most of the available information on residual nuclei production in spallation or fragmentation reactions has been obtained using radiochemical or spectroscopic methods. Unfortunately, these techniques only provide isobaric information on the produced nuclei, and the isotopic production cross sections for only a few shielded nuclides. A few years ago, a new experimental technique based on the combined use of inverse kinematics and a high-resolution magnetic spectrometer was proposed at GSI. This new technique allows for the isotopic identification of all reaction residues. For the last several years, a large experimental program has been underway at GSI, which uses the abovementioned technique, to measure the isotopic production cross sections and kinematic properties of all residual nuclides produced in spallation reactions. The high-quality data it provides has allowed us to improve our present understanding on this reaction mechanism, to draw some important conclusions about the production of radioactive nuclear beams or to investigate some basic nuclear a

e-mail: [email protected]

structure features. In this paper we review some of the highlights of the GSI program.

2 Experiments and results The experiments have been carried out at the SIS synchrotron at GSI (Germany). Primary beams of 238 U, 208 Pb, 197 Au, 136 Xe and 56 Fe accelerated at energies between 300 and 1000 A MeV impinged on a liquid hydrogen or deuteron target. At these energies all reaction residues are predominantly fully stripped, bare ions. The achromatic high resolution magnetic spectrometer FRS [5] equipped with an energy degrader, two position-sensitive scintillators and a multi-sampling ionisation chamber made it possible to identify the mass and atomic number of all the residual nuclides with half lives longer than 200 ns. This technique provided resolutions of A/ΔA ≈ 400 and Z/ΔZ ≈ 150, and final production cross sections could be evaluated with near 10% accuracy. The high resolution of the magnetic spectrometer also enabled us to determine the recoil velocity of the reaction residues. This information is relevant both to investigating the nature of the reaction mechanism responsible of the production of the residual nuclei and for characterising radiation-induced damages in the accelerator window or structural materials on an ADS. More details about these experiments can be found in references [6,7,8, 9] and a complete set of data in [10]. In fig. 1, all residues measured in the reactions 208 Pb(1 A GeV) + p [6,9] and 238 U(1 A GeV) + p, d, Ti [11,12, 13,14] are presented in form of a chart of the nuclides

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with a colour code according to five cross sections ranges whose lower limits are indicated. More than 1100 different nuclei were identified in each reaction. Spallation residues populate two different regions of the chart of the nuclides. The high-Z region corresponds to the spallation-evaporation residues which populate the so called evaporation-residue corridor. The low-Z region represents medium-mass residues produced in spallationfission reactions. Though inherently different, both fission and evaporation contribute to the production of residues.

3 Implications for the production of radioactive nuclear beams These data are also relevant to understanding the expected yields of exotic beams, with a view to finding the reaction mechanisms best suited to extending the present limits of the nuclide chart. The accuracy of the new data has improved our understanding of these mechanisms and allowed to explore the prospects of producing rare isotopes in different regions of the nuclide chart. In the next sections we present some examples of these investigations.

3.1 Production of heavy neutron-rich nuclei Recent investigations reveals large fluctuations in the N/Z and excitation-energy distribution of the final residues of fragmentation reactions at relativistic energies. Specifically, proton-removal channels have been investigated in cold-fragmentation reactions [15], where protons only are abraded from the projectile while the induced excitation energy is below the particle-emission threshold. These reactions could produce heavy neutron-rich nuclei beyond the present limits of the chart of the nuclides. Using the abrasion-ablation model, these reactions can be explained as a two-step process. The interaction between projectile and target leads to a projectile-like residue with a given excitation energy which then statistically de-excites by particle evaporation or by fission. A new analytical formulation of the abrasion-ablation model, the code COFRA [15], has been developed to calculate the expected low production cross sections of extremely neutron-rich nuclei which cannot be reached with Monte Carlo codes. The results of these calculations have been benchmarked with the new available data, showing the reliability of the model predictions. These calculations have also been used to estimate the expected production of heavy neutron-rich nuclei in future rare-beam facilities.

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Figure 2 shows the calculated production cross sections of heavy neutron-rich nuclei that can be obtained in the fragmentation of 238 U, 208 Pb and 174 W. Great progress is expected in this region of the chart of the nuclides, where the r-process path may even be reached near the waiting point N = 126. 3.2 Production of heavy neutron-deficient nuclei Heavy-exotic nuclei can be produced in fusion-evaporation reactions or by fragmentation(spallation) of heavy nuclei. Both reaction mechanisms lead mainly to the production of neutron-deficient residues and in fact they have been used to extend the proton drip-line up to Z = 86 and the 1 μs proton half life line until Z = 82. The main difficulty in producing heavier neutron-deficient isotopes is the significant decrease in the survival probability of the compound nucleus due to the fission channel. Theoretically, survival probability against fission is expected to increase in this region of the chart of the nuclides due to the presence of the neutron shell N = 126. However, the measured data show no such increase in the production cross sections of heavy neutron-deficient isotopes around N = 126 (see fig. 3). This is thought to be due to a cancellation between shell stabilisation and the enhancement of collective excitations at saddle [16], as discussed in sect. 4. 3.3 Production of medium-mass neutron-rich nuclei Fission has been widely used to produce medium-mass neutron-rich nuclei to the present frontiers of the nuclide chart [17]. The isotopic distribution of fission-produced residues can be understood in terms of the potential governing this process. The Coulomb term of the nuclear potential is responsible for the neutron excess of the stable fissile nuclei. The asymmetry term preserves the N/Z ratio in the fission process, which results in a large neutron

115 120 125 130 135 140 145 150

Neutron number Fig. 3. Production cross sections of Ra isotopes produced in the reaction 238 U(1 A GeV)+d compared with model calculations using a Fermi gas level density (dotted line), a level density including ground state shell effects (dashed line) and ground state shell effects and collective excitations (solid line).

excess in the final residues with respect to the valley of beta stability. Shell effects and fluctuations in the N/Z due to temperature could lead to the production of even more neutron-rich residues. In order to investigate the fluctuations in N/Z and mass asymmetry induced by the temperature of the fissioning system, several simulations were carried out using the fission code of ref. [18], which again was benchmarked with the new experimental data. Figure 4 represents the distributions of residues after the fission of 238 U at different excitation energies in form of a chart of the nuclides. As excitation energy increases, shell effects (double humped distribution) disappear and the fluctuations in mass asymmetry and N/Z increase, populating a greater variety of neutron-rich residues. However, at high excitation energies neutron evaporation sets in, and the residue distribution moves to the neutron-deficient side. These calculations show that for producing the greatest variety of neutron-rich nuclei, the optimum excitation energy of the fissioning system is around 50 MeV.

4 Nuclear structure investigated with spallation reactions Manifestations of nuclear structure such us even-odd effects or shell closure are known to disappear as the temperature of the nucleus increases. Consequently, signs of nuclear structure are not expected in high-energy reactions such as fragmentation or spallation. However, the accurate measurement of the production yields of residual nuclei in these reactions have revealed complex nuclearstructure phenomena, indicating that the final residual nuclei in high-energy reactions are produced after long evaporation chains of very hot nuclei. The final isotopic composition of the residues then, is determined during the last steps of the evaporation chain, when the nuclei are sufficiently cold and their decay widths are sensitive

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4.1 Even-odd staggering in the production yields of spallation residues Figure 5 illustrates the production cross sections of light projectile-like residues from the reaction 238 U + Ti at 1 A GeV [19]. The data are sampled according to the neutron excess N − Z for even-mass (left panel) and oddmass nuclei (right panel), revealing a complex structure. Even-mass nuclei display a clear even-odd effect, which is particularly strong for N = Z nuclei, while odd-mass nuclei show a reversed even-odd effect with enhanced production of odd-Z nuclei, specially those nuclei with larger N − Z values. However, the reversed even-odd effect for nuclei with N − Z = 1 vanishes at Z = 16, and an enhanced production of even-Z nuclei can again be observed for Z > 16. Finally, all observed structural effects seem to vanish as the mass of the fragment increases. Most of these observations were interpreted using the statistical model framework, including a consistent de-

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to structural effects. Investigation of the production yields from highly-excited nuclei could be a rich source of information about nuclear-structure phenomena in slightlyexcited nuclei found at the end of their evaporation process. Two manifestations of nuclear structure, pairing and collective excitations, have been observed in the production yields of spallation and fragmentation residues.

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scription of pairing and shell effects in both binding energies and level densities of the parent and daughter nuclei. With odd-mass residues, the even-odd staggering in the production cross sections can be understood as a manifestation of pairing correlations in the particle separation energies. The number of particle-bound states in the final residual nuclei follows the observed staggering in the production yields. However, in describing even-odd staggering in even-mass nuclei, the number of available states in the daughter nucleus along the evaporation chain must be taken into account along with those in the mother nucleus. In both cases and for heavier nuclei, gamma emission becomes a competitive decay channel in the last deexcitation steps, being responsible for the vanishing of the even-odd staggering as mass increases. In spite of this success, particularly strong staggering observed in the final yields on the N = Z chain could not be reproduced. This is still an unresolved question, but could be due to phenomena such as the Wigner energy, alpha clustering or neutron-proton correlations (see ref. [19] for a detailed discussion). 4.2 Collective excitations in residual nuclei across the shell N = 126 Shell effects also modify binding energies and level densities. As with pairing correlations, they should also appear

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Fig. 5. Formation cross sections of the projectile-like residues from the reaction 238 U + Ti, 1 A GeV. The data are given for specific values of N − Z. The chain N = Z shows the strongest even-odd effect, while the chain N − Z = 5 shows the strongest reversed even-odd effect.

during the last steps of the evaporation chain for nuclei near a shell closure. The measured production cross sections of residual nuclides in reactions induced by 238 U projectiles drew attention to the region of the nuclide chart that crosses the neutron shell N = 126, which proved to be very interesting. In this region, the final production cross section of residual nuclei is governed by the competition between neutron or proton evaporation and fission. In fact, the measured cross sections represent the survival probability against fission. Higher fission barriers should lead to an enhanced production cross section of those nuclei (see sect. 3.2). However, no evidence of such an enhancement is observed in the measured cross sections of radium isotopes produced in the reaction 238 U(1 A GeV)+d (fig. 3). Several calculations were carried out using the statistical de-excitation model in an effort to understand these results. The dashed line in fig. 3 indicates the results of calculations that consistently account for shell effects, both in the binding energies and the level densities, while the dotted line represents a calculation where these effects are not accounted for. An enhanced production of radium isotopes around N = 126 was clearly predicted by the calculations but not corroborated by the measured data. The astonishing lack of stabilisation against fission for magic or near magic nuclei was interpreted as an indication of the level-density enhancement due to rotational collective excitations [16]. The large deformation of the mother nucleus at the saddle point favours the appearance of rotational bands above the fission barrier. These collective levels are added to the intrinsic levels of the nucleus, leading to a level density increase at saddle that favours the fission decay channel. The magnitude of this effect compensates for stabilisation against fission due to the presence of shell effects, which modify the binding energy and fission barrier. The solid line in fig. 3 represents a calculation where shell effects are accounted for consistently in both binding energies and level densities, and

collective excitation at the saddle point are added to single particle level densities according to ref. [16].

5 Conclusion The combined use of inverse kinematics with a high-resolution magnetic spectrometer is a powerful technique for investigating spallation reactions, allowing for a precise isotopic identification of all projectile-like residues with a half-life longer than 200 ns. With this technique we could establish the production cross sections with near 10% accuracy. The large experimental program at GSI enabled us to investigate these reactions using key projectiles that represent different regions of the chart of the nuclides, in particular 238 U, 208 Pb, 136 Xe and 56 Fe at energies between 1000 and 300 A MeV. More than 1000 different nuclides were measured and identified for each of these reactions. The high sensitivity of the residual nuclides final production cross sections to the reaction mechanism provided new and detailed information about the underlying physics of spallation reactions, which has been used to develop and improve model calculations. These reactions models are presently being coupled with complex transport codes to describe the interaction of relativistic projectiles with thick targets. The aim of these calculations is to design target assemblies for neutron production in accelerator driven systems, to be used for nuclear waste transmutation or for the production of non-stable nuclides in future rare-beam facilities. For this purpose, the present data are vital to optimising the production of exotic nuclei in different regions of the chart of the nuclides. A comprehensive analysis of these results lead us to expect important progress in the production of heavy neutron-rich nuclides, which will result in a considerable expansion of the present limits of the chart of the nuclides.

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In contrast, the production of heavy neutron-deficient nuclides will be limited by the extensive depopulation of the final yields due to the fission decay channel. However, fission still remains the optimum reaction mechanism for producing medium-weight neutron-rich isotopes. Finally, and unexpectedly, spallation reactions can also be a rich source of information to the investigation of nuclear structure. Nuclear structure, specifically, pairing correlations and shell effects, appear in the final yields of residual nuclides produced in these reactions. The challenge ahead is to develop and use theoretical models to quantitatively interpret these results, in order to better understand the complex nuclear-structure behind them.

Most of the results presented in this paper were obtained by a German-French-Spanish collaboration and in particular by P. Armbruster, M. Bernas, A. Boudard, E. Casarejos, T. Enqvist, S. Leray, J. Pereira, F. Rejmund, M.V. Ricciardi, C. Stephan, K.H. Schmidt, J. Taieb and L. TassanGot. The work was supported by the following grants ECEuratom FIKW-CT-2000-00031, MCyT FPA2002-04181-C0401 and XuGa PGIDIT03PXIC20605PN.

References 1. C.D. Bowman et al., Nucl. Instrum. Methods Phys. Res. A 320, 336 (1992). 2. C. Rubbia et al., preprint CERN/AT/95-44(ET), 1995. 3. Study Group on Radioactive Nuclear Beams, OECD Megascience Forum, 2000 (http://www.iupap.org/ reports/c12report.html). 4. NuPECC Report “Radioactive Nuclear Beam Facilities”, April 2000. 5. H. Geissel et al., Nucl. Instr. Methods B 70, 286 (1992). 6. W. Wlazlo et al., Phys. Rev. Lett. 84, 5736 (2000). 7. J. Benlliure et al., Nucl. Phys. A 683, 513 (2001). 8. F. Rejmund et al., Nucl. Phys. A 683, 540 (2001). 9. T. Enqvist et al., Nucl. Phys. A 686, 481 (2001). 10. http://www-w2k.gsi.de/charms/data.htm. 11. J. Taieb et al., Nucl. Phys. A 724, 413 (2003). 12. M. Bernas et al., Nucl. Phys. A 725, 213 (2003). 13. E. Casarejos et al., Phys. At. Nuclei 66, 1413 (2003). 14. J. Pereira et al.Nucl. Phys. A 734, (2004). 15. J. Benlliure et al., Nucl. Phys. A 660, 87 (1999). 16. A.R. Junghans et al., Nucl. Phys. A 629, 635 (1998). 17. M. Bernas et al., Phys. Lett. B 415, 111 (1997). 18. J. Benlliure et al., Nucl. Phys. A 628, 458 (1998). 19. M.V. Ricciardi et al., Nucl. Phys. A 733, 299 (2004).

Eur. Phys. J. A 25, s01, 763–764 (2005) DOI: 10.1140/epjad/i2005-06-146-5

EPJ A direct electronic only

TARGISOL: An ISOL-database on the web O. Tengblad1,a , M. Turrion1 , and L.M. Fraile2 1 2

Instituto de Estructura de la Materia, CSIC, Serrano 113 bis, E-28006 Madrid, Spain ISOLDE, PH department, CERN, CH-1211 Geneva 23, Switzerland Received: 12 September 2004 / c Societ` Published online: 5 July 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. An essential requisite for an efficient production of short-lived nuclei in an Isotope Separation On-Line (ISOL) facility is the fast release and extraction of the radioactive isotopes. In order to control the variables affecting the design and development of the target matrices and ion-sources, a database management system, called DifEfIsol, containing the relevant information of this diffusion-effusion process has been built. The Oracle database is constructed within an Open-URL framework directly reachable from any Web-browser at http://www.targisol.csic.es. The database includes the diffusion and desorption data of most elements in a range of materials. About 2400 entries are presently stored in the database. These data are used as input to a Monte Carlo simulation program that presently is being tested. This paper presents the database and the Web application as a tool for diffusion-effusion studies. PACS. 07.05.Rm Data presentation and visualization: algorithms and implementation – 51.20.+d Viscosity, diffusion, and thermal conductivity – 29.25.-t Particle sources and targets

1 Introduction The production of radioactive isotopes is getting more difficult the further out from the line of stability the scientific interest is moving. Many elements, due to their specific chemical properties, are difficult to release from the production target in amounts sufficient for an experimental study. There are presently in the world several projects for the construction of the next generation Radioactive Nuclear Beam facilities. These new facilities will have higher primary beam energies and intensities in order to reach further away from stability and to increase the production yields. However, in order to be able to study more exotic (i.e. very short lived) isotopes one has to optimise not only the production but also the release of the produced isotopes out of the target matrix and to secure an efficient transport up to the experiment.

2 The extraction process In the case of ISOL facilities a requisite for the efficient delivery of short-lived nuclei to the experiment is the fast release of the radioactive ions from the target-ion sourcesystem. The experimentally determined release curves of different elements from specific targets contain components due to the container surface sticking time as well a

e-mail: [email protected]

as due to the diffusion out of the target material. The development of analytical methods to simulate this release allows us to understand and if possible determine the relative contribution of each mechanism. We are thus here interested in the transport of the atoms produced by the ISOL method from the place of creation in the target up to the extraction electrode. In this transport there are losses of ions due to radioactive decay. To minimize loss of ions the delay time should be short compared to the lifetime of the atoms. This delay is due to the diffusion out of the target material and to the collisions with the surface of the target material and with the enclosure, this latter we define as effusion. The solid state diffusion is governed by Ficks laws, which have been solved for various boundary conditions [1,2, 3]. The temperature is an essential parameter in this diffusion process. The diffusion rate increases rapidly with increasing temperature, however the target must be kept within a certain temperature range during the process in order not to breakdown. The temperature (T ) dependence of the diffusion can be described by the Arrhenius equation: D(T ) = D0 e−Ea /kT ,

(1)

where D0 is a constant dependent on the target material and of the properties of the diffusing material, Ea the activation energy and k Boltzman’s constant. Once the created particle has diffused to the surface, the subsequent effusion is determined by the average number of collisions with the surface of the target and enclosure, the mean

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sticking time per wall collision, τsorp , and the mean flight time between two wall collisions. The sticking time, is as the diffusion a function of temperature as described by the Frenkel equation [3]: τsorp (T ) = τ0 e−ΔHsorp /kT ,

(2)

where τ0 is a surface-dependent constant in the range of ≈ 10−13 s, ΔHsorp the desorption enthalpy. When no experimental data exist, the desorption enthalpy can be deduced using the semi-empirical model of Eichler et al. [4]. The database is thus stored with the characteristic parameters of the diffusion and effusion processes which then can be used for the simulation of the whole release process (diffusion, effusion and decay).

3 Database and Web application The advent of the Internet and advanced computer capability has produced a new generation of Web-based applications. In this context a database plays the vital role of storing and accessing the parameters of interest. Webbased applications are intended to facilitate the use of the computational resources located in different physical sites, thereby allowing users at different locations to easily access information and communicate with each other. Webbased applications thus offer scientists the opportunity to share their data and information with others within the research community by providing a suite of collaboration tools. The TARGISOL-database [5] contains a collection of tables (entities) connected in a series of relationships that reflects the process and the delay parameters involved in the production and delivery of intense beams of rare isotopes. For the diffusion process, eq. (1), the parameters included in the database are: the constant D0 , the activation energy Ea , the diffusion coefficient D, and the temperature T for which the diffusion D of an element (Z) in a certain material (Z-target) has been measured. The parameters contained in the database related to the effusion process, eq. (2), is the desorption enthalpy ΔHsorp . All the data contained in the database can be traced back to the reference in original work. Apart from diffusion, effusion and yield entities, there is complementary information stored in the database. A table with general information about each element allows to access atomic, physical and thermal properties of the selected element. All entities are connected via logical relationships making it possible to access any combination of them. The data of the database are, in order to maintain the quality of the stored information, collected from the literature and from several research organizations under the criteria of being published in refereed journals or books. The database is managed by a relational database management

system, RDBMS, and can be accessed through the userinterface both by a retrieval system and/or applications programs. An internet browser-based user interface to the Oracle Relational Database, Rdb, has been created to provide a quick and simple querying procedure. To enhance communication with the database a Web application has been integrated. Standard HTML pages and embedded PL/SQL code constitute an Oracle PSP file. The PSP files are actually stored in the Oracle Rdb and provide direct query access to it so that the process to retrieve information becomes quick and secure. The HTML pages use forms that include test entries, check boxes, and radio buttons. These graphical tools provide the interactive interface to the user. The PSP files contain server-side script commands that build an SQL search string based on the user selection and input. After an user submits a query request from the web page, the PSP script commands execute on the database via the PL/SQL gateway, the database retrieves the data which uses the PL/SQL Toolkit to return the data in HTML format. Graphical representations of retrieved data is embedded in the HTML page using Java Applets.

4 Summary With the evolution of Internet technology, there is an ever increasing interest in using the Web as a new platform for scientific applications. For Web applications a database plays the vital role of storing and accessing the simulation data. DifEfIsol Database and Web-Application provides an intelligent Web interface so that scientists can access release parameters of the extraction of radioactive ions from a target-ion-source-system using a standard Web browser from remote sites. DifEfIsol will be very useful for the next generation of Radioactive Ion Beam (RIB) facilities because target-ion source systems can be simulated with different composition, geometry, temperature, beam energy in advance for optimum design of new targets This work was supported by the European Union under contract HPRI-CT-2001-50033.

References 1. J. Crank, The Mathematics of Diffusion (Clarendon Press, Oxford, 1956). 2. M. Fujioka, Y. Arai, Nucl. Instrum. Methods 186, 409 (1981). 3. R. Kirchner, Nucl. Instrum. Methods B 70, 186 (1992). 4. B. Eichler, S. Huebener, H. Rossbach, Zfk Rossendorf Reports 560 and 561 (1985). 5. TARGISOL: http://www.targisol.csic.es/

12 Conference summary 12.1 Neutron-rich nuclei

Eur. Phys. J. A 25, s01, 767–771 (2005) DOI: 10.1140/epjad/i2005-06-004-6

EPJ A direct electronic only

Concluding remarks of the ENAM’04 Conference ¨ oa J. Ayst¨ Department of Physics, P.O. Box 35 (YFL), FIN-40014 University of Jyv¨ askyl¨ a, Finland Received: 1 February 2005 / c Societ` Published online: 12 April 2005 –  a Italiana di Fisica / Springer-Verlag 2005 Abstract. In this talk a summary of the program and scientific highlights of the ENAM2004 conference will be presented.

1 Introduction To start, I would like to congratulate Witek Nazarewicz, Carl Gross, and the team from Oak Ridge for putting together and running this magnificent conference. Of course they could not have done this without the active role of participants in the conference, who are to be thanked as well. The conference program has been really outstanding and extremely interesting, and has demonstrated the scientific impact of the field in an important way. I am in this situation because it has been a tradition of the ENAM conferences that the chairman of the previous conference delivers the summary talk. I am sure Witek Nazarewicz is looking forward to this honorable duty in four years time in Poland when our colleagues will be organizing the next conference. There also seems to be another tradition not decided by us, namely the stormy weather during one of the days of the conference. I remember, last time in Finland, we also had a major thunderstorm during the last session of the conference, and this tradition seems to be following us everywhere. The progress in our field since the last ENAM conference has been fast and noticeable. I think that this progress is speeding up with these conferences. One way to observe the progress is simply to look at the numbers and the statistics of this conference. We had 280 participants, 84 oral talks, 43 oral poster talks, and 162 posters. The oral poster presentations, a new feature of ENAM, was a very good idea indeed. The presentations were very informative and provided an opportunity for many more participants to actually present their work. The presentations have been of very high quality. Electronic presentations really provide an extremly efficient tool for bringing the information to the audience. Also, the posters have been of a very high quality, and I have seen that the discussions have been very lively in the poster sessions. In particular, the younger participants have been able to a

e-mail: [email protected]

communicate their results and interact with the rest of the conference participants. The conference covered basically all of its traditional areas. I could not help noticing that the community working in nuclear spectroscopy, especially in in-beam spectroscopy, has been directing its interests toward nuclei far from stability and contributing in an important way to this conference. I estimated that about 30% of the conference contributions have come from the field of in-beam spectroscopy, providing a nice complementary addition to the field. The development in the field has been driven by a number of advances, but not least by the new facilities that are being planned and constructed and taken into operation. In particular in this conference, the MSU Cyclotron Laboratory and RIKEN have shown up in a very strong way without forgetting other facilities like HRIBF, REXISOLDE, TRIUMF, and many others. One typical feature in this field is that much of the research we do, is done in large collaborations and this also, I think, is an important factor. Collaborations are spread across the seas and we seem to have the ability to do our research today in a nearly optimal way with regard to our the resources and infrastructure. In the following, I will discuss the conference content itself. As mentioned, we had close to 250 presentations, and therefore it will be impossible to give a comprehensive summary in a short time. What I am reviewing here is a summary which is, of course, strongly biased, being based on my personal impressions and taste, as well as on my knowledge of different areas of this field. I did attend all sessions; I learned a lot, and, in fact, you will see throughout this presentation that I will try to bring up some of the highlights of this conference which struck me the most. The progress has been very strong and powered by the constant development of the equipment and computing power. Several of the new methods that were discussed at the previous ENAM conference are now in full use to produce physics.

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2 Masses The conference started traditionally with the session on atomic masses. We are now in a fortunate situation that the new atomic mass tables were introduced just prior to this conference, representing a collection of the best atomic mass values. There are two components in the tables, stable and radioactive atomic masses, as discussed by Aaldert Wapstra. As compared to the old table, the new table has a large amount of new information. David Lunney gave a beautiful presentation on the masses, emphasizing the fast progress in this field over the last couple of years. There are many new developments in experimental techniques that have led to this. For example, the ion traps with a new feature, e.g., to introduce the ions into a trap in an efficient and fast way has opened up a possibility to develop a major new tool in mass measurements for radioactive isotopes. Relative precision can typically reach the lower end of the 10−8 range for nuclides with half-lives less than 100 ms. Several examples, such as 22 Mg, 22,33,34 Ar, 68 Se, 72 Kr, and 74 Rb, mainly from the ISOLTRAP group but also from the Canadian Penning Trap group at Argonne, were presented and discussed at this conference. Also, a new Penning trap at Jyv¨ askyl¨a has started to work, and the very first results on masses of refractory fission products were presented at this conference by Ari Jokinen. There was a remarkable result reported by Cyril Bachelet concerning the mass of 11 Li, a very exotic short-lived nucleus, whose mass was measured by the MISTRAL spectrometer to a precision of 5 keV. The actual mass-measurement factory, one could say, is the experimental storage ring of GSI, which has recently produced a large number of new masses for neutron-rich nuclei. By its nature, this technique is universal and will, in the future, be a very important technology for mass measurements of very exotic nuclei. We also heard from GANIL, where a large number of new masses near the neutron drip line at N ∼ 20 were reported by Herve Savajols. Many other techniques were reported and discussed. One of them applied accelerated radioactive ions and the household appliances at HRIBF to measure masses of exotic copper and germanium isotopes close to doubly magic 78 Ni. In theory, the development of mean-field theories, providing a global approach to connect masses to effective interactions, has provided important tools for mass predictions, for example, in astrophysics. In the future, there is also a need to address the local structure effects in binding energies to understand the physics behind the fine structures. Stephane Goriely presented his overview talk giving a very nice description of the current situation on the different theories for the mass calculations. As he stated, the future challenge lies in a unified description of masses and other nuclear properties. One example discussed was the evolution of the N = 82 shell-gap as a function of the proton number. It was shown that different models deviate significantly from each other. It is of significant interest to extend the experimental measurements down towards the lighter elements, as reported by a recent experiment at ISOLDE where the mass of 130 Ag had been deduced from a beta end-point measurement.

Because mass measurement techniques have advanced in a major way in recent years, one may ask the question: why and where do we need these new accurate masses? In fact, there are many requirements for high precision. At this conference we have heard about testing the validity of the Standard Model in various ways. In experiments on superallowed Fermi-decays, a very accurate measurement of mass differences or decay energies, e.g. much better than one keV, is required. I think John Hardy was asking for a 100 electron volt or better precision. This is, of course, a very challenging, but not an impossible task, for example, for Penning traps. Typically, in some cases in astrophysics, especially when resonant capture reactions are studied, the accuracies have to be well below 10 keV. Nuclear structure studies require an accuracy somewhere around 100 keV or better. If one looks globally over the distant wings of the nuclidic mass surface, something like a half of a MeV is still acceptable and useful.

3 Moments and radii From masses we move on to moments and radii. Spinpolarized radioactive beams at high and low energy, as reported by ISOLDE and GANIL, have become important tools in structure studies of nuclei close to N = 8, 20, and 28, as described in the presentations of Gerda Neyens and Magdalena Kowalska. Many important studies close to the magic neutron numbers far from stability on the neutron-rich side have been made by these groups. There has been major progress in studies of moments and radii of refractory neutron-rich nuclei. They have become available, as reported by Jon Billowes, for collinear laser spectroscopy, mainly thanks to the recently developed cooling and bunching techniques for short-lived radioactive ions. There is also resonant laser ion source spectroscopy that has been applied to study the coexistence of shapes in lead nuclei at ISOLDE. Two outstanding results were reported at this conference, namely the accurate measurements of the charge radii of 6 He and 9 Li by Peter Mueller and Wilfried N¨ ortersh¨ auser, respectively. These experiments will eventually lead the way for future measurements in the same quantities for two important halo nuclei, 8 He and 11 Li. There were, in addition, several experimental results on studies of matter radii and matter distributions of exotic nuclei done by various experimental setups at RIKEN, GSI, GANIL, and MSU. Also, we heard about the g-factor measurements with neutron-rich radioactive beams as reported, for example, by the Oak Ridge and Munich groups. It is clear that in the future we need systematic studies over a broad range in proton and neutron numbers. In particular, I would like to express a wish to get radii in the island of inversion region near N = 20. There are measurements by the ISOLDE group on the neutron-rich magnesium isotopes up to 28 Mg; but now the challenge is to go further. One of the outstanding results presented at this conference was the measurement of the quadrupole moment of 11 Li. The accuracy for the experimental ratio of the

¨ o: Concluding remarks . . . J. Ayst¨ 11

Li to 9 Li quadrupole moment has been improved significantly over the years. The quadrupole moment of 11 Li is 10% higher than the one of 9 Li, which indicates that halo neutrons must partially be in the d5/2 orbital, a result that confirms the recent reaction experiment at GSI.

4 Radioactivity Hubert Grawe gave a nice overview of the nuclear structure changes along the N = 50 neutron shell, starting from the 78 Ni region up to 100 Sn. He pointed out the importance of l = 2 core polarization as a mechanism leading to isomerism and, in general, the important role of the monopole interaction in the structures of these nuclei. Radioactivity studies continue to be a rich source of information on single-particle states near the magic numbers far from stability. For example, Paul Mantica’s overview talk discussed a number of experiments that have been done on the beta decays of aluminum and sodium nuclei, mapping the levels and spins on both sides of the N = 20 magic neutron number. Another presentation related to these nuclei, more specifically to the lifetime measurements of their excited states, was given by Henryk Mach. Isomeric decays, as discussed by Robert Grzywacz, were demonstrated as an important spectroscopic tool at the previous ENAM2001 conference. They have been effectively used to probe nuclear structures and states of medium and high spin very far from stability. At this conference, Ivan Mukha reported the discovery of the highest spin beta-decaying isomer discovered so far, 94 Ag. The story is just beginning, and it seems to me that this one isomer will, in the future, provide us a rich laboratory of nuclear structure and radioactive decay studies. Experimental activity in the proton decay studies has somewhat diminished due to the natural reason that there are fewer and fewer new cases to be studied. It was satisfying to observe that the theory effort in the field of proton and two-proton decay is substantial and extremely important, as reported by Cary Davids, Alexander Volya, and Jimmy Rotureau and co-workers. For experiments, there are new techniques which provide a complementary approach to get additional information on the excited states preceding the proton decay, as discussed by Andrew Robinson. Two-proton radioactivity was reviewed by Marek Pfutzner. In fact, a few weeks after the previous ENAM conference the first evidence for two-proton radioactivity of 45 Fe was observed at GANIL and at GSI. It seems that there are other interesting candidates for true diproton (or 2 He) radioactivity which still remain to be uncovered. In this connection, we have already heard about a new two-proton emitter, 54 Zn, presented by Bertram Blank. To unravel the decay mechanism, one really needs new detection systems for energy and angular correlation measurements. When the experiments advance very far from stability, it remains important to obtain information on gross decay properties, but as a second step, we will have to aim at high-resolution, high-sensitivity experiments to uncover the increasing complexity of radioactive decays.

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5 Clusters and drip line There were two interesting sessions on drip-line nuclei, especially on the role of clusters in nuclear structure that was reviewed very nicely by Y. Kanada-En’yo. She showed convincingly that clustering really plays an essential role in structures of unstable light nuclei as well as in some stable nuclei. In fact, even 12 C, in the framework of cluster physics, stays in the news both from a theoretical as well as from an experimental point of view. Recently, there has been plenty of new information reported at the conference on the states of 12 C at about 10 MeV excitation energy. This new information will also have an impact on the triple-alpha process leading to the formation of carbon in stars. The clusters and the mean field do coexist and both need to be considered at the same time to understand the structures observed in light nuclei. A specific problem concerning the concept of a tetra neutron was discussed both in the experimental talk of Miguel Marques and the theoretical presentation of Steven Pieper. It seems that some more work is needed since our current rational understanding of nuclear force and nuclear interaction does not allow a bound tetra neutron. It was interesting to hear from Michael Thoennessen that there are still about 200 nuclei to be discovered near the proton drip line. Two of these were presented by Andreas Stolz, who presented evidence of new nuclei 62 Ge and 64 Se. There has been a considerable amount of work done at Jyv¨ askyl¨a on alpha decays near the proton drip line, as reported by Juha Uusitalo.

6 Nuclear structure and spectroscopy The main general subject of the conference, nuclear structure and spectroscopy, covered about 30% of the program. It included several interesting presentations. The main theme currently is the study of neutron-rich nuclei at and near the classical closed neutron shells, but far from stability. There are several different experimental approaches that were presented; the accelerated radioactive ion beam experiments were reported mainly by teams from REX-ISOLDE at CERN and the HRIBF at Oak Ridge. In both, Coulomb excitation and transfer reactions have been employed in experiments near N = 20, 50, and 82. There were also a number of experimental results reported from RIKEN and MSU using the fragmentation technique. Since fragmentation is a universal production method, it allows studies of many exotic nuclei simultaneously and with high sensitivity, but it lacks the high accuracy of in-beam spectroscopy. A continuing important role of the network of stable beam facilities was demonstrated by several contributions from Argonne, Legnaro, Jyv¨ askyl¨a, and elsewhere. The successful future of this field calls for a constant development of tracking methods for gamma rays and charged particles. I will briefly highlight some examples of studies presented at the conference. The first results employing

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Coulomb excitation of n-rich Mg isotopes from REXISOLDE were reported by Heiko Scheit. The B(E2) value observed for 30 Mg was found to be in some discrepancy with the values derived earlier from the high-energy experiments at GANIL and MSU. The newest data, presented by Robert Varner and David Radford, yielded B(E2) values for Sn and Te isotopes. The experimental values for Sn at N = 80, 82, and 84 are reproduced rather nicely by the theory. Also, we heard about an interesting experiment at RIKEN on 30 Ne, which had been done with a beam intensity of only 0.3 ions/s. It detected, for the first time, the first 2+ excited state at 790 keV in 30 Ne, which is very similar to 32 Mg. It seems to have, if based on the energy argument alone, a similar collectivity as that of 32 Mg. Level lifetime measurements employing the recoil shadow technique, reported by Hiro Sakurai, also from RIKEN, was very interesting. The anomalously small B(E2) value for 16 C suggests a strong contribution of neutron matter to this excitation. This was also discussed by James Vary, who presented theoretical calculations based on the no-core shell model that reproduced the experimental value very nicely. There was an interesting presentation by Janne Pakarinen, which concerned the probing of the famous 0+ state askyl¨a using the recoil structures in 186 Pb studied at Jyv¨ decay tagging. The group had identified a new rotational band based on one of the excited 0+ states. More work is needed here to clarify the picture, but there has been a lot of progress in this area. We heard of several new results from Legnaro, as reported by Andres Gadea. The PRISMA spectrometer, coupled with the CLARA Ge-array, is now in full operation and is going to provide us with a large amount of spectroscopic information on neutron-rich nuclei via transfer reactions in the coming years. Frank Becker reported on a larger number of results from the GSI RISING setup. For example, they have measured the first B(E2) values for neutron-rich 54–58 Cr nuclei. This conference has convincingly shown that we have made many significant developments in nuclear structure theory. Several of these were discussed in review talks, such as the ab initio no-core shell model overview talk of James Vary. No-core shell-model calculations employing realistic two- and three-body interactions were also discussed by Peter Navratil. Coupled-cluster calculations were extensively reviewed by Piotr Piecuch, and microscopic models for exotic nuclei were treated in an extensive way by Michael Bender. Wojtek Satula discussed a special treatment of the isospin degree of freedom in nuclear structure calculations. It seems that any given theory framework is becoming increasingly tested against many observables at the same time, including binding energies, excited states, as well as nuclear bulk properties. It is obvious that the predictive power of theories has been significantly improved, which will eventually lead the way to new and better formulated physics searches far from stability.

7 Heavy elements At the time of the ENAM2001 conference, the heaviest element observed was the one with Z = 112, and then we had this mysterious Z = 118 result. Since those days, the community has become extremely active, and heavy element research has gained new momentum in many ways. For example, during the last year or two, two new elements were named, Z = 110 as darmstadtium, and Z = 111 as roentgenium. Several new results were discussed by Dieter Ackermann, Vladimir Utyonkov, and Paul Greenlees. The Berkeley activity in this field is back on track, and the LISE spectrometer at GANIL has entered the field as another new player. There were some really exciting new results from RIKEN, namely the discovery of a new element 278 113 by Kosuke Morita and his team. This result was reported by Dieter Ackermann. It was a pity that there was no Japanese presentation of this beautiful result. In-beam spectroscopy studies of transfermium elements have been askyl¨a pushed to more new nuclei around 252 No at Jyv¨ and Argonne. We had an interesting presentation by Heinz Gaeggeler on the chemistry of the superheavy elements. He presented exciting results on the chemistry of the element 112 done at GSI and on the chemistry of Dubnium, which was produced as a decay product in the decay chain of element 115 observed in Dubna. It is important that chemists participate in the research, because they will be very helpful in assigning the Z of the new elements. If we look at the upper corner of the nuclear chart, it has many interesting new features. There is the socalled nobelium region which is actively researched by the Jyv¨ askyl¨a and Argonne groups for excited and microscopic structures. We have several new elements and isotopes produced in cold fusion reactions at GSI and at RIKEN and, finally, more than 30 new isotopes, all produced at Dubna in hot fusion reactions. The decay chains of the latter nuclides end up in unknown isotopes. Connecting these chains to the known upper part of the nuclear chart will be a challenge for future studies in this field.

8 Reactions Reactions were discussed in penetrating ways. The field is developing very rapidly, although difficulties related to the beam quality, the energy, and angular resolution need constant attention. There were several reports on low-energy radioactive ion beam experiments concerning the fusion reactions of neutron-rich nuclei. The proof for the expected enhancement of fusion was shown by Walter Loveland for the 132 Sn + 64 Ni reaction at sub-barrier energies. The first spectroscopy results by transfer reactions at the new VAMOS facility at SPIRAL were presented by Wilton Catford. Several high-energy experiments were described. Knock-out reactions used for extracting spectroscopy factors along the isotones were described by Alexandra Gade of MSU with an intriguing difference in valence neutron orbital occupation observed between 22 O and 32 Ar. Deeply

¨ o: Concluding remarks . . . J. Ayst¨

bound states in 32 Ar possess a very small reduction factor compared to loosely bound 22 O. Also, scattering experiments used to extract radii and halos of drip-line nuclei were presented by Wolfgang Mittig and several other contributions. A special technique relying on scattering of radioactive beams from a polarized hydrogen target was introduced by Hide Sakai who demonstrated the sensitivity of the reaction in probing the radial extension of the spin-orbit part of the nuclear potential.

9 Nuclear astrophysics Nuclear astrophysics was presented in a very lively presentation by Art Champagne. We often discuss the importance of nuclear physics in astrophysics, and I just want to agree with the statement of Hendrik Schatz that the role of nuclear physics should not be underestimated in astrophysics. Several key reaction rates continue to be of interest in this field, and some of them mentioned at the conference were 7 Be(p, γ), 14 N(p, γ), 18 F(p, α), 22 Na(p, γ), and so on. Also, many new important results concerning the masses of the rp-process waiting-point nuclei were presented. The masses of 68 Se and 72 Kr have been measured accurately at the Canadian Penning Trap and ISOLTRAP, as reported by Jason Clark and Frank Herfurth, respectively. Also, very detailed reviews on the r-process, both for experimental and theoretical aspects, were provided by Hendrik Schatz, Karl-Ludwig Kratz, as well as by Stephane Goriely and Gabriel Martinez-Pinedo.

10 Fundamental symmetries Klaus Jungmann provided us with a highly interesting tour through the different possibilities we have concerning studies of fundamental symmetries and interactions at the current nuclear physics facilities and accelerators. A few of these subjects were specifically presented at the conference: T and CP violation was discussed by Jonathan

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Engel, correlations in beta decays by John Behr, and the unitarity of the CKM matrix by John Hardy. These experiments are all very difficult and not many of us are involved. However, they are important experiments and definitely should be very strongly supported at our facilities.

11 Radioactive ion beams and applications Production methods and technologies for radioactive ion beams have advanced tremendously, leading to the success of many of the experiments presented at this conference. This subject was not reviewed at this conference. However, a few important new developments were presented. Piet Van Duppen, from Leuven, reviewed the current status and future developments of laser ion source technology for the production of radioactive beams. While in the past only the ISOLDE at CERN and Louvain la Neuve in Belgium were utilizing this technique, it is now becoming more common and several laboratories are adapting to it. Another important general development related to radioactive ion beam manipulation was presented by Guy Savard from Argonne. Applications, in small scale, were presented as well, but although they are important, they are normally not discussed in detail at this conference. In this connection, we enjoyed a presentation by Jose Benlliure on nuclear cross section measurements for transmutaion of nuclear waste.

12 Conclusion In summary, this conference has shown that our field is indeed in good shape, and we have a very enthusiastic community. I would like to underline that theoretical efforts have been significant, and they are able to offer challenges for the experiments which I think are particularly important. We are living in exciting times, during which new facilities are developing throughout the whole world. There is great promise for an excellent ENAM 2008 conference in Poland. Thank you.

Eur. Phys. J. A 25, s01, 773 (2005) DOI: 10.1140/epjad/i2005-06-211-1

EPJ A direct electronic only

Erratum Identification of mixed-symmetry states in odd-A

93

Nb

C.J. McKay1 , J.N. Orce1,a , S.R. Lesher1 , D. Bandyopadhyay1 , M.T. McEllistrem1 , C. Fransen2 , J. Jolie2 , A. Linnemann2 , N. Pietralla2,3 , V. Werner2 , and S.W. Yates1,4 1 2 3 4

Department of Physics & Astronomy, University of Kentucky, Lexington, KY 40506-0055, USA Institut f¨ ur Kernphysik, Universit¨ at zu K¨ oln, 50937 K¨ oln, Germany Nuclear Structure Laboratory, Department of Physics & Astronomy, SUNY, Stony Brook, NY 11794-3800, USA Department of Chemistry, University of Kentucky, Lexington, KY 40506-0055, USA

Original article: Eur. Phys. J. A 25, s01, 377–379 (2005) DOI: 10.1140/epjad/i2005-06-047-7 Received: 26 July 2005 / c Societ` Published online: 1 August 2005 –  a Italiana di Fisica / Springer-Verlag 2005

Following the acceptance for publication of the paper entitled Identification of mixed-symmetry states in odd-A 93 Nb, the authors realized that some mistakes in the data analysis had occurred. As mentioned in the original paper, from an experiment using the 94 Zr(p, 2n)93 Nb reaction, multipolarities and spin assignments were determined. The de-excited γ-rays were detected using the HORUS spectrometer, comprised of 16 HPGe detectors. Here, nine correlation groups are available in order to determine the spins through angular-correlation analysis. Later, the authors realised that there was a problem with the efficiency of the correlation groups where the cluster detector was primarily involved. This problem led to unreliable quadrupole mixing ratios, δ, and therefore to the incorrect identification of mixed-symmetry states. The problem has been resolved by using only seven correlation groups. At present, the authors cannot confirm the identification of any mixed-symmetry states since the data are being reanalised. The new analysis and conclusions of this work will be published in a forthcoming paper.

a

Conference presenter; e-mail: [email protected]

Author index Abdullin F.Sh. → Oganessian Yu.Ts. Abu-Ibrahim B. → Kanungo R. Abu-Ibrahim B. → Kanungo R. Achouri N.L. → Gr´evy S. Ackermann D.: Beyond darmstadtium —Status and perspectives of superheavy element research 577 Ackermann D. → Block M. Ackermann D. → Nara Singh B.S. Added N. → Lichtenth¨ aler R. Adhikari S., Samanta C., Basu C., Ray S., Chatterjee A. and Kailas S.: Entrance channel dependence in compound nuclear reactions with loosely bound nuclei 299 Adhikari S. → Kanungo R. Adhikari S. → Kanungo R. Adimi N. → Blank B. Agrawal B.K., Shlomo S. and Kim Au V.: Breathing mode energy and nuclear matter incompressibility coefficient within relativistic and non-relativistic models 525 Aguilera R. E. → Barr´ on-Palos L. Aksouh F. → Blank B. Aksouh F. → Kiselev O.A. Aksouh F. → Scheit H. Alamanos N. → Giot L. Alford W.P. → Behr J.A. Al-Khalili J.S. → Sarazin F. Alvarez C. → Scheit H. Ames F. → Delahaye P. Ames F. → Scheit H. Amro H. → Liang J.F. Amro H. → Shapira D. Amzal N. → Eeckhaudt S. Amzal N. → Greenlees P.T. Amzal N. → Keyes K.L. Andersson L.-L. → Ekman J. Andreyev A.N. → Chakrawarthy R.S. Ang´elique J.C. → Gr´evy S. Ang´elique J.C. → L´epine-Szily A. Angelique J.C. → Pain S.D. Angulo C. → Ter-Akopian G.M. Aoi N. → Hatano M. Aoi N. → Iwasaki H. Aoi N. → Michimasa S. Aoi N. → Ong H.J. Aoi N. → Yamada K. Aprahamian A. → Boutachkov P. Aprahamian A. → Kautzsch T. Aprahamian A. → Popa G. Aprahamian A. → Schatz H. Arazi A. → Lichtenth¨ aler R. Arndt O. → Kautzsch T. Arndt O. → K¨ oster U. Arndt O. → Kratz K.-L. Arndt O. → Schatz H.

Arndt O. → Shergur J. Ashery D. → Behr J.A. Ashley S.F. → Chakrawarthy R.S. Ashwood N.I. → Pain S.D. Asztalos S.J. → Fong D. Atkin E. → Pollacco E. Atramentov O.V. → Vary J.P. Audi G. → Bachelet C. Audi G. → Gu´enaut C. Audi G. → Gu´enaut C. Audi G. → Herfurth F. Audi G. → L´epine-Szily A. Audi G. → Rodr´ıguez D. Audi G. → Weber C. Auger F. → Giot L. Auger G. → Khouaja A. Aumann T. → Cortina-Gil D. Aumann T. → Datta Pramanik U. Austin R.A.E. → Sarazin F. ¨ o J.: Concluding remarks of the ENAM’04 Conference Ayst¨ 767 ¨ o J. → Jokinen A. Ayst¨ ¨ o J. → Kankainen A. Ayst¨ ¨ o J. → Penttil¨ Ayst¨ a H. ¨ Ayst¨o J. → Per¨aj¨ arvi K. ¨ o J. → Rinta-Antila S. Ayst¨ ¨ o J. → Rodr´ıguez D. Ayst¨ ¨ o J. → Scheit H. Ayst¨ Baba H. → Ideguchi E. Baba H. → Iwasaki H. Baba H. → Michimasa S. Baba H. → Ong H.J. Baba H. → Yamada K. Bachelet C., Audi G., Gaulard C., Gu´enaut C., Herfurth F., Lunney D., De Saint Simon M., Thibault C. and the ISOLDE Collaboration: Mass measurement of short-lived halo nuclides 31 Bachelet C. → Sewtz M. Baiborodin D. → Khouaja A. Baiborodin D. → Savajols H. Baktash C. → Jones K.L. Baktash C. → Radford D.C. Baktash C. → Stone N.J. Baktash C. → Varner R.L. Baktash C. → Yu C.-H. Baktash C. → Zamfir N.V. Balabanski D.L. → Tonev D. Ball G.C. → Chakrawarthy R.S. Ball G.C. → Sarazin F. Ban G. → Rodr´ıguez D. Bandyopadhyay D. → McKay C.J. Bandyopadhyay D. → McKay C.J. Banu A. → Becker F.

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Banu A. → Karny M. Banu A. → Kavatsyuk M. Baran A., L  ojewski Z. and Sieja K.: Ground-state properties of superheavy elements in macroscopicmicroscopic models 611 Barber R.C. → Clark J.A. Barber R.C. → Sharma K.S. Bardayan D.W., Blackmon J.C., G´ omez del Campo J., Kozub R.L., Liang J.F., Ma Z., Shapira D., Sahin L. and Smith M.S.: New 19 Ne resonance observed using an exotic 18 F beam 643 Bardayan D.W. → Jones K.L. Bardayan D.W. → Thomas J.S. Barea J. → Hirsch J.G. Baron P. → Pollacco E. Baronick J.P. → Pollacco E. Barrett B.R. → Stetcu I. Barrett B.R. → Vary J.P. Barr´ on-Palos L., Ch´ avez L. E., Huerta H. A., Ortiz M.E., Murillo O. G., Aguilera R. E., Mart´ınez Q. E., Moreno E., Policroniades R. R. and Varela G. A.: 12 C + 12 C cross-section measurements at low energies 645 Barton C.J. → Radford D.C. Barton C.J. → Zamfir N.V. Barton C. → Stone N.J. Bastin B. → Gr´evy S. Bastin J.E. → Eeckhaudt S. Bastin J.E. → Greenlees P.T. Basu C. → Adhikari S. Basu P. → Chinmay Basu,Adhikari S. Batchelder J.C., Tantawy M., Bingham C.R., Danchev M., Fong D.J., Ginter T.N., Gross C.J., Grzywacz R., Hagino K., Hamilton J.H., Karny M., Krolas W., Mazzocchi C., Piechaczek A., Ramayya A.V., Rykaczewski K.P., Stolz A., Winger J.A., Yu C.-H. and Zganjar E.F.: Study of fine structure in the proton radioactivity of 146 Tm 149 Batchelder J.C. → Gross C.J. Batchelder J.C. → Grzywacz R. Batchelder J.C. → Mazzocchi C. Batchelder J.C. → Tantawy M.N. Batchelder J.C. → Yu C.-H. Batchelder J. → Radford D.C. Batist L. → Karny M. Batist L. → Kavatsyuk M. Batist L. → Mukha I. Baumann T. → Cortina-Gil D. Baumann T. → Stolz A. Bazin D. → Gade A. Beaumel D. → Pollacco E. Beausang C.W. → Grahn T. Becchetti F.D. → Boutachkov P. Becheva E. → Pollacco E. Beck C. → Keyes K.L. Beck D. → Block M. Beck D. → Gu´enaut C. Beck D. → Gu´enaut C. Beck D. → Herfurth F.

Beck D. → Rodr´ıguez D. Beck D. → Weber C. Beck D. → Yazidjian C. Beck T. → Becker F. Becker F., Banu A., Beck T., Bednarczyk P., Doornenbal P., Geissel H., Gerl J., G´ orska M., Grawe H., Grebosz J., Hellstr¨ om M., Kojouharov I., Kurz N., Lozeva R., Mandal S., Muralithar S., Prokopowicz W., Saito N., Saito T.R., Schaffner H., Weick H., Wheldon C., Winkler M., Wollersheim H.J., Jolie J., Reiter P., Warr N., B¨ urger A., H¨ ubel H., Simpson J., Bentley M.A., Hammond G., Benzoni G., Bracco A., Camera F., Million B., Wieland O., Kmiecik M., Maj A., Meczynski W., Stycze´ n J., Fahlander C. and Rudolph D.: Status of the RISING project at GSI 719 Becker F. → Karny M. Becker F. → Kavatsyuk M. Becker J.A. → Chakrawarthy R.S. Bednarczyk P. → Becker F. Bednarczyk P. → Keyes K.L. Bednarczyk P. → Tonev D. Beene J.R. → Liang J.F. Beene J.R. → Radford D.C. Beene J.R. → Shapira D. Beene J.R. → Stone N.J. Beene J.R. → Varner R.L. Beene J.R. → Yu C.-H. Beghini S. → Corradi L. Beghini S. → Trotta M. Behera B.R. → Chinmay Basu,Adhikari S. Behera B.R. → Corradi L. Behera B.R. → Trotta M. Behr J.A., Gorelov A., Melconian D., Trinczek M., Alford W.P., Ashery D., Bricault P.G., Courneyea L., D’Auria J.M., Deutsch J., Dilling J., Dombsky M., Dub´e P., Gl¨ uck F., Gryb S., Gu S., H¨ ausser O., Jackson K.P., Lee B., Mills A., Paradis E., Pearson M., Pitcairn R., Prime E., Roberge D. and Swanson T.B.: Weak interaction symmetries with atom traps 685 Behrens T. → Scheit H. Benczer-Koller N., Kumbartzki G., Cooper J.R., Mertzimekis T.J., Taylor M.J., Bernstein L., Hiles K., Maier-Komor P., McMahan M.A., Phair L., Powell J., Speidel K.-H. and Wutte D.: First g-factor measurement using a radioactive 76 Kr beam 203 Benczer-Koller N. → Stone N.J. Bender M. and Heenen P.-H.: Microscopic models for exotic nuclei 519 Bender M. → Terasaki J. Benjamim E.A. → Lichtenth¨ aler R. Benjelloun M. → Khouaja A. Benlliure J.: Spallation reactions for nuclear waste transmutation and production of radioactive nuclear beams 757 Benlliure J. → Cortina-Gil D. Bentley M.A. → Becker F. Benzoni G. → Becker F. Bergmann U.C. → K¨oster U. Bernstein L. → Benczer-Koller N.

Author index

Bey A. → Blank B. Beyer C.J. → Fong D. Beyer C.J. → Hwang J.K. Bierman J.D. → Liang J.F. Bierman J.D. → Shapira D. Bildstein V. → Scheit H. Billowes J.: Developments in laser spectroscopy at the Jyv¨askyl¨ a IGISOL 187 Billowes J. → Penttil¨ a H. Bingham C.R. → Batchelder J.C. Bingham C.R. → Gross C.J. Bingham C.R. → Grzywacz R. Bingham C.R. → Mazzocchi C. Bingham C.R. → Radford D.C. Bingham C.R. → Stone N.J. Bingham C.R. → Tantawy M.N. Bingham C. → Yu C.-H. Blackmon J.C. → Bardayan D.W. Blackmon J.C. → Jones K.L. Blackmon J.C. → Thomas J.S. Blank B., Adimi N., Bey A., Canchel G., Dossat C., Fleury A., Giovinazzo J., Matea I., De Oliveira F., Stefan I., Geogiev G., Gr´evy S., Thomas J.C., Borcea C., Cortina D., Caamano M., Stanoiu M. and Aksouh F.: First observation of 54 Zn and its decay by two-proton emission 169 Blank B. → Clark J.A. Blank B. → Robinson A.P. Blank B. → Seweryniak D. Blaum K. → Block M. Blaum K. → Gu´enaut C. Blaum K. → Gu´enaut C. Blaum K. → Herfurth F. Blaum K. → Kowalska M. Blaum K. → Rodr´ıguez D. Blaum K. → Weber C. Blaum K. → Weber C. Blaum K. → Yazidjian C. Blazhev A. → Grawe H. Blazhev A. → Karny M. Blazhev A. → Kavatsyuk M. Blazhev A. → Mukha I. Blazkiewicz A., Oberacker V.E. and Umar A.S.: 2-D lattice HFB calculations for neutron-rich zirconium isotopes 543 Bleile A. → Kiselev O.A. Block M., Ackermann D., Beck D., Blaum K., Breitenfeldt M., Chauduri A., Doemer A., Eliseev S., Habs D., Heinz S., Herfurth F., Heßberger F.P., Hofmann S., Geissel H., Kluge H.-J., Kolhinen V., Marx G., Neumayr J.B., Mukherjee M., Petrick M., Plass W., Quint W., Rahaman S., Rauth C., Rodr´ıguez D., Scheidenberger C., Schweikhard L., Suhonen M., Thirolf P.G., Wang Z., Weber C. and the SHIPTRAP Collaboration: The ion-trap facility SHIPTRAP 49 Block M. → Weber C. Blomeley L. → Ryjkov V.L. Blumenfeld Y. → Pollacco E. Bochkarev O.V. → Kiselev O.A.

777

Bogomolov S.L. → Oganessian Yu.Ts. Boie H. → Scheit H. Bollen G. → Gu´enaut C. Bollen G. → Gu´enaut C. Bollen G. → Herfurth F. Bollen G. → Ringle R. Bollen G. → Rodr´ıguez D. Bollen G. → Scheit H. Bollen G. → Schury P. Bollen G. → Sun T. Bollen G. → Weber C. Bonaccorso A.: Unbound exotic nuclei studied via projectile fragmentation reactions 293 Bonaccorso A.: Exotic nuclei within the INFN-PI32 network 753 Bonetti R. → Romoli M. Bonomo C. → Tumino A. Borcea C. → Blank B. Borcea R. → Gr´evy S. Boretzky K. → Datta Pramanik U. Borge M.J.G. → Cortina-Gil D. Borge M.J.G. → Mach H. Borremans D. → Kowalska M. Borycki P.J. → Dobaczewski J. Bouchat V. → Pain S.D. Bouchat V. → Ter-Akopian G.M. Bouchez E. → Eeckhaudt S. Bouchez E. → Greenlees P.T. Boudreau C. → Clark J.A. Boujrad A. → Pollacco E. Boutachkov P., Rogachev G.V., Goldberg V.Z., Aprahamian A., Becchetti F.D., Bychowski J.P., Chen Y., Chubarian G., DeYoung P.A., Kolata J.J., Lamm L.O., Peaslee G.F., Quinn M., Skorodumov B.B. and Wohr A.: Isobaric analog states of neutron-rich nuclei. Doppler shift as a measurement tool for resonance excitation functions 259 Boutami R. → Mach H. Bracco A. → Becker F. Brand H. → Yazidjian C. Breitenfeldt M. → Block M. Bricault P.G. → Behr J.A. Bricault P. → Ryjkov V.L. Brodeur M. → Ryjkov V.L. Brown B.A. → Gade A. Brown B.A. → Honma M. Brown B.A. → Kautzsch T. Brown B.A. → Korgul A. Brown B.A. → Lisetskiy A.F. Brown B.A. → Nara Singh B.S. Brown B.A. → Shergur J. Br¨ uchle W. → Karny M. Br¨ uchle W. → Kavatsyuk M. Buchinger F. → Clark J.A. Buchinger F. → Ryjkov V.L. Buchinger F. → Sharma K.S. Buklanov G.V. → Oganessian Yu.Ts. B¨ urger A. → Becker F. Burkard K. → Karny M.

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The European Physical Journal A

Burkard K. → Kavatsyuk M. Burns M.J. → Keyes K.L. Bushaw B.A. → N¨ ortersh¨auser W. Buta A. → Gr´evy S. Butler P.A. → Eeckhaudt S. Butler P.A. → Greenlees P.T. Butler P.A. → Mach H. Butler P.A. → Scheit H. Bychowski J.P. → Boutachkov P. Caamano M. → Blank B. Caama˜ no M. → Mittig W. Caballero L. → Catford W.N. aler R. Camargo O. jr. → Lichtenth¨ Camera F. → Becker F. Camera F. → Tonev D. Campbell C.M. → Gade A. Campbell P. → Penttil¨ a H. Canchel G. → Blank B. Caprio M.A. → Radford D.C. Caprio M.A. → Zamfir N.V. Caraley A.L. → Liang J.F. Caraley A.L. → Shapira D. Carpenter M.P. → Robinson A.P. Carpenter M.P. → Seweryniak D. Casandjian J.M. → L´epine-Szily A. Casten R.F. → McCutchan E.A. Casten R.F. → Werner V. Casten R.F. → Zamfir N.V. Catford W.N., Lemmon R.C., Labiche M., Timis C.N., Orr N.A., Caballero L., Chapman R., Chartier M., Rejmund M., Savajols H. and the TIARA Collaboration: First experiments on transfer with radioactive beams using the TIARA array 245 Catford W.N. → Jones K.L. Catford W.N. → Pain S.D. Catford W. → Khouaja A. Catford W. → Savajols H. Catherall R. → K¨ oster U. Caurier E. → Navr´ atil P. Cederk¨ all J. → K¨ oster U. Cederk¨ all J. → Mach H. Cederk¨all J. → Scheit H. Cederwall B. → Ideguchi E. Cerny J. → Per¨ aj¨ arvi K. Chakrawarthy R.S., Walker P.M., Smith M.B., Andreyev A.N., Ashley S.F., Ball G.C., Becker J.A., Daoud J.J., Garrett P.E., Hackman G., Jones G.A., Litvinov Y., Morton A.C., Pearson C.J., Svensson C.E., Williams S.J. and Zganjar E.F.: Discovery of a new 2.3 s isomer in neutron-rich 174 Tm 125 Champagne A.E.: Amazing developments in nuclear astrophysics 623 Chapman R. → Catford W.N. Chapman R. → Keyes K.L. Chartier M. → Catford W.N. Chartier M. → Khouaja A. Chartier M. → L´epine-Szily A. Chartier M. → Mittig W.

Chartier M. → Savajols H. Chatillon A. → Eeckhaudt S. Chatillon A. → Greenlees P.T. Chatterjee A. → Adhikari S. Chatterjee R. → Rotureau J. Chauduri A. → Block M. Ch´avez L. E. → Barr´on-Palos L. Chauvin N. → Sewtz M. Chen Y.J. → Zhu S.J. Chen Y. → Boutachkov P. Cherubini S. → Tumino A. Chiba M. → Kanungo R. Chiba M. → Kanungo R. Chinda T. → Takechi M. Chinda T. → Tanaka K. Chinmay Basu,Adhikari S., Basu P., Behera B.R., Ray S., Ghosh S.K. and Datta S.K.: Observation of preequilibrium alpha particles at extreme backward angles from 28 Si + nat Si and 28 Si + 27 Al reactions at E < 5 MeV/A 277 Chizhov A.Yu. → Trotta M. Chubarian G. → Boutachkov P. Chulkov L.V. → Cortina-Gil D. Chulkov L.V. → Kiselev O.A. Church J.A. → Gade A. Chuvilskaya T.V., Kurgalin S.D., Okunev I.S. and Tchuvil’sky Yu.M.: Search for P -odd time reversal noninvariance in nuclear processes 699 Chuvilskaya T.V. and Shirokova A.A.: Yield of low-lying high-spin states at optimal charge-particle reactions 279 Cizewski J.A. → Jones K.L. Cizewski J.A. → Thomas J.S. Clark J.A., Barber R.C., Blank B., Boudreau C., Buchinger F., Crawford J.E., Greene J.P., Gulick S., Hardy J.C., Hecht A.A., Heinz A., Lee J.K.P., Levand A.F., Lundgren B.F., Moore R.B., Savard G., Scielzo N.D., Seweryniak D., Sharma K.S., Sprouse G.D., Trimble W., Vaz J., Wang J.C., Wang Y., Zabransky B.J. and Zhou Z.: Investigating the rp-process with the Canadian Penning trap mass spectrometer 629 Clark J.A. → Sharma K.S. Clarke N.M. → Pain S.D. Clement R.R.C. → Schatz H. Cole J.D. → Fong D. Cole J.D. → Gore P.M. Cole J.D. → Hwang J.K. Cole J.D. → Zhu S.J. Cooper J.R. → Benczer-Koller N. Corradi L., Stefanini A.M., Szilner S., Beghini S., Behera B.R., Farnea E., Gadea A., Fioretto E., Haas F., Latina A., Marginean N., Montagnoli G., Pollarolo G., Scarlassara F., Trotta M., Ur C. and the PRISMA-CLARA Collaboration: Multinucleon transfer reactions studied with the heavy-ion magnetic spectrometer PRISMA 427 Corradi L. → Trotta M. Cortina D. → Blank B.

Author index

Cortina D. → Datta Pramanik U. Cortina-Gil D., Fernandez-Vazquez J., Aumann T., Baumann T., Benlliure J., Borge M.J.G., Chulkov L.V., Datta Pramanik U., Forss´en C., Fraile L.M., Geissel H., Gerl J., Hammache F., Itahashi K., Janik R., Jonson B., Mandal S., Markenroth K., Meister M., Mocko M., M¨ unzenberg G., Ohtsubo T., Ozawa A., Prezado Y., Pribora V., Riisager K., Scheit H., Schneider R., Schrieder G., Simon H., Sitar B., Stolz A., Strmen P., S¨ ummerer K., Szarka I. and Weick H.: One-neutron knockout of 23 O 343 Cortina-Gil D. → Kiselev O.A. Cortina-Gil M.-D. → Giot L. Cortina-Gil M.D. → Mittig W. Courneyea L. → Behr J.A. Courtin S. → Trotta M. Covello A. → Korgul A. Crawford J.E. → Clark J.A. Crawford J.E. → Sharma K.S. Crawford J. → Ryjkov V.L. Crespo L´opez-Urrutia J.R. → Sikler G. Crider B. → Fetea M.S. Cunsolo A. → L´epine-Szily A. Curtis N. → Pain S.D. Danchev M. → Batchelder J.C. Danchev M. → Radford D.C. Danchev M. → Stone N.J. Danchev M. → Yu C.-H. Daniel A.V. → Gore P.M. Daniel A.V. → Luo Y.X. Daniel A.V. → Zhu S.J. Daniel A. → Fong D. Daniel A. → Hwang J.K. Daoud J.J. → Chakrawarthy R.S. Darby I. → Pakarinen J. Darius G. → Rodr´ıguez D. Datta S.K. → Chinmay Basu,Adhikari S. Datta Pramanik U., Aumann T., Boretzky K., Cortina D., Elze Th.W., Emling H., Geissel H., Hellstr¨ om M., Jones K.L., Khiem L.H., Kratz J.V., Kulessa R., Leifels Y., M¨ unzenberg G., Nociforo C., Palit R., Scheit H., Simon H., S¨ ummerer K., Typel S., Walus W. and Weick H.: Studies of light neutron-rich nuclei near the drip line 339 Datta Pramanik U. → Cortina-Gil D. Daugas J.M. → Gr´evy S. D’Auria J.M. → Behr J.A. Davids C.N. → Robinson A.P. Davids C.N. → Seweryniak D. Davids C.N. → Shergur J. Davids C. → Volya A. Davies A.D. → Tripathi V. Davies D.A. → Schury P. Davinson T. → Robinson A.P. Davinson T. → Scheit H. Davinson T. → Seweryniak D. Dax A. → N¨ ortersh¨ auser W. Dean D.J. → Shergur J.

779

Dean D.J. → Stoitcheva G. Dean D.J. → Wloch M. Dean S. → Mukha I. de Angelis G. → Tonev D. De Baerdemacker S. → Fortunato L. de Faria P.N. → Lichtenth¨ aler R. De Francesco A. → Romoli M. Delahaye P., Ames F., Podadera I., Savreux R. and Wenander F.: Recent developments of the radioactive beam preparation at REX-ISOLDE 739 Delahaye P. → Gu´enaut C. Delahaye P. → Gu´enaut C. Delahaye P. → Herfurth F. Delahaye P. → Rodr´ıguez D. Delahaye P. → Scheit H. deLima A.P. → Jones E.F. Demichi K. → Ong H.J. Demichi K. → Yamada K. Demonchy C.E. → Khouaja A. Demonchy C.E. → Mittig W. Demonchy C.E. → Savajols H. Demonchy Ch.E. → Giot L. a H. Dendooven P. → Penttil¨ Dendooven P. → Rinta-Antila S. Denisov V.Yu.: Entrance-channel potentials for hot fusion reactions 619 Denke R. → Lichtenth¨ aler R. De Oliveira F. → Blank B. De Oliveira F. → Gr´evy S. De Rosa A. → Romoli M. De Saint Simon M. → Bachelet C. Dessagne Ph. → Mach H. Deutsch J. → Behr J.A. Dewald A. → Grahn T. Dewald A. → Tonev D. DeYoung P.A. → Boutachkov P. Dilling J. → Behr J.A. Dilling J. → Ryjkov V.L. Dilling J. → Sikler G. Dillmann I. → K¨oster U. Dimitrov V. → Zhu S.J. Dinca D.-C. → Gade A. Di Pietro M. → Romoli M. Dlouhy Z. → Khouaja A. Dlouhy Z. → Savajols H. Dobaczewski J., Borycki P.J., Nazarewicz W. and Stoitsov M.: On the non-unitarity of the Bogoliubov transformation due to the quasiparticle space truncation 541 Dobaczewski J. → Stoitsov M.V. Dobaczewski J. → Terasaki J. Dobrovolsky A.V. → Kiselev O.A. Doemer A. → Block M. Doemer A. → Schury P. Dombr´adi Zs. → Ong H.J. Dombsky M. → Behr J.A. Donangelo R. → Fong D. Donangelo R. → Gore P.M. Donangelo R. → Hwang J.K.

780

The European Physical Journal A

Donangelo R. → Luo Y.X. Donzaud C. → L´epine-Szily A. Doornenbal P. → Becker F. D¨oring J. → Karny M. D¨oring J. → Kavatsyuk M. D¨oring J. → Mukha I. Dorvaux O. → Greenlees P.T. Dorvaux O. → Ter-Akopian G.M. Dossat C. → Blank B. Draayer J.P. and Feng Pan,Gueorguiev V.G.: Extended pairing model revisited 511 Draayer J.P. → Popa G. Drake G.W.F. → N¨ ortersh¨ auser W. Drigert M.W. → Zhu S.J. Drouart A. → Pollacco E. Druillole F. → Pollacco E. Dub´e P. → Behr J.A. Dubois M. → K¨oster U. Duchˆene G. → Keyes K.L. Dupak J. → Stone N.J. Durand D. → Rodr´ıguez D. Durantel F. → K¨ oster U. du Rietz R. → Ekman J. Eberth J. → Scheit H. Edelbruck P. → Pollacco E. Eeckhaudt S., Amzal N., Bastin J.E., Bouchez E., Butler P.A., Chatillon A., Eskola K., Gerl J., Grahn T., G¨ orgen A., Greenlees P.T., Herzberg R.-D., Hessberger F.P., H¨ urstel A., Ikin P.J.C., Jones G.D., Jones P., Julin R., Juutinen S., Kettunen H., Khoo T.L., Korten W., Kuusiniemi P., Le Coz Y., Leino M., Lepp¨ anen A.-P., Nieminen P., Pakarinen J., Perkowski J., Pritchard A., Reiter P., Rahkila P., Scholey C., Theisen Ch., Uusitalo J., Van de Vel K., Wilson J. and Wollersheim H.J.: In-beam gamma-ray spectroscopy of 254 No 605 Eeckhaudt S. → Grahn T. Eeckhaudt S. → Greenlees P.T. Eeckhaudt S. → Lepp¨ anen A.-P. Eeckhaudt S. → Pakarinen J. Eeckhaudt S. → Uusitalo J. Egelhof P. → Kiselev O.A. Ekman J., Andersson L.-L., Fahlander C., Johansson E.K., du Rietz R. and Rudolph D.: News on mirror nuclei in the sd and f p shells 363 Elekes Z. → Iwasaki H. Elekes Z. → Ong H.J. Elekes Z. → Yamada K. Eliseev S.A. → Kankainen A. Eliseev S. → Block M. Elomaa V.-V. → Penttil¨ a H. Elze Th.W. → Datta Pramanik U. Emhofer S. → Scheit H. Emling H. → Datta Pramanik U. Enders J. → Gade A. Engel J.: Time-reversal violation in heavy octupoledeformed nuclei 691 Engel J. → Terasaki J.

Enqvist T. → Kettunen H. Enqvist T. → Lepp¨anen A.-P. Enqvist T. → Pakarinen J. Enqvist T. → Uusitalo J. Epp S. → Sikler G. Eronen T. → Jokinen A. Eronen T. → Kankainen A. Eronen T. → Penttil¨ a H. Eshpeter B. → Sarazin F. Eskola K. → Eeckhaudt S. Eskola K. → Greenlees P.T. Eskola K. → Kettunen H. Eskola K. → Lepp¨anen A.-P. Eskola K. → Uusitalo J. Estrade A. → Schatz H. Ewald G. → N¨ortersh¨auser W. Faestermann T. → Karny M. Faestermann T. → Kavatsyuk M. Fahlander C. → Becker F. Fahlander C. → Ekman J. Falahat S. → Kautzsch T. Fallon P. → Fong D. Fang D.Q. → Kanungo R. Fang D.Q. → Kanungo R. Farnea E. → Corradi L. Fedorov D.V. → Garrido E. Feng Pan,Draayer J.P. → Gueorguiev V.G. Feng Pan,Gueorguiev V.G. → Draayer J.P. Fernandez J. → Giot L. Fernandez-Vazquez J. → Cortina-Gil D. Ferrer R. → Weber C. Fetea M.S., Nikolova V. and Crider B.: Chiral symmetry in odd-odd neutron-deficient Pr nuclei 437 Figuera P. → Tumino A. Finlay P. → Sarazin F. Fioretto E. → Corradi L. Fioretto E. → Trotta M. Fitting J. → Scheit H. Fitzgerald R.P. → Jones K.L. Fitzgerald R.P. → Thomas J.S. Fitzler A. → Tonev D. Fl´echard X. → Rodr´ıguez D. Fleury A. → Blank B. Fogelberg B. → Korgul A. Fogelberg B. → Mach H. Fomichev A.S. → Ter-Akopian G.M. Fomichev A. → Mittig W. Fong D., Hwang J.K., Ramayya A.V., Hamilton J.H., Beyer C.J., Li K., Gore P.M., Jones E.F., Luo Y.X., Rasmussen J.O., Zhu S.J., Wu S.C., Lee I.Y., Fallon P., Stoyer M.A., Asztalos S.J., Ginter T.N., Cole J.D., Ter-Akopian G.M., Daniel A. and Donangelo R.: Investigations of short half-life states from SF of 252 Cf 465 Fong D.J. → Batchelder J.C. Fong D. → Grzywacz R. Fong D. → Hwang J.K. Fong D. → Luo Y.X.

Author index

Fong D. → Mazzocchi C. Fong D. → Tantawy M.N. Fong D. → Zhu S.J. Forss´en C. → Cortina-Gil D. Forss´en C. → Navr´ atil P. Forstner O. → Scheit H. Fortunato L., De Baerdemacker S. and Heyde K.: Soft triaxial rotor in the vicinity of γ = π/6 and its extensions 439 Foti A. → L´epine-Szily A. Fox S.P. → Kankainen A. Fraile L.M.: Recent highlights from ISOLDE@CERN 723 Fraile L.M. → Cortina-Gil D. Fraile L.M. → Mach H. Fraile L.M. → Scheit H. Fraile L.M. → Tengblad O. Fraile L. → K¨ oster U. Franchoo S. → K¨ oster U. Franchoo S. → Scheit H. Frank A. → Hirsch J.G. Frank N.H. → Stolz A. Fransen C. → McKay C.J. Fransen C. → McKay C.J. Frauendorf S. → Zhu S.J. Freeman S.J. → Robinson A.P. Freeman S.J. → Seweryniak D. Freer M. → Pain S.D. Fritioff T. → Podadera I. Fuentes B. → Radford D.C. Fujiwara H. → Sumikama T. Fukuchi T. → Ideguchi E. Fukuchi T. → Iwasaki H. Fukuchi T. → Odahara A. Fukuda M. → Sumikama T. Fukuda M. → Takechi M. Fukuda M. → Tanaka K. Fukuda N. → Nakamura T. Fukutani H. → Sharma K.S. F¨ ul¨ op Zs. → Ong H.J. Fulton B.R. → Pain S.D. Fynbo H.O.U. → Scheit H. Fynbo H. → Mach H. Gade A., Bazin D., Brown B.A., Campbell C.M., Church J.A., Dinca D.-C., Enders J., Glasmacher T., Hansen P.G., Hu Z., Kemper K.W., Mueller W.F., Olliver H., Perry B.C., Riley L.A., Roeder B.T., Sherrill B.M., Terry J.R., Tostevin J.A. and Yurkewicz K.L.: Spectroscopic factors in exotic nuclei from nucleonknockout reactions 251 Gadea A.: First results of the CLARA-PRISMA setup installed at LNL 421 Gadea A. → Corradi L. Gadea A. → Tonev D. Gadea A. → Trotta M. G¨aggeler H.W.: Chemical properties of transactinides 583 Galindo-Uribarri A. → Liang J.F.

781

Galindo-Uribarri A. → Radford D.C. Galindo-Uribarri A. → Shapira D. Galindo-Uribarri A. → Stone N.J. Galindo-Uribarri A. → Varner R.L. Galindo-Uribarri A. → Yu C.-H. Galindo-Uribarri A. → Zamfir N.V. Gall B. → Greenlees P.T. Gargano A. → Korgul A. Garrett P.E. → Chakrawarthy R.S. Garrett P.E. → Sarazin F. Garrido E., Fedorov D.V. and Jensen A.S.: Borromean nuclei and three-body resonances 323 Gaubert G. → K¨oster U. Gaudefroy L. → K¨oster U. Gaulard C. → Bachelet C. Gebauer B. → Keyes K.L. Geissel H. → Becker F. Geissel H. → Block M. Geissel H. → Cortina-Gil D. Geissel H. → Datta Pramanik U. Geissel H. → Kiselev O.A. Gelberg A. → Luo Y.X. Gelin M. → Mittig W. Gelin M. → Pollacco E. Geogiev G. → Blank B. George S. → Herfurth F. Georgieva A. → Popa G. Gerl J. → Becker F. Gerl J. → Cortina-Gil D. Gerl J. → Eeckhaudt S. Gerl J. → Greenlees P.T. Gerl J. → Nara Singh B.S. Gerl J. → Scheit H. Gernh¨ auser R. → Scheit H. Gersch G. → Scheit H. Ghosh S.K. → Chinmay Basu,Adhikari S. Giarmana O. → Gr´evy S. Gibelin J. → Ong H.J. Gibelin J. → Yamada K. Gikal B.N. → Oganessian Yu.Ts. Gillibert A. → Giot L. Gillibert A. → Khouaja A. Gillibert A. → L´epine-Szily A. Gillibert A. → Mittig W. Gillibert A. → Pollacco E. Gillibert A. → Savajols H. Ginter T.N. → Batchelder J.C. Ginter T.N. → Fong D. Ginter T.N. → Luo Y.X. Ginter T.N. → Stolz A. Giot L., Roussel-Chomaz P., Alamanos N., Auger F., Cortina-Gil M.-D., Demonchy Ch.E., Fernandez J., Gillibert A., Jouanne C., Lapoux V., Mackintosh R.S., Mittig W., Nalpas L., Pakou A., Pita S., Pollacco E.C., Rodin A., Rusek K., Savajols H., Sida J.L., Skaza F., Stepantsov S., Ter-Akopian G., Thompson I. and Wolski R.: Study of the groundstate wave function of 6 He via the 6 He(p, t)α transfer reaction 267

782

The European Physical Journal A

Giot L. → Khouaja A. Giot L. → Savajols H. Giovinazzo J. → Blank B. Glasmacher T. → Gade A. Glodariu T. → Romoli M. Gl¨ uck F. → Behr J.A. Gnedin O.Y. → Yakovlev D.G. Goldberg V.Z. → Boutachkov P. Goldring G. → Nara Singh B.S. Golovkov M.S. → Ter-Akopian G.M. Gomes P.R.S. → Trotta M. G´ omez del Campo J. → Bardayan D.W. Gomez del Campo J. → Liang J.F. Gomez del Campo J. → Radford D.C. Gomez Del Campo J. → Shapira D. Gomez del Campo J. → Varner R.L. Gomi T. → Ong H.J. Gomi T. → Yamada K. Gono Y. → Odahara A. Gore P.M., Jones E.F., Hamilton J.H., Ramayya A.V., Zhang X.Q., Hwang J.K., Luo Y.X., Li K., Zhu S.J., Ma W.C., Rasmussen J.O., Lee I.Y., Stoyer M., Cole J.D., Daniel A.V., Ter-Akopian G.M., Oganessian Yu.Ts., Donangelo R. and Gupta J.B.: Unexpected rapid variations in odd-even level staggering in gamma-vibrational bands 471 Gore P.M. → Fong D. Gore P.M. → Hwang J.K. Gore P.M. → Jones E.F. Gore P.M. → Luo Y.X. Gore P.M. → Zhu S.J. Gorelov A. → Behr J.A. G¨ orgen A. → Eeckhaudt S. G¨orgen A. → Greenlees P.T. Goriely S., Samyn M., Pearson J.M. and Khan E.: Recent progress in mass predictions 71 Goriely S.: Global microscopic models for r-process calculations 653 G´orska M. → Becker F. G´ orska M. → Grawe H. G´orska M. → Karny M. G´orska M. → Kavatsyuk M. G¨otte S. → N¨ ortersh¨auser W. Gour J.R. → Wloch M. Grahn T., Dewald A., M¨ oller O., Beausang C.W., Eeckhaudt S., Greenlees P.T., Jolie J., Jones P., Julin R., Juutinen S., Kettunen H., Kr¨ oll T., Kr¨ ucken R., Leino M., Lepp¨ anen A.-P., Maierbeck P., Meyer D.A., Nieminen P., Nyman M., Pakarinen J., Petkov P., Rahkila P., Saha B., Scholey C. and Uusitalo J.: RDDS lifetime measurement with JUROGAM + RITU 441 Grahn T. → Eeckhaudt S. Grahn T. → Greenlees P.T. Grahn T. → Kettunen H. Grahn T. → Lepp¨ anen A.-P. Grahn T. → Pakarinen J. Grahn T. → Uusitalo J.

Grawe H., Blazhev A., G´ orska M., Mukha I., Plettner C., Roeckl E., Nowacki F., Grzywacz R. and Sawicka M.: Shell structure from 100 Sn to 78 Ni: Implications for nuclear astrophysics 357 Grawe H. → Becker F. Grawe H. → Karny M. Grawe H. → Kavatsyuk M. Grawe H. → Mukha I. Grebosz J. → Becker F. Greene J.P. → Clark J.A. Greene J.P. → Sharma K.S. Greene J. → Romoli M. Greenlees P.T., Amzal N., Bastin J.E., Bouchez E., Butler P.A., Chatillon A., Dorvaux O., Eeckhaudt S., Eskola K., Gall B., Gerl J., Grahn T., G¨ orgen A., Hammond N.J., Hauschild K., Herzberg R.-D., Heßberger F.P., Humphreys R.D., H¨ urstel A., Jenkins D.G., Jones a¨ a G.D., Jones P., Julin R., Juutinen S., Kankaanp¨ H., Keenan A., Kettunen H., Khalfallah F., Khoo T.L., Korten W., Kuusiniemi P., Le Coz Y., Leino M., Lepp¨ anen A.-P., Muikku M., Nieminen P., Pakarinen J., Rahkila P., Reiter P., Rousseau M., Scholey C., Theisen Ch., Uusitalo J., Wilson J. and Wollersheim H.-J.: In-beam and decay spectroscopy of transfermium elements 599 Greenlees P.T. → Eeckhaudt S. Greenlees P.T. → Grahn T. Greenlees P.T. → Kettunen H. Greenlees P.T. → Lepp¨anen A.-P. Greenlees P.T. → Uusitalo J. Greenlees P. → Pakarinen J. Greife U. → Jones K.L. Greife U. → Thomas J.S. Greiner W. → Gridnev K.A. Greiner W. → Gridnev K.A. Gr´evy S., Negoita F., Stefan I., Achouri N.L., Ang´elique J.C., Bastin B., Borcea R., Buta A., Daugas J.M., De Oliveira F., Giarmana O., Jollet C., Laurent B., Lazar M., Li´enard E., Mar´echal F., Mr´azek J., Pantelica D., Penionzhkevich Y., Pi´etri S., Sorlin O., Stanoiu M., Stodel C. and St-Laurent M.G.: Observation of the 44 0+ S 111 2 state in Gr´evy S. → Blank B. Gridnev D.K. → Gridnev K.A. Gridnev D.K. → Gridnev K.A. Gridnev K.A., Gridnev D.K., Kartavenko V.G., Mitroshin V.E., Tarasov V.N., Tarasov D.V. and Greiner W.: Stability island near the neutron-rich 40 O isotope 353 Gridnev K.A., Torilov S.Yu., Gridnev D.K., Kartavenko V.G., Greiner W. and Hamilton J.: Model of binding alpha-particles and applications to superheavy elements 609 Griesel T. → Kautzsch T. Grigorenko L.V. → Ter-Akopian G.M. Grinyer G.F. → Sarazin F. Grishechkin S.K. → Ter-Akopian G.M. Gross C.J., Rykaczewski K.P., Shapira D., Winger J.A., Batchelder J.C., Bingham C.R., Grzywacz R.K.,

Author index

Hausladen P.A., Krolas W., Mazzocchi C., Piechaczek A. and Zganjar E.F.: A novel way of doing decay spectroscopy at a radioactive ion beam facility 115 Gross C.J. → Batchelder J.C. Gross C.J. → Grzywacz R. Gross C.J. → Liang J.F. Gross C.J. → Radford D.C. Gross C.J. → Shapira D. Gross C.J. → Stone N.J. Gross C.J. → Tantawy M.N. Gross C.J. → Thomas J.S. Gross C.J. → Varner R.L. Gross C.J. → Yu C.-H. Gross C.J. → Zamfir N.V. Gross M. → Habs D. Grothkopp P. → Ryjkov V.L. Gryb S. → Behr J.A. Grzywacz R., Karny M., Rykaczewski K.P., Batchelder J.C., Bingham C.R., Fong D., Gross C.J., Krolas W., Mazzocchi C., Piechaczek A., Tantawy M.N., Winger J.A. and Zganjar E.F.: Discovery of the new proton emitter 144 Tm 145 Grzywacz R.: The structure of nuclei near 78 Ni from isomer and decay studies 89 Grzywacz R.K. → Gross C.J. Grzywacz R. → Batchelder J.C. Grzywacz R. → Grawe H. Grzywacz R. → Mazzocchi C. Grzywacz R. → Tantawy M.N. Gu S. → Behr J.A. Gu´enaut C., Audi G., Beck D., Blaum K., Bollen G., Delahaye P., Herfurth F., Kellerbauer A., Kluge H.-J., Lunney D., Schwarz S., Schweikhard L. and Yazidjian C.: Is N = 40 magic? An analysis of ISOLTRAP mass measurements 33 Gu´enaut C., Audi G., Beck D., Blaum K., Bollen G., Delahaye P., Herfurth F., Kellerbauer A., Kluge H.-J., Lunney D., Schwarz S., Schweikhard L. and Yazidjian C.: Extending the mass “backbone” to short-lived nuclides with ISOLTRAP 35 Gu´enaut C. → Bachelet C. Gu´enaut C. → Herfurth F. Gu´enaut C. → Sewtz M. Gueorguiev V.G. and Feng Pan,Draayer J.P.: Application of the extended pairing model to heavy isotopes 515 Guglielmetti A. → Romoli M. Guimar˜ aes V. → Lichtenth¨ aler R. Gulbekian G.G. → Oganessian Yu.Ts. Gulick S. → Clark J.A. Gulick S. → Sharma K.S. Gulino M. → Tumino A. Gupta J.B. → Gore P.M. Gwinner G. → Ryjkov V.L. Haas F. → Corradi L. Haas F. → Keyes K.L. Haas F. → Trotta M. Habs D., Gross M., Heinz S., Kester O., Kolhinen V.S., Neumayr J., Schramm U., Sch¨ atz T., Szerypo J., Thi-

783

rolf P. and Weber C.: Development of a Penning trap system in Munich 57 Habs D. → Block M. Habs D. → Scheit H. Hackman G. → Chakrawarthy R.S. Hackman G. → Sarazin F. Hager U. → Jokinen A. Hager U. → Kankainen A. Hager U. → Penttil¨ a H. Hager U. → Per¨aj¨ arvi K. Hagino K. → Batchelder J.C. Hakala J. → Jokinen A. Hakala J. → Kankainen A. Hakala J. → Penttil¨ a H. Hakala J. → Per¨aj¨ arvi K. Halbert M.L. → Radford D.C. Halbert M.L. → Varner R.L. Hallmann O. → K¨oster U. Hamilton J.H. → Batchelder J.C. Hamilton J.H. → Fong D. Hamilton J.H. → Gore P.M. Hamilton J.H. → Hwang J.K. Hamilton J.H. → Jones E.F. Hamilton J.H. → Luo Y.X. Hamilton J.H. → Mazzocchi C. Hamilton J.H. → Tantawy M.N. Hamilton J.H. → Zhu S.J. Hamilton J. → Gridnev K.A. Hammache F. → Cortina-Gil D. Hammond G. → Becker F. Hammond N.J. → Greenlees P.T. Hammond N. → Robinson A.P. Hammond N. → Seweryniak D. Hanappe F. → Pain S.D. Hanappe F. → Ter-Akopian G.M. Hannawald M. → Kautzsch T. Hansen P.G. → Gade A. Hardy J.C. and Towner I.S.: Superallowed 0+ → 0+ β decay and CKM unitarity: A new overview including more exotic nuclei 695 Hardy J.C. → Clark J.A. Harlin C. → Shapira D. Hartley D.J. → Radford D.C. Hartley D.J. → Tantawy M.N. Hasan M. → Vary J.P. Hasegawa H. → Ong H.J. Hasegawa H. → Yamada K. Hashimoto Y. → Inakura T. Hass M. → Nara Singh B.S. Hatano M., Sakai H., Wakui T., Uesaka T., Aoi N., Ichikawa Y., Ikeda T., Itoh K., Iwasaki H., Kawabata T., Kuboki H., Maeda Y., Matsui N., Ohnishi T., Onishi T.K., Saito T., Sakamoto N., Sasano M., Satou Y., Sekiguchi K., Suda K., Tamii A., Yanagisawa Y. and Yako K.: First experiment of 6 He with a polarized proton target 255 Hauschild K. → Greenlees P.T. Hausladen P.A. → Gross C.J. Hausladen P.A. → Liang J.F.

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Hausladen P.A. → Shapira D. Hausladen P.A. → Varner R.L. Hausladen P.A. → Yu C.-H. Hausladen P.A. → Zamfir N.V. Hausladen P. → Radford D.C. H¨ausser O. → Behr J.A. Hayes A.C. → Vary J.P. Hecht A.A. → Clark J.A. Heenen P.-H. → Bender M. Heinz A. → Clark J.A. Heinz A. → Romoli M. Heinz A. → Sharma K.S. Heinz S. → Block M. Heinz S. → Habs D. Helariutta K. → Kettunen H. Hellstr¨ om M. → Becker F. Hellstr¨ om M. → Datta Pramanik U. Hellstr¨ om M. → Kiselev O.A. Henderson D. → Romoli M. Hennrich S. → Kautzsch T. Hennrich S. → Kratz K.-L. Herbane M. → Rodr´ıguez D. Herfurth F., Audi G., Beck D., Blaum K., Bollen G., Delahaye P., George S., Gu´enaut C., Herlert A., Kellerbauer A., Kluge H.-J., Lunney D., Mukherjee M., Rahaman S., Schwarz S., Schweikhard L., Weber C. and Yazidjian C.: Recent high-precision mass measurements with the Penning trap spectrometer ISOLTRAP 17 Herfurth F. → Bachelet C. Herfurth F. → Block M. Herfurth F. → Gu´enaut C. Herfurth F. → Gu´enaut C. Herfurth F. → Rodr´ıguez D. Herfurth F. → Weber C. Herfurth F. → Weber C. Herfurth F. → Yazidjian C. Herlert A. → Herfurth F. Herzberg R.-D. → Eeckhaudt S. Herzberg R.-D. → Greenlees P.T. Hess H. → Scheit H. Heßberger F.P. → Block M. Hessberger F.P. → Eeckhaudt S. Heßberger F.-P. → Greenlees P.T. anen A.-P. Heßberger F.P. → Lepp¨ Hessberger F.P. → Nara Singh B.S. Heyde K. → Fortunato L. Hiles K. → Benczer-Koller N. Himpe P. → Kowalska M. Hirata D. → Khouaja A. Hirata D. → L´epine-Szily A. Hirsch J.G., Frank A., Barea J., Van Isacker P. and Vel´azquez V.: Bounds on the presence of quantum chaos in nuclear masses 75 Hitt G.W. → Stolz A. Hjorth-Jensen M. → Wloch M. Hoff P. → Mach H. Hoffman C.R. → Mukha I. Hoffman C.R. → Tripathi V.

Hofmann S. → Block M. Hofmann S. → Nara Singh B.S. Hokoiwa N. → Ideguchi E. Honma M., Otsuka T., Brown B.A. and Mizusaki T.: Shell-model description of neutron-rich pf -shell nuclei with a new effective interaction GXPF1 499 Horiuchi H. → Kanada-En’yo Y. Horoi M. → Lisetskiy A.F. Hosmer P.T. → Schatz H. Hoteling N. → Robinson A.P. Hoteling N. → Seweryniak D. Hoteling N. → Shergur J. Houarner Ch. → Pollacco E. Hu Z. → Gade A. Huang W. → Kankainen A. H¨ ubel H. → Becker F. Huber G. → Scheit H. Huerta H. A. → Barr´on-Palos L. Huet-Equilbec C. → K¨ oster U. Hughes R.O. → Zamfir N.V. Huikari J. → Kankainen A. Huikari J. → Penttil¨ a H. Huikari J. → Per¨aj¨ arvi K. Huikari J. → Rinta-Antila S. Humphreys R.D. → Greenlees P.T. Hurst A. → Scheit H. H¨ urstel A. → Eeckhaudt S. H¨ urstel A. → Greenlees P.T. Hussein M.S. → Lichtenth¨ aler R. Huyse M. → Scheit H. Hwang J.K., Ramayya A.V., Hamilton J.H., Fong D., Beyer C.J., Li K., Gore P.M., Jones E.F., Luo Y.X., Rasmussen J.O., Zhu S.J., Wu S.C., Lee I.Y., Stoyer M.A., Cole J.D., Ter-Akopian G.M., Daniel A. and Donangelo R.: Half-life measurement of excited states in neutron-rich nuclei 463 Hwang J.K. → Fong D. Hwang J.K. → Gore P.M. Hwang J.K. → Jones E.F. Hwang J.K. → Luo Y.X. Hwang J.K. → Mazzocchi C. Hwang J.K. → Radford D.C. Hwang J.K. → Tantawy M.N. Hwang J.K. → Zhu S.J. Ichikawa Y. → Hatano M. Ichikawa Y. → Iwasaki H. Ideguchi E., Niikura M., Ishida C., Fukuchi T., Baba H., Hokoiwa N., Iwasaki H., Koike T., Komatsubara T., Kubo T., Kurokawa M., Michimasa S., Miyakawa K., Morimoto K., Ohnishi T., Ota S., Ozawa A., Shimoura S., Suda T., Tamaki M., Tanihata I., Wakabayashi Y., Yoshida K. and Cederwall B.: Study of high-spin states in the 48 Ca region by using secondary fusion reactions 429 Ikeda K. → Masui H. Ikeda T. → Hatano M. Ikin P.J.C. → Eeckhaudt S. Iliev S. → Oganessian Yu.Ts.

Author index

Imagawa H. → Inakura T. Imai N. → Ong H.J. Imai N. → Yamada K. Inakura T., Imagawa H., Hashimoto Y., Yamagami M., Mizutori S. and Matsuyanagi K.: Soft octupole vibrations on superdeformed states in nuclei around 40 Ca suggested by Skyrme-HF and self-consistent RPA calculations 545 Inakura T. → Yoshida K. Inglima G. → Romoli M. IS378 Collaboration → Kratz K.-L. IS393 Collaboration → Kratz K.-L. IS403 Collaboration → Kankainen A. ISOLDE Collaboration → Bachelet C. ISOLDE Collaboration → Mach H. ISOLDE Collaboration → Rinta-Antila S. ISOLDE Collaboration → Shergur J. ISOLDE IS333 Collaboration → Kautzsch T. ISOLDE/IS333 Collaboration → Kratz K.-L. Isaev N.B. → Kiselev O.A. Iseri Y. → Takashina M. Ishida C. → Ideguchi E. Ishihara M. → Iwasaki H. Ishihara M. → Ong H.J. Itahashi K. → Cortina-Gil D. Itkis I.M. → Trotta M. Itkis M.G. → Oganessian Yu.Ts. Itkis M.G. → Trotta M. Itoh K. → Hatano M. Ivanov O. → Scheit H. Iwakoshi T. → Sumikama T. Iwanicki J. → Scheit H. Iwasa N. → Iwasaki H. Iwasa N. → Kanungo R. Iwasa N. → Kanungo R. Iwasa N. → Michimasa S. Iwasaki H., Aoi N., Takeuchi S., Ota S., Sakurai H., Tamaki M., Onishi T.K., Takeshita E., Ong H.J., Iwasa N., Baba H., Elekes Z., Fukuchi T., Ichikawa Y., Ishihara M., Kanno S., Kanungo R., Kawai S., Kubo T., Kurita K., Michimasa S., Niikura M., Saito A., Satou Y., Shimoura S., Suzuki H., Suzuki M.K., Togano Y., Yanagisawa Y. and Motobayashi T.: Intermediate-energy Coulomb excitation of the neutron-rich Ge isotopes around N = 50 415 Iwasaki H. → Hatano M. Iwasaki H. → Ideguchi E. Iwasaki H. → Michimasa S. Iwasaki H. → Ong H.J. Iwasaki H. → Yamada K. Izumikawa T. → Takechi M. Izumikawa T. → Tanaka K. Jackson K.P. → Behr J.A. Jacquot B. → K¨ oster U. Janas Z. → Karny M. Janas Z. → Kavatsyuk M. Janas Z. → Mukha I.

785

J¨ anecke J. and O’Donnell T.W.: Symmetry energies and the curvature of the nuclear mass surface 79 Janik R. → Cortina-Gil D. Janssens R.V.F. → Robinson A.P. Janssens R.V.F. → Seweryniak D. Jardin P. → K¨oster U. Jenkins D.G. → Greenlees P.T. Jenkins D. → Kankainen A. Jensen A.S. → Garrido E. Jiang C.L. → Romoli M. Johansson E.K. → Ekman J. Johnson C.W. → Ter´an E. Johnson M.S. → Jones K.L. Johnson M.S. → Thomas J.S. Johnston-Theasby F. → Pakarinen J. Jokinen A., Eronen T., Hager U., Hakala J., Kopecky ¨ o J.: S., Nieminen A., Rinta-Antila S. and Ayst¨ Ion manipulation and precision measurements at JYFLTRAP 27 Jokinen A. → Kankainen A. Jokinen A. → Mach H. Jokinen A. → Penttil¨ a H. Jokinen A. → Per¨aj¨ arvi K. Jokinen A. → Podadera I. Jokinen A. → Rinta-Antila S. Jokinen A. → Rodr´ıguez D. Jolie J. → Becker F. Jolie J. → Grahn T. Jolie J. → McKay C.J. Jolie J. → McKay C.J. Jolie J. → Werner V. Jollet C. → Gr´evy S. Jollet C. → Mach H. Jones E.F., Hamilton J.H., Gore P.M., Ramayya A.V., Hwang J.K. and deLima A.P.: Identification of levels in 162,164 Gd and decrease in moment of inertia between N = 98–100 467 Jones E.F. → Fong D. Jones E.F. → Gore P.M. Jones E.F. → Hwang J.K. Jones E.F. → Luo Y.X. Jones E.F. → Zhu S.J. Jones G.A. → Chakrawarthy R.S. Jones G.D. → Eeckhaudt S. Jones G.D. → Greenlees P.T. Jones K.L., Baktash C., Bardayan D.W., Blackmon J.C., Catford W.N., Cizewski J.A., Fitzgerald R.P., Greife U., Johnson M.S., Kozub R.L., Livesay R.J., Ma Z., Nesaraja C.D., Shapira D., Smith M.S., Thomas J.S. and Visser D.: Developing techniques to study A ∼ 132 nuclei with (d, p) reactions in inverse kinematics 283 Jones K.L. → Datta Pramanik U. Jones K.L. → Liang J.F. Jones K.L. → Shapira D. Jones K.L. → Thomas J.S. Jones P. → Eeckhaudt S. Jones P. → Grahn T. Jones P. → Greenlees P.T.

786

The European Physical Journal A

Jones P. → Kettunen H. Jones P. → Lepp¨ anen A.-P. Jones P. → Pakarinen J. Jones P. → Uusitalo J. Jonson B. → Cortina-Gil D. Jonson B. → Scheit H. Jouanne C. → Giot L. Julin R. → Eeckhaudt S. Julin R. → Grahn T. Julin R. → Greenlees P.T. Julin R. → Kettunen H. Julin R. → Lepp¨ anen A.-P. Julin R. → Pakarinen J. Julin R. → Uusitalo J. Jungclaus A. → Karny M. Jungclaus A. → Kavatsyuk M. Jungmann K.: Fundamental symmetries and interactions —Some aspects 677 Jurado B. → Mittig W. Jurado B. → Savajols H. Juutinen S. → Eeckhaudt S. Juutinen S. → Grahn T. Juutinen S. → Greenlees P.T. Juutinen S. → Kettunen H. Juutinen S. → Lepp¨ anen A.-P. Juutinen S. → Pakarinen J. Juutinen S. → Uusitalo J. Kailas S. → Adhikari S. Kanada-En’yo Y., Kimura M. and Horiuchi H.: Cluster structure in stable and unstable nuclei 305 Kankaanp¨ a¨ a H. → Greenlees P.T. Kankaanp¨ a¨ a H. → Kettunen H. Kankainen A., Eliseev S.A., Eronen T., Fox S.P., Hager U., Hakala J., Huang W., Huikari J., Jenkins D., Jokinen A., Kopecky S., Moore I., Nieminen A., Novikov Yu.N., Penttil¨ a H., Popov A.V., Rinta-Antila S., Schatz H., Seliverstov D.M., Vorobjev G.K., Wang ¨ o J. and the IS403 Collaboration: BetaY., Ayst¨ delayed gamma and proton spectroscopy near the Z = N line 129 Kankainen A. → Penttil¨ a H. Kankainen A. → Rinta-Antila S. Kanno S. → Iwasaki H. Kanno S. → Michimasa S. Kanno S. → Ong H.J. Kanno S. → Yamada K. Kanungo R., Chiba M., Abu-Ibrahim B., Adhikari S., Fang D.Q., Iwasa N., Kimura K., Maeda K., Nishimura S., Ohnishi T., Ozawa A., Samanta C., Suda T., Suzuki T., Wang Q., Wu C., Yamaguchi Y., Yamada K., Yoshida A., Zheng T. and Tanihata I.: A new view to the structure of 19 C 261 Kanungo R., Chiba M., Abu-Ibrahim B., Adhikari S., Fang D.Q., Iwasa N., Kimura K., Maeda K., Nishimura S., Ohnishi T., Ozawa A., Samanta C., Suda T., Suzuki T., Wang Q., Wu C., Yamaguchi Y., Yamada K., Yoshida A., Zheng T. and Tanihata I.: Observation of a two-proton halo in 17 Ne 327 Kanungo R. → Iwasaki H.

Karny M., Batist L., Banu A., Becker F., Blazhev A., Burkard K., Br¨ uchle W., D¨ oring J., Faestermann T., G´orska M., Grawe H., Janas Z., Jungclaus A., Kavatsyuk M., Kavatsyuk O., Kirchner R., La Commara M., Mandal S., Mazzocchi C., Miernik K., Mukha I., Muralithar S., Plettner C., Plochocki A., Roeckl E., Romoli M., Rykaczewski K., Sch¨adel M., Schmidt K., ˙ Schwengner R. and Zylicz J.: Beta-decay studies near 100 Sn 135 Karny M. → Batchelder J.C. Karny M. → Grzywacz R. Karny M. → Kavatsyuk M. Karny M. → Mazzocchi C. Kartavenko V.G. → Gridnev K.A. Kartavenko V.G. → Gridnev K.A. Karvonen P. → Penttil¨ a H. Karvonen P. → Per¨aj¨ arvi K. Kat¯o K. → Masui H. Kautzsch T., W¨ ohr A., Walters W.B., Kratz K.-L., Pfeiffer B., Hannawald M., Shergur J., Arndt O., Hennrich S., Falahat S., Griesel T., Keller O., Aprahamian A., Brown B.A., Mantica P.F., Stoyer M.A., Ravn H.L. and the ISOLDE IS333 and Rochester CHICO/Gammasphere Collaborations: Structure of neutron-rich even-even 124,126 Cd 117 Kavatsyuk M., Kavatsyuk O., Batist L., Banu A., Becker F., Blazhev A., Br¨ uchle W., Burkard K., D¨ oring J., Faestermann T., G´ orska M., Grawe H., Janas Z., Jungclaus A., Karny M., Kirchner R., La Commara M., Mandal S., Mazzocchi C., Mukha I., Muralithar S., Plettner C., Plochocki A., Roeckl E., Romoli M., ˙ Sch¨adel M., Schwengner R. and Zylicz J.: Beta-decay spectroscopy of 103,105 Sn 139 Kavatsyuk M. → Karny M. Kavatsyuk O. → Karny M. Kavatsyuk O. → Kavatsyuk M. Kawabata T. → Hatano M. Kawai S. → Iwasaki H. Kawai S. → Ong H.J. Keenan A. → Greenlees P.T. Keenan A. → Kettunen H. Keller O. → Kautzsch T. Kellerbauer A. → Gu´enaut C. Kellerbauer A. → Gu´enaut C. Kellerbauer A. → Herfurth F. Kellerbauer A. → Rodr´ıguez D. Kellerbauer A. → Weber C. Kemper K.W. → Gade A. Kenneally J.M. → Oganessian Yu.Ts. Kenneally J.M. → Stoyer M.A. Kepinski J.F. → Podadera I. K´epinski J.F. → Sewtz M. Kester O. → Habs D. Kester O. → Scheit H. Kettunen H., Enqvist T., Eskola K., Grahn T., Greenlees P.T., Helariutta K., Jones P., Julin R., Juutinen S., Kankaanp¨ a¨a H., Keenan A., Koivisto H., Kuusiniemi P., Leino M., Lepp¨ anen A.-P., Miukku M., Nieminen P., Pakarinen J., Rahkila P. and Uusitalo J.: Decay

Author index

studies of neutron-deficient odd-mass At and Bi isotopes 181 Kettunen H. → Eeckhaudt S. Kettunen H. → Grahn T. Kettunen H. → Greenlees P.T. Kettunen H. → Lepp¨ anen A.-P. Kettunen H. → Pakarinen J. Kettunen H. → Uusitalo J. Keyes K.L., Papenberg A., Chapman R., Ollier J., Liang X., Burns M.J., Labiche M., Spohr K.-M., Amzal N., Beck C., Bednarczyk P., Haas F., Duchˆene G., Papka P., Gebauer B., Kokalova T., Thummerer S., von Oertzen W. and Wheldon C.: Spectroscopy of Ne and Na isotopes: Preliminary results from a EUROBALL + Binary Reaction Spectrometer experiment 431 Khalfallah F. → Greenlees P.T. Khan E. → Goriely S. Khiem L.H. → Datta Pramanik U. Khoo T.L. → Eeckhaudt S. Khoo T.L. → Greenlees P.T. Khoo T.L. → Robinson A.P. Khoo T.L. → Seweryniak D. Khouaja A., Villari A.C.C., Benjelloun M., Auger G., Baiborodin D., Catford W., Chartier M., Demonchy C.E., Dlouhy Z., Gillibert A., Giot L., Hirata D., L´epine-Szily A., Mittig W., Orr N., Penionzhkevich Y., Pitae S., Roussel-Chomaz P., Saint-Laurent M.G. and Savajols H.: Reaction cross-sections and reduced strong absorption radii of nuclei in the vicinity of closed shells N = 20 and N = 28 223 Khouaja A. → Savajols H. Kim Au V. → Agrawal B.K. Kimura K. → Kanungo R. Kimura K. → Kanungo R. Kimura M. → Kanada-En’yo Y. Kinnard V. → Ter-Akopian G.M. Kirchner R. → Karny M. Kirchner R. → Kavatsyuk M. Kirchner R. → Mukha I. Kirchner R. → N¨ ortersh¨auser W. Kiselev O.A., Aksouh F., Bleile A., Bochkarev O.V., Chulkov L.V., Cortina-Gil D., Dobrovolsky A.V., Egelhof P., Geissel H., Hellstr¨ om M., Isaev N.B., Komkov B.G., M´ atos M., Moroz F.V., M¨ unzenberg G., Mutterer M., Mylnikov V.A., Neumaier S.R., Pribora V.N., Seliverstov D.M., Sergueev L.O., Shrivastava A., S¨ ummerer K., Weick H., Winkler M. and Yatsoura V.I.: Investigation of nuclear matter distribution of the neutron-rich He isotopes by proton elastic scattering at intermediate energies 215 Kitagawa A. → Takechi M. Kluge H.-J. → Block M. Kluge H.-J. → Gu´enaut C. Kluge H.-J. → Gu´enaut C. Kluge H.-J. → Herfurth F. Kluge H.-J. → N¨ ortersh¨ auser W. Kluge H.-J. → Rodr´ıguez D. Kluge H.-J. → Weber C. Kluge H.-J. → Weber C.

787

Kmiecik M. → Becker F. Kniajeva G.N. → Trotta M. Kobayasi M., Nakatsukasa T., Matsuo M. and Matsuyanagi K.: Collective path connecting the oblate and prolate local minima in proton-rich N = Z nuclei around 68 Se 547 K¨ock F. → Scheit H. Koike T. → Ideguchi E. Koivisto H. → Kettunen H. Kojouharov I. → Becker F. Kojouharov I. → Nara Singh B.S. Kokalova T. → Keyes K.L. Kolata J.J. → Boutachkov P. Kolata J.J. → Liang J.F. Kolata J.J. → Shapira D. Kolata J. → Lichtenth¨ aler R. Kolhinen V.S. → Habs D. Kolhinen V.S. → Rinta-Antila S. Kolhinen V.S. → Rodr´ıguez D. Kolhinen V. → Block M. Komatsubara T. → Ideguchi E. Komkov B.G. → Kiselev O.A. Kondratiev N.A. → Trotta M. Koopmans K.A. → Sarazin F. Kopecky S. → Jokinen A. Kopecky S. → Kankainen A. Kopecky S. → Penttil¨ a H. Korgul A., Mach H., Brown B.A., Covello A., Gargano A., Fogelberg B., Schuber R., Kurcewicz W., WernerMalento E., Orlandi R. and Sawicka M.: On the structure of the anomalously low-lying 5/2+ state of 135 Sb 123 Korgul A. → Mach H. Korsheninnikov A.A. → Ter-Akopian G.M. Korten W. → Eeckhaudt S. Korten W. → Greenlees P.T. K¨ oster U., Arndt O., Bergmann U.C., Catherall R., Cederk¨all J., Dillmann I., Dubois M., Durantel F., Fraile L., Franchoo S., Gaubert G., Gaudefroy L., Hallmann O., Huet-Equilbec C., Jacquot B., Jardin P., Kratz K.L., Lecesne N., Leroy R., Lopez A., Maunoury L., Pacquet J.Y., Pfeiffer B., Saint-Laurent M.G., Stodel C., Villari A.C.C. and Weissman L.: ISOL beams of neutron-rich oxygen isotopes 729 K¨oster U. → Mach H. K¨oster U. → Scheit H. Kowalska M., Yordanov D., Blaum K., Borremans D., Himpe P., Lievens P., Mallion S., Neugart R., Neyens G. and Vermeulen N.: Laser and β-NMR spectroscopy on neutron-rich magnesium isotopes 193 Kowalski K. → Wloch M. Koyama R. → Takechi M. Kozhuharov C. → Weber C. Kozub R.L. → Bardayan D.W. Kozub R.L. → Jones K.L. Kozub R.L. → Thomas J.S. Kozulin E.M. → Trotta M. Kratz J.V. → Datta Pramanik U.

788

The European Physical Journal A

Kratz K.-L., Pfeiffer B., Arndt O., Hennrich S., W¨ ohr A., the ISOLDE/IS333, IS378 and IS393 Collaborations: r-process isotopes in the 132 Sn region 633 Kratz K.-L. → Kautzsch T. Kratz K.L. → K¨ oster U. Kratz K.-L. → Schatz H. Kratz K.-L. → Shergur J. Krolas W. → Batchelder J.C. Krolas W. → Gross C.J. Krolas W. → Grzywacz R. Kr´olas W. → Mazzocchi C. Krolas W. → Radford D.C. Kr´olas W. → Tantawy M.N. Krolas W. → Yu C.-H. Kr¨ oll T. → Grahn T. Kr¨ oll T. → Scheit H. Kr¨ ucken R. → Grahn T. ucken R. → Scheit H. Kr¨ Kr¨ ucken R. → Werner V. Krupko S.A. → Ter-Akopian G.M. Kubo T. → Ideguchi E. Kubo T. → Iwasaki H. Kubo T. → Ong H.J. Kubo T. → Yamada K. Kuboki H. → Hatano M. Kubono S. → Michimasa S. Kudo S. → Tanaka K. K¨ uhl Th. → N¨ ortersh¨ auser W. Kulessa R. → Datta Pramanik U. Kulp W.D. → Sarazin F. Kumar A., Orce J.N., Lesher S.R., McKay C.J., McEllistrem M.T. and Yates S.W.: Lifetime measurements and low-lying structure in 112 Sn 443 Kumbartzki G. → Benczer-Koller N. Kumbartzki G. → Stone N.J. Kurcewicz W. → Korgul A. Kurcewicz W. → Mach H. Kurgalin S.D. → Chuvilskaya T.V. Kurita K. → Iwasaki H. Kurita K. → Michimasa S. Kurita K. → Ong H.J. Kurita K. → Yamada K. Kurokawa M. → Ideguchi E. Kurokawa M. → Michimasa S. Kurpeta J. → Per¨ aj¨ arvi K. Kurz N. → Becker F. Kuusiniemi P. → Eeckhaudt S. Kuusiniemi P. → Greenlees P.T. Kuusiniemi P. → Kettunen H. Kuusiniemi P. → Lepp¨ anen A.-P. Kuusiniemi P. → Nara Singh B.S. Kuusiniemi P. → Uusitalo J. Kwan E. → Stolz A. Labalme M. → Rodr´ıguez D. Labiche M. → Catford W.N. Labiche M. → Keyes K.L. Labiche M. → Pain S.D. La Cognata M. → Tumino A.

La Commara M. → Karny M. La Commara M. → Kavatsyuk M. La Commara M. → Mukha I. La Commara M. → Romoli M. Lalazissis G.A. → Vretenar D. Lamia L. → Tumino A. Lamm L.O. → Boutachkov P. Lapoux V. → Giot L. Lapoux V. → Pollacco E. Lapoux V. → Ter-Akopian G.M. Larochelle Y. → Liang J.F. Larochelle Y. → Radford D.C. Larochelle Y. → Tantawy M.N. Larochelle Y. → Varner R.L. Latina A. → Corradi L. Latina A. → Trotta M. Lauer M. → Scheit H. Laurent B. → Gr´evy S. Lavergne L. → Pollacco E. Lawton D. → Ringle R. Lawton D. → Schury P. Lawton D. → Sun T. Lazar M. → Gr´evy S. Leberthe G. → Pollacco E. Leccia E. → Sewtz M. Lecesne N. → K¨oster U. Lecouey J.L. → Pain S.D. Le Coz Y. → Eeckhaudt S. Le Coz Y. → Greenlees P.T. Le Du D. → Sewtz M. Lee B. → Behr J.A. Lee D. → Per¨aj¨ arvi K. Lee I.Y. → Fong D. Lee I.Y. → Gore P.M. Lee I.Y. → Hwang J.K. Lee I.Y. → Luo Y.X. Lee I.Y. → Zhu S.J. Lee J.K.P. → Clark J.A. Lee J.K.P. → Sharma K.S. Lee J. → Ryjkov V.L. Leifels Y. → Datta Pramanik U. Leino M. → Eeckhaudt S. Leino M. → Grahn T. Leino M. → Greenlees P.T. Leino M. → Kettunen H. Leino M. → Lepp¨anen A.-P. Leino M. → Pakarinen J. Leino M. → Uusitalo J. Lemmon R.C. → Catford W.N. Lemmon R.C. → Pain S.D. L´epine-Szily A., Lima G.F., Villari A.C.C., Mittig W., Lichtenth¨ aler R., Chartier M., Orr N.A., Ang´elique J.C., Audi G., Casandjian J.M., Cunsolo A., Donzaud C., Foti A., Gillibert A., Hirata D., Lewitowicz M., Lukyanov S., MacCormick M., Morrissey D.J., Ostrowski A.N., Sherrill B.M., Stephan C., Suomij¨ arvi T., Tassan-Got L., Vieira D.J. and Wouters J.M.: Anomalous behaviour of matter radii of proton-rich Ga, Ge, As, Se and Br nuclei 227

Author index

L´epine-Szily A. → Khouaja A. L´epine-Szily A. → Lichtenth¨ aler R. Lepp¨ anen A.-P., Uusitalo J., Eeckhaudt S., Enqvist T., Eskola K., Grahn T., Heßberger F.P., Greenlees P.T., Jones P., Julin R., Juutinen S., Kettunen H., Kuusiniemi P., Leino M., Nieminen P., Pakarinen J., Perkowski J., Rahkila P., Scholey C. and Sletten G.: Alpha-decay study of 218 U; a search for the sub-shell closure at Z = 92 183 Lepp¨anen A.-P. → Eeckhaudt S. Lepp¨anen A.-P. → Grahn T. Lepp¨anen A.-P. → Greenlees P.T. Lepp¨anen A.-P. → Kettunen H. Lepp¨anen A.-P. → Pakarinen J. Lepp¨anen A.-P. → Uusitalo J. Leroy R. → K¨ oster U. Lesher S.R. → Kumar A. Lesher S.R. → McKay C.J. Lesher S.R. → McKay C.J. Leslie J.R. → Sarazin F. Leterrier L. → Pollacco E. Levand A.F. → Clark J.A. Le Ven V. → Pollacco E. Levenfish K.P. → Yakovlev D.G. Lewitowicz M. → L´epine-Szily A. Lhersonneau G. → Rinta-Antila S. Li K. → Fong D. Li K. → Gore P.M. Li K. → Hwang J.K. Li K. → Zhu S.J. Liang J.F., Shapira D., Gross C.J., Varner R.L., Amro H., Beene J.R., Bierman J.D., Caraley A.L., GalindoUribarri A., Gomez del Campo J., Hausladen P.A., Jones K.L., Kolata J.J., Larochelle Y., Loveland W., Mueller P.E., Peterson D., Radford D.C. and Stracener D.W.: Sub-barrier fusion induced by neutron-rich radioactive 132 Sn 239 Liang J.F. → Bardayan D.W. Liang J.F. → Radford D.C. Liang J.F. → Romoli M. Liang J.F. → Shapira D. Liang J.F. → Thomas J.S. Liang J.F. → Varner R.L. Liang J.F. → Yu C.-H. Liang X. → Keyes K.L. Lichtenth¨ aler R., L´epine-Szily A., Guimar˜ aes V., Perego C., Placco V., Camargo O. jr., Denke R., de Faria P.N., Benjamim E.A., Added N., Lima G.F., Hussein M.S., Kolata J. and Arazi A.: Radioactive Ion beams in Brazil (RIBRAS) 733 Lichtenth¨ aler R. → L´epine-Szily A. Liddick S.N. → Mazzocchi C. Liddick S.N. → Schatz H. Liddick S.N. → Tripathi V. Lieb P. → Scheit H. Li´enard E. → Gr´evy S. Li´enard E. → Rodr´ıguez D. Lievens P. → Kowalska M. Liljeby L. → Scheit H.

789

Lima G.F. → L´epine-Szily A. Lima G.F. → Lichtenth¨ aler R. Lindroos M. → Podadera I. Linnemann A. → McKay C.J. Linnemann A. → McKay C.J. Lisetskiy A.F., Brown B.A. and Horoi M.: Exotic nuclei near 78 Ni in a shell model approach 95 Litvinov Y. → Chakrawarthy R.S. Liu Z. → Robinson A.P. Liu Z. → Seweryniak D. Livesay R.J. → Jones K.L. Livesay R.J. → Thomas J.S. Lloyd R. → Vary J.P. Lobanov Yu.V. → Oganessian Yu.Ts. L  ojewski Z. → Baran A. Lopez A. → K¨oster U. Lougheed R.W. → Oganessian Yu.Ts. Loveland W.: Fusion studies with RIBs 233 Loveland W. → Liang J.F. Loveland W. → Shapira D. Lozeva R. → Becker F. Lugiez F. → Pollacco E. Lukyanov A. L´epine-Szily S. → Savajols H. Lukyanov S. → L´epine-Szily A. Lundgren B.F. → Clark J.A. Lunney D.: Latest trends in the ever-surprising field of mass measurements 3 Lunney D. → Bachelet C. Lunney D. → Gu´enaut C. Lunney D. → Gu´enaut C. Lunney D. → Herfurth F. Lunney D. → Podadera I. Lunney D. → Sewtz M. Lunney D. → Weber C. Luo Y.X., Rasmussen J.O., Hamilton J.H., Ramayya A.V., Gelberg A., Stefanescu I., Hwang J.K., Zhu S.J., Gore P.M., Fong D., Jones E.F., Wu S.C., Lee I.Y., Ginter T.N., Ma W.C., Ter-Akopian G.M., Daniel A.V., Stoyer M.A. and Donangelo R.: Shape transitions and triaxiality in neutron-rich odd-mass Y and Nb isotopes 469 Luo Y.X. → Fong D. Luo Y.X. → Gore P.M. Luo Y.X. → Hwang J.K. Luo Y.X. → Zhu S.J. Lutter R. → Scheit H. Ma W.C. → Gore P.M. Ma W.C. → Luo Y.X. Ma W.C. → Zhu S.J. Ma Z. → Bardayan D.W. Ma Z. → Jones K.L. Ma Z. → Thomas J.S. MacCormick M. → L´epine-Szily A. Mach H., Fraile L.M., Tengblad O., Boutami R., Jollet C., Pl´ociennik W.A., Yordanov D.T., Stanoiu M., Borge M.J.G., Butler P.A., Cederk¨ all J., Dessagne Ph., Fogelberg B., Fynbo H., Hoff P., Jokinen A., Korgul A., K¨oster U., Kurcewicz W., Marechal F., Motobayashi

790

The European Physical Journal A

T., Mrazek J., Neyens G., Nilsson T., Pedersen S., Poves A., Rubio B., Ruchowska E. and the ISOLDE Collaboration: New structure information on 30 Mg, 31 Mg and 32 Mg 105 Mach H. → Korgul A. Mackintosh R.S. → Giot L. Maeda K. → Kanungo R. Maeda K. → Kanungo R. Maeda Y. → Hatano M. Mahboub D. → Pain S.D. Maierbeck P. → Grahn T. Maier-Komor P. → Benczer-Koller N. Maj A. → Becker F. Mallion S. → Kowalska M. Mandal S. → Becker F. Mandal S. → Cortina-Gil D. Mandal S. → Karny M. Mandal S. → Kavatsyuk M. Mantica P.F.: β-decay studies of neutron-rich nuclei 83 Mantica P.F. → Kautzsch T. Mantica P.F. → Mazzocchi C. Mantica P.F. → Schatz H. Mantica P.F. → Tripathi V. Mar´echal F. → Gr´evy S. Marechal F. → Mach H. Marginean N. → Corradi L. Marginean N. → Tonev D. Markenroth K. → Cortina-Gil D. Marketin T. → Paar N. Marqu´es Moreno Fco. Miguel: Multineutron clusters 311 Marsh B. → Penttil¨ a H. Martin B. → Romoli M. Mart´ınez-Pinedo G.: Shell-model applications in supernova physics 659 Mart´ınez Q. E. → Barr´ on-Palos L. Marx G. → Block M. Marx G. → Weber C. Mas J. → Varner R.L. Masone V. → Romoli M. Masui H., Myo T., Kat¯ o K. and Ikeda K.: Study of dripline nuclei with a core plus multi-valence nucleon model 505 Matea I. → Blank B. Materna T. → Ter-Akopian G.M. M´ atos M. → Kiselev O.A. Matsubara H. → Takechi M. Matsui N. → Hatano M. Matsumasa T. → Takechi M. Matsuo M., Mizuyama K. and Serizawa Y.: Di-neutron correlations in medium-mass neutron-rich nuclei near the dripline 563 Matsuo M. → Kobayasi M. Matsuta K. → Sumikama T. Matsuta K. → Takechi M. Matsuta K. → Tanaka K. Matsuyama Y.U. → Ong H.J. Matsuyama Y.U. → Yamada K. Matsuyanagi K. → Inakura T. Matsuyanagi K. → Kobayasi M.

Matsuyanagi K. → Yoshida K. Mauger F. → Rodr´ıguez D. Maunoury L. → K¨oster U. Mayet P. → Scheit H. Mazur A.I. → Vary J.P. Mazzocchi C., Grzywacz R., Batchelder J.C., Bingham C.R., Fong D., Hamilton J.H., Hwang J.K., Karny M., Kr´olas W., Liddick S.N., Morton A.C., Mantica P.F., Mueller W.F., Rykaczewski K.P., Steiner M., Stolz A. and Winger J.A.: Beta-delayed γ and neutron emission near the double shell closure at 78 Ni 93 Mazzocchi C. → Batchelder J.C. Mazzocchi C. → Gross C.J. Mazzocchi C. → Grzywacz R. Mazzocchi C. → Karny M. Mazzocchi C. → Kavatsyuk M. Mazzocchi C. → Mukha I. Mazzocchi C. → Tantawy M.N. Mazzocco M. → Romoli M. McCutchan E.A., Zamfir N.V. and Casten R.F.: Groundstate properties and phase/shape transitions in the IBA 435 McCutchan E.A. → Werner V. McCutchan E.A. → Zamfir N.V. McEllistrem M.T. → Kumar A. McEllistrem M.T. → McKay C.J. McEllistrem M.T. → McKay C.J. McKay C.J., Orce J.N., Lesher S.R., Bandyopadhyay D., McEllistrem M.T., Fransen C., Jolie J., Linnemann A., Pietralla N., Werner V. and Yates S.W.: Identification of mixed-symmetry states in odd-A 93 Nb 377 McKay C.J., Orce J.N., Lesher S.R., Bandyopadhyay D., McEllistrem M.T., Fransen C., Jolie J., Linnemann A., Pietralla N., Werner V. and Yates S.W.: Identification of mixed-symmetry states in odd-A 93 Nb 773 (Erratum) McKay C.J. → Kumar A. McMahan M.A. → Benczer-Koller N. Meczynski W. → Becker F. Meister M. → Cortina-Gil D. Melconian D. → Behr J.A. Melconian D. → Sarazin F. Mertzimekis T.J. → Benczer-Koller N. M´ery A. → Rodr´ıguez D. Meyer D.A. → Grahn T. Mezentsev A.N. → Oganessian Yu.Ts. Michel N., Nazarewicz W., Ploszajczak M. and Rotureau J.: Shell-model description of weakly bound and unbound nuclear states 493 Michel N., Nazarewicz W. and Ploszajczak M.: Effects of the continuum coupling on spin-orbit splitting 503 Michimasa S., Shimoura S., Iwasaki H., Tamaki M., Ota S., Aoi N., Baba H., Iwasa N., Kanno S., Kubono S., Kurita K., Kurokawa M., Minemura T., Motobayashi T., Notani M., Ong H.J., Saito A., Sakurai H., Takeuchi S., Takeshita E., Yanagisawa Y. and Yoshida A.: Study of single-particle states in 23 F using proton transfer reaction 367 Michimasa S. → Ideguchi E.

Author index

Michimasa S. → Iwasaki H. Michimasa S. → Ong H.J. Michimasa S. → Yamada K. Miernik K. → Karny M. Mihara M. → Sumikama T. Mihara M. → Takechi M. Mihara M. → Tanaka K. Millener D.J.: Beta decays of 8 He, 9 Li, and 9 C 97 Million B. → Becker F. Mills A. → Behr J.A. Minamisono K. → Sumikama T. Minamisono T. → Sumikama T. Minamisono T. → Takechi M. Minamisono T. → Tanaka K. Minemura T. → Michimasa S. Minemura T. → Ong H.J. Minemura T. → Yamada K. Mitroshin V.E. → Gridnev K.A. Mittig W., Demonchy C.E., Wang H., Roussel-Chomaz P., Jurado B., Gelin M., Savajols H., Fomichev A., Rodin A., Gillibert A., Obertelli A., Cortina-Gil M.D., Caama˜ no M., Chartier M. and Wolski R.: Reactions induced beyond the dripline at low energy by secondary beams 263 Mittig W. and Villari A.C.C.: GANIL and the SPIRAL2 project 737 Mittig W. → Giot L. Mittig W. → Khouaja A. Mittig W. → L´epine-Szily A. Mittig W. → Savajols H. Mittig W. → Ter-Akopian G.M. Miukku M. → Kettunen H. Miyakawa K. → Ideguchi E. Mizusaki T. → Honma M. Mizutori S. → Inakura T. Mizutori S. → Yoshida K. Mizuyama K. → Matsuo M. Moazen B.H. → Thomas J.S. Mocko M. → Cortina-Gil D. Mocko M. → Stolz A. M¨ oller O. → Grahn T. M¨ oller O. → Tonev D. Momota S. → Takechi M. Momota S. → Tanaka K. Montagnoli G. → Corradi L. Montagnoli G. → Trotta M. Montes F. → Schatz H. Moody K.J. → Oganessian Yu.Ts. Moody K.J. → Stoyer M.A. Moore E.F. → Romoli M. Moore I. → Kankainen A. Moore I. → Penttil¨ a H. aj¨ arvi K. Moore I. → Per¨ Moore R.B. → Clark J.A. Moreno E. → Barr´ on-Palos L. Morimoto K. → Ideguchi E. Moro A.M. → Nunes F.M. Moroz F.V. → Kiselev O.A. Morrissey D.J. → L´epine-Szily A.

791

Morrissey D.J. → Schury P. Morton A.C. → Chakrawarthy R.S. Morton A.C. → Mazzocchi C. Morton A.C. → Schatz H. Motobayashi T. → Iwasaki H. Motobayashi T. → Mach H. Motobayashi T. → Michimasa S. Motobayashi T. → Ong H.J. Motobayashi T. → Yamada K. Mr´azek J. → Gr´evy S. Mrazek J. → Mach H. Mrazek J. → Savajols H. Mueller P.E. → Liang J.F. Mueller P.E. → Radford D.C. Mueller P.E. → Shapira D. Mueller P.E. → Varner R.L. Mueller W.F. → Gade A. Mueller W.F. → Mazzocchi C. Mueller W.F. → Schatz H. Mueller W.F. → Tripathi V. Muikku M. → Greenlees P.T. Mukha I., Roeckl E., Grawe H., D¨ oring J., Batist L., Blazhev A., Hoffman C.R., Janas Z., Kirchner R., La Commara M., Dean S., Mazzocchi C., Plettner C., Tabor S.L. and Wiedeking M.: Study of the (21+ ) isomer in 94 Ag 131 Mukha I. → Grawe H. Mukha I. → Karny M. Mukha I. → Kavatsyuk M. Mukhamedzhanov A.M. → Nunes F.M. Mukherjee G. → Robinson A.P. Mukherjee G. → Seweryniak D. Mukherjee M. → Block M. Mukherjee M. → Herfurth F. Mukherjee M. → Weber C. M¨ unch M. → Scheit H. M¨ unzenberg G. → Cortina-Gil D. M¨ unzenberg G. → Datta Pramanik U. M¨ unzenberg G. → Kiselev O.A. Muralithar S. → Becker F. Muralithar S. → Karny M. Muralithar S. → Kavatsyuk M. Murillo O. G. → Barr´on-Palos L. Musumarra A. → Tumino A. Mutterer M. → Kiselev O.A. Mylnikov V.A. → Kiselev O.A. Myo T. → Masui H. Nagatomo T. → Sumikama T. Nakamura T. and Fukuda N.: Breakup reactions of halo nuclei 325 Nakashima Y. → Sumikama T. Nakashima Y. → Takechi M. Nakatsukasa T. and Yabana K.: Unrestricted TDHF studies of nuclear response in the continuum 527 Nakatsukasa T. → Kobayasi M. Nakatsukasa T. → Ohta H. Nalpas L. → Giot L. Nalpas L. → Pollacco E.

792

The European Physical Journal A

Nalpas L. → Ter-Akopian G.M. Nara Singh B.S., Hass M., Goldring G., Ackermann D., Gerl J., Hessberger F.P., Hofmann S., Kojouharov I., Kuusiniemi P., Schaffner H., Sulignano B. and Brown B.A.: Parity non-conservation in the γ-decay of polarized 17/2− isomers in 93 Tc 703 Naviliat-Cuncic O. → Rodr´ıguez D. Navr´ atil P., Ormand W.E., Forss´en C. and Caurier E.: Ab initio no-core shell model calculations using realistic two- and three-body interactions 481 Navr´ atil P. → Stetcu I. Navr´ atil P. → Vary J.P. Nazarewicz W. → Dobaczewski J. Nazarewicz W. → Michel N. Nazarewicz W. → Michel N. Nazarewicz W. → Stoitcheva G. Nazarewicz W. → Stoitsov M.V. Nazarewicz W. → Terasaki J. Negoita A.G. → Vary J.P. Negoita F. → Gr´evy S. Nesaraja C.D. → Jones K.L. Nesaraja C.D. → Thomas J.S. Neugart R. → Kowalska M. Neumaier S.R. → Kiselev O.A. Neumayr J.B. → Block M. Neumayr J. → Habs D. Neyens G. → Kowalska M. Neyens G. → Mach H. Nguyen Van Giai → Yamagami M. Niedermaier O. → Scheit H. Nieminen A. → Jokinen A. Nieminen A. → Kankainen A. Nieminen A. → Penttil¨ a H. Nieminen A. → Rinta-Antila S. Nieminen P. → Eeckhaudt S. Nieminen P. → Grahn T. Nieminen P. → Greenlees P.T. Nieminen P. → Kettunen H. Nieminen P. → Lepp¨ anen A.-P. Nieminen P. → Pakarinen J. Nieminen P. → Uusitalo J. Niikura M. → Ideguchi E. Niikura M. → Iwasaki H. Nikolova V. → Fetea M.S. Nikolskii E.Yu. → Ter-Akopian G.M. Nikˇsi´c T. → Paar N. Nikˇsi´c T. → Vretenar D. Nilsson T. → Mach H. Nilsson T. → Scheit H. Ninane A. → Pain S.D. Nishimura S. → Kanungo R. Nishimura S. → Kanungo R. Nociforo C. → Datta Pramanik U. Nogga A. → Vary J.P. Normand G. → Pain S.D. N¨ortersh¨ auser W., Bushaw B.A., Dax A., Drake G.W.F., Ewald G., G¨ otte S., Kirchner R., Kluge H.-J., K¨ uhl Th., Sanchez R., Wojtaszek A., Yan Z.-C. and Zim-

mermann C.: Measurement of the nuclear charge radii of 8,9 Li 199 Notani M. → Michimasa S. Notani M. → Ong H.J. Notani M. → Yamada K. Novikov Yu.N. → Kankainen A. Nowacki F. → Grawe H. Nummela S. → Rinta-Antila S. Nunes F.M., Moro A.M., Mukhamedzhanov A.M. and Summers N.C.: Progress on reactions with exotic nuclei 295 Nunes F.M. → Summers N.C. Nyman M. → Grahn T. Nyman M. → Pakarinen J. Nyman M. → Uusitalo J. Oberacker V.E. → Blazkiewicz A. Oberacker V.E. → Umar A.S. Obertelli A. → Mittig W. Odahara A., Wakabayashi Y., Fukuchi T., Gono Y. and Sagawa H.: High-spin shape isomers and the nuclear Jahn-Teller effect 375 O’Donnell T.W. → J¨anecke J. Oganessian Yu.Ts., Utyonkov V.K., Lobanov Yu.V., Abdullin F.Sh., Polyakov A.N., Shirokovsky I.V., Tsyganov Yu.S., Gulbekian G.G., Bogomolov S.L., Gikal B.N., Mezentsev A.N., Iliev S., Subbotin V.G., Sukhov A.M., Voinov A.A., Buklanov G.V., Subotic K., Zagrebaev V.I., Itkis M.G., Patin J.B., Moody K.J., Wild J.F., Stoyer M.A., Stoyer N.J., Shaughnessy D.A., Kenneally J.M., Wilk P.A. and Lougheed R.W.: New elements from Dubna 589 Oganessian Yu.Ts. → Gore P.M. Oganessian Yu.Ts. → Stoyer M.A. Oganessian Yu.Ts. → Ter-Akopian G.M. Ogura M. → Sumikama T. Ohnishi T. → Hatano M. Ohnishi T. → Ideguchi E. Ohnishi T. → Kanungo R. Ohnishi T. → Kanungo R. Ohta H., Nakatsukasa T. and Yabana K.: Light exotic nuclei studied with the parity-projected Hartree-Fock method 549 Ohtsubo T. → Cortina-Gil D. Ohtsubo T. → Takechi M. Ohtubo T. → Tanaka K. Oinonen M. → Rodr´ıguez D. Oinonen M. → Scheit H. Okolowicz J. → Rotureau J. Okunev I.S. → Chuvilskaya T.V. Olivier L. → Pollacco E. Ollier J. → Keyes K.L. Olliver H. → Gade A. Ong H.J., Imai N., Aoi N., Sakurai H., Dombr´ adi Zs., Saito A., Elekes Z., Baba H., Demichi K., F¨ ul¨ op Zs., Gibelin J., Gomi T., Hasegawa H., Ishihara M., Iwasaki H., Kanno S., Kawai S., Kubo T., Kurita K., Matsuyama Y.U., Michimasa S., Minemura T., Motobayashi T., Notani M., Ota S., Sakai H.K., Shimoura

Author index

S., Takeshita E., Takeuchi S., Tamaki M., Togano Y., Yamada K., Yanagisawa Y. and Yoneda K.: Inelastic proton scattering on 16 C 347 Ong H.J. → Iwasaki H. Ong H.J. → Michimasa S. Ong H.J. → Yamada K. Onishi K. T. → Yamada K. Onishi T. → Tanaka K. Onishi T.K. → Hatano M. Onishi T.K. → Iwasaki H. Orce J.N. → Kumar A. Orce J.N. → McKay C.J. Orce J.N. → McKay C.J. Orlandi R. → Korgul A. Ormand W.E. → Navr´ atil P. Ormand W.E. → Vary J.P. Orr N.A. → Catford W.N. Orr N.A. → L´epine-Szily A. Orr N.A. → Pain S.D. Orr N. → Khouaja A. Orr N. → Savajols H. Ortiz M.E. → Barr´on-Palos L. Osborne C.J. → Sarazin F. Osborne C.J. → Sikler G. Ostrowski A.N. → L´epine-Szily A. Ota S. → Ideguchi E. Ota S. → Iwasaki H. Ota S. → Michimasa S. Ota S. → Ong H.J. Ota S. → Yamada K. Otsuka T. → Honma M. Ottarson J. → Schury P. Ouellette M. → Schatz H. Ozawa A. → Cortina-Gil D. Ozawa A. → Ideguchi E. Ozawa A. → Kanungo R. Ozawa A. → Kanungo R. Ozawa A. → Tanaka K. Ozawa A. → Yamada K. Paar N., Nikˇsi´c T., Marketin T., Vretenar D. and Ring P.: Self-consistent relativistic QRPA studies of soft modes and spin-isospin resonances in unstable nuclei 531 Pacquet J.Y. → K¨ oster U. Padilla E. → Radford D.C. Padilla E. → Yu C.-H. Padilla-Rodal E. → Varner R.L. Page R. → Pakarinen J. Pain S.D., Catford W.N., Orr N.A., Angelique J.C., Ashwood N.I., Bouchat V., Clarke N.M., Curtis N., Freer M., Fulton B.R., Hanappe F., Labiche M., Lecouey J.L., Lemmon R.C., Mahboub D., Ninane A., Normand G., Soi´c N., Stuttge L., Timis C.N., Tostevin J.A., Winfield J.S. and Ziman V.: Experimental evidence of a ν(1d5/2 )2 component to the 12 Be ground state 349 Pakarinen J., Darby I., Eeckhaudt S., Enqvist T., Grahn T., Greenlees P., Johnston-Theasby F., Jones P.,

793

Julin R., Juutinen S., Kettunen H., Leino M., Lepp¨anen A.-P., Nieminen P., Nyman M., Page R., Raddon P., Rahkila P., Scholey C., Uusitalo J. and Wadsworth R.: Probing the three shapes in 186 Pb using in-beam γ-ray spectroscopy 449 Pakarinen J. → Eeckhaudt S. Pakarinen J. → Grahn T. Pakarinen J. → Greenlees P.T. Pakarinen J. → Kettunen H. Pakarinen J. → Lepp¨anen A.-P. Pakarinen J. → Uusitalo J. Pakou A. → Giot L. Pal U.K. → Scheit H. Paleni A. → Tonev D. Palit R. → Datta Pramanik U. Palit R. → Ter-Akopian G.M. Pantea M. → Scheit H. Pantelica D. → Gr´evy S. Papenberg A. → Keyes K.L. Papenbrock T.: Wave function factorization of shell-model ground states 507 Papenbrock T. → Wloch M. Papka P. → Keyes K.L. Paradis E. → Behr J.A. Parascandolo P. → Romoli M. Pardo R.C. → Romoli M. Pasini M. → Scheit H. Patin J.B. → Oganessian Yu.Ts. Patin J.B. → Stoyer M.A. Paul B. → Pollacco E. Pavan J. → Radford D.C. Pavan J. → Stone N.J. Pavan J. → Yu C.-H. Pearson C.J. → Chakrawarthy R.S. Pearson J.M. → Goriely S. Pearson M. → Behr J.A. Peaslee G.F. → Boutachkov P. Pedersen S. → Mach H. Pejovic P. → Tonev D. Pellegrini E. → Schatz H. Pellegriti M.G. → Tumino A. Penionzhkevich Y. → Gr´evy S. Penionzhkevich Y. → Khouaja A. Penionzhkevich Y. → Savajols H. Penttil¨ a H., Billowes J., Campbell P., Dendooven P., Elomaa V.-V., Eronen T., Hager U., Hakala J., Huikari J., Jokinen A., Kankainen A., Karvonen P., Kopecky S., Marsh B., Moore I., Nieminen A., Popov A., ¨ o J.: Performance Rinta-Antila S., Wang Y. and Ayst¨ of IGISOL 3 745 Penttil¨ a H. → Kankainen A. arvi K. Penttil¨ a H. → Per¨aj¨ Penttil¨ a H. → Rinta-Antila S. Per¨aj¨ arvi K., Cerny J., Hager U., Hakala J., Huikari J., Jokinen A., Karvonen P., Kurpeta J., Lee D., Moore ¨ o J.: Production I., Penttil¨ a H., Popov A. and Ayst¨ of beams of neutron-rich nuclei between Ca and Ni using the ion-guide technique 749 Per¨aj¨ arvi K. → Rinta-Antila S.

794

The European Physical Journal A

Perego C. → Lichtenth¨ aler R. Perevozchikov V.V. → Ter-Akopian G.M. Perkowski J. → Eeckhaudt S. Perkowski J. → Lepp¨ anen A.-P. Perry B.C. → Gade A. Peters W. → Stolz A. Peterson D. → Liang J.F. Petkov P. → Grahn T. Petkov P. → Tonev D. Petrache C. → Tonev D. Petrick M. → Block M. Pfeiffer B. → Kautzsch T. Pfeiffer B. → K¨ oster U. Pfeiffer B. → Kratz K.-L. Pfeiffer B. → Schatz H. Pfeiffer B. → Shergur J. Pf¨ utzner M.: Two-proton emission 165 Phair L. → Benczer-Koller N. Piechaczek A. → Batchelder J.C. Piechaczek A. → Gross C.J. Piechaczek A. → Grzywacz R. Piechaczek A. → Radford D.C. Piechaczek A. → Tantawy M.N. Piecuch P. → Wloch M. Pierroutsakou D. → Romoli M. Pietralla N. → McKay C.J. Pietralla N. → McKay C.J. Pi´etri S. → Gr´evy S. Pita S. → Giot L. Pita S. → Savajols H. Pitae S. → Khouaja A. Pitcairn R. → Behr J.A. Pizzone R.G. → Tumino A. Placco V. → Lichtenth¨ aler R. Plass W. → Block M. Plettner C. → Grawe H. Plettner C. → Karny M. Plettner C. → Kavatsyuk M. Plettner C. → Mukha I. Plochocki A. → Karny M. Plochocki A. → Kavatsyuk M. Pl´ociennik W.A. → Mach H. Ploszajczak M. → Michel N. Ploszajczak M. → Michel N. Ploszajczak M. → Rotureau J. Podadera I., Fritioff T., Jokinen A., Kepinski J.F., Lindroos M., Lunney D. and Wenander F.: Preparation of cooled and bunched ion beams at ISOLDE-CERN 743 Podadera I. → Delahaye P. Podlech H. → Scheit H. Pokrovsky I.V. → Trotta M. Pollacco E., Beaumel D., Roussel-Chomaz P., Atkin E., Baron P., Baronick J.P., Becheva E., Blumenfeld Y., Boujrad A., Drouart A., Druillole F., Edelbruck P., Gelin M., Gillibert A., Houarner Ch., Lapoux V., Lavergne L., Leberthe G., Leterrier L., Le Ven V., Lugiez F., Nalpas L., Olivier L., Paul B., Raine B., Richard A., Rouger M., Saillant F., Skaza F., Tripon

M., Vilmay M., Wanlin E. and Wittwer M.: MUST2: A new generation array for direct reaction studies 287 Pollacco E.C. → Giot L. Pollarolo G. → Corradi L. Policroniades R. R. → Barr´on-Palos L. Polyakov A.N. → Oganessian Yu.Ts. Popa G., Aprahamian A., Georgieva A. and Draayer J.P.: Systematics in the structure of low-lying, non-yrast band-head configurations of strongly deformed nuclei 451 Popescu S. → Vary J.P. Popov A.V. → Kankainen A. Popov A. → Penttil¨ a H. Popov A. → Per¨aj¨ arvi K. Poves A. → Mach H. Powell J. → Benczer-Koller N. Prezado Y. → Cortina-Gil D. Pribora V.N. → Kiselev O.A. Pribora V. → Cortina-Gil D. Prime E. → Behr J.A. Prinke A. → Schury P. PRISMA-CLARA Collaboration → Corradi L. Pritchard A. → Eeckhaudt S. Prokopowicz W. → Becker F. Quinn M. → Boutachkov P. Quint W. → Block M. Quint W. → Weber C. Raabe R. → Ter-Akopian G.M. Raddon P. → Pakarinen J. Radford D.C., Baktash C., Barton C.J., Batchelder J., Beene J.R., Bingham C.R., Caprio M.A., Danchev M., Fuentes B., Galindo-Uribarri A., Gomez del Campo J., Gross C.J., Halbert M.L., Hartley D.J., Hausladen P., Hwang J.K., Krolas W., Larochelle Y., Liang J.F., Mueller P.E., Padilla E., Pavan J., Piechaczek A., Shapira D., Stracener D.W., Varner R.L., Woehr A., Yu C.-H. and Zamfir N.V.: Coulomb excitation and transfer reactions with neutron-rich radioactive beams 383 Radford D.C. → Liang J.F. Radford D.C. → Stone N.J. Radford D.C. → Varner R.L. Radford D.C. → Yu C.-H. Radford D.C. → Zamfir N.V. Rafalski M. → Satula W. Rahaman S. → Block M. Rahaman S. → Herfurth F. Rahaman S. → Weber C. Rahkila P. → Eeckhaudt S. Rahkila P. → Grahn T. Rahkila P. → Greenlees P.T. Rahkila P. → Kettunen H. Rahkila P. → Lepp¨anen A.-P. Rahkila P. → Pakarinen J. Rahkila P. → Uusitalo J. Raine B. → Pollacco E.

Author index

Ramayya A.V. → Batchelder J.C. Ramayya A.V. → Fong D. Ramayya A.V. → Gore P.M. Ramayya A.V. → Hwang J.K. Ramayya A.V. → Jones E.F. Ramayya A.V. → Luo Y.X. Ramayya A.V. → Tantawy M.N. Ramayya A.V. → Zhu S.J. Rasmussen J.O. → Fong D. Rasmussen J.O. → Gore P.M. Rasmussen J.O. → Hwang J.K. Rasmussen J.O. → Luo Y.X. Rasmussen J.O. → Zhu S.J. Rauth C. → Block M. Ravn H.L. → Kautzsch T. Ray S. → Adhikari S. Ray S. → Chinmay Basu,Adhikari S. Reeder P. → Schatz H. Rehm K.E. → Romoli M. Reiter P. → Becker F. Reiter P. → Eeckhaudt S. Reiter P. → Greenlees P.T. Reiter P. → Scheit H. Rejmund M. → Catford W.N. Repnow R. → Scheit H. Ressler J.J. → Zamfir N.V. Richard A. → Pollacco E. Richter A. → Scheit H. Riisager K. → Cortina-Gil D. Riley L.A. → Gade A. Ring P. → Paar N. Ring P. → Vretenar D. Ringle R., Bollen G., Lawton D., Schury P., Schwarz S. and Sun T.: The LEBIT 9.4 T Penning trap system 59 Ringle R. → Schury P. Ringle R. → Sun T. Rinollo A. → Tumino A. Rinta-Antila S., Wang Y., Dendooven P., Huikari J., Jokinen A., Kankainen A., Kolhinen V.S., Lhersonneau G., Nieminen A., Nummela S., Penttil¨ a H., Per¨ aj¨ arvi ¨ o J. and the ISOLDE K., Szerypo J., Wang J.C., Ayst¨ Collaboration: Structure of doubly-even cadmium nuclei studied by β − decay 119 Rinta-Antila S. → Jokinen A. Rinta-Antila S. → Kankainen A. Rinta-Antila S. → Penttil¨ a H. Roberge D. → Behr J.A. Robinson A.P., Davids C.N., Seweryniak D., Woods P.J., Blank B., Carpenter M.P., Davinson T., Freeman S.J., Hammond N., Hoteling N., Janssens R.V.F., Khoo T.L., Liu Z., Mukherjee G., Scholey C., Shergur J., Sinha S., Sonzogni A.A., Walters W.B. and Woehr A.: Recoil decay tagging study of 146 Tm 155 Robinson A. → Seweryniak D. Rochester CHICO/Gammasphere Collaboration → Kautzsch T. Rodin A.M. → Ter-Akopian G.M. Rodin A. → Giot L.

795

Rodin A. → Mittig W. ¨ o J., Beck Rodr´ıguez D., Kolhinen V.S., Audi G., Ayst¨ D., Blaum K., Bollen G., Herfurth F., Jokinen A., Kellerbauer A., Kluge H.-J., Oinonen M., Schatz H., Sauvan E. and Schwarz S.: Mass measurement on the rp-process waiting point 72 Kr 41 Rodr´ıguez D., M´ery A., Darius G., Herbane M., Ban G., Delahaye P., Durand D., Fl´echard X., Labalme M., Li´enard E., Mauger F. and Naviliat-Cuncic O.: The LPCTrap for the measurement of the β-ν correlation in 6 He 705 Rodr´ıguez D. → Block M. Roeckl E. → Grawe H. Roeckl E. → Karny M. Roeckl E. → Kavatsyuk M. Roeckl E. → Mukha I. Roeder B.T. → Gade A. Rogachev G.V. → Boutachkov P. Romano S. → Tumino A. Romoli M., Mazzocco M., Vardaci E., Di Pietro M., De Francesco A., Bonetti R., De Rosa A., Glodariu T., Guglielmetti A., Inglima G., La Commara M., Martin B., Masone V., Parascandolo P., Pierroutsakou D., Sandoli M., Scopel P., Signorini C., Soramel F., Stroe L., Greene J., Heinz A., Henderson D., Jiang C.L., Moore E.F., Pardo R.C., Rehm K.E., Wuosmaa A. and Liang J.F.: The EXODET apparatus: Features and first experimental results 289 Romoli M. → Karny M. Romoli M. → Kavatsyuk M. Rotureau J., Chatterjee R., Okolowicz J. and Ploszajczak M.: Microscopic theory of the two-proton radioactivity 173 Rotureau J. → Michel N. Rouger M. → Pollacco E. Rousseau M. → Greenlees P.T. Rousseau M. → Savajols H. Roussel-Chomaz P. → Giot L. Roussel-Chomaz P. → Khouaja A. Roussel-Chomaz P. → Mittig W. Roussel-Chomaz P. → Pollacco E. Roussel-Chomaz P. → Savajols H. Roussel-Chomaz P. → Ter-Akopian G.M. Rowley N. → Trotta M. Rubio B. → Mach H. Ruchowska E. → Mach H. Rudolph D. → Becker F. Rudolph D. → Ekman J. Rudolph K. → Scheit H. Rusek K. → Giot L. Ryjkov V.L., Blomeley L., Brodeur M., Grothkopp P., Smith M., Bricault P., Buchinger F., Crawford J., Gwinner G., Lee J., Vaz J., Werth G., Dilling J. and the TITAN Collaboration: TITAN project status report and a proposal for a new cooling method of highly charged ions 53 Rykaczewski K.P. → Batchelder J.C. Rykaczewski K.P. → Gross C.J. Rykaczewski K.P. → Grzywacz R.

796

The European Physical Journal A

Rykaczewski K.P. → Mazzocchi C. Rykaczewski K.P. → Tantawy M.N. Rykaczewski K. → Karny M. Sagaidak R.N. → Trotta M. Sagawa H., Zhou X.R., Zhang X.Z. and Toshio Suzuki: Deformations and electromagnetic moments of light exotic nuclei 535 Sagawa H. → Odahara A. Saha B. → Grahn T. Sahin L. → Bardayan D.W. Saillant F. → Pollacco E. Saint-Laurent M.G. → Khouaja A. Saint-Laurent M.G. → K¨ oster U. Saito A. → Iwasaki H. Saito A. → Michimasa S. Saito A. → Ong H.J. Saito A. → Yamada K. Saito N. → Becker F. Saito T.R. → Becker F. Saito T. → Hatano M. Sakai H.K. → Ong H.J. Sakai H. → Hatano M. Sakamoto N. → Hatano M. Sakuragi Y. → Takashina M. Sakurai Hiroyoshi: Spectroscopy on neutron-rich nuclei at RIKEN 403 Sakurai H. → Iwasaki H. Sakurai H. → Michimasa S. Sakurai H. → Ong H.J. Sakurai H. → Yamada K. Samanta C. → Adhikari S. Samanta C. → Kanungo R. Samanta C. → Kanungo R. Samyn M. → Goriely S. Sanchez R. → N¨ ortersh¨auser W. Sandoli M. → Romoli M. Santi P. → Schatz H. Sarazin F., Al-Khalili J.S., Ball G.C., Hackman G., Walker P.M., Austin R.A.E., Eshpeter B., Finlay P., Garrett P.E., Grinyer G.F., Koopmans K.A., Kulp W.D., Leslie J.R., Melconian D., Osborne C.J., Schumaker M.A., Scraggs H.C., Schwarzenberg J., Smith M.B., Svensson C.E., Waddington J.C. and Wood J.L.: Halo neutrons and the β-decay of 11 Li 99 Sasaki M. → Takechi M. Sasano M. → Hatano M. Sato S. → Takechi M. Satou Y. → Hatano M. Satou Y. → Iwasaki H. Satula W., Wyss R. and Rafalski M.: Cranking in isospace 559 Satula W., Wyss R. and Zdu´ nczuk H.: Using high-spin data to constrain spin-orbit term and spin-fields of Skyrme forces 551 Sauvan E. → Rodr´ıguez D. Savajols H., Jurado B., Mittig W., Baiborodin D., Catford W., Chartier M., Demonchy C.E., Dlouhy Z., Gillibert A., Giot L., Khouaja A., Lukyanov

A. L´epine-Szily S., Mrazek J., Orr N., Penionzhkevich Y., Pita S., Rousseau M., Roussel-Chomaz P. and Villari A.C.C.: New mass measurements at the neutron drip-line 23 Savajols H. → Catford W.N. Savajols H. → Giot L. Savajols H. → Khouaja A. Savajols H. → Mittig W. Savard G.: Ion manipulation with cooled and bunched beams 713 Savard G. → Clark J.A. Savard G. → Sharma K.S. Savreux R. → Delahaye P. Sawicka M. → Grawe H. Sawicka M. → Korgul A. Scarlassara F. → Corradi L. Scarlassara F. → Trotta M. Sch¨adel M. → Karny M. Sch¨adel M. → Kavatsyuk M. Schaffner H. → Becker F. Schaffner H. → Nara Singh B.S. Schatz H., Hosmer P.T., Aprahamian A., Arndt O., Clement R.R.C., Estrade A., Kratz K.-L., Liddick S.N., Mantica P.F., Mueller W.F., Montes F., Morton A.C., Ouellette M., Pellegrini E., Pfeiffer B., Reeder P., Santi P., Steiner M., Stolz A., Tomlin B.E., Walohr A.: The half-life of the doublyters W.B. and W¨ magic r-process nucleus 78 Ni 639 Schatz H. → Kankainen A. Schatz H. → Rodr´ıguez D. Sch¨atz T. → Habs D. Scheidenberger C. → Block M. Scheit H., Niedermaier O., Bildstein V., Boie H., Fitting J., von Hahn R., K¨ ock F., Lauer M., Pal U.K., Podlech H., Repnow R., Schwalm D., Alvarez C., Ames F., Bollen G., Emhofer S., Habs D., Kester O., Lutter R., Rudolph K., Pasini M., Thirolf P.G., Wolf B.H., Eberth J., Gersch G., Hess H., Reiter P., Thelen O., Warr N., Weisshaar D., Aksouh F., Van den Bergh P., Van Duppen P., Huyse M., Ivanov O., Mayet P., ¨ o J., Butler P.A., Cederk¨ Van de Walle J., Ayst¨ all J., Delahaye P., Fynbo H.O.U., Fraile L.M., Forstner O., Franchoo S., K¨ oster U., Nilsson T., Oinonen M., Sieber T., Wenander F., Pantea M., Richter A., auser R., Schrieder G., Simon H., Behrens T., Gernh¨ Kr¨oll T., Kr¨ ucken R., M¨ unch M., Davinson T., Gerl J., Huber G., Hurst A., Iwanicki J., Jonson B., Lieb P., Liljeby L., Schempp A., Scherillo A., Schmidt P. and Walter G.: Coulomb excitation of neutron-rich beams at REX-ISOLDE 397 Scheit H. → Cortina-Gil D. Scheit H. → Datta Pramanik U. Schempp A. → Scheit H. Scherillo A. → Scheit H. Schiller A. → Stolz A. Schmidt K. → Karny M. Schmidt P. → Scheit H. Schneider R. → Cortina-Gil D. Scholey C. → Eeckhaudt S.

Author index

Scholey C. → Grahn T. Scholey C. → Greenlees P.T. Scholey C. → Lepp¨ anen A.-P. Scholey C. → Pakarinen J. Scholey C. → Robinson A.P. Scholey C. → Uusitalo J. Scholl C. → Werner V. Scholl C. → Werner V. Schramm U. → Habs D. Schrieder G. → Cortina-Gil D. Schrieder G. → Scheit H. Schuber R. → Korgul A. Schumaker M.A. → Sarazin F. Schury P., Bollen G., Davies D.A., Doemer A., Lawton D., Morrissey D.J., Ottarson J., Prinke A., Ringle R., Sun T., Schwarz S. and Weissman L.: Precision experiments with rare isotopes with LEBIT at MSU 51 Schury P. → Ringle R. Schury P. → Sun T. Schwalm D. → Scheit H. Schwarz S. → Gu´enaut C. Schwarz S. → Gu´enaut C. Schwarz S. → Herfurth F. Schwarz S. → Ringle R. Schwarz S. → Rodr´ıguez D. Schwarz S. → Schury P. Schwarz S. → Sun T. Schwarz S. → Weber C. Schwarz S. → Yazidjian C. Schwarzenberg J. → Sarazin F. Schweikhard L. → Block M. Schweikhard L. → Gu´enaut C. Schweikhard L. → Gu´enaut C. Schweikhard L. → Herfurth F. Schwengner R. → Karny M. Schwengner R. → Kavatsyuk M. Scielzo N.D. → Clark J.A. Scopel P. → Romoli M. Scraggs H.C. → Sarazin F. Sekiguchi K. → Hatano M. Seliverstov D.M. → Kankainen A. Seliverstov D.M. → Kiselev O.A. Sergueev L.O. → Kiselev O.A. Serizawa Y. → Matsuo M. Seweryniak D., Davids C.N., Robinson A., Woods P.J., Blank B., Carpenter M.P., Davinson T., Freeman S.J., Hammond N., Hoteling N., Janssens R.V.F., Khoo T.L., Liu Z., Mukherjee G., Shergur J., Sinha S., Sonzogni A.A., Walters W.B. and Woehr A.: Particle-core coupling in the transitional proton emitters 145,146,147 Tm 159 Seweryniak D. → Clark J.A. Seweryniak D. → Robinson A.P. Seweryniak D. → Shergur J. Sewtz M., Bachelet C., Gu´enaut C., K´epinski J.F., Leccia E., Le Du D., Chauvin N. and Lunney D.: A MISTRAL spectrometer accoutrement for the study of exotic nuclides 37

797

Shapira D., Liang J.F., Gross C.J., Varner R.L., Beene J.R., Galindo-Uribarri A., Gomez Del Campo J., Mueller P.E., Stracener D.W., Hausladen P.A., Harlin C., Kolata J.J., Amro H., Loveland W., Jones K.L., Bierman J.D. and Caraley A.L.: Measurement of evaporation residue cross sections from reactions with radioactive neutron-rich beams 241 Shapira D. → Bardayan D.W. Shapira D. → Gross C.J. Shapira D. → Jones K.L. Shapira D. → Liang J.F. Shapira D. → Radford D.C. Shapira D. → Tantawy M.N. Shapira D. → Thomas J.S. Shapira D. → Varner R.L. Shapira D. → Zamfir N.V. Sharma K.S., Vaz J., Barber R.C., Buchinger F., Clark J.A., Crawford J.E., Fukutani H., Greene J.P., Gulick S., Heinz A., Lee J.K.P., Savard G., Zhou Z. and Wang J.C.: Atomic mass ratios for some stable isotopes of platinum relative to 197 Au 45 Sharma K.S. → Clark J.A. Shaughnessy D.A. → Oganessian Yu.Ts. Shaughnessy D.A. → Stoyer M.A. Shehadeh B. → Vary J.P. Shergur J., Hoteling N., W¨ ohr A., Walters W.B., Arndt O., Brown B.A., Davids C.N., Dean D.J., Kratz K.-L., Pfeiffer B., Seweryniak D. and the ISOLDE Collaboration: New level information on Z = 51 isotopes, 111 Sb60 and 134,135 Sb83,84 121 Shergur J. → Kautzsch T. Shergur J. → Robinson A.P. Shergur J. → Seweryniak D. Sherrill B.M. → Gade A. Sherrill B.M. → L´epine-Szily A. Shimoura S. → Ideguchi E. Shimoura S. → Iwasaki H. Shimoura S. → Michimasa S. Shimoura S. → Ong H.J. Shimoura S. → Yamada K. Shinosaki W. → Takechi M. SHIPTRAP Collaboration → Block M. SHIPTRAP Collaboration → Weber C. Shirokov A.M. → Vary J.P. Shirokova A.A. → Chuvilskaya T.V. Shirokovsky I.V. → Oganessian Yu.Ts. Shlomo S. → Agrawal B.K. Shrivastava A. → Kiselev O.A. Sida J.L. → Giot L. Sidorchuk S.I. → Ter-Akopian G.M. Sieber T. → Scheit H. Sieja K. → Baran A. Signorini C. → Romoli M. Sikler G., Crespo L´ opez-Urrutia J.R., Dilling J., Epp S., Osborne C.J. and Ullrich J.: A high-current EBIT for charge-breeding of radionuclides for the TITAN spectrometer 63 Simon H. → Cortina-Gil D. Simon H. → Datta Pramanik U.

798

The European Physical Journal A

Simon H. → Scheit H. Simpson J. → Becker F. Sinha S. → Robinson A.P. Sinha S. → Seweryniak D. Sitar B. → Cortina-Gil D. Skaza F. → Giot L. Skaza F. → Pollacco E. Skorodumov B.B. → Boutachkov P. Slepnev R.S. → Ter-Akopian G.M. Sletten G. → Lepp¨anen A.-P. Smith M.B. → Chakrawarthy R.S. Smith M.B. → Sarazin F. Smith M.S. → Bardayan D.W. Smith M.S. → Jones K.L. Smith M.S. → Thomas J.S. Smith M. → Ryjkov V.L. Soi´c N. → Pain S.D. Sonzogni A.A. → Robinson A.P. Sonzogni A.A. → Seweryniak D. Soramel F. → Romoli M. Sorlin O. → Gr´evy S. Speidel K.-H. → Benczer-Koller N. Spence J.R. → Vary J.P. Spitaleri C. → Tumino A. Spohr K.-M. → Keyes K.L. Sprouse G.D. → Clark J.A. Stahl S. → Weber C. Stanoiu M. → Blank B. Stanoiu M. → Gr´evy S. Stanoiu M. → Mach H. Stefan I. → Blank B. Stefan I. → Gr´evy S. Stefanescu I. → Luo Y.X. Stefanini A.M. → Corradi L. Stefanini A.M. → Trotta M. Steiner M. → Mazzocchi C. Steiner M. → Schatz H. Stepantsov S.V. → Ter-Akopian G.M. Stepantsov S. → Giot L. Stephan C. → L´epine-Szily A. Stetcu I., Barrett B.R., Navr´ atil P. and Vary J.P.: Effective operators in the NCSM formalism 489 Stetcu I. → Vary J.P. St-Laurent M.G. → Gr´evy S. Stodel C. → Gr´evy S. Stodel C. → K¨ oster U. Stoica S. → Vary J.P. Stoitcheva G., Nazarewicz W. and Dean D.J.: Shell model analysis of intruder states and high-K isomers in the f p shell 509 Stoitsov M.V., Dobaczewski J., Nazarewicz W. and Terasaki J.: Large-scale HFB calculations for deformed nuclei with the exact particle number projection 567 Stoitsov M. → Dobaczewski J. Stoitsov M. → Terasaki J. Stolz A., Baumann T., Frank N.H., Ginter T.N., Hitt G.W., Kwan E., Mocko M., Peters W., Schiller A.,

Sumithrarachchi C.S. and Thoennessen M.: Discovery of 60 Ge and 64 Se 335 Stolz A. → Batchelder J.C. Stolz A. → Cortina-Gil D. Stolz A. → Mazzocchi C. Stolz A. → Schatz H. Stolz A. → Tripathi V. Stone J.R. → Stone N.J. Stone N.J., Stuchbery A.E., Danchev M., Pavan J., Timlin C.L., Baktash C., Barton C., Beene J.R., BenczerKoller N., Bingham C.R., Dupak J., Galindo-Uribarri A., Gross C.J., Kumbartzki G., Radford D.C., Stone J.R. and Zamfir N.V.: First nuclear moment measurement with radioactive beams by recoil-in-vacuum 132 Te 205 method: g-factor of the 2+ 1 state in Stoyer M.A., Patin J.B., Kenneally J.M., Moody K.J., Shaughnessy D.A., Stoyer N.J., Wild J.F., Wilk P.A., Utyonkov V.K. and Oganessian Yu.Ts.: Random probability analysis of recent 48 Ca experiments 595 Stoyer M.A. → Fong D. Stoyer M.A. → Hwang J.K. Stoyer M.A. → Kautzsch T. Stoyer M.A. → Luo Y.X. Stoyer M.A. → Oganessian Yu.Ts. Stoyer M. → Gore P.M. Stoyer M. → Zhu S.J. Stoyer N.J. → Oganessian Yu.Ts. Stoyer N.J. → Stoyer M.A. Stracener D.W. → Liang J.F. Stracener D.W. → Radford D.C. Stracener D.W. → Shapira D. Stracener D.W. → Varner R.L. Stracener D.W. → Zamfir N.V. Strmen P. → Cortina-Gil D. Stroe L. → Romoli M. Stuchbery A.E. → Stone N.J. Stuttge L. → Pain S.D. Stuttge L. → Ter-Akopian G.M. Stycze´ n J. → Becker F. Subbotin V.G. → Oganessian Yu.Ts. Subotic K. → Oganessian Yu.Ts. Suda K. → Hatano M. Suda T. → Ideguchi E. Suda T. → Kanungo R. Suda T. → Kanungo R. Suda T. → Takechi M. Suhonen M. → Block M. Sukhov A.M. → Oganessian Yu.Ts. Sulignano B. → Nara Singh B.S. Sumikama T., Iwakoshi T., Nagatomo T., Ogura M., Nakashima Y., Fujiwara H., Matsuta K., Minamisono T., Mihara M., Fukuda M., Minamisono K. and Yamaguchi T.: Alignment correlation term in mass A = 8 system and G-parity irregular term 709 Sumikama T. → Tanaka K. Sumithrarachchi C.S. → Stolz A. S¨ ummerer K. → Cortina-Gil D. S¨ ummerer K. → Datta Pramanik U.

Author index

S¨ ummerer K. → Kiselev O.A. Summers N.C. and Nunes F.M.: 7 Be breakup on heavy and light targets 647 Summers N.C. → Nunes F.M. Sun T., Schwarz S., Bollen G., Lawton D., Ringle R. and Schury P.: Commissioning of the ion beam buncher and cooler for LEBIT 61 Sun T. → Ringle R. Sun T. → Schury P. Suomij¨ arvi T. → L´epine-Szily A. Suzuki H. → Iwasaki H. Suzuki M.K. → Iwasaki H. Suzuki T. → Kanungo R. Suzuki T. → Kanungo R. Suzuki T. → Takechi M. Suzuki T. → Tanaka K. Svensson C.E. → Chakrawarthy R.S. Svensson C.E. → Sarazin F. Swanson T.B. → Behr J.A. Szanto de Toledo A. → Trotta M. Szarka I. → Cortina-Gil D. Szerypo J. → Habs D. Szerypo J. → Rinta-Antila S. Szilner S. → Corradi L. Szilner S. → Trotta M. Tabor S.L. → Mukha I. Tabor S.L. → Tripathi V. Tajima N.: Continuum effects on the pairing in neutron drip-line nuclei studied with the canonical-basis HFB method 571 Takahashi M. → Takechi M. Takashina M., Sakuragi Y. and Iseri Y.: Effect of halo structure on 11 Be + 12 C elastic scattering 273 Takechi M., Fukuda M., Mihara M., Chinda T., Matsumasa T., Matsubara H., Nakashima Y., Matsuta K., Minamisono T., Koyama R., Shinosaki W., Takahashi M., Takizawa A., Ohtsubo T., Suzuki T., Izumikawa T., Momota S., Tanaka K., Suda T., Sasaki M., Sato S. and Kitagawa A.: Reaction cross-sections for stable nuclei and nucleon density distribution of proton drip-line nucleus 8 B 217 Takechi M. → Tanaka K. Takeshita E. → Iwasaki H. Takeshita E. → Michimasa S. Takeshita E. → Ong H.J. Takeshita E. → Yamada K. Takeuchi S. → Iwasaki H. Takeuchi S. → Michimasa S. Takeuchi S. → Ong H.J. Takeuchi S. → Yamada K. Takizawa A. → Takechi M. Tamaki M. → Ideguchi E. Tamaki M. → Iwasaki H. Tamaki M. → Michimasa S. Tamaki M. → Ong H.J. Tamaki M. → Yamada K. Tamii A. → Hatano M. Tanaka K., Fukuda M., Mihara M., Takechi M., Chinda T., Sumikama T., Kudo S., Matsuta K., Minamisono

799

T., Suzuki T., Ohtubo T., Izumikawa T., Momota S., Yamaguchi T., Onishi T., Ozawa A., Tanihata I. and Zheng Tao: Nucleon density distribution of proton drip-line nucleus 17 Ne 221 Tanaka K. → Takechi M. Tanihata I. → Ideguchi E. Tanihata I. → Kanungo R. Tanihata I. → Kanungo R. Tanihata I. → Tanaka K. Tanihata I. → Yamada K. Tantawy M.N., Bingham C.R., Mazzocchi C., Grzywacz R., Kr´olas W., Rykaczewski K.P., Batchelder J.C., Gross C.J., Fong D., Hamilton J.H., Hartley D.J., Hwang J.K., Larochelle Y., Piechaczek A., Ramayya A.V., Shapira D., Winger J.A., Yu C.-H. and Zganjar E.F.: Study of the N = 77 odd-Z isotones near the proton-drip line 151 Tantawy M.N. → Grzywacz R. Tantawy M. → Batchelder J.C. Tarasov D.V. → Gridnev K.A. Tarasov O.B.: LISE++ development: Application to projectile fission at relativistic energies 751 Tarasov V.N. → Gridnev K.A. Tassan-Got L. → L´epine-Szily A. Taylor M.J. → Benczer-Koller N. Tchuvil’sky Yu.M. → Chuvilskaya T.V. Tengblad O., Turrion M. and Fraile L.M.: TARGISOL: An ISOL-database on the web 763 Tengblad O. → Mach H. Ter-Akopian G.M., Fomichev A.S., Golovkov M.S., Grigorenko L.V., Krupko S.A., Oganessian Yu.Ts., Rodin A.M., Sidorchuk S.I., Slepnev R.S., Stepantsov S.V., Wolski R., Korsheninnikov A.A., Nikolskii E.Yu., Roussel-Chomaz P., Mittig W., Palit R., Bouchat V., Kinnard V., Materna T., Hanappe F., Dorvaux O., Stuttge L., Angulo C., Lapoux V., Raabe R., Nalpas L., Yukhimchuk A.A., Perevozchikov V.V., Vinogradov Yu.I., Grishechkin S.K. and Zlatoustovskiy S.V.: New insights into the resonance states of 5 H and 5 He 315 Ter-Akopian G.M. → Fong D. Ter-Akopian G.M. → Gore P.M. Ter-Akopian G.M. → Hwang J.K. Ter-Akopian G.M. → Luo Y.X. Ter-Akopian G.M. → Zhu S.J. Ter-Akopian G. → Giot L. Ter´an E. and Johnson C.W.: A statistical spectroscopy approach for calculating nuclear level densities 673 Terasaki J., Engel J., Bender M., Dobaczewski J., Nazarewicz W. and Stoitsov M.: Skyrme-QRPA calculations of multipole strength in exotic nuclei 539 Terasaki J. → Stoitsov M.V. Terry J.R. → Gade A. Theisen Ch. → Eeckhaudt S. Theisen Ch. → Greenlees P.T. Thelen O. → Scheit H. Thibault C. → Bachelet C. Thirolf P.G. → Block M. Thirolf P.G. → Scheit H.

800

The European Physical Journal A

Thirolf P. → Habs D. Thoennessen M.: Remarks about the driplines 333 Thoennessen M. → Stolz A. Thomas J.C. → Blank B. Thomas J.S., Bardayan D.W., Blackmon J.C., Cizewski J.A., Fitzgerald R.P., Greife U., Gross C.J., Johnson M.S., Jones K.L., Kozub R.L., Liang J.F., Livesay R.J., Ma Z., Moazen B.H., Nesaraja C.D., Shapira D., Smith M.S. and Visser D.W.: Single-neutron excitations in neutron-rich N = 51 nuclei 371 Thomas J.S. → Jones K.L. Thompson I. → Giot L. Thummerer S. → Keyes K.L. TIARA Collaboration → Catford W.N. Timis C.N. → Catford W.N. Timis C.N. → Pain S.D. Timlin C.L. → Stone N.J. TITAN Collaboration → Ryjkov V.L. Togano Y. → Iwasaki H. Togano Y. → Ong H.J. Togano Y. → Yamada K. Tomlin B.E. → Schatz H. Tomlin B.E. → Tripathi V. Tonev D., de Angelis G., Petkov P., Dewald A., Gadea A., Pejovic P., Balabanski D.L., Bednarczyk P., Camera F., Fitzler A., M¨ oller O., Marginean N., Paleni A., Petrache C., Zell K.O. and Zhang Y.H.: Check for chirality in real nuclei 447 Torilov S.Yu. → Gridnev K.A. Toshio Suzuki → Sagawa H. Tostevin J.A. → Gade A. Tostevin J.A. → Pain S.D. Towner I.S. → Hardy J.C. Trimble W. → Clark J.A. Trinczek M. → Behr J.A. Tripathi V., Tabor S.L., Mantica P.F., Hoffman C.R., Wiedeking M., Davies A.D., Liddick S.N., Mueller W.F., Stolz A., Tomlin B.E. and Volya A.: Voyage to the “Island of Inversion”: 29 Na 101 Tripon M. → Pollacco E. Trotta M., Stefanini A.M., Beghini S., Behera B.R., Chizhov A.Yu., Corradi L., Courtin S., Fioretto E., Gadea A., Gomes P.R.S., Haas F., Itkis I.M., Itkis M.G., Kniajeva G.N., Kondratiev N.A., Kozulin E.M., Latina A., Montagnoli G., Pokrovsky I.V., Rowley N., Sagaidak R.N., Scarlassara F., Szanto de Toledo A., Szilner S., Voskressensky V.M. and Wu Y.W.: Fusion hindrance and quasi-fission in 48 Ca induced reactions 615 Trotta M. → Corradi L. Tsyganov Yu.S. → Oganessian Yu.Ts. Tumino A., Spitaleri C., Bonomo C., Cherubini S., Figuera P., Gulino M., La Cognata M., Lamia L., Musumarra A., Pellegriti M.G., Pizzone R.G., Rinollo A. and Romano S.: Quasi-free 6 Li(n, α)3 H reaction at low energy from 2 H break-up 649 Turrion M. → Tengblad O. Typel S.: The Trojan-Horse method for nuclear astrophysics 665

Typel S. → Datta Pramanik U. Uesaka T. → Hatano M. Ullrich J. → Sikler G. Umar A.S. and Oberacker V.E.: TDHF studies with modern Skyrme forces 553 Umar A.S. → Blazkiewicz A. Ur C. → Corradi L. Urrego-Blanco J.-P. → Varner R.L. Utsuno Y.: Anomalous magnetic moment of 9 C and shell quenching in exotic nuclei 209 Utyonkov V.K. → Oganessian Yu.Ts. Utyonkov V.K. → Stoyer M.A. Uusitalo J., Eeckhaudt S., Enqvist T., Eskola K., Grahn T., Greenlees P.T., Jones P., Julin R., Juutinen S., anen A.Kettunen H., Kuusiniemi P., Leino M., Lepp¨ P., Nieminen P., Nyman M., Pakarinen J., Rahkila P. and Scholey C.: Alpha-decay studies using the JYFL gas-filled recoil separator RITU 179 Uusitalo J. → Eeckhaudt S. Uusitalo J. → Grahn T. Uusitalo J. → Greenlees P.T. Uusitalo J. → Kettunen H. Uusitalo J. → Lepp¨anen A.-P. Uusitalo J. → Pakarinen J. Van den Bergh P. → Scheit H. Van de Vel K. → Eeckhaudt S. Van de Walle J. → Scheit H. Van Duppen P. → Scheit H. Van Isacker P. → Hirsch J.G. Vardaci E. → Romoli M. Varela G. A. → Barr´on-Palos L. Varner R.L., Beene J.R., Baktash C., Galindo-Uribarri A., Gross C.J., Gomez del Campo J., Halbert M.L., Hausladen P.A., Larochelle Y., Liang J.F., Mas J., Mueller P.E., Padilla-Rodal E., Radford D.C., Shapira D., Stracener D.W., Urrego-Blanco J.-P. and Yu C.-H.: Coulomb excitation measurements of transition strengths in the isotopes 132,134 Sn 391 Varner R.L. → Liang J.F. Varner R.L. → Radford D.C. Varner R.L. → Shapira D. Vary J.P., Atramentov O.V., Barrett B.R., Hasan M., Hayes A.C., Lloyd R., Mazur A.I., Navr´ atil P., Negoita A.G., Nogga A., Ormand W.E., Popescu S., Shehadeh B., Shirokov A.M., Spence J.R., Stetcu I., Stoica S., Weber T.A. and Zaytsev S.A.: Ab initio No-Core Shell Model —Recent results and future prospects 475 Vary J.P. → Stetcu I. Vaz J. → Clark J.A. Vaz J. → Ryjkov V.L. Vaz J. → Sharma K.S. Vel´azquez V. → Hirsch J.G. Vermeulen N. → Kowalska M. Vieira D.J. → L´epine-Szily A. Villari A.C.C. → Khouaja A. Villari A.C.C. → K¨oster U. Villari A.C.C. → L´epine-Szily A.

Author index

Villari A.C.C. → Mittig W. Villari A.C.C. → Savajols H. Vilmay M. → Pollacco E. Vinogradov Yu.I. → Ter-Akopian G.M. Visser D.W. → Thomas J.S. Visser D. → Jones K.L. Voinov A.A. → Oganessian Yu.Ts. Volya A. and Davids C.: Nuclear pairing and Coriolis effects in proton emitters 161 Volya A. → Tripathi V. von Brentano P. → Werner V. von Brentano P. → Werner V. von Hahn R. → Scheit H. von Oertzen W. → Keyes K.L. Vorobjev G.K. → Kankainen A. Voskressensky V.M. → Trotta M. Vretenar D., Lalazissis G.A., Nikˇsi´c T. and Ring P.: Relativistic mean-field models with medium-dependent meson-nucleon couplings 555 Vretenar D. → Paar N. Waddington J.C. → Sarazin F. Wadsworth R. → Pakarinen J. Wakabayashi Y. → Ideguchi E. Wakabayashi Y. → Odahara A. Wakui T. → Hatano M. Walker P.M. → Chakrawarthy R.S. Walker P.M. → Sarazin F. Walter G. → Scheit H. Walters W.B. → Kautzsch T. Walters W.B. → Robinson A.P. Walters W.B. → Schatz H. Walters W.B. → Seweryniak D. Walters W.B. → Shergur J. Walus W. → Datta Pramanik U. Wang H. → Mittig W. Wang J.C. → Clark J.A. Wang J.C. → Rinta-Antila S. Wang J.C. → Sharma K.S. Wang Q. → Kanungo R. Wang Q. → Kanungo R. Wang Y. → Clark J.A. Wang Y. → Kankainen A. Wang Y. → Penttil¨ a H. Wang Y. → Rinta-Antila S. Wang Z. → Block M. Wanlin E. → Pollacco E. Wapstra A.H.: Atomic Mass Evaluation 2003 9 Warr N. → Becker F. Warr N. → Scheit H. Weber C., Audi G., Beck D., Blaum K., Bollen G., Herfurth F., Kellerbauer A., Kluge H.-J., Lunney D. and Schwarz S.: Effects of the pairing energy on nuclear charge radii 201 Weber C., Blaum K., Block M., Ferrer R., Herfurth F., Kluge H.-J., Kozhuharov C., Marx G., Mukherjee M., Quint W., Rahaman S., Stahl S. and the SHIPTRAP Collaboration: FT-ICR: A non-destructive detection for on-line mass measurements at SHIPTRAP 65 Weber C. → Block M.

801

Weber C. → Habs D. Weber C. → Herfurth F. Weber T.A. → Vary J.P. Weick H. → Becker F. Weick H. → Cortina-Gil D. Weick H. → Datta Pramanik U. Weick H. → Kiselev O.A. Weisshaar D. → Scheit H. Weissman L. → K¨oster U. Weissman L. → Schury P. Wenander F. → Delahaye P. Wenander F. → Podadera I. Wenander F. → Scheit H. Werner V., Scholl C. and von Brentano P.: A measure for triaxiality from K (shape) invariants 453 Werner V., von Brentano P., Casten R.F., Scholl C., McCutchan E.A., Kr¨ ucken R. and Jolie J.: Alternative interpretation of E0 strengths in transitional regions 455 Werner V. → McKay C.J. Werner V. → McKay C.J. Werner-Malento E. → Korgul A. Werth G. → Ryjkov V.L. Wheldon C. → Becker F. Wheldon C. → Keyes K.L. Wiedeking M. → Mukha I. Wiedeking M. → Tripathi V. Wieland O. → Becker F. Wild J.F. → Oganessian Yu.Ts. Wild J.F. → Stoyer M.A. Wilk P.A. → Oganessian Yu.Ts. Wilk P.A. → Stoyer M.A. Williams S.J. → Chakrawarthy R.S. Wilson J. → Eeckhaudt S. Wilson J. → Greenlees P.T. Winfield J.S. → Pain S.D. Winger J.A. → Batchelder J.C. Winger J.A. → Gross C.J. Winger J.A. → Grzywacz R. Winger J.A. → Mazzocchi C. Winger J.A. → Tantawy M.N. Winkler M. → Becker F. Winkler M. → Kiselev O.A. Wittwer M. → Pollacco E. Wloch M., Dean D.J., Gour J.R., Piecuch P., HjorthJensen M., Papenbrock T. and Kowalski K.: Ab initio coupled cluster calculations for nuclei using methods of quantum chemistry 485 Woehr A. → Radford D.C. Woehr A. → Robinson A.P. Woehr A. → Seweryniak D. Wohr A. → Boutachkov P. W¨ohr A. → Kautzsch T. W¨ohr A. → Kratz K.-L. W¨ohr A. → Schatz H. W¨ohr A. → Shergur J. Wojtaszek A. → N¨ortersh¨auser W. Wolf B.H. → Scheit H. Wollersheim H.J. → Becker F.

802

The European Physical Journal A

Wollersheim H.J. → Eeckhaudt S. Wollersheim H.-J. → Greenlees P.T. Wolski R. → Giot L. Wolski R. → Mittig W. Wolski R. → Ter-Akopian G.M. Wood J.L. → Sarazin F. Woods P.J. → Robinson A.P. Woods P.J. → Seweryniak D. Wouters J.M. → L´epine-Szily A. Wu C. → Kanungo R. Wu C. → Kanungo R. Wu S.C. → Fong D. Wu S.C. → Hwang J.K. Wu S.C. → Luo Y.X. Wu Y.W. → Trotta M. Wuosmaa A. → Romoli M. Wutte D. → Benczer-Koller N. Wyss R. → Satula W. Wyss R. → Satula W. Xu R.Q. → Zhu S.J. Yabana K. → Nakatsukasa T. Yabana K. → Ohta H. Yako K. → Hatano M. Yakovlev D.G., Levenfish K.P. and Gnedin O.Y.: Pycnonuclear reactions in dense stellar matter 669 Yamada K., Motobayashi T., Aoi N., Baba H., Demichi K., Elekes Z., Gibelin J., Gomi T., Hasegawa H., Imai N., Iwasaki H., Kanno S., Kubo T., Kurita K., Matsuyama Y.U., Michimasa S., Minemura T., Notani M., Onishi K. T.,Ong H.J., Ota S., Ozawa A., Saito A., Sakurai H., Shimoura S., Takeshita E., Takeuchi S., Tamaki M., Togano Y., Yanagisawa Y., Yoneda K. and Tanihata I.: Reduced transition probabilities for the first 2+ excited state in 46 Cr, 50 Fe, and 54 Ni 409 Yamada K. → Kanungo R. Yamada K. → Kanungo R. Yamada K. → Ong H.J. Yamagami M.: Collective excitations induced by pairing anti-halo effect 569 Yamagami M. and Nguyen Van Giai: Pairing effects on the collectivity of quadrupole states around 32 Mg 573 Yamagami M. → Inakura T. Yamagami M. → Yoshida K. Yamaguchi T. → Sumikama T. Yamaguchi T. → Tanaka K. Yamaguchi Y. → Kanungo R. Yamaguchi Y. → Kanungo R. Yan Z.-C. → N¨ortersh¨ auser W. Yanagisawa Y. → Hatano M. Yanagisawa Y. → Iwasaki H. Yanagisawa Y. → Michimasa S. Yanagisawa Y. → Ong H.J. Yanagisawa Y. → Yamada K. Yang L.M. → Zhu S.J. Yates S.W. → Kumar A. Yates S.W. → McKay C.J.

Yates S.W. → McKay C.J. Yatsoura V.I. → Kiselev O.A. Yazidjian C., Beck D., Blaum K., Brand H., Herfurth F. and Schwarz S.: Commissioning and first on-line test of the new ISOLTRAP control system 67 Yazidjian C. → Gu´enaut C. Yazidjian C. → Gu´enaut C. Yazidjian C. → Herfurth F. Yoneda K. → Ong H.J. Yoneda K. → Yamada K. Yordanov D.T. → Mach H. Yordanov D. → Kowalska M. Yoshida A. → Kanungo R. Yoshida A. → Kanungo R. Yoshida A. → Michimasa S. Yoshida K., Inakura T., Yamagami M., Mizutori S. and Matsuyanagi K.: Microscopic structure of negativeparity vibrations built on superdeformed states in sulfur isotopes close to the neutron drip line 557 Yoshida K. → Ideguchi E. Yu C.-H., Baktash C., Batchelder J.C., Beene J.R., Bingham C., Danchev M., Galindo-Uribarri A., Gross C.J., Hausladen P.A., Krolas W., Liang J.F., Padilla E., Pavan J. and Radford D.C.: Coulomb excitation of odd-A neutron-rich radioactive beams 395 Yu C.-H. → Batchelder J.C. Yu C.-H. → Radford D.C. Yu C.-H. → Tantawy M.N. Yu C.-H. → Varner R.L. Yu C.-H. → Zamfir N.V. Yukhimchuk A.A. → Ter-Akopian G.M. Yurkewicz K.L. → Gade A. Zabransky B.J. → Clark J.A. Zagrebaev V.I. → Oganessian Yu.Ts. Zamfir N.V., Hughes R.O., Casten R.F., Radford D.C., Barton C.J., Baktash C., Caprio M.A., GalindoUribarri A., Gross C.J., Hausladen P.A., McCutchan E.A., Ressler J.J., Shapira D., Stracener D.W. and Yu C.-H.: 132 Te and single-particle density-dependent pairing 389 Zamfir N.V. → McCutchan E.A. Zamfir N.V. → Radford D.C. Zamfir N.V. → Stone N.J. Zaytsev S.A. → Vary J.P. Zdu´ nczuk H. → Satula W. Zell K.O. → Tonev D. Zganjar E.F. → Batchelder J.C. Zganjar E.F. → Chakrawarthy R.S. Zganjar E.F. → Gross C.J. Zganjar E.F. → Grzywacz R. Zganjar E.F. → Tantawy M.N. Zhang X.Q. → Gore P.M. Zhang X.Q. → Zhu S.J. Zhang X.Z. → Sagawa H. Zhang Y.H. → Tonev D. Zheng T. → Kanungo R. Zheng T. → Kanungo R. Zheng Tao → Tanaka K. Zhou X.R. → Sagawa H.

Author index

Zhou Z. → Clark J.A. Zhou Z. → Sharma K.S. Zhu S.J., Hamilton J.H., Ramayya A.V., Gore P.M., Rasmussen J.O., Dimitrov V., Frauendorf S., Xu R.Q., Hwang J.K., Fong D., Yang L.M., Li K., Chen Y.J., Zhang X.Q., Jones E.F., Luo Y.X., Lee I.Y., Ma W.C., Cole J.D., Drigert M.W., Stoyer M., TerAkopian G.M. and Daniel A.V.: Soft chiral vibrations in 106 Mo 459

Zhu S.J. → Fong D. Zhu S.J. → Gore P.M. Zhu S.J. → Hwang J.K. Zhu S.J. → Luo Y.X. Ziman V. → Pain S.D. Zimmermann C. → N¨ortersh¨auser W. Zlatoustovskiy S.V. → Ter-Akopian G.M. ˙ Zylicz J. → Karny M. ˙ Zylicz J. → Kavatsyuk M.

803