Proceedings of the International Workshop on the New Applications Of Nuclear Fission: Bucharest, Romania, 7-12 September 2003

M uc 11 er

NEW

APPLICATIONS

OF

MLJCl—S^FP F=ISSIOiNI

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Proceedings of the International Workshop on the

NEW

APPLICATIONS

Bucharest, Romania

OF

7 - 1 2 September 2003

editors

A. C. Mueller Institut de Physique Nucleaire, France

M. Mirea National Institute for Physics and Nuclear Engineering, Romania

L. Tassan-Got Institut de Physique Nucleaire, France

\[p World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONGKONG • TAIPEI • CHENNAI

Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401^02, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

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NEW APPLICATIONS OF NUCLEAR FISSION Copyright © 2004 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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Organized by

IDRANAP (Inter-Disciplinary Research and Applications Based on Nuclear and Atomic Physics) European Center of Excellence from the "Horia Hulubei" National R&D Institute for Physics and Nuclear Engineering

Sponsored by

European Commission under contract ICA1-CT-2000-70023 and Romanian Ministry of Education and Research

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PREFACE This volume contains the lectures and contributions presented at the International Workshop "New Applications of Nuclear Fission" (NANUF03), held at Bucharest, in Romania, from 7 September to 12 September 2003. NANUF03 is the 4 th international meeting in a series organized by the European Commission Center of Excellence IDRANAP (InterDisciplinary Research and Applications Based on Nuclear and Atomic Physics) from the "Horia Hulubei" National Institute for Physics and Nuclear Engineering (IFIN-HH). The European Commission, under contract ICA1-CT-2000-70023, generously sponsored this meeting. The workshop topics covered new experimental and theoretical studies focused on the modern developments of nuclear fission aiming at various applications in a wide range of fields. It was an occasion to bring together scientists working in different fields related to nuclear fission in order to disseminate experience and knowledge in the benefit of the community. The main topics of the workshop were: radioactive beam facilities based on nuclear fission; nuclear waste transmutations and the future accelerator driven systems; fission and spallation nuclear data and modeling; experimental and theoretical advances in the study of nuclear fission; fusion reactions and decay modes of superheavy nuclei; stability against fission and many body systems and superasymmetric and multicluster fission. A few contributions presented by very young researchers emerging from connected domains were also accepted. The atmosphere during the workshop was stimulating due to the scientific level of the excellent lectures and the interesting contributions, offering an excellent frame for discussions and raising new suggestions and ideas. The opening address was given by Dr. E. Dragulescu, General Director of the National Institute for Physics and Nuclear Engineering, and the IDRANAP European Center of Excellence was presented by Dr. F. Buzatu, the Scientific Director. The meeting took benefits from the presence of Dr. L. Biro, Minister Secretary of State with Nuclear Safety, who presented a documented image of the nuclear energy in Romania and emphasized the importance of a durable development based on nuclear power plants. Prof. A.C. Mueller illustrated the importance of international

VII

VIM

collaborations in the context offered by the 6 European Framework Program and contributed to enhance the synergies within Romanian researchers. Special thanks are addressed to Prof. Yu.P. Gangrsky who presented the concluding remarks in an outstanding manner. We also thank to the International Advisory Committee consisting of Y. Abe (Kyoto), F. Buzatu (Bucharest), R. Casten (Yale), M. Ciocanescu (Pitesti), E. Dragulescu (Bucharest), C. Gheorghiu (Pitesti), W. Greiner (Frankfurt am Main), J.H. Hamilton (Nashville), S. Hofmann (Darmstadt), M.G. Itkis (Dubna), G. Muenzenberg (Darmstadt), Y. Nagame (Tokai), W. von Oertzen (Berlin), Yu.Ts. Oganessian (Dubna), D.N. Poenaru (Bucharest), A.V. Ramayya (Nashville), W. Scheid (Giessen), K.-H. Schmidt (Darmstadt) and P. Schuck (Orsay). The scientific secretary, Dr. Amalia Pop, and the technical secretary, Mrs. Alia Orascu, have done an extremely valuable and complex activity for the preparation of the meeting and managed difficult matters during the workshop efficiently, contributing essentially to the success. We want to thank Mr. E. Pauna, Mr. A. Sokolov and Mr. G. Chisner for their technical assistance. A special acknowledgement is dedicated to Mr. M. Duma and Mrs. Cristina Aiftimiei for their activity concerning the web design. A.C. Mueller M. Mirea

CONTENTS

Preface

vii

Fission Approach to Heavy Particle Radioactivities D.N. Poenaru. R.A. Gherghescu and W. Greiner

1

MYRRHA, a Multipurpose European ADS for R&D H.A. Abderrahim

9

Fusion-fission Dynamics and Synthesis of the Superheavy Elements Y.Abe

14

Quasifission of the Dinuclear System G.G. Adamian, N.V. Antonenko and W. Scheid

25

Microscopic Optical Potential for Nuclear Transmutation, Fusion Reactors and ADS Projects M. Avrigeanu, V. Avrigeanu, M. Duma, W. von Oertzen and A. Plompen

31

Identification of Excited 10Be Clusters Born in Ternary Fission of 262Cf A. V. Daniel. G.M. Ter-Akopian, G.S. Popeko, A.S. Fomichev, A.M. Rodin, Yu. Ts. Oganessian, J.H. Hamilton, A.V. Ramayya, J. Kormicki, J.K. Hwang, D. Fong, P. Gore, J.D. Cole, M. Jandel, L Krupa, J. Kliman, J.O. Rasmussen, A.O. Macchiavelli, I.Y. Lee, S.-C. Wu, M.A. Stoyerand R. Donangelo

41

Production of Photofission Fragments and Study of their Nuclear Structure Yu. P. Gangrsky and Yu. E. Penionzhkevich

48

Variation of Charge Density in Fusion Reactions R.A. Gherghescu, D.N. Poenaru and W. Greiner

54

IX

X

Parent Di-Nuclear Quasimolecular States as Exotic Resonant States N. Grama, C. Grama and I. Zamfirescu

60

Fission Investigations and Evaluation Activities at IRMM F.-J. Hambsch. S. Oberstedt, G. Vladuca and A. Tudora

67

Investigation of GeV Proton-Induced Spallation Reactions D. Hilscher. C.-M. Herbach, U. Jahnke, V.G. Tishchenko, J. Galin, B. Lott, A. Letourneau, A. Peghaire, D. Filges, F. Goldenbaum, K. Nunighoff, H. Schaal, G. Sterzenbach, M. Wohlmuther, L Pienkowski, W.U. Schroder and J. Joke

75

Evidence for Transient Effects in Fission B. Jurado. K.-H. Schmidt, C. Schmitt, A. Kelic, J. Benlliure andA.R. Junghans

82

Traps for Fission Product Ions at IGISOL S. Kopecky. T. Eronen, U. Hager, J. Hakala, J. Huikari, A. Jokinen, V.S. Kolhinen, A. Nieminen, H. Penttila, S. Rinta-Antila, J. Szerypo and J. Aysto

89

Triple-Humped Fission Barrier and Clusterization in the Actinide Region A. Krasznahorkay. M. Csatlos, J. Gulyas, M. Hunyadi, A. Krasznahorkay Jr., Z. Mate, P.G. Thirolf, D. Habs, Y. Eisermann, G. Graw, R. Hertenberger, H.J. Maier, O. Schaile, H.F. Wirth, T. Faestermann, M.N. Harakeh, M. Heil, F. Kaeppeler and R. Reifarth

95

Microscopic Analysis of the a-Decay in Heavy and Superheavy Nuclei D.S. Delion, A. Sandulescu and W. Greiner

101

Searching for Critical Point Nuclei in Fission Products N. V. Zamfir. E.A. McCutchan and R.F Casten

110

Fission Barriers in the Quasi-Molecular Shape Path G. Rover. C. Bonilla, K. Zbiri and R.A. Gherghescu

118

XI

Probing the 11Li Halo Structure by Two-Neutron Interferometry Experiments M. Petrascu. A. Constantinescu, I. Cruceru, M. Giurgiu, A. Isbasescu, H. Petrascu, I. Tanihata, T. Kobayashi, K. Morimoto, K. Katori, A. Ozawa, K. Yoshida, T. Suda and S. Nishimura

124

Dissipation in a Wide Range of Mass-Asymmetries M. Mirea

132

Physics with SPIRAL and SPIRAL 2 M. Lewitowicz

138

Two-Proton Radioactivity of 45Fe C. Borcea

146

Optimization of ISOL UCX Targets for Fission Induced by Fast Neutrons or Electrons O. Bajeat. S. Essabaa, F. Ibrahim, C. Lau, Y. Huguet, P. Jardin, N. Lecesne, R. Leroy, F. Pellemoine, M.G. Saint-Laurent, A.C.C. Villari, F. Nizery, A. Piukis, D. Ridikas, J.M. Gautier and M. Mirea

155

The ALTO Project: A 50 MeV Electron Beam at IPN Orsay O. Bajeat. J. Arianer, P. Ausset, J.M. Buhour, J.N. Cayla, M. Chabot, F. Clapier, J.L. Coacolo, M. Ducourtieux, S. Essabaa, H. Lefort, F. Ibrahim, M. Kaminski, J.C. Lescornet, J. Lesrel, A. Said, S. M'Garrech, J. P. Prestel, B. Waastand G. Bienvenu

160

Sensibility of Isomeric Ratios and Excitation Functions to Statistical Model Parameters for the (4'68He,n,3n)-Reactions T.V. Chuvilskaya. A.A. Shirokova andM. Herman

162

Fragment Mass Distribution of the 239Pu(d,pf) Reaction via the Superdeformed (3-vibrational Resonance K. Nishio. H. Ikezoe, Y. Nagame, S. Mitsuoka, I. Nishinaka, L Duan, K. Satou, M. Asai, H. Haba, K. Tsukada, N. Shinohara and S. Ichikawa

164

XII

Fingerprints of Finite Size Effects in Nuclear Multifregimentation Ad. R. Raduta andAI. H. Raduta

166

Systematics of the Alpha-Decay to Vibrational 2+ States S. Peltonen. J. Suhonen and D.S. Delion

170

Analysis of a Neutron-Rich Nuclei Source Based on Photofission M. Mirea. L. Groza, O. Bajeat, F Clapier, S. Essabaa, F. Ibrahim, A.C. Mueller, J. Proust, N. Pauwels and S. Kandry-Rody

172

Numerical Code for Symmetric Two-Center Shell Model P. Stoica

174

Deformed Open Quantum Systems A. Isar

176

Decommissioning the Research Nuclear Reactor VVR-S Magurele-Bucharest: Analyze, Justification and Selection of Decommissioning Strategy M. Dragusin, V. Popa, A. Boicu, C. Tuca. I. lorga and C. Mustata

178

K-Shell Vacancy Production and Sharing in (0.2-1.75) MeV/u Fe, Co + Cr Collisions C. Ciortea, I. Piticu, D. Fluerasu. D.E. Dumitriu, A. Enulescu, MM. GugiuandA.T. Radu

181

Some Fission Yields for 235U(n,f), 239Pu(n,f), 238U(n,f) Reactions in ZE Neutron Spectrum C. Garlea and I. Garlea

183

Recalibration of Some Sealed Fission Chambers—France in MARK III, Mol, Belgium Facility H.A. Abderahim, I. Garlea. C. Kelerman and C. Garlea

185

XIII

Muon Decay, a Possibility for Precise Measurements of Muon Charge Ratio in the Low Energy Range (< 1 GeV/c) B. Mitrica. A. Bercuci, I.M. Brancus, J. Wentz, M. Petcu, H. Rebel, C. Aiftimiei, M. Duma and G. Toma

190

Research and Development Activities as Support for Decommissioning of the Research Reactor VVR-S Magurele M. Dragusin

193

Light Heavy-Ion Dissipative Collisions at Low Energy A. Pop. A. Andronic, I. Berceanu, M. Duma, D. Moisa, M. Petrovici, V. Simion, G. Imme, G. Lanzano, A- Pagano, G. Raciti, R. Coniglione, A. Del Zoppo, P. Piatelli, P. Sapienza, N. Colonna, G. d'Erasmo and A. Pantaleo

195

Estimates of the a Rates for Deformed Superheavy Nuclei /. Silisteanu, W. Scheid, M. Rizea andA.O. Silisteanu

197

List of Participants

201

FISSION A P P R O A C H TO HEAVY PARTICLE RADIOACTIVITIES

D. N. POENARU AND R. A. GHERGHESCU Horia Hulubei National Institute of Physics and Nuclear Engineering, RO-077125, Bucharest-Magurele, Romania, E-mail: [email protected] W. GREINER Frankfurt Institute for Advanced Studies, J. W. Goethe Universitat, Pf 111932, D-60054 Frankfurt am Main, Germany Heavy particle radioactivity predicted in 1980 was experimentally confirmed since 1984. The obtained until now data on half-lives and branching ratios relative to a-decay of 14 C, 1 8 ' 2 0 O, 2 3 F, 22,24-26Nei 28,30Mg a n d 32,34g; rad i 0 activities are in good agreement with predicted values within the analytical superasymmetric fission (ASAF) model. The strong shell effect may be further exploited to search for new cluster emitters.

1. Introduction In order to predict heavy particle radioactivities in 1980 and to arrive at a unified approach of cluster decay modes, alpha disintegration, and cold fission, before the first experimental confirmation3 in 1984, we developed and used a series of fission theories in a wide range of mass asymmetry, namely: fragmentation theory, numerical (NuSAF) and analytical (ASAF) superasymmetric fission models, and a semiempirical formula for a-decay (see the multiauthored book * and the references therein). As normally expected, being intermediate phenomena between fission and a-decay, cluster radioactivities have been treated 2 ' 1 either as extremely asymmetric cold fission phenomena or in a similar way to a-decay, but with heavier emitted particles 4 ' 5 . The main difference from model to model consists in the method used to calculate the preformation probability or the half-life. There are also different relationships for the nuclear radii, interaction potentials, as well as for the frequency of assaults on the potential barrier. Particularly useful has been the ASAF model, improved successively

1

2

since 1980, allowing us to predict the half-lives and branching ratios relative to a-decay for more than 150 different kinds of cluster radioactivities, including all cases experimentally determined so far. Several other models have been introduced since 1985 (see the cited papers in Refs. 1 and 6). The performed measurements 7 _ 1 4 of cluster decay modes, showing a good agreement with calculated half-lives within analytical superasymmetric fission model, are included in a comprehensive half-life systematics 15 from which other possible candidates for future experiments may be obtained. The experimental data on half-lives and branching ratios relative to a-decay of 1 4 C, 1 8 ' 2 0 O, 2 3 F , 22,24-26^ 28,30Mg a n d 32,34Si r a d i o a c . tivities are in good agreement with predicted values within the analytical superasymmetric fission (ASAF) model. The fine structure 16 was predicted 17 before the discovery of 1989 in Orsay. The measurements 18 with superconducting magnetic spectrometer SOLENO were repetead with the best accuracy ever obtained 19 in 1995.

2. Cold fission In the usual mechanism of fission, a significant part (about 25-35 MeV) of the released energy Q is used to deform and excite the fragments (which subsequently cool down by neutron and 7-ray emissions); hence the total kinetic energy of the fragments, TKE, is always smaller than Q. Since 1980 a new mechanism has been experimentally observed - cold fission10 characterized by a very high TKE, practically exhausting the Q-value, and a compact scission configuration. Experimental data have been collected in two regions of nuclei: (a) thermal neutron induced fission on some targets like 233,235Uj 238 Np) 239,241 p U ) 245 C n i ) ^ t h e spontaneous fission of 252

Cf; (b) the bimodal 2 1 spontaneous mass-symmetrical fission of 2 5 8 Fm,

259,260 M d ; 258,262 NO;

& n d

260104

T h e y i e M

rf

t h e c o l d

fisgion

m e c hanism

is comparable to that of the usual fission events in the latter region, but it is much lower (about five-six orders of magnitude) in the former. We have systematically studied the cold fission process viewed as cluster radioactivity within our ASAF model. 22 ' 23 The cold fission properties of transuranium nuclei are dominated by the interplay between the magic number of neutrons, N = 82, and protons, Z = 50, in one or both fragments. The best conditions for symmetric cold fission are fulfilled by 2 6 4 Fm, leading to identical doubly magic fragments 132 Sn. A spectrum of the 234 U halflives versus the mass and atomic numbers of the fragments illustrates the idea of a unified treatment of different decay modes over a wide range of

3

mass asymmetry. Three distinct groups, a-decay, cluster radioactivities, and cold fission, can be seen, in good agreement with experimental results. 3. Region of cluster emitters From the energetical point of view (released energy Q > 0) the area of heavy particle radioactivity is extended well beyond that of a-decay. Nevertheless, the largest branching ratio with respect to a emission experimentally determined up to now is ba = Ta/T ~ 10~ 9 . At the limit of experimental sensitivity, the smallest branching ratio measured already is of the order of 10~ 16 for 34 Si decay of 242 Cm and the longest upper limit of the halflife (for 24 - 26 Ne radioactivity of 2 3 2 Th) is T > 10 2 9 2 s. Consequently we

126 „ • Be

0

C

B

0

sNe oMg H S i

82

Figure 1. Part of the nuclear chart showing the predicted (within ASAF model) emitters and t h e most probable emitted heavy particles from nuclei heavier than the doubly magic 2 0 8 P b , the region where successful experiments have been performed. The line of beta-stability is marked with black squares. The selection condition was T < 10 3 0 s, ba > 1 ( T 1 7 .

selected from the very large number of cluster emitters those fulfilling simultaneously the conditions T < 10 30 s and ba > 1 0 - 1 7 . The nuclear chart of cluster emitters obtained in such a way for N > 126 and Z > 82 is plotted in Fig. 1. This is the region in which successful experiments have been performed. The cluster emitters 221 Fr, 2 2 1 - 2 2 4 - 2 2 6 Ra, 225 Ac, 228, 23 o Th) 23ip a j 230,232-236 U ; 236,238p U i

a n d

242 Cm ^

e

j t h e r p^gfofe

o r n o t far

from

stabil

.

ity nuclei. Few examples from the total of about 300 stable nuclides found in nature are shown in Fig. 1. Following Green, the line of beta stability can be approximated by A={Z-

100)/0.6 + y/(Z - 100) 2 /0.36 + 200Z/0.3

(1)

Another island of very proton-rich cluster emitters above the doubly magic 100 Sn is not shown on the above mentioned figure.

4

4. Shell effects The surface of calculated half-lives (within ASAF model) of heavy nuclei against 14 C radioactivity and the measured points are plotted in Fig. 2. A strong shell effect can be seen: as a rule the shortest value of the halflife (maximum of 1/T) is obtained when the daughter nucleus has a magic number of neutrons (Nj = 126) and/or protons {Z& = 82). For 14 C decay

Figure 2. The surface of calculated half-lives (within ASAF model) of heavy nuclei against 1 4 C radioactivity and the measured points. Daughter nuclei are P b isotopes. The peak of maximum probability (shortest half-life) corresponds to 2 2 2 R a for which the daughter is the doubly magic 2 0 8 P b .

modes the peak of maximum probability (shortest half-life) corresponds to 222 Ra for which the daughter is the doubly magic 2 0 8 Pb. As can be seen in table 1, from 26 identified emitters and 9 determined upper limits (u) one has: • 9 +2u — doubly magic daughter g^8Pb126 • 9 — magic proton number Za = 82 • 6 + 4u — magic neutron number N^ = 126. There are only 2+3u exceptions: Zd ^ 82 Nd ^ 126: 'Ac - • i 4 C 8 + I^Biiag; i n - • 1 0 JNei4 + 8 0 U g l 2 8 , 233 U -* 2 |Mg 1 6 + 2 ° 5 Hg 125 ; 23*U -+ 2 «Mg 16 + 80 M g,127) a n d 2 3 6 U -+ 28.Mg16 + 2 ° 8 Hg 128 .

225

5

We continue to present the shell effects in the next section. Table 1. Performed experiments. Prom 26 identifications and 9 upper limits 24 + 6 belong to this table. Magic nucleon numbers of the daughter. Par is an abreviation for parent. Zd == 82

Par. 222

Ra

Fragments 14

C8

8

Ra

14

8

223

Ra

14

224

Ra

i Pbl26

lo

228

20O 8 U 23F

15 8 Pbl26

Pa

14 14

c8 c8

C8

i9Pb

230'pj1

24

Ne

231

Pa

24

Ne

207

Tli26

Th

26

Ne

206

Hg126

|2°Pb 2

|2 Pb §°9Pb

Ne

i Pbl26

234n

24

Ne

§2°Pb

|§ 8 Pb!26

236

TJ

24

Ne

|2XPb

Ne

I^PblSe

235

TJ

25

Ne

l2°Pb

Mg

i8Pbl26

238pu

28

Mg

i2°Pb

232-[j

24

Ne

233 "[J

25

Ne

234

U

26

236pu

28

238pu

30 34

Ra

C8

i Pb

14

24

22

Cm

i Pbl26

226

C8

Ne

M g

Si20

I^PblSe 8

8

§§ Pbl26

Fragments

221^.

7

233 TJ

230 TJ

242

8

Nd = 126 Par.

Fragments

221

i Pb!26

231

Par.

8

226Th

Th

Zd = 82

Nd = 126

232

207 206

T1 1 2 6

Hgl26

234 TJ

28

M g

206

Hgl26

236 TJ

30

M g

206

Hgl26

Np

30

M g

238pu

32

237

T1126

Si

206

Hgi26

206

Hgl26

240pu

34

Si20

241

34

Si20

Am

207

207

T1126

i8Pbl26

5. N e w candidates By comparing the systematics of calculated values and of experimental data one can list 15 other possible candidates for future experiments: 220,222,223Fr; 223,224Ac> a n d 225 T h M u c e m i t t e r s ; 2 2 9 Th for 2 0 O radioactivity; 2 2 9 Pa for 22 Ne decay mode; 2 3 0 ' 2 3 2 Pa, 231 U, and 2 3 3 Np for 24 Ne radioactivity; 2 3 4 Pu for 26 Mg decay mode; 234 - 235 Np and 235,237pu ^ 2 8 M g emitters, as well as 238>239Am and 2 3 9 _ 2 4 1 Cm for 32 Si radioactivity. Also 33 Si decay of 2 4 1 Cm could be observed. In the table 2 one may see • 3 cases with doubly magic daughter g28Pbi26 • 6 with magic proton number Zd = 82 • 8 with magic neutron number Nd = 126. There are nine exceptions with Zd ^ 82 Nd ^ 126: 220m. _v 14/"1 i 206npi . * r ->• 6 ^ 8 + 81 1 1 1 2 5 ,

222r\. _v 14/~< _i_ 208x1 *T -t 6 <^8 + 81 i l 1 2 7 )

223

224

Fr -+ i 4 C 8 + i? 9 Tl 1 2 8 ; Th -»• i 4 C 8 + l^PoiaT; 232 Pa -+ 2 4 Ne 1 4 + 1? 8 T1 127 ; 225

Ac -»• £ 4 C 8 + H°Bi 127 ; Pa -> 2 4 Ne 1 4 + I? 6 T1 125 ; 234 Np -> 2 lMg 1 6 + I° 6 T1 1 2 5 ,

230

6 Table 2. Candidates for new experiments; 14 cases with magic nucleon numbers of the daughter out of the total number 23. Zd = 82 Par. 234pu 240 241

Cm Cm

and

Zd = 82

Nd = 126 Par.

Fragments 26Mg 32 33

238

Si Si

208pbl26 8

§0 Pb 1 2 6 i8Pbl26

14

Fragments

229Th

20

24

231U 235pu

28

237pu

28

Par.

O

209Pb

Ne

7

223Ac

§§ Pb

C8

209B;126

229pa

207Th26

24

209

Mg

|07pb

233Np

Mg

9

§° Pb

239Cm

32 Si

|07pb

239

241 C m

32

|09pb

Si

Fragments 14

22Ne

235Np

A m - • ? 2 Mg 1 8 +

6. Emission of

Nd = 126

Am

Ne

Bii26

28Mg

207Tll26

32 Si

207Tll26

2 6

° T1125.

C in competition with

12

C

14

In 1984 there was a discussion: why C and not the three alphas 12 C is emitted from 223 Ra? Based on alpha-like theory one would expect a three-a structure to be preformed and emitted with maximum probability. On the other hand let us have a closer look at the following equation expressing the halflife in terms of three model-dependent quantities (frequency of assaults, preformation probability, and the penetrability of the external part of the barrier): T=l

~T

=

~^P

l

°ST = iosF-^gS-\ogP

(2)

where F = In 2/v with v denoting the frequency of assaults on the barrier in the process of quantum penetrability. As may be seen in Fig. 3, despite a slightly smaller preformation probability, the Q-value is higher and the potential barrier for emission of 14 C is smaller so that a higher penetrability makes a shorter half-life. The shell effects of the emitted particle 64Cg with magic neutron number are also playing a role. 7. Half life estimation with the universal curve The preformation probability can be calculated within a fission model as a penetrabilty of the internal part of the barrier, which corresponds to still overlapping fragments. With good approximation, by assuming v = constant and S — S(Ae), one can obtain the universal curve for any kind of cluster decay mode, including a decay: logT = - logP - 22.169 + 0.598(Ae - 1)

(3)

7

12

13 223

'

45

14

I

•

Ra - -

40 35 7 30

15

I

—

'

Q(MeV) log T(s) -logs log P -logF(s)

- "••••^

16

I

'

j S'

~

^^

^f

25 2U

-

15

_

• ^ ^ ^

^

^

—

^ ^ " " N ^ ^

_

— — —

It)

""" "~

•

— 1

45 :

222

|

1

|

1

|

1

Ra

:

40 /

3b y

'

^ ~ ^

s

v ^"

—<\ T V -

30 25

^

20

/

s

15 10 =

12

^^^Sw

,

i

13

S

,

\-~T~

14

i

15

16

Figure 3. Q-values, halflives T, and the three model dependent quantities (F = the preexponential factor, 5 = preformation probability, and P = the penetrability of external part of the barrier) versus the mass number Ae of the emitted carbon (Ze = 6 ) cluster from 2 2 3 R a (top) and 2 2 2 R a (bottom).

where the penetrability of the external part of the barrier is easily calculated - logP = Q.22&7Z{nAZdZeRbfl2

[arccos y/r - y/r(l - r)

with r = Rt/Rb, Rt = 1.2249(Ad/3 + Al/3), HA = AdAe/A.

Rb = 1.43998ZdZe/Q,

(4)

and

Acknowledgments This work was partly supported by the Centre of Excellence IDRANAP under contract ICA1-CT-2000-70023 with European Commission, Brussels, by

8 U N E S C O ( U V E - R O S T E Contract 875.737.2), by Gesellschaft fur Schwerionenforschung (GSI), D a r m s t a d t , by Bundesministerium fur Bildung u n d Forschung (BMBF), Bonn, a n d by Ministry of Education a n d Research, Bucharest.

References 1. D.N. Poenaru, W. Greiner, in Nuclear Decay Modes, (IOP Publishing, Bristol, 1996), Chap. 6, pp. 275-336. 2. A. Sandulescu, D. N. Poenaru and W. Greiner, Sov. J. Part. Nucl. 1 1 , 528 (1980). 3. H. J. Rose and G. A. Jones, Nature 307, 245 (1984). 4. R. Blendowske, T. Pliessbach and H. Walliser, Chap. 7 in Ref.1, pp. 337-349. 5. R. G. Lovas, R. J. Liotta, A. Insolia, K. Varga and D. S. Delion, Phys. Rep. 294, 265 (1998). 6. D. N. Poenaru and W. Greiner (Eds), Handbook of Nuclear Properties (Clarendon Press, Oxford, 1996). 7. P. B. Price, Annu. Rev. Nucl. Part. Sci. 39, 19 (1989); P. B. Price and S. W. Barwick, Ch. 8 in Ref.23, Vol. II, p. 205. 8. W. Henning and W. Kutschera, Ch. 7 in Ref.23, Vol. II, p. 188. 9. E. Hourany, Ch. 8 in Ref.1, p. 350. 10. R. Bonetti and A. Guglielmetti, Ch. 9 in Ref.1, p. 370. 11. Pan Qiangyan et al., High Energy Phys. Nucl. 23, 1039 (1999); Chinese Phys. Lett. 16, 251 (1999); Phys. Rev. C 62, 044612 (2001). 12. R. Bonetti, C. Carbonini, A. Guglielmetti, M. Hussonnois, D. Trubert and C. Le Naour, Nucl. Phys. A 686, 64 (2001). 13. S. P. Tretyakova et al. Radiat. Meas. 34, 241 (2001); A. A. Ogloblin et al., Phys. Rev. 6 1 , 034301 (2000). 14. A. Enulescu et al. Radiat. Meas. 28, 555 (1997). 15. D.N. Poenaru, Y. Nagame, R.A. Gherghescu, W. Greiner, Phys. Rev., C65 (2002) 054308; Erratum C66 049902. 16. M. Mirea and R. K. Gupta, in Heavy Elements and Related New Phenomena Vol. II (World Scientific, Singapore, 1999) p. 673. 17. M. Greiner and W. Scheid, J. Phys. G, 12, L229 (1986). 18. D. N. Poenaru and W. Greiner (Eds), Experimental Techniques in Nuclear Physics (Walter de Gruyter, Berlin, 1997). 19. E. Hourany et al. Phys. Rev. C 52, 267 (1995); E. Hourany, I. H. Plonski and D. N. Poenaru, Ch. 4 in Ref.18, p. 117. 20. C. Signarbieux et al., J. Phys. Lett. (Paris) 42, L437 (1981). 21. E.K. Hulet et al., Phys. Rev. Lett. 56, 313 (1986). 22. D. N. Poenaru, J. A. Maruhn, W. Greiner, M. Iva§cu, D. Mazilu and R. Gherghescu, Z. Phys. A 328, 309 (1987). 23. D. N. Poenaru, M. Iva§cu and W. Greiner, Ch. 7 in Particle Emission from Nuclei, Vol. Ill (CRC, Boca Raton, FL, 1989) p. 203.

MYRRHA, A MULTIPURPOSE EUROPEAN ADS FOR R&D HAMID AIT ABDERRAfflM* SCK-CEN, Boeretang 200, B-2400 Mol, Belgium

1.

Introduction

Since 1997 SCK»CEN is developing MYRRHA in collaboration with various European laboratories as a multipurpose Accelerator Driven System (ADS) for R&D applications [1]. In its present status, the MYRRHA project is based on the coupling of a (350 MeV- 5 mA) LINAC proton accelerator with a liquid Pb-Bi windowless spallation target and a neutron multiplying sub-critical core (SC) cooled by Pb-Bi in a pool type configuration (see Fig. 1). 2.

Spallation target

The spallation target circuit (see Fig. 2) is fully separated from the core coolant as a vacuum tight unit whose internal heat production is removed to the SC pool. For achieving high performance core characteristics, we had to cope with a drastic geometrical constraint during the spallation target design. Indeed, the available central hole in the core four housing the spallation source is limited to roughly 10 cm diameter and that lead to a current density of -130 uA/cm2 on the hypothetical window target. Therefore, we decided to design the MYRRHA spallation target as a windowless target. The choice of using a 350 MeV protons is also putting a constraint in terms of heat deposition in the target. Indeed, the proton penetration in the Pb-Bi is limited to 13 cm leading to a heat deposition of -1.4 MW in a volume of 0.5 liter. This led us to choose the solution of a liquid Pb-Bi target. 3.

Sub-critical core

The SC has fast neutron spectrum properties and the capability of housing several islands with thermal spectrum regions located in In-Pile Sections (IPS) in or at the periphery of the fast core. The fast core is fuelled with typical fast reactor fuel pins arranged in hexagonal assemblies with an active length of 600

[email protected], [email protected]

9

10 mm. The three central hexagons are housing the spallation module. The MOX Proton B e a m Tube

m\

•-I.' *r\

•1

•

r -1

••

-if

J! t

t

I-

i

3I

•Tl:

>* f w-

Spallation L o o p :for-Pb-Bi

^

•

Subcritical Core •Ylth Spallation I'arget

'A Double-Vessel f o r Lead-Bismuth Eutectic Coolant

Figure 1. MYRRHA spallation loop cut-away.

fuel has Pu contents of 30% and 20%. The Pu isotopic vector is the one typical resulting from the U0 2 LWR reprocessing. 4.

Containment building

The facility is designed to be operated to a large extent thanks to remote handling. Therefore, the design called for a dedicated building containment arrangement as illustrated in Fig. 3. A remote handling system based on the Man-In-The-Loop principle implemented with two bi-lateral force reflecting servo-manipulators working under Master-Slave mode has been recommended on basis of similar implementation in fusion projects. The slave servo-manipulators will be

11 commanded by remote operators using kinematically identical master manipulators supported with CCTV feedback. The manipulators will have

VACUUM PUMPING DUCT ELECTRICAL MOTOR • HYDRAULIC PRIMARY DRIVE GUIDERAILFDR MOUNTING INTO CORE LM CONDITIO!!!) VESSEL

CO-AXIAL LM FEED

SUCTION POINT OF MHDPUMP DRAG LIMITED FLOW ANNULAR SECTION

SPALLATION SOURCE FEED

IMPELLER SECTION

LM-LM HEAT EXCHANGER

Figure 2. MYRRH A spallation loop cut-away.

additional robotic capabilities to maximize operational capabilities. The slave manipulators will be positioned close to the task environment by means of remotely controlled transporters with sufficient reach and degrees of freedom to position the slave at all relevant locations around the MYRRHA machine. The concept relies on the ability of the servo-manipulators and the video feedback systems to create a sense of presence for the operators at the task location. In practice all of the MYRRHA maintenance tasks will be performed directly by personnel using the arms, a range of cameras and cranes in much the same way

12 as if they were next to the MYRRHA machine themselves. The remote manipulators and transporters will have computer controlled features which will enhance and simplify the operations. 5.

Objectives

The MYRRHA project team is developing a multipurpose neutron source for R&D applications on the basis of an ADS. This project is intended to fit into the European strategy towards an ADS Demo facility for nuclear waste transmutation. It is also intended to be a European, fast-neutron-spectrum, irradiation facility allowing various applications such as: ADS concept demonstration, MAs transmutation studies, LLFPs transmutation studies, radioisotope production for medical applications, material research for fission and fusion reactors, fuel research for innovative concepts, safety studies for ADS

Figure 3. Internal view of the MYRRHA System containment building

13 6.

Conclusions

The present time schedule of MYRRHA is to be put in service around 2012. This planning is subject to modification depending on the outcome of the detailed engineering design that would reveal an important need for R&D support program for the present design and on the approval procedure in combination with the availability of the corresponding funding. MYRRHA is a challenging facility from many points of views therefore we are convinced that it will trigger a renewal of R&D activities within the fission community. Its development will attract young talented researchers and engineers looking for challenges. It will be a new irradiation facility for research and in Europe for future innovative energy systems. References 1.

C. Rubbia, H.A. Abderrahim, M. Bjornberg, B. Carluec, G. Gherardi, E.G. Romero, W. Gudowski, G. Heusener, H. Leeb, W. von Lensa, G. Locatelli, J. Magill, J.M. Martinez-Val, S. Monti, A. Mueller, M. Napolitano, A. Perez-Navarro, M. Salvatores, J.C. Soares and J.B. Thomas, in A European Roadmap for Developing Accelerator Driven Systems (ADS) for Nuclear Waste Incineration, ENEA, Roma, 2001.

FUSION-FISSION D Y N A M I C S A N D S Y N T H E S I S OF T H E SUPERHEAVY ELEMENTS

YASUHISA ABE Yukawa Institute for Theoretical Physics, Kyoto Univ., 606-8502, Kyoto

Dissipation in nuclear collective motions is testified through anomalous neutron multiplicities emitted prior fission. Its importance is also shown in fusion of massive systems and thereby in the synthesis of the superheavy elements. It is recommended to keep in mind the important role of the dissipation and its associated fluctuation in nuclear collective motions such as nuclear fission.

1. Introduction The measurements of multiplicities of neutrons, gamma rays etc. emitted prior scission in fusion-fission reactions 1 clarify that the life time of nuclear fission is much longer than that expected from Bohr-Wheeler formula. Therefore, a dynamical treatment of the process is required. Following the pioneering work by Kramers with the dissipation-fluctuation dynamics 2 , the fissioning degree of freedom is described with the viewpoint of Brownian motion under incessant interactions with the heat bath particles, i.e., with nucleons in the thermal equilibrium in the present case. In the dynamical description, the fission width is no more constant in time, but has a transient feature, as well as the reduction factor, so-called Kramers factor. Both effectively result in a longer life time, consistent with anomalous multiplicities measured 3 . In fusion process, shape evolution of the sticked configuration formed by the target and projectile nuclei to the spherical compound nucleus is again expected to be governed by the dissipation-fluctuation dynamics. Actually, in very heavy systems it is known experimentally that there exists a hindrance in fusion4, which is inferred to be due to the dissipation of incident kinetic energy during the processes leading to the spherical compound nucleus. That is, the Coulomb barrier is not enough for determination of fusion probability, but an extra-energy above the barrier height is required for the system to fuse. This is understood by the properties of the energy

14

15 surface of the Liquid Drop Model in heavy systems. After overcoming the Coulomb barrier, the ions touch with each other. But the sticked configuration with a pear shape is located outside of the conditional saddle point or outside of the ridgeline. Therefore, in order to form the spherical compound nucleus, the system has to overcome one more barrier 5 . Naturally, in such a situation, the kinetic energy carried in by the incident projectile has been more or less dissipated, i.e., the composite system is heated up 6 . Thus, the shape evolution toward the spherical shape or toward the re-separation can be considered as a Brownian motion with the heat bath inside like in the fission process. Dynamical features of the fission process is briefly reminded in section 2. In section 3, the two-step model 7 for fusion of massive heavy-ion systems is recapitulated where the fusion probability is given by a product of the sticking and the formation probabilities. The former is that for the system to overcome the Coulomb barrier to stick each other, while the latter that for the system to overcome the conditional saddle to form the spherical shape. In section 4, residue cross sections for the superheavy elements with Z—113 and 114 are predicted by combining the survival probability which is calculated with the statistical theory of decay 8 . A summary is given at the end.

2. Dynamical features of nuclear fission Experimental multiplicities of pre-scission neutron increase monotonically as excitation energy of the compound nucleus increases, while the calculations with the statistical theory of fission decay and of neutron emission show a kind of saturation 9 . This is inferred due to a fast decrease of fission life in higher total angular momenta which come into play as energy increases. Therefore, a mechanism is looked for, which makes the fission decay life to be longer. Since Bohr-Wheeler theory is considered to be based on "equilibrium statistical mechanics", a non-equilibrium statistical dynamical approach should be applied, as mentioned in the Introduction. Kramers proposed the equation for time evolution of the distribution function for the collective coordinate and associated momentum, which is now called Kramers equation 2 . Furthermore, he solved it in a quasi-stationary regime to obtain the formula for the decay rate which is almost the same as that by Bohr-Wheeler except an additional pre-exponential factor, so-called Kramers factor, which is given as follows,

16 rK = K(x)-rBW,

K(x) = Vx2 + l - x ,

x = 0/2-u,

P = "(/m,

(1)

where 7, m and UJ denote the friction coefficient, the inertia mass and the curvature of the barrier, respectively. rBW denotes the decay rate given by the conventional Bohr-Wheeler theory. Kramers factor always reduces the decay rate, i.e., makes the fission life longer. If we solve time evolution of the distribution function with Kramers equation, we always obtain a time-dependent decay rate which starts with zero at the beginning and, after a while, approaches to the Kramers stationary limit given in Eq. (1). This means that there is a dead time in fission decay, which gives an additional time for the decay life time. The dead time, of course, depends on an initial distribution, but does not depend strongly on the excitation energy. Both, the dead time and the Kramers factor, make the fission life longer than that given by Bohr-Wheeler theory. For realistic calculations of fission dynamics, we employ a multi-dimensional Langevin equation which is equivalent to Kramers equation and easy to solve numerically 10,11 . dpi dV 1 d -^- = - g - ~ 2 a r ( — = (m lij

)ijPj,

m

!

_x )ikPjPk ~ Uj (m

)jkPk + 9ijRj (t), (2)

T = gikQjk,

where repeated indices are assumed to sum up. V(q) is the potential energy, which is calculated as the sum of a generalized surface energy, a Coulomb energy for diffused surface and a centrifugal potential. The tensors rriij and jij denote the inertia mass and the friction tensors, respectively. The former is taken to be hydrodynamical one calculated with Werner-Wheeler approximation 12 , while the latter is so-called one body model (OBM), i.e., one-body wall-and-window formula13, gtj denotes the strength of the random force associated to the friction through the dissipation-fluctuation theorem (D-F theorem) which is given in the last line of Eq. (2), with temperature T of the heat bath. B4 denotes random number which is assumed to be Gaussian with the following properties; (Ri{t)) = 0, (Ri(t) • Rj(t')) = 6ij • 6{t - t'), where ( ) denotes the average over all the realizations of Gaussian random numbers. A coupling

17

to neutron evaporation is made through the temperature which defines the strength of the fluctuation force through the D-F theorem. This means that the temperature T depends on time due to the cooling by successive neutron evaporation. Examples of time-dependent fission decay rates are shown in Fig. 1, where the transient feature is seen as well as the cooling effect which makes Kramers limit itself time-dependent. Neutron multiplicities calculated with the results of the dynamical calculations of fission turned out to be in a good agreement with the measured energy-dependence of the multiplicities, as given in Refs. 3 and 10. This means that the present dynamical approach well describes the fission life time indicated by the experiments. There is another physical quantity which depends more directly on dynamics of fissioning degree of freedom. That is the total kinetic energy of fission fragments (TKE) which carry information of dynamical process from the saddle point to the scission point. The comparison between the calculated results and the measurements is also made in Refs. 3, 10 and 11. Average values of TKE are well reproduced, but the variances of the distributions are not completely well reproduced. Nevertheless, it would be satisfactory, considering that the present model is limited to the mass symmetric configurations, while the data includes those of mass asymmetric components. Actually, three dimensional calculations including mass asymmetry degree of freedom which was made later 14 turned out to fill out the above insufficiency. Other physical quantities such as gamma ray emitted prior fission

0.004 N

i i—| i I i | i I i | i I i | i i i | i—i—r

0

"J

000 0

I i i i I i i i I i i i I i i i I i i i 20

40

60

80

120x10

Time [ s ]

Figure 1. Calculated fission decay widths V = r • h are for 2 0 0 P b system with J=40ft and 50ft. Bold solid lines are calculated at the scission point while thin solid lines at the saddle point. Dashed lines denote Kramers limits which depend on time through time-dependence of the temperature due to cooling by neutron evaporation.

18 have been shown to have the similar tendency 15 . And recent systematic study has shown that OBM would be modified about by factor 1/2, but not by order of magnitude 16 . At the same time, recent direct measurements of fission life time by crystal blocking method have indicated a possibility that the fission life is much longer than that discussed above 17 . In brief, it can be concluded that collective motions of excited nuclei are governed by the D-F dynamics with quite a strong energy dissipation comparative to OBM, or even stronger. 3. Fusion dynamics of massive systems : Two Step Model

P'.AE UK shck V cm'

[E )=Prt. (£ ) form*'

cm'

jiii/on *•

cm'

m Etm Coulomb barrier

s

-E

vB

'

E*

v.. A

-Q

B*

^E^+Q

Figure 2. One-dimensional schematic presentation of the two-step process, where the Coulomb barrier and the conditional saddle point are displayed for formation of the compound nucleus.

In view of the strong dissipation in fissioning motion as testified in section 2, the collective motion leading to the spherical compound nuclei, i.e., the fusion process is expected to similarly suffer the dissipation due to the interactions with thermal nucleonic motions, because the sticked configuration is more or less internally excited. In heavier systems like nuclei of the superheavy elements, sticked configurations with a pear-shaped configuration are located outside a conditional saddle point, or a ridge line, which has to be overcome for the system to reach the spherical shape of the compound nucleus, as schematically shown in Fig. 2. Thus, the dissipation

19 during this process would be a main origin for the fusion hindrance observed in massive systems 18 . (In lighter heavy ion systems, sticked configurations are already inside the conditional saddle point, and thus, they automatically slide down to the spherical compound nuclei. Therefore, the effects of the dissipation do not show up themselves distinctively in contrast to the massive systems.) The probability for the formation of the compound nucleus has to be calculated by D-F dynamics, i.e., by the Langevin equation 2 in the same way as that for the fission, while the initial conditions are different, i.e., the starting point of dynamical evolution is the outside of the saddle, or the ridge line. And the mass-asymmetry coordinate is indispensably necessary, corresponding to various combinations of a projectile and a target which define the asymmetry of the initial configuration. Here, we notice that there are possibilities in how to choose an initial momentum conjugate to the distance coordinate between the mass centers of the pear-shape configuration, which depends on the approaching process up to the contact point. Dynamics of the process overcoming of the Coulomb barrier determines the momentum as well as the probability for sticking of a projectile and a target of the incident channel. This means that the fusion probability Pfusion is given by the product of the two probabilities; the formation and the sticking probabilities, Pformation and Psticking-

-* fusion

— * sticking ' •* formation-

\y)

A naive choice for Psticking is a quantum tunneling probability of the Coulomb barrier, i.e., a transmission coefficient which is often used as Pfusion in lighter heavy ion systems. The choice conserves the energy. Another one is a classical passing over the Coulomb barrier under frictional force, which does not conserve the energy. In other words, the system is being internally heated during the approaching process toward the contact point. One of the realizations is so-called Surface Friction Model(SFM) which was proposed for the description of the Deep-Inelastic Collisions with a fair success 19 . We employ the model for the approaching process up to the contact point, not for the whole collision process. Then, there is a problem of connection between the two processes, the approaching and the formation processes, i.e., the connection between twobody collision phase and one-body shape evolution phase. Since we extend SFM so as to include the fluctuation associated to the surface friction, the radial momentum at the contact point results in a distribution, actually a Gaussian distribution which is due to the Gaussian nature assumed for the

20

fluctuation force6. Generally the distribution is given as follows,

(p-p)x\* 2fj,-T

(4)

where p denotes the average momentum left at the contact point. This distribution gives an initial condition for subsequent shape evolution of the united system, i.e., initial values of the momentum for the shape evolution. Thus, the method is called "statistical connection". Practically, formation probabilities obtained with various values of the initial radial momenta are convoluted with the Gaussian distribution, which gives rise to the final formation probability for a given incident kinetic energy. For realistic calculations of Pformation, we need at least two degrees of freedom for shape description as stated above, i.e., the distance between two mass centers and the mass-asymmetry. In the following, we will see results obtained with the two-dimensional model for shape evolution 20 . Of course, the neck degree of freedom is also expected to play an important role, which is discussed elsewhere21.

'"Fe +

e

208

Pb

O

*

a

n»i«, (Experiment) ''ruao- (ln,Calculation)

o

U 10

1

10

10

-3 10

~215

220

225

230~

235

240

245 250 E t m (MeV)

Figure 3. Comparison of calculated fusion excitation function with the experimental one for 5 8 Fe+ 2 0 8 Pb system.

With these fusion probabilities for relevant total angular momenta J's, we calculate fusion excitation functions, according to the usual formula,

21 ^fusion

= 7rX 2 J2(2J

+ 1) • Pfusion,

(5)

where X denotes the de-Broglie wave length corresponding to the incident energy. An example is shown in Fig. 3 for 5 6 Fe+ 2 0 8 Pb system, where measured experimental data are available 22 . It is remarkable that the calculations reproduce the data very well, without adjusting any parameter 8 . This strongly indicates that the two-step model describes the fusion process in massive systems with a realistic accuracy. (Note that the data show very small cross sections, exemplifying the fusion hindrance.) 4. Predictions of excitation functions for residue cross sections of SHE Experimentally, cross sections for SHE are well known to be extremely small 23 , which is well expected from the fusion hindrance explained in the previous section. But there is the other factor which plays an important role in determining the residue cross sections, i.e., the survival probability Psurvivai against fission. It is given by the ratio between neutron decay and fission decay widths, and expected to be extremely small, because of a large fission decay probability due to the fact that the fissility parameter is close to 1 in nuclei for SHE. A new statistical decay code KEWPIE is recently developed which is suitable for cases with such small probabilities 24 . The code is checked through applications to various cases, for example, to the excitation functions of xn reactions in 4 8 Ca+ 2 0 8 Pb system. With PSUrvivai calculated with the code and Pfusion of the two-step model, excitation functions of residues are calculated with usual formula of the compound nucleus theory of reactions,

ares

— ?r*

2 ^ ( 2 J + ^)Pfusion

' Psurvivai

(6)

There are a few parameters in the statistical theory, such as masses, or shell correction energies of compound nuclei of SHE, the level density parameter, the shell damping energy etc. The second one is calculated systematically with Toke and Swiatecki formula 25 , while the last one is taken to be that given by Ignatyuk et al 26 . For the first ones, we adopted those from the table given by P. M0ller et al 27 . The reduced friction strength is taken to be 5xl0 2 0 /sec, consistent with OBM, while the transient time is neglected, because of the extremely small phase space around the spherical shape which is expected not to require a long time for the equilibration

22 -7

xlO £0.3 ,8

1

* •

Sp.25

I

a

ev«D (lnjExperiment Gsi) a *J (ln,Experiinent Riken) o

U

(ln,Calculation)

0.2

0.15

0.1 0.05

232

234

236

238

240

242

244

246

248

250

Figure 4. Comparison of the excitation function of In reaction with RIKEN data (open squares) for 6 4 Ni+ 2 0 8 Pb system. Solid dots denote GSI data.

there. Calculated cross sections are compared with the precise data recently measured at RIKEN for In excitation function of 6 4 Ni+ 2 0 8 Pb system 28 . The peak position in Ecm is accurately reproduced, but the absolute value of the peak height obtained is much larger than the experiment. In view of the good reproduction of the fusion excitation function discussed in previous section, we consider that Pfusion 1S more or less realistic, and thus, that Psurvive should be improved. As a practical treatment, we introduce a scaling factor which reduces absolute values of shell correction energies of SHE. (Note that there are variety of predictions of the shell correction energy, which indicates the existence of ambiguities in theoretical predictions.) If it is taken to be 0.4, the absolute value of the peak height is reproduced, together with the shape of the peak, as shown in Fig. 4. Although the factor might have a system-dependence, we keep it constant for SHE in order to keep the characteristic system-dependence of the mass table adopted and to avoid introducing an arbitrariness in the predictions. The energy positions and the heights of the measured peaks for Z=108, 111 and 112 in addition to Z=110, are also well reproduced with the same factor 8 . In Fig. 5, predicted excitation functions are displayed for In residues of two incident systems for Z=113 and one incident system for Z=114. Note that scales

23

in the abscissa are different between Z=113 and 114 cases. These are the first predictions by the calculations with the dynamical model for fusion, combined with the refined calculations of statistical decays. Experiments are eagerly desired to confirm the present predictions. xlO

xlO

275

270

275

280

285 290

Figure 5. Predictions of In excitation functions for the superheavy elements with Z = 1 1 3 and 114.

5. S u m m a r y Dissipation in nuclear collective motions is now well established, firstly through heavy-ion induced fission and secondly through fusion leading to SHE. It is also worth notifying here that for syntheses of SHE, the fluctuation associated to the energy dissipation plays an essential role, because small fusion probabilities necessary for the formation of the compound nuclei are determined by small fractions of Langevin trajectories, not by the mean trajectory. Thus, D-F dynamics is not only essential for fusion-fission process in heavy ion reactions, but also crucial for the synthesis of SHE. Therefore, it is recommended to keep in mind the importance of D-F dynamics in any applications involving nuclear collective motions such as in-

24 duced nuclear fission. T h e present a u t h o r likes t o acknowledge t h a t most of t h e materials given here are obtained through collaborations with T . Wada, N. Carjan, D. Boilley, B. Giraud, C.W. Shen, G. Kosenko a n d B. Bouriquet. Discussions with Profs. W . J . Swiatecki and A. Sobiczewski are also greatly acknowledged. He appreciates the supports given by R I K E N theory group, and also communications and encouragement by experimentalists of GANIL, GSI, D u b n a , R I K E N and J A E R I . This work is partially supported by t h e Grant-in-Aids of J S P S ( No. 13640278 a n d P-01741).

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

D. Hilscher and H. Rossner, Ann. Phys. (Fr.) 17, 471 (1992). H.A. Kramers, Phyaica VIIA 284 (1940). T. Wada, Y. Abe and N. Carjan, Phys. Rev. Lett. 70 3538 (1993). A.B. Quint et al., Z. Phys. A346, 199 (1993). Y. Abe, Eur. Phys. J. A 1 3 143 (2002). G. Kosenko, C.W. Shen and Y. Abe, J. Nucl. Radiochem. Sci. 3 19 (2002), Y. Abe et al., Prog. Theor. Phys. Suppl. N o . 146 104 (2002), see also ref. 3. 7. C. Shen, G. Kosenko and Y. Abe, Phys. Rev. C66 061602(R) (2002). 8. B. Bouriquet, G. Kosenko and Y. Abe, submitted to Phys. Rev. Letters. 9. D. Hinde, D. Hilscher and H. Rossner, Nucl. Phys. A 5 0 2 497c (1989). 10. Y. Abe, C. Gregoire and H. Delagrange, J. de Physique 47 C4-329 (1986). 11. Y. Abe et al., Phys. Reports C275 Nos. 2 and 3 (1996). 12. K.T.R. Davies, A.J. Sierk and J.R. Nix, Phys. Rev. C13 2385 (1976). 13. J. Blocki et al., Ann. Phys. (NY) 113 330 (1978). 14. Y. Abe, Proc. 3rd IN2P3-RIKEN symp. on Heavy Ion Collisions, Tokyo, Oct. 1994 (World Scientific, 1995) p. 127. 15. P. Paul and M. Thoennessen, Ann. Rev. Nucl. Part. Sci. 44 65 (1994). 16. G.D. Adeev and P.N. Nadtocky, Physics of Atomic Nuclei 66 618 (2003). 17. M. Morjean, et al., Nucl. Phys. A630 200 (1998). 18. W.J. Swiatecki, Physica Scripta 24 113 (1981). 19. D.H.E. Gross and H. Kalinowski, Phys. Reports C45 175 (1978). 20. K. Sato et al., Z. Phys. A288 383 (1978). 21. J.D. Bao, D. Boilley and Y. Abe, to be published. 22. M.G. Itkis, et al., Proc. Int. Workshop on Fusion Dynamics at the Extremes, Dubna, 25-27 May, 2000 (World Scientific, 2001) p. 93. 23. S. Hofmann and G. Miinzenberg, Rev. Mod. Phys. 72 733 (2000). 24. B. Bouriquet, D. Boilley and Y. Abe, to appear in Comp. Phys. Gomm. 25. J. Toke and W.J. Swiatecki, Nucl. Phys. A372 141 (1981). 26. A.V. Ignatyuk et al., Sov. J. Nucl. Pnys. 21 255 (1975). 27. P. M0ller et al., Atomic Data and Nuclear Data Tables 59 185 (1995). 28. K. Morita, private communications.

QUASIFISSION OF T H E D I N U C L E A R S Y S T E M

G. G. ADAMIAN 1 , N. V. ANTONENKO 1 AND W. SCHEID 2 Joint Institute for Nuclear Research, 141980 Dubna, Russia Institut fur Theoretische Physik, Justus-Liebig-Universitat, Giessen, Germany Quasifission and fusion are treated with master equations describing the evolution of the dinuclear system in the charge and mass asymmetries. Agreement of the calculated results with experimental data of fusion reactions leading to superheavy nuclei is found.

1. Introduction The production of superheavy elements can be well described with the dinuclear system (DNS) concept x ~ 4 . The DNS model assumes a system of two touching nuclei which exchange nucleons by transfer up to the moment that the compound nucleus is formed. During this process the DNS can decay which we denote as quasifission, distinguishing it from the fission of the compound nucleus. Quasifission has been measured by Itkis et al 5 in heavy ion collisions used for the production of superheavy elements 6 . This article is devoted to the description of quasifission within the DNS concept 7 . We like to mention that the DNS model has also been successfully applied to nuclear structure phenomena connected with cluster effects 8 . 2. Master Equations for Nucleon Transfer For the description of the quasifission process we choose master equations for the transfer of nucleons between the nuclei of the DNS. As coordinates we take the nucleon numbers of the light cluster, namely Z\ = Z, Ni = N and Ai = A = Z + N. The corresponding numbers of the heavy cluster are Zi = Ztot -Zi,N2= Ntot - Nx and A2 = Atot - Ax, where Ztot, Ntot and Atot are the total charge, neutron and mass numbers of the DNS, respectively. The starting point for the derivation of the master equations is the shell-model Hamiltonian of the DNS, H = H0 + Vint, where H0 is the sum of the Hamiltonians of the DNS nuclei and Vint their interaction. Denoting

25

26

the fragmentation by Z, N and Ztot -Z, Ntot-N, we introduce the unperturbed states of the DNS, \Z,N,n), solving H0\Z,N,n) = E%
jPz,N{n,t)=

Y.

HZ,N,n\Z',N',n')[Pz,!N,(n',t)-PZtN(n,t)]

Z',N',n'

-[A%N(n)

+ Az%(n)]Pz,N(n,t).

(1)

The transition rate A is calculated in time-dependent perturbation theory:

X(Z,N,n\Z',N',n')

=

^-t\(Z,N,n\Vint\Z',N',n')\2 sm*[At(EZ>N-EZ'N)/2h]

where the time interval At = 10~ 22 s is larger than the relaxation time of the mean field but considerably smaller than the reaction time. The quantities AZN(n) and AZN(n) are the rates for quasifission and for the fission of the heavy nucleus with Ztot — Z and Ntot — N in the DNS, respectively. Because of the single-particle character of the interaction energy Vint, the transition rates are only non-zero between states which differ by one particle-hole pair. In order to simplify the system of the differential equations, we assume that the DNS is in thermal equilibrium, and factorize Pz,N{n,t) in the form Pz,N(n,t) = Pz,N(t)$z,N(n,T), where $z>N(n,T) is the probability for finding the DNS in the state n at a local temperature T(Z, N) and is normalized to unity. Summing over the DNS states n, we finally obtain the master equations used in the calculations 7 :

jtPzAt) = *z~+t* pz+iMt) + *£% Pz-iMt) + A g - ^ Pz,N+i(t) + A g ' + ^

Pz,N-i(t)

- (A { -' 0 ) + A ( + ' 0 ) + A ( 0 '- } + A j ° # + A"Z{N + Afz%) Pz,N(t)

(3)

27

with ( m ( T ) = nm(T), A A

( ± - 0 )

m

_

1

S T

Z , N ( T ) - ^ - ^

A(°>±)m-

A

^(

T

:

Z

n2(T) = nn2(T) ) \2r,o(T^(l

\ n

\gni,n2\

V ^ l n

r,

|2„ m n

) = E Ag J V (n)*z, A r (n,T) >

-en2)/2H]

( T W ^ ^ ^

n?(T)(l-n,(r))

.

)2/4

„ ^ u s i n 2 [ A ^ ( e n i -e„ 3 )/2fi]

A ^ ( T )= ^ A ^ W $ ^ ( n , T ) .

n

n

Here, p n i ,„2 are transition matrix elements and eni, e„2 are single-particle energies of the DNS nuclei. This system of equations has to be solved with the initial condition Pz,jv(0) = 5z,Zi • SfftN.. The rates for the transfer of a proton or neutron from the heavy nucleus to the light one {&ZH , &Z'N ) a n d m opposite direction ( A ^ \ Az'x ) depend on the temperature-dependent Fermi occupation numbers nm(T) and nn2(T) of the single-particle states. The decay rate AqJN(T) of the DNS for quasifission depends on the height Bqf of the quasifission potential barrier at -R& = Rm + 1.5 fm where Rm is the internuclear distance of the DNS nuclei in the potential minimum. The decay rate is treated with the Kramers formula 7 . 3. Charge and Mass Yields The charge and mass yields for quasifission can be calculated as to

q

YzMh) = A J,N j Pz,N{t)dt,

(4)

o 20

where t0 w (3 — 4) • 10~ s is the reaction time which is at least ten times larger than the time of deep-inelastic collisions. This time is determined by considering the balance equation for the probabilities: to A

Y,( Z,N Z,N

+ ^zZt-z,Ntot-N)

[PzMt)dt J Q

= 1 - 5>z,Jv(*o).

(5)

Z,N

The sum on the right hand side of (5) contains the fusion probability PCN = Y^z
28

which is short compared with the decay time of the compound nucleus. The mass and charge yields of quasifission products are given as Y(A) = 52Yz,A-z(to),

y(Z) = £ r z , ; v ( t o ) .

Z

(6)

N

4. Variance of Total Kinetic Energy The average total kinetic energy (TKE) of the quasifission products and its dispersion depend strongly on the deformation of the fragments. For nearly symmetric dinuclear systems with A = At0t/2 ± 20, we found deformations which are about 3-4 times larger than the deformations of the nuclei in their ground states. These large polarizations of the DNS nuclei have to be regarded to explain the experimental TKEs of the quasifission fragments. We assume that the distribution of the fragments as a function of Z, N and the deformations can be written as W = W(Z,N,fr,fa)

= Yz,N(to)w01(Z,N)w02(Ztot

- Z,Ntot - N). (7)

The distributions of the deformations /?i and /?2 are chosen as Gaussian distributions at fixed values of Z and N: wp(Z,N)

= ^i=exp(-(/?-(/?))2/(2aJ)),

(8)

The determination of ai from the experimental spectra is described in detail in Ref. 7. Using the distribution W and setting TKE = Vc(Rb) + VN(Rb) with the radius Rb at the position of the quasifission barrier, we get the variance of the TKE as 'TKE (A) «

^(TKEfl^^Yz^zitoy^Yz^.zito) z "2=<,32> z e - (TKE{A)f + (4 L(A))l + {*%E(A))l

(9)

with (j = 1, 2) 4,Yz,A-z(to)/Y,Yz,A-z(h).

(10)

/3l = 0 2 =

5. Results for Hot Fusion Reactions Here we discuss the mass yields and the variances of the TKE of the fragments in the reactions with 4 8 Ca projectiles incident on actinide targets where data were measured by Itkis et al. 5 in Dubna. Fig. 1 shows the

29 •

1

'

i —•

"i - •

i—•—r '!Ca+23!U :

-

•

1 \

'

J

•J,

0.00 20

40

f \ hr 1

\

{ .

m

"* 100

60

120

60

40

140

80

A

100

1200

• «• •• •

1000

£

400

110 A

120

130 140

•

• •

70

•"

mm

/*• 48,-, , 248 „ i

100

140

800

$ 600

90

120

80

.,!_ 90

Ca+ Cm i i . i i , i 100 110 120 130 140 150 A

Figure 1. The calculated (solid lines) mass yield (upper part) and variance of the T K E (lower part) of the quasifission products as a function of mass number A of the light fragment for the hot fusion reactions 4 8 C a + 2 3 8 U -> 2 8 6 112 (left hand side) and 48 Ca+ 2 4 8 Cm—> 2 9 6 116 (right hand side) at a bombarding energy corresponding to an excitation energy of the compound nucleus of 33.4 and 37 MeV, respectively. The experimental data 6 are shown by solid points.

calculated mass yields Y (A) and the variances of the TKE of the fragments as functions of the mass number for the hot fusion reactions 4 8 Ca + 238 U —• 286 112 (left figures) and 4 8 Ca + 248 Cm -» 296 116 (right figures) in comparison with experimental data. The calculated data in the figure are related to the primary fragments before neutron emission. Near the initial mass number A=48 the quasifission events overlap with the products of deepinelastic collisions and were taken out in the experimental analysis since it is difficult to discriminate them from deep-inelastic events. The calculated peak near the initial mass number contains only quasifission events because we disregard angular momenta larger than the critical one which belong to deep-inelastic and quasi-elastic collisions. Maxima in the mass yields arise due to shell effects in the dinuclear system. For A > 48, the maximum yield of the quasifission products appears around the nucleus 2 0 8 Pb for the heavy fragments where the driving potential has several minima. The height of the peak around A — 80 in the mass yield of the 4 8 Ca + 238 U reaction is 4.5 times larger than the height

30

of the peaks in the symmetric mass region. The minima in the dependence of a\KE on A in Fig. 1 rise due to stiff nuclei in the DNS like Zr, Sn and Pb. The absolute height of the calculated a TKE a g r e e s w e u with the experimental data. The fluctuations due to the deformations contribute much more to the variance of the TKE than the fluctuations by the transfer of nucleons which come only into play for very asymmetric dinuclear systems. Beside the calculation for hot fusion reactions we also carried out calculations of quasifission yields and TKE variances for reactions with a 58 Fe beam, for cold fusion reactions with Pb targets and for reactions with lighter nuclei, e.g. 40 Ar + 165 Ho (for details see Ref. 7). Special interest we paid to the relative contribution of the fusion-fission process with respect to the quasifission. This contribution is mainly determined by the fusion probability and increases with incident energy, but remains small in the reactions considered. Therefore, the quasifission process mainly gives the yield of nearly symmetric products. For example, for the reaction 4 8 Ca (Ec.m. = 193 MeV) + 238 U (see Fig. 1) the calculated cross section of the yield of quasifission fragments with mass numbers Atot/2 ± 20 is about 4.5 mb in good agreement with the measured value of about 5 mb. Acknowledgments This work was supported in part by Volkswagen-Stiftung, DFG and RFBR. References 1. V.V. Volkov, Izv. AN SSSR ser. fiz 50, 1879 (1986). 2. G.G. Adamian, N.V. Antonenko and W. Scheid, Nucl. Phys. A618, 176 (1997). 3. G.G. Adamian, N.V. Antonenko and W. Scheid, Unexpected isotopic trends in synthesis of superheavy nuclei, preprint (2003); Isotopic trends in production of superheavy nuclei in cold fusion reactions, preprint (2003). 4. Proceedings of the Symposium on Nuclear Clusters: from Light Exotic to Superheavy Nuclei (Rauischholzhausen, Germany, 2002), ed. R.V. Jolos and W. Scheid (EP Systema, Debrecen, 2003). 5. M.G. Itkis et al. in Ref. 4, p. 315. 6. Yu. Ts. Oganessian et al, Eur. Phys. J. A13, 135 (2002); ibidem A15, 201 (2002). 7. G.G. Adamian, N.V. Antonenko and W. Scheid, Phys. Rev. C68, 034601 (2003). 8. T.M Shneidman et al, Phys. Rev. C65, 024308 (2002).

MICROSCOPIC OPTICAL POTENTIAL FOR NUCLEAR TRANSMUTATION, FUSION REACTORS, AND ADS PROJECTS M. AVRIGEANU1, V. AVRIGEANU, M. DUMA Association EURATOM-MEC-Romania, "Horia Hulubei" National Institute for Physics and Nuclear Engineering, P.O.BoxMG-6, 76900Bucharest, Romania W. VON OERTZEN Freie Universitat Berlin, Fachbereich Physik, Arnimallee 14, 14195 Berlin, and Hahn-Meitner-Institut, Glienicker Strasse 100, 14109 Berlin, Germany A. PLOMPEN European Commission, Joint Research Centre, Institute for Reference Materials and Measurements, Retieseweg, B-2440 Geel, Belgium

Progress on the use of the double-folding method for calculations of microscopic real potentials for complex particles is reported as well as their use within nuclear data evaluation of actual interest for radiation damage estimation and radioactive waste transmutation projects. The effective nucleon-nucleon interaction involved for opticalpotential calculation and analysis has been used also within multistep direct calculations.

1.

Introduction

Among the high-priority elements for the accelerator driven systems (ADS) and fusion-reactor projects are also Zr, Mo and Li, so that the corresponding nuclear data for nucleon-, deuteron-, and a-particle interactions are of actual interest for radiation damage estimation and radioactive waste transmutation projects. It is why this work reports on the progress of using the double-folding (DF) microscopic real potentials [1] for nucleons [2], deuterons and a-particles[3] on isotopes of these elements, within reaction cross sections calculations. The microscopic real optical potential, calculated within the DF model [1] by using a realistic effective nucleon-nucleon (NN) interaction and updated structure models for a-particles [4], provides a good description of differential data of the elastic scattering of a-particles on A-100 nuclei [3], including Zr mavrig @ ifin .nipne.ro 31

32

and Mo isotopes, over a large energy range from -15 MeV to 142 MeV. It is thus validated the use of the microscopic potentials in the nuclear data evaluation. Next, in order to improve the calculations of the D-Li neutron source term, the update of the d+6,7Li data evaluation is carried on by calculation of the elastic scattering of deuteron on 6'7Li, for incident energies up to 50 MeV, by using a microscopic optical model potential (OMP). On the other hand, the effective nucleon-nucleon (NN) interaction involved within optical potential calculation and analysis can be used in multistep direct (MSD) calculations. The main point could be the description of experimental doubledifferential cross sections without use of any free parameter. 2.

Double-folding method calculation of nuclear potential for complex particles

Since the IFMIF project requests nuclear-data evaluation for D incident on Li for D-energies up to 50 MeV, we have analyzed and proved [2,4] the possibility of using the DF method for calculation of the nuclear induced reactions on medium nuclei, as well as potential for complex particles (e.g. 23 H, 3,4He) emitted in neutron of interest [5] for evaluation of nuclear data for D on 6'7Li. The basic input for the calculations of the double-folded OP are the nuclear densities of the colliding nuclei and the effective nucleon-nucleon (NN) interaction. Several types of the most recent densities associated to a-particle have been used in addition to the most known expression of Satchler and Love [6], namely the experimental Tanihata densities [7], the realistic densities derived from the cluster-orbital shell model approximation [8] (COSMA), and the microscopic Baye density. The energy- and density-dependent (DDM3Y and BDM3Y) effective Paris and Reid NN have been considered with an explicit treatment of the exchange potential [9]. 6,7

3.

Microscopic optical potential for a-particles interacting with 90Zr

The microscopic real OPs have been validated through the comparison with the phenomenological OPs and the description of the systematics of the experimental a-particle elastic-scattering angular distributions. It is important to underline that no adjustable parameter or normalization constant are involved within the microscopic calculations. The volume integrals of the real phenomenological [10] and of the microscopic potentials for a+90Zr based on the Tanihata density and DDM3Y-Paris effective interaction have been found in the best agreement. Calculated differential elastic scattering cross sections of ce+90Zr at incident energies of 40, 59.1, 79.5, 99.5, 118, and 141.7 MeV using the DDM3Y-Paris effective NN interactions with both Tanihata and COSMA

33

t>

30 60 90 120 150

30

CO

30 60 90 120 150

90 120 150 180 30

60

*cm

30 60 90 120 150 180

93 120 150 180 30

60

SO 120 150 180

^

Figure 1. Comparison of measured and calculated deuteron-6Li elastic-scattering angular distributions at incident energies between 3 and 50 MeV.

densities are presented in comparison with the experimental data. It has been thus shown that the present microscopic potential is able to describe the experimental angular distributions of elastic scattered a-particle over a large incident energy range. Moreover, a comparative analysis shows that the microscopic elastic-scattering and total reaction cross-sections are in good agreement with those predicted by the phenomenological optical potentials along the whole energy range analyzed. This final comparison validates the procedure of calculating microscopic optical potential and its use in applications. 4.

Calculation of Deuterium-Lithium cross sections for energies up to 50 MeV Nuclear density distributions. The deuteron density distribution has been

34

.1 [ « Atrarmfd»(}97Bi t | _ \ 30 60 90 120150 30 60 90 120 150 30 60 90 120 150180

30 60 90 120150

30 60 90 120 150

30 60 90 120150 180

30 60 90 120150

30 60 90 120 150 180

^.m [defifl Figure 2. As for Fig. 1, but for the target nucleus 7Li and incident energies between 3 and 14.7 MeV .

obtained following the analysis of both the deuteron ground state wave functions given by either Satchler [11], Lacombe et al. [12] or Machleidt [13], and the experimental charge density [14]. We have considered only the S-state of the deuteron ground state wave function, so that the effective NN-interaction used in the double folding procedure has no tensor component Therefore in the present work we have used the Machleidt wave function for calculations of the deuteron density distribution. The nuclear density distribution of the target nuclei 6,7Li has been described by means of a gaussian forms with the parameters obtained from the analysis of the electron scattering data [15,16] and also from the shell model calculations [17]. Finally the Bray et al. [16]

35

density distribution for 6Li target and Satchler and Love [6] density distribution for 7Li target have been chosen. The effective NN interaction. Several versions like the M3Y and different types of its density dependence like DDM3Y, BDM3Y, and CDM3Y effective interactions [18] were developed and used to fit nucleon- and nucleus-nucleus elastic-scattering angular distributions. The most popular M3Y forms are based on the G-matrix elements of the Reid [19] or Paris [20] NN potential in an oscillator basis. Since the M3Y effective interaction is characteristic for the nuclear density around 1/3 of the normal matter density, its choice could be considered appropriate for the deuteron scattering which is localized in the nuclear surface [21] at lower incident energies (3-15 MeV). In this work we have chosen the Paris M3Y effective interaction for the complete consistency with the density distribution of the deuteron whose ground-state wave function has been obtained from Paris effective interaction. For higher incident energies of the deuterons incident on 6Li, e.g. above 25 MeV, the density dependence of the effective NN-interaction has been also taken into account. It has been modeled by looking for the proper account of the saturation properties of nuclear matter [1] within a corresponding Hartree-Fock calculation, and accounts for the reduction in the strength of the interaction that occurs as the density of the surrounding medium increases. The density-dependent DDM3Y and BDM3Y effective NN interactions have been obtained by multiplying with the density-dependent function F(p) adjusted by reproducing the saturation point of the nuclear matter and a compressibility modulus of K-230 MeV. Moreover, in addition to the density dependence it was also introduced an energy-dependent factor as a linear function of the incident energy per nucleon E, of the form g(E)=l-y/E. The coefficient yhas the values 0.002 and 0.003 for the M3Y-Reid [1,18] and M3Y-Paris [19] interactions, respectively. Finally, for 50 MeV deuterons incident on 6Li target we built the semi-microscopic DFM real potential based on the Machleidt S wave function of deuteron, Bray et al. density distribution for 6Li and the above-given BDM3Y Paris effective NNinteraction. Elastic scattering ansular distributions. The real DF potential calculated with the ingredients described above has been applied for description of the deuteron scattering data at low energies, in conjunction with Woods-Saxon imaginary and spin-orbit potentials. The present calculations have been compared with the deuteron-6,7Li elastic-scattering angular distributions [22,23] measured at incident energies between 3 and 50 MeV for the target nucleus 6Li (Fig. 1), and between 3 and 14.7 MeV for the target nucleus 7Li (Fig. 2).

36

The scattering cross sections are calculated by using the code [24] SCAT2 modified to include the DF potential as OMP real-part option, with no adjustable parameter or normalization constant. CRC analysis for the deuteron exchange. The general feature of experimental d+6'7Li elastic-scattering angular distributions at low incident energies is an increase in the yield at large angles. The scattering in the backward direction determines the optical model parameters to be used for the description of the elastic scattering data. Nevertheless, adjusting the parameters or the type of the optical model to the case under consideration does not always help to provide a satisfactory correspondence to the pronounced maxima at very large angles. In attempts to interpret the data in such cases the direct exchange processes has been employed [25]. Reactions of interest in which exchange effects are supposed to be of significance are the elastic scattering of both deuterons and alpha particles by 6Li, nucleus which has the simplest alpha cluster structure, i.e. an alpha particle loosely bound to a deuteron or a p-n pair [26].

1

90-Z r

110 r

•i.io' ^10°

o 1 "O10

1

1

(P>n)

1

1

1 1

i

Trabandf89 -default (g=A/13; P=0) "~g=A/13;p-Dllg73 —I I I 1 1

20

1

Ep=80MeV]

40 En [MeV]

60

80

Figure 3. Comparison of experimental and MSD cross sections for the (p,xn) reactions on Zr.

37

20

40

60

80

100

120

140

Figure 4. Comparison of experimental and MSD cross sections for the (p,xn) reactions on 100Mo.

In the case of deuteron elastic scattering on 6Li at energies of 14.7 and 19.6 MeV (Fig. 1) search for the imaginary and spin-orbit OMP parameters led to a good description of the forward angles, while at larger angles the disagreement has been obvious. It seems that not merely accidental since it is in line with the experimental angular distributions obtained by Bingham et al. [27] and Abramovich et al. [28]. The results are improved by taking into account also the coupled reaction channel (CRC) model predictions of the code FRESCO [29]. Thus the maximum of the angular distribution at extremely backward angles is reproduced fairly well by the CRC. The coupling routes taken into account in the present analysis involve both a-particle and the sequential deuteron exchange in the 6Li nucleus, by using Timofeyuk and Thompson [30] spectroscopic factor for the a-particle in 6Li and Rudchik et al. [23] spectroscopic factor of the deuteron in the a-particle. It appears [25] that the exchange-effects probability has to decrease strongly with increasing energy of the incident particle, e.g. for the deuteron increased energy the characteristic momentum with which it captures the aparticle to form the ground state of 6Li must increase as well. At the same time the binding energy of the cluster 6H=a+d is only 1.47 MeV, the relative

38

effective momentum between its constituents not being large. Thus, the experimental elastic angular distribution [23] of 50 MeV deuterons on 6Li has been described only by pure elastic scattering calculations, as long as the experimental data are measured only up to 155 degrees 5.

Quantum-statistical MSD processes at low and intermediate energies on 90Zr and 100Mo

The quantum mechanical formalism developed by Feshbach, Kerman and Koonin [31] (FKK) for the multistep processes has been extensively used to describe a large amount of experimental data covering a broad energy range. The assumptions and simplifying approximations considered in the application of the FKK theory have been analyzed and important refinements of calculations have been made (e.g. [32] and references therein). One of the important assumptions concerns the effective NN interaction, which is taken as a single Yukawa term with 1 frn range, its strength V0 being considered as the only free parameter of the FKK theory. However, it should be noted that, even when a consistent standard parameter set has been used as well as several other effects have been taken into account, the systematics of the phenomenological V0 values still show discrepancies. Such uncertainties of the phenomenological effective NN-interaction strengths may reflect the eventual scaling of Vo compensating for some effects which have been neglected and should be added to the theory. Thus, the use a more realistic effective NN interaction, which should be consistent with the corresponding OP real part of the OM, has been stated as one of the open problems in the theoretical description of the MSD nuclear reactions. Through the trial to provide a reliable strength to be used within the FKK theory instead of the free parameter V0, we expect to overcome the uncertainties in fitting an effective interaction directly to MSD processes data. Thus an 1Yequivalent NN interaction strength V0eq obtained from the DDM3Y-Paris effective interaction has been used within MSD calculations which describes without any free parameter the experimental double-differential cross sections, the nucleon emission spectra from the (p,n) and (p,p') reactions on 90Zr (Fig. 3) and I00Mo (Fig. 4) isotopes at the incident energies of 80 MeV, 100 MeV, and 120 MeV, and makes possible predictions of MSD double-differential cross sections and nucleon emission spectra corresponding to (n,n') and (n,p) reactions on 90Zr and 100 Mo isotopes at the incident energies of 80 MeV, 100 MeV, and 120 MeV, where no experimental data exist.

39

Acknowledgments This is where one acknowledge funding bodies etc. Note that section numbers are not required for Acknowledgments, Appendix or References. This work was supported at IFIN-HH by the Contract of Association between EURATOM and MEC-Bucharest No. ERB-5005-CT-990101, and by the EC/JRC/IRMM project PA No. 59 during a three-month visit at IRMM-Geel, and the EC/FP5/INC02 project IDRANAP/WP12 of IFIN-HH during three-month visits at HMI-Berlin. M.A. gratefully acknowledges the warm hospitality at IRMM-Geel and HMIBerlin. References 1. Dao T. Khoa, W. von Oertzen and H.G. Bohlen, Phys. Rev. C49, 1652 (1994); Dao T. Khoa, W. von Oertzen and A.A. Ogloblin, Nucl. Phys. A602, 98 (1996); Dao T. Khoa and G.R.Satchler, Nucl. Phys. A668, 3 (2000). 2. M. Avrigeanu, A.N. Antonov, H. Lenske and I. Stetcu, Nucl. Phys. A693, 616 (2001). 3. M .Avrigeanu, W. von Oertzen, A.J.M. Plompen and V. Avrigeanu, Nucl. Phys. A723, 104 (2003). 4. M. Avrigeanu, G.S. Anagnostatos, A.N. Antonov and J. Giapitzakis, Phys. Rev. C62, 017001 (2000); M. Avrigeanu, G.S. Anagnostatos, A.N. Antonov and J. Gapitzakis, Phys. Rev. C62, 017001 (2000); M. Avrigeanu, G.S. Anagnostatos, A.N. Antonov and V. Avrigeanu, J.Nucl. Sci. Technol. S2, 595 (2002); Int. J. Modern Phys. E l l , 249 (2002). 5. A.Yu. Konobeyev, Yu.A. Korovin, P.E. Pereslavtsev, U. Fisher, and U. von Mollendorff, Nucl. Sci. Eng. 139, 1 (2001). 6. G.R. Satchler and W.G. Love, Phys. Rep. 55, 183 (1979). 7. I. Tanihata et al., Phys. Lett. B289, 261 (1992). 8. M.V. Zhukov et al., Phys. Rep. 231, 151 (1993). 9. Dao T. Khoa, Phys. Rev. C63, 034007 (2001). 10. L.W. Put and A.M.J. Paans, Nucl. Phys. A291, 93 (1977); L.McFadden and G.R. Satchler, Nucl. Phys. A84, 177 (1966); M. Nolte, H. Machner and J. Bojowald, Phys. Rev. C 36, 1312 (1987); V. Avrigeanu, P.E. Hodgson and M. Avrigeanu, Phys. Rev. C 49, 2136 (1994). 11. G.R. Satchler, Phys. Lett. B36, 169 (1971). 12. M. Lacombe et al, Phys. Lett. B101, 139 (1981). 13. R. Machleidt, Adv. Nucl. Phys. 19, 189 (1989). 14. D. Abbot et al, Eur. Phys. J. A7, 421 (2000).

40

15. G.C. Li, I. Sick, R.R. Whitney and M.R. Yearian, Nucl. Phys. A162, 583 (1971); T. Sinha, Subinit Roy, and C. Samanta, Phys. Rev. C48, 785 (1993). 16. K.H. Bray, et al, Nucl. Phys. A189 (1972) 35. 17. A.A. Korsheninnikov et al, Nucl. Phys. A617, 45 (1997); M. El-Azab Farid and M.A. Hassanain, Nucl. Phys. A697, 183 (2002). 18. M.E. Brandan and G.R. Satchler, Phys. Rep. 285, 143 (1997); Dao T. Khoa, Phys. Rev. C63, 034007 (2001). 19. G. Bertsch, J. Borysowicz, H. McManus and W.G. Love, Nucl. Phys. A284, 399 (1977). 20. N. Anantaraman, H. Toki and G. Bertsch, Nucl. Phys. A398, 279 (1983). 21. M. Avrigeanu, A. Harangozo, V. Avrigeanu, A.N.Antonov, Phys.Rev.C 54,2538(1996); 56,1633(1997). 22. S.N. Abramovich et al, Yad. Phys. 40, 842 (1976), and EXFOR-A0117 data-file entry; D.L. Powell et al, Nucl. Phys. A147, 65 (1970), and EXFOR-A1432 data-file entry; H.G. Bingham et al, Nucl. Phys. A173, 265 (1971), and EXFOR-A1431 data-file entry; H. Ludecke et al, Nucl.Phys. A109, 676 (1968), and EXFOR-F0002 data-file entry; S. Matsuki et al, Jap. Phys. J. 26, 1344 (1969), and EXFOR-A1435 data-file entry; V.I. Chuev et al, J. de Phys. 32 (1971) C6. 23. A.T. Rudchik, A. Budzanoki et al. Nucl. Phys. A602, 211 (1996). 24. O. Bersillon, Centre d'Etudes de Bruyeres-le-Chatel Note CEA-N-2227, 1992. 25. V.Z. Goldberg, K.A. Gridnev, E.F. Hefter, and B.G. Novatskii, Phys. Lett. B58, 405 (1975). 26. T. Yoshimura et al.,Nucl. Phys. A641, 3 (1998). 27. H.G. Bingham et al, Nucl. Phys. A173, 265 (1971), and EXFOR A1431 data-file entry. 28. S.N. Abramovich et al, Yad. Phys. 40, 842 (1976), and EXFOR A0117 data-file entry. 29. I.J. Thompson, Comput. Phys. Reports 7, 167 (1988). 30. N.K. Timofeyuk and I.J. Thompson, Phys. Rev. C61, 044608 (2000). 31. H. Feshbach, A. Kerman and S. Koonin, Ann. Phys. (NY) 125, 429 (1980). 32. M.B. Chadwick et al., Acta Phys. Slovaca 49, 365 (1999).

IDENTIFICATION OF EXCITED 10BE CLUSTERS BORN IN TERNARY FISSION OF 252CF A. V. DANIEL, G. M. TER-AKOPIAN, G. S. POPEKO, A. S. FOMICHEV, A. M. RODIN AND YU. TS. OGANESSIAN Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, Dubna 141980, Russia J. H. HAMILTON, A. V. RAMAYYA, J. KORMICKI, J. K. HWANG, D. FONG AND P. GORE Department of Physics, Vanderbilt University, Nashville, TN 37235, USA J. D. COLE Idaho National Engineering and Environmental Laboratory, Idaho Falls, ID 83415, USA M. JANDEL, L. KRUPA AND J. KLMAN Institute of Physics, Slovak Academy of Sciences, Dubravska cesta 6, Bratislava, Slovak Republic and FLNR, JINR, Dubna, Russia J. O. RASMUSSEN, A. O. MACCHIAVELLI, I. Y. LEE AND S. -C. WU Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA M. A. STOYER Lawrence Livermore National Laboratory, Livermore, CA 94550, USA R. DONANGELO Instituto de Fisica Universidade, Federal do Rio de Janeiro, Rio de Janeiro, 21945-970, Brazil Ternary fission of 252Cf was studied at Gammasphere with using eight AExE particle telescopes. The 3368 keV gamma transition from the first excited state in 10Be was undoubtedly found. The ratio of the population probabilities for these two levels was estimated as 0.160±0.025. The nuclear temperature of the neck region near the scission point was estimated as 1.0±0.2 MeV. No evidence was found for 3368 keV y rays emitted from a triple molecular state.

41

42

1.

Introduction

The interest to nuclear fission accompanied by light charged particle (LCP) emission is connected with the possibility to obtain additional data about the fission mechanism. In spite of intensive investigations of these phenomena (see reviews1'2 and papers cited there a good quantitative explanation of the observed kinematical characteristics and yield of LCPs has not been achieved. Mainly, theoretical models concentrated only on the explanation of a-particle emission in the fission for which the main experimental data have been obtained. More recently, information about the kinematical characteristics of heavy LCPs and their yields were improved3'4 for the 252Cf spontaneous fission. The problem still remained is a relatively high energy limit above which heavy LCPs were measured. A more direct way allowing the exploring of the fission nucleus characteristics may be based on the assumption5 that the LCPs could be emitted in their excited states. If thermal equilibrium is maintained near the scission point then population of the LCPs in excited state can be connected with the nuclear temperature. Reports of the observation of the 3368 keV y ray corresponding to the 10Be 2+—>0+ transition in a ternary fission experiment with 252 Cf have been made6'7. There was some evidence that the y peak of 10Be was seen without Doppler broadening. Taking into consideration the lifetime 125 fs of 2+ level in 10Be it means 6 ' 7 that the 10Be stays at rest for an unusual long time or y rays are emitted predominantly in the orthogonal direction to the 10Be momentum. It was not the undoubted result because of the poor energy resolution of Nal detectors used in the experiment. This idea has been tested by using data of y-y-y coincidences obtained at the experiment made on the Gammashpere8 with high energy resolution. The data gave support for that result, but with limited statistics and no direct LCPs identification. The possibility that the 10Be nucleus may stay between two fission fragments for a long time ~10"13s to create a so-called triple nuclear molecule opens up exciting possibility discussed in9. 2.

Experiment

The experiment has been carried out at the Lawrence Berkeley National Laboratory by using Gammasphere and eight light charged particle detectors. Gammasphere was set to record y rays with energy less then ~5.4 MeV. The efficiency varied from a maximum value ~17% to ~4.6% at the y energy 3368 keV. A sample of 252Cf giving ~4xl 06 spontaneous fissions per second was installed in the center of the reaction chamber, which was placed in a hollow

43

sphere inside Gammasphere. The source was prepared from a Cf specimen that was deposited in a 5 mm spot on a 1.8 micron titanium foil and was tightly covered on both sides by gold foils to exclude the coming out of fission fragments from source. Eight similar AExE Si detector telescopes were used to measure LCPs emitted in the ternary fission. They were arranged in the reaction chamber with four telescopes centered at the polar angle 0=30° (azimuth angles cp = 45°, 135°, 225° and 315°, and four at 0 =150° (azimuth angles were the same). Each AE detector had an area 10x10 mm2 and thickness slightly varying between 9 u and 10.5 u. Each E detector was 400 (i thick and was 20x20 mm2 in area. The distance from the source to AE detector was 27 mm and from )E detector to E detector was 13 mm in all telescopes. 3.

Results and Discussion

The resolution of the AZsxE telescopes allowed us to well identify helium, beryllium, boron and carbon nuclei, when energy deposition in the E detector was greater then 5 MeV. From this value 5 MeV, we calculated the lower primary energy of the LCPs registered in the experiment, as 9, 20, 24, 32 MeV for He, Be, B, and C LCPs, respectively. The lithium region was shadowed by the random coincidence of the ternary helium LCPs with the 252Cf a-decay particles. The detection of prompt y rays coinciding with the Be LCPs permits to search y rays corresponding to the transition from the first excited state in 10Be. The energy resolution of the AE detectors does not allow the separation of beryllium isotopes in the AExE plot, but experimental results presented in10 show that the yield of beryllium LCPs emitting in the 252Cf spontaneous fission consist of 10Be on -80%. In Fig. 1 the dotted line shows the spectrum of y rays in coincidence with the beryllium accompanied 252Cf spontaneous fission. The solid line on this figure demonstrates the same spectrum after applying a Doppler correction. The distinct peak in the last spectrum at the energy 3368 keV corresponds to the 2+->0+ transition in 10Be. The width FWHM=65.7±4.5 keV was calculated for the peak by using a Gaussian fitting. This width is compatible with the value FWHM=62.1 keV obtained by the Monte Carlo simulation of the procedure introducing a Doppler correction for the y rays emitting from the moving 10Be nucleus. The simulation has been done taking into consideration the experimental kinetic energy distribution of 10Be, the Gammasphere energy resolution and the real 3d-position of all gamma and particle detectors. For comparison, the dotted line in the Fig. 1 shows the spectrum of yrays

44

coinciding with the emission of helium nuclei. It reflects, to some extent, the background from the y rays emitted from fission fragments. One infers from Fig. 1 that the 3368 keV peak restored after Doppler correction (see the solid line histogram) is smeared in the raw spectrum (dashed line histogram) over an energy range extending from about 3000 keV to 3700 keV. Comparison made in Fig. 2 between the spectrum of y rays coinciding with Be LCPs and the spectrum obtained by Monte Carlo simulation gives evidence that the 3368 keV y rays are mainly emitted by moving 10Be

5000

Figure 1: The solid and dashed lines show the spectra of y rays coinciding with Be LCPs after and before the Doppler shift correction, respectively. The dotted line shows the spectrum of y rays coinciding with He LCPs. The last spectrum was normalized to the total number of counts obtained in the whole spectrum associated with the Be LCPs E _ 9 0 _ 5900 ke V.

nuclei. In the raw spectrum of y rays recorded in coincidence with Be LCPs we do not see any distinct peak near 3368 keV, which could be associated with y emission from stationary 10Be nuclei (see Figs. 1 and 2). Obviously, yrays emitted from the moving 10Be in directions almost orthogonal to the 10Be momentum result in a broad bump centered on the maximum of the 3368 keV peak. To get rid of this bump we picked out only such events where the angles between the trajectories of y rays and 10Be nuclei were less than 45° or greater than 135°. The resulting spectrum obtained after the background subtraction is shown in Fig. 3. The energy region around 3368 keV now has a clear zero. In

45 1 20

37

15

-_4 :!

Counts

1

10

-

:f;

-\

!*r

; j

5

0

| %-H": -i t 1; - ;.; 2 Z\ . . 3000

Iffr

(!."«- +H4i

+

'"J-

'M.rir ~* A riT' .

, i . 3100

.

!

4

i

:

'?•

. . ir

\ , :

m~u >'••i: h .n. iU^-U-jJl'dt J;;j !

I i i -,iA':'' '' 1 ! j i

:

'

! x

•

^ •

"

,

... bP

!

r

M":

fi

U Hirr^-rf-i": rn 4

'4 1 1 1 1 1 1 I 3200 3300

. 1 1 1 1 3400 E, k.V

i

L_i

I_I

.

1• l

• i

u , ; , r.^Ti'

• • 1—i

i

t

,,.. i

q- ; ' i

1 i

J 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Figure 2: Histogram drawn with a dotted line shows the spectrum of y rays coinciding with Be LCPs. It is obtained from the dashed line histogram of Fig. 1 after the subtraction of the background shown by the dotted line in Fig. 1. The solid and dashed line histograms demonstrate me spectra simulated using experimental angular distribution of 3368 keV y and under the assumption of isotropic y emission from 10Be, correspondingly. Both spectra were normalized to the number of counts obtained in the first one in the energy range 3000-3800 keV.

[!

•1

![A/ Hi 3000

3100

3200

3300

AJ 3400 E.keV

3500

3600

i 3700

3800

Figure 3: Histogram shows the spectrum of y rays detected at angles <45° or >135° to the Be momentum.

other words, there is a lack of any y line which could be attributed to the emission from 10Be standing in a triple nuclear molecule. Using results on Fig. 1 we estimated the population ratio of the excited 2+ to the ground-state 0+ levels in 10Be as 0.160+0.025. Having spin and energy of these two states and assuming thermal equilibrium near the scission point, this value allows one to estimate the temperature parameter as 1.0+0.2 MeV using

46

Boltzmann distribution. Most likely it is the estimation of the nuclear temperature of the neck region at the scission point. The upper limit for the probability that 10Be emits its y rays being in rest makes only 2% of this ratio. This result is valid for 10Be LCPs having at infinity the kinetic energy more than 20 MeV. One can not exclude that the decay channel of the hypothetical triple molecule is characterized by the low kinetic energy of the 10Be LCPs which was unreachable in our experiment. The Gammasphere experiment13 relied solely on the observation of y-y-y coincidence events, a possibility still remains open that a narrow ypeak characteristic to the motionless 10Be can be found if the low energy part of the energy distribution of 10Be LCPs is detected. The present result excludes any possibility that an effect of triple quasi molecular state, involving beryllium LCPs, could be observed in 6,7 where the energy cut off was 26 MeV for these clusters. Acknowledgments Work at Joint Institute for Nuclear Research was supported in part by the US Department of Energy contract \#DE-AC011- 00NN4125, BBW1 Agreement No.~3498 (CRDF grant RPO-10301-INEEL) and by the joint RFBR-DFG grant (RFBR No. 02-02-04004, DFG No. 436RUS 113/673/0-1(R)). Work at Vanderbilt University, LBNL, LLNL and INEEL are supported by U.S. Department of Energy under Grant No. DE-FG05-88ER40407 and Contract Nos. W-7405-ENG48, DE- AC03-76SF00098 and DE-AC07-76ID01570. References 1. I. Halpern, Ann. Rev. Nucl Sci. 21, 245 (1971). 2. C. Wagemans, The Nuclear Fission Process, (CRS Press, Boca Raton, FL, USA, 1989), chap. 12. 3. M. Mutterer et al, Proc. Int. 3rd Conf. DANF'96, Casta Papernicka, Slovakia, edited by J. Kliman and B. Pustylnik, (JINR, Dubna, 1996), pp. 250-261. 4. Yu. N. Kopach et al, 5He, 7He and 8Li, E = 2.26 MeV, Intermediate Ternary Particles in the Spontaneous Fission of252Cf., (Preprint GSI 200210, 2002). 5. G. Valskii, Sov. J. Nucl. Phys. 24, 140 (1976). 6. P. Singer et al, Proc. Int. 3rd Conf. DANF' 96, Casta Papernicka, Slovakia, edited by J. Kliman and B. Pustylnik, (JINR, Dubna, 1996), pp. 262-269.

47

7. M. Mutterer et al, Proc. Int. Conf. Fission and Properties of Neutron-Rich Nuclei, edited by J.H. Hamilton and A.V. Ramayya (World Scientific, Singapore, 1998), p. 119. 8. A. V. Ramayya et al., Phys. Rev. Lett. 81, 81 (1998). 9. W. Greiner, Acta Physica Slovaca 49, 9 (1999). 10. V. A. Rubchenya and S. G. Yavshits, Z Phys. A329, 217 (1988).

PRODUCTION OF PHOTOFISSION FRAGMENTS AND STUDY OF THEIR NUCLEAR STRUCTURE YU.P.GANGRSKY+ AND YU.E.PENIONZHKEVICH Joint Institute for Nuclear Research, Dubna, Russia

Fission fragments of heavy nuclei (Z > 90) are neutron-rich isotopes of the elements from Zn (Z = 30) to Nd (Z = 60) with a neutron number of 45 - 90. The large neutron excess in the fission fragments under study (in some cases there are 10 - 15 more neutrons, than in the nuclei situated in the (3-stability valley) could lead to an essential change in their structure and radioactive decay characteristics. The abnormal ratio of protons and neutrons in such nuclei reflects on spin-orbit interactions and can lead to another order of nucleon shell filling. This change will manifest itself in the appearance of new magic numbers of protons or neutrons, new regions of deformation, of new islands of isomerism. A striking example of such phenomena is found in light neutronrich nuclei of 31Na and 32Mg at the magic number N = 20. Contrary to our knowledge about nuclear structure, these nuclei are strongly deformed [1,2]. The same situation could occur in the case of very neutron-rich isotopes of Cu and Zn near N = 50 as well as Ag and Cd near N = 82. The high energy of p-decay can result in the appearance of new, much rare, modes of radioactive decay. They are emission of a neutron pair or an aparticle after P-decay (|32n or pa). These decay modes are an important source of new information about nuclear structure. Thus the spectroscopic properties of fission fragments are very various. They are relatively poorly known, and researching them (measurement of the nuclear moments, the level spectra, the decay schemes e. c.) allows one to establish the way in which nuclear structure changes with the increasing neutron excess. A wide set of experimental devices should be used to obtain this information. Study of the nuclear structure of fission fragments is one of the main directions of the DRIBs project, being developed in the Flerov Laboratory of Nuclear Reactions JINR. The aim of this project is the production of intense beams of accelerated radioactive nuclei in a wide range of Z and A - from He to rare-earth elements. Light neutron-rich nuclei (up to Na) will be obtained in the

[email protected] 48

49

fragmentation of bombarding ions on the 4-meter isochronous cyclotron U400M, and nuclei of a medium mass number - in the fission of uranium on the electron accelerator microtron MT-25. Nuclei chosen for study will be massseparated and transported to be accelerated in another 4-meter isochronous, cyclotron U-400. Study of reactions induced by neutron-rich or neutron-deficient nuclei essentially enlarges information about their structure. It is impossible to judge some details of this structure from radioactive decay characteristics. A striking example is observation of an unusual wide space distribution of neutrons in some neutron-rich nuclei (neutron halo), first in n Li and then in others [3]. These data were obtained from measurement of cross-sections for different reactions (fusion, stripping, nucleon exchange) with neutron-rich nuclei. Such multidirection investigation of the properties of nuclei far from the P-stability valley definitely widens our knowledge about the changes in nuclear structure with the growing neutron excess and about the appearing of new phenomena. Reactions with neutron-rich nuclei can be also used for obtaining more neutron-rich nuclei. Really, the compound-nuclei formed in these reactions contain the neutron excess, and the evaporation of charged particles increases this excess. By this technique it is possible to get the most neutron-rich nuclei and to draw near the boundary of nucleon stability. The success of study of fission fragments structure, especially the most neutron-rich fragments, depends to a great degree on their yields. These are determined by their distribution on mass and atomic numbers (A and Z). But there is poor information about these parameters in photofission as compared with neutron fission. Worthy of mention are only investigations performed in Gent (Belgium) [4,5]. The main contribution to the photofission fragment yield is induced by the energy range of 10 - 15 MeV (it is the position of the giant dipole resonance in heavy nuclei). This energy range also determines the excitation energy of fissioning nuclei. At such excitation energy, the mass spectra of the photofission fragments are asymmetric with the mean mass numbers 99 and 139 for the light and heavy groups of fragments. To get more detailed information about the isotopic yields we measured the isotopic distributions of Kr and Xe fragments independent yields in the photofission of 238U and other heavy nuclei by bremsstrahlung with the boundary energy of 25 MeV [6]. The method of transporting fission fragments by a gas flow and stopping in a cryostat with liquid nitrogen was used. The independent yields of Kr (A = 89 - 93) and Xe (A = 137 - 143) fragments at the photofission of 232Th, 238U, 237Np and 244Pu were measured by

50

the method (Table 1). The dependences of these yields on the mass number of fission fragments are approximated by Gauss curves. Table 1. Independent yields of Kr and Xe fission fragments. Fragment 89

Kr 91 Kr 92 Kr 93 Kr

232

Xe Xe Xe 140 Xe 141 Xe 142 Xe 143 Xe 139

244

U(Y,f)

Fft 0,10(2) 0,62(5) 0,59(5) 0,15(2)

Yal 0,29(1) 1,00 0,80(2) 0,25(2)

Yfr 0,18(2) 0,60(5) 0,46(4) 0,15(2)

0,85(1) 1,00 0,85(7) 0,19(1) 0,09(1)

0,53(4) 0,63(5) 0,53(5) 0,12(1) 0,06(1)

0,27(3) 0,65(3) 1,00 0,94(7) 0,53(3) 0,26(2) 0,08(2)

0,16(2)[51 0,38(4) 0,59(5) 0,56(5) 0,31(3) 0,16(2) 0,05(1)

,37

138

238

Th(y,f)

YIA 0,15(2) 1,00 0,95(1) 0,25(1)

Pu(Y,f)

iid

1ft

0,84(4) 1,00 1,03(8) 0,73(4) 0,46(4) 0,24(4)

0,47(4) 0,56(5) 0,57(5) 0,41(4) 0,26(3) 0,14(2)

The parameters of these distributions for 232Th, 238U and 242Pu photofission nuclear reactions are tabulated in Table 2 (the magnitude of the A for 238U is in good agreement with that obtained in work [4,5]). For comparison the similar parameters are presented for the fission of 235U, 233U and 238 Uby the neutrons. A comparison of those parameters permits a number of conclusions to be drawn: 1.

2.

3.

The average mass number for Kr and Xe fragments shows a slight increase as the Z and A of the fissioning nucleus increases. It is close to the magnitude of the A for the fission of 238U induced by 14.7 MeV neutrons, but substantially larger than that for the fission of 235U and 233U induced by thermal neutrons. This points to the fact that an increase in the neutron excess of the fissioning nucleus results in an increase in the A (this excess can be characterized by the ratio (N-Z)/N, which is tabulate in Table 2). At the same time the distribution dispersion shows a noticeable increase as the atomic number of the fissioning nucleus increases (for example, it increases by a factor of 1.5 from 232Th to 244Pu). This means that the yields of the most neutron-rich fragments differ significantly. For example, the yield of 143Xe for the photofission of 244Pu is one order of magnitude larger than for the photofission of 232Th, this difference increasing rapidly as the number of neutrons in the fragment increases. The deviation of the measured yields from the Gaussian distribution as well as their even-odd distinctions is not great and lies within the limits of experimental error.

51 The Kr and Xe fragments produced in the fission of 232Th are complementary, i.e. they are produced in the_same fission event.^A. comparison of the sum of their average mass numbers ( A (Xe) = 138.9 and A (Kr) = 91.3) with the mass number of the fissioning nucleus (A = 232) allows the number of neutrons emitted from those fragments to be determined. This number proves to be equal to v = 1.8(2). With the fractional yields of 91Kr and 139Xe equal to 0.8 and 0.85 respectively, it is in good agreement with reported numbers of fission neutrons from fragments of a specified mass number and their excitation energy dependence. From those data it follows that in this region of fragment mass numbers the ratio of the numbers of neutrons from the light and heavy fragments is 1.3 and has only a weak dependence on excitation energy. This corresponds to v = 1.0 for Kr isotopes and v = 0.8 for Xe isotopes.

Table 2. Isotopic distribution parameters of Kr and Xe fission fragments. Reaction

(N-Z)/N

U(Y,f)

0,366 0,370

Pu(Y,f) 235 Ufy,f) 233 U(n,f) 235 U(n,f) 238 U(n,f)

0,373 0,357 0,352 0,364 0,379

232

Th(y,f)

238

244

A

a

A

91,3(2) 91,1(2)

1-1(1) 1,3(1)

138,9(2) 139,4(2) 138,9(3) 139,7(2) 137,4(4) 137,8(1) 138,4(1) 139,5(1)

89,4(3) 89,3(1) 90,1(1) 91,5(1)

References

Xe

Kr

1,3(1) 1,5(1) 1,5(1) 1,6(1)

CT

1,2(1) 1,5(1)

* * [51

1,8(2) 1,4(1) 1,5(1) 1,6(1) 1,8(2)

* [5] [11 [11 [11

"This work

The magnitudes of v obtained allow one to determine the fragment charge shift relative to the unchanged charge distribution Z0/A0, which corresponds to the ratio of the atomic to mass number of the fissioning nucleus. For a fragment of atomic number Z, the charge shift is expressed as:

AZ = ^ ( A + v ) - Z .

(1)

4> The thus obtained magnitudes of the AZ for the average mass numbers of Kr and Xe fragments produced in the photofission of 232Th, 238U and 244Pu are tabulated in Table 3. They prove to be close to the corresponding magnitudes of the AZ for the neutron-induced fission of heavy nuclei.

52

Using these measured yields, we can estimate more correctly the yields for another fission fragments. Examples of some interesting nuclei and their yields are presented in Table 4. One of these nuclei was studied. The rare mode decay, emission of delayed neutron pair (f52n) was observed at the photofission of 238U at the boundary energy of bremsstrahlung 10 MeV. It is, probably, 136Sb, the intensity of p2nbranch is about 1CT3.

Table 3. Charge shifts of Kr and Xe fission fragments relative unchanged charge distribution. 238

232

Zo/Ao

^PuM

U(Yi) 0,387

Th(Y,f) 0,388

Z

36

54

36

54

A

91,3(2)

138,9(2)

91,1(2)

139,4(2)

V

1,0

0,8

1,0

0,8

AZ

-0,19(8)

+0,20(8)

-0,36(9)

+0,25(8)

0,385 54 139,7(2) 0,8 +0,13(6)

Table 4. Exotic fission fragments. Fission fragment and its peculiarities 80 Zn - closed neutron shell W=50 81 Ge - closed neutron shell N=50 131 In - closed neutron shell N=S2 132 Sn - double magic nuclei Z=50, N=S2 134 Sn - 2 neutrons over closed shell 100 Zr - beginning of deformation region 104 Zr - strongly deformed nuclei 160 Sm - strongly deformed nuclei 136 Sb - delayed two-neutron emitter 140 J - delayed a-emitter

7,1/f

Y, 1/s (DRIBs)

IO"6

103

3-10

-5

io-3

3-10 6

108 3

3-10" 8-10"4 IO"2 5-10"4

3-10 8

IO"

10' IO5 106

IO' 6 IO-5

10' 10' 5-10 7

Thus photofission reactions of heavy nuclei are a very handy and promising way for the production of intense beams of the most neutron-rich nuclides. The small stopping power of the y-rays allows one to use thick targets. But the low excitation energy of the fissioning nuclei and of the fission fragments results in the small values of the evaporated neutrons. This compensates for the photofission cross sections being smaller as compared with the cross sections for fission induced by charged particles and neutrons. Moreover electron accelerators are simpler and much cheaper than charged particle accelerators and atomic reactors.

53

These examples show the wide field of activity in the study of the neutronrich nuclei structure, and the DRIBs project is the first step on this way. References 1. 2. 3. 4. 5. 6.

G. Huber, F. Touchard, S. Biittgenbach et. al., Phys. Rev. C18, 2342 (1978). D. Guillemaud-Mtieller, C. Detraz, M. Langevin et. al., Nucl. Phys. A426, 37 (1984). I. Tanihata, H. Hamagaki, O. Mashimoto et. al., Phys. Rev. Lett. 55, 2676 (1985). H. Jacobs, H. Tierens, D. De Frenne et. al., Phys. Rev. C21, 237 (1980). D. De Frenne, H. Tierens, B. Proot et. al., Phys. Rev. C26, 1356 (1982). Yu.P. Gangrsky, S.N. Dmitriev, V.I. Zhemenik et. al., Particles and Nuclei Letters 6, 5 (2000).

VARIATION OF C H A R G E D E N S I T Y I N F U S I O N REACTIONS

R. A. GHERGHESCU AND D. N. POENARU Horia Hulubei National Institute for Physics and Nuclear Engineering, RO-76900, Bucharest-Magurele, Romania, E-mail: [email protected] W. GREINER Institut fur Theoretische Physik der J. W. Goethe Universitdt, Robert Mayer Str. 8-10, Frankfurt am Main, Germany

Target and projectile charge densities are treated as free parameters in the calculation of the deformation energy. Different charge density paths are proposed as a result of geometrically related law of variation of the number of protons in the non-overlapped volumes of the two partners. As a result of minimization along the distance between the two centers fusion barriers differences reach up to 4 MeV for light nuclei and 8 MeV for superheavy synthesis.

1. Introduction Changes of the charge density in the superposed target and projectile configuration are equivalent with the atomic number changes in isobaric reactions. Such systems have been studied already for intermediate nuclei l. At low energy it is shown that the dependence on charge asymmetry could decide between fusion and deep-inelastic processes. Another result of the charge influence is the increase of the cross section with the charge product of the projectile and target for the same synthesized nucleus in subbarrier fusion reactions 2 . This work reveals the changes which occur within the overlapping configuration with the variation of the projectile and target charge density. It will be shown that the fusion barrier is more sensitive to charge density variations in the last part of the reaction, close to the total overlapping configuration. There is a relation between the magnitude of the volume and the shape of the non-overlapped part of the projectile on one hand and the charge density variation on the other hand. Consequently the macroscopic and microscopic energies are affected.

54

55

2. Geometry related charge density path We consider the spheroidal shape (ai, &i, zs) with a\, 61 semiaxes and zs separation plane as having the same charge density as it were a whole nucleus {Alx,Zlx), i. e. the charge density of the shape is determined by its geometric correspondence to (A l x , Zix); thus Zyx is the atomic number if the heavy fragment is a complete spheroid with (ai, 61) semiaxes. Variation of atomic to mass numbers Z\xjA\x must also comply to: , Z\x Mx

Z0

Z\x

Z\

AQ

A\X

AI

where ZQ,A0 and Z\, A\ are the final and initial values of the target nucleus. A variation law fulfilling these conditions could be: Z\x Alx

1 A0 - A1

(A^-A^^

+ A0

iAo-A^)^

(2)

A\

For A\x — A0 we have Z\x = Z0 and for Aix = Ai results Z\x — Z\. We emphasize that Aix, Z±x, A^x and Zix are not the real mass and atomic numbers, but the ones which correspond to whole non-intersected nuclei having the same semiaxes as the real intersected ones. For the same fusion reaction, an spheroidal projectile can change its shape parameters (02,62) in different ways along the overlapping region: it can preserve its initial 620 semiaxis or 62 can become larger up to the limit where 62 = bo, the semiaxis of the compound nucleus. Between these two limits, 62 can take any values, provided that the volume V2 does not become larger then its initial value. Consequently, the corresponding intermediary atomic number Z2j changes according to the above considerations. In Fig. 1, upper part, the variation of Zix with the normalized distance between centers Rn — (R — Rf)/(Rt — Rf) is presented, where Rf and Rt are the final and the tangent configuration distance between centers. Different curves correspond to different laws of variation for the small semiaxis of real intermediary nucleus (A 2 j, Z 2 j). The plots refer to a superheavy nucleus synthesis: 5 4 Cr+ 2 3 8 U -¥ 292 116. The middle plot refers to the real intermediary atomic number variation Z^i with Rn. Variations in the last part of the fusion process ( Rn < 0.4) are due to volume differences. The smallest value for the V-z volume is for 62 = &2o(292H6) at the same Rn, the situation where the projectile preserves its initial semiaxis. The lower plot represents the proton density variation. The larger the volume, the lower the charge density, as can be seen. The highest proton density corresponds

56 120

^=Ro(2Kiif) 132=0.9 . R 0 Q 1 6 ) 1)2=0.8 ;R,(Z9Z116) •••• b2=b2„rcr)

100 & 80

N

60 40

iV

.T T — 20 0.0 0.2 0.4 0.6 0.8 1.0 60 50

^.Rol^HJ) bj-ao-RgPHle) — b2=o.s -Kfoie) • • • • b2=b2„( Cr)

•

40

N '30 20 \i 10

¥<

0.0 0.2 0.4 0.6 0.8 1.0 0.08 2BS b2=R„( 116) b2=0.9.R 0 C,116)

••••

b2=b2 0 rcr)

CM

,0-0.07

0.06 0.0 0.2 0.4 0.6 0.8 1.0

(R-Rf)/(Rt-R{) Figure 1. Hypothetic Z%x, real Zii atomic number and proton density variation of the target along a fusion reaction.

to &2 = &2o(292H6), when the non-overlapped part of the projectile remains almost at its initial shape.

3. Total deformation energy The microscopic potential which follows the equipotentiality on the nuclear surface is generated by the spheroidally deformed two center oscillators:

57 V(r)t

z) ={V1(p,z)

= \m0uj2pip2 + | m 0 < ( z + 2i) 2 ,Vl

in which v\ and v2 are the space regions where the two potentials are acting. These Hilbert space regions are defined by: V1(p,z)=V2{p,z)

(4)

with i = l , 2. The shape and the volume of v\ and v2 depend on the overlapping grade and (Ai,Zi)-target and (A 2 ,Z 2 )-projectile. Any change in the oscillator frequencies is converted to a change in V\ and v2. The four frequencies define the shape; when using the volume conservation a,ib2=R3 and hu>i=AlA^ ' , where Ri=r0Ai' , one obtains the shape dependence of the frequencies: m 0 < = (at/bi)2/3 • m^li = ( a ^ ) 2 / 3 • 54.5/i?? m0w2zi = (bi/atf/3 • mowgi = ( 6 , / a i ) 4 / 3 • 54.5/i??

{

°>

The influence of the charge density on the potential manifests through the above equations. In such a way the variation of the charge density is expressed by the variation of the four frequencies via the spheroid semiaxes. The single particle energy levels are used to calculate the shell corrections by the Strutinsky method. The macroscopic energy Emacro is computed as the sum of the Coulomb Ec 3 and the nuclear Yukawa-plus-exponential term Ey 4- For two intersected nuclei system shape, the Coulomb energy can be written as 5 : 2TT

E

C = Y (fiiFci

+ p\2Fci + 2pelpe2Fcl2)

(6)

where Fa are shape dependent expressions. The Y + E energy Ey is 5 : EY = T-1[csiFEY1

+ cs2FEY2 + 2{cslcs2fl2FEY12]

(7)

A-KTQ

For the intermediate surface coefficients csu and c s2 i, with the general expression: csji = o s ( l - Kl2i) we use An, Zu from Eq. 2, with Ijt = (Nji — Zjj)/Aji

(8) where j=l, 2.

58

The total macroscopic deformation energy is given by: Emacro = (EC ~ E{°]) + (EY - E{°})

(9)

4. Results and discussion Results are presented for the light nuclei fusion reaction 36 Ar+ 6 6 Fe —^102Ru. All the curves are drawn after minimization against the %-parameter. The figures show only the variation as a function of &2- 36 Ar is a spherical nucleus, with the initial radius i? 20 ( 36 Ar)=3.3 fm, 66 Fe has an spheroidal deformation of j3fFe) =0.027 and 102 Ru is deformed with (3^°2Ru)=0.189. The projectile 36 Ar maintains its spherical shape for the four possible paths. During the overlapping process, the 36 Ar radius becomes R? if the projectile preserves its spherical shape. The i? 2 = &o(102R-u) curves correspond to the situation when the projectile ends the fusion process with its radius equal with the small semiaxis of 102 Ru. Differences are more significant in the last part of the fusion process. Microscopic influence and total deformation energy is depicted in Fig. 2 for 102 Ru synthesis and four charge density variation paths. Rn takes values far beyond the touching distance {Rn > 1), in order to comprise the whole cold fusion barrier. The variation of Esheii (upper plot) nears 2 MeV and is more pronounced in the last part of the fusion process, as (R — Rf)/(Rt — Rf) approaches zero. There is a mixed behaviour of the four curves. The lowest values are successively reached by i?2=&o(102R.u) at the beginning of the process, then by i? 2 =0.8& 0 ( 102 Ru) followed by 0.9&0(102Ru) curve in the last part. The total sum Eb = Emacro + Esheu is shown in the lower plot of Fig. 2. Differences of about 4 MeV are visible when Rn approaches zero, and the situation when the projectile enlarge its dimensions as to seize synthesized nucleus size and shape are favoured (R2 = 6 0 ( 102 Ru)). 5. Conclusion Charge density influence on cold fusion barriers manifests itself through geometrical parameters characterizing the target and projectile nuclei within the overlapping region. Changes of semiaxis ratios and magnitude triggers a modification in proton density over the non-overlapped volume of the projectile. As a free coordinate, charge density can lower the cold fusion deformation energy, as a result of minimization against 62 and \i • This

59

•••

R 2 -b„( 10z Ru) R2=0.9.b0( Ru) R2-O.S .bnl'^Ru) Rz-R^'Ar)

(R-Rf)/(Rt-Rf) Figure 2. Shell correction Es/ieu and fusion barrier Et, for the four charge density paths as in Fig. 1 for the synthesis of 102Ru. kind of influence is especially active in the last part of the fusion process, when the projectile is already half embedded in the target (Rn <0.5) up to total synthesis. For light nuclei cold fusion, the energy variation in the last part of the deformation path reaches 4 MeV for 102 Ru by the reaction 36Ar+66Fe ^ I M p ^

References 1. 2. 3. 4. 5.

M. Colonna et al. Phys. Rev. C57, 1410 (1998). T. Rumin, K. Hagino and N. Takigawa, Phys. Rev. C63: 044603 (2001). K. T. Davies and A. J. Sierk, J. Comp. Phys., 18, 311 (1975). H. J. Krappe, J. R. Nix and A. J. Sierk, Phys. Rev. C20, 992 (1979). D. N. Poenaru, M. Ivascu and D. Mazilu, Comp. Phys. Gomm. 19, 205 (1980).

P A R E N T D I - N U C L E A R QUASIMOLECULAR STATES AS EXOTIC R E S O N A N T STATES

N. G R A M A , C. G R A M A , A N D I. Z A M F I R E S C U Horia Hulubei

National

Institute MG-6,

of Physics Bucharest,

and Nuclear Romania

Engineering,

P.O.Box

The properties of the parent quasimolecular states are deduced from the general properties of the exotic resonant states found by the Riemann surface approach to S-matrix poles.

1.

Introduction

Di-nuclear quasimolecular states (QMS) represent the most important cluster phenomenon in nuclear physics. They are nuclear resonant states (RS) excited in heavy-ion reactions, having special properties: a) QMS are highly excited RS in nuclei above the threshold Eth of two-body decay into the cluster constituents; b) The reduced width of QMS for decay into cluster constituents is large, while the reduced widths for decay into other channels are small; c) QMS have good spins and parities (Jn); d) QMS excitation energies are situated around the top of the total barrier (EQMS — Ecoui + Ecentrifugai), in a region of high level density. Their widths TQMS are of the order of hundred of keV; e) For a given J there are several QMS. The energy centroids of QMS with the same J form a straight line in the plane Eex vs J(J +1), appropriate to a rotational band. As suggested by Feshbach 1 the narrow QMS with the same J* are fragments of a di-nuclear parent quasimolecular state (PQMS) with a width of several MeV. In spite of the great deal of research work done in the field of QMS there are main open questions still left 2 : (1) Stability against the dissolution into the complex neighboring compound nuclear states in a region of a high level density; (2) The QMS wave function is localized in the barrier region. It is a great puzzle to understand how a short range nuclear attraction

60

61 can be operative in order to generate a RS having the wave function localized outside the potential well, in the region of the barrier. The present work answers the above questions. By using an usual potential we are looking for the possibility to generate a class of exotic RS (ERS) that could be candidates for PQMS, i.e. RS which have the wave function localized in the region of the barrier, particularly stable with respect to the dissolution into the neighboring compound nucleus resonant states. In order to do this we have to identify all classes of RS and to study their properties. The existence of different types of RS must be reflected in the existence of different types of S-matrix poles. Consequently it is important to find a method to identify simultaneously all the S-matrix poles. Let us consider the non-relativistic scattering of a charged particle by a central potential V(r) = QVnii") + Vbar(r) where the short range complex nuclear potential Vn of strength g 6 C has a square or a Woods-Saxon form-factor, and Vbar is a potential barrier. The S-matrix poles are the solutions k = ki(g) of the equation Ti+(g,k) = 0 where Ti+(g,k) is the Jost function, / is the orbital angular momentum, k is the wave number and g is the potential strength, provided that Ti-{g,k) ^ 0. Here Ti+(g, k) and Ti-{g,k) are the denominator and numerator, respectively, of the S-matrix element 3 . The pole function k = fc; (g) is a multiple-valued function defined on the complex g-plane. The S-matrix poles distribution in the fc-plane as a function of the potential strength g has been extensively studied by using the pole trajectory method: a particular path in the complex <7-plane is chosen and the corresponding trajectory of the S-matrix poles in the &-plane is determined. The pole trajectory method does not provide all S-matrix poles, some important poles being lost, and one can never be sure that the same pole is followed (see references in Ref. 4). In order to get a better description of the function k = ki (g) the Riemann surface approach to S-matrix poles 4 ' 5 will be used. It consists in constructing the Riemann surface Rg' over the g-plane, on which the pole function ki(g) is single valued and analytic. A schematic illustration of the method is given in fig. 1. In fig. (lb) the sheets of the Riemann surface over the ^-plane and their images in the fc-plane are represented. Having located the branch points in the g-plane, cuts have been taken in the g-plane along the branch-lines. In this way all the sheet En of the Riemann surface Rg have been separated.

62

Figure 1. a) The multiple-valued function k —fc;(flf)defined on the complex g-plane and its distinct values in the &-plane. b) The single-valued function k = ki(g) denned on the Riemann surface over the complex g-plane. The branchpoints indicated by * and the branch-lines that join the sheets are shown. The border of any sheet image in the A;-plane £ „ ' was obtained by letting g trace a path along the cuts on the corresponding Riemann sheet £„ , without crossing them, and along a circle of large radius joining the cuts. Taking into account that one branch and only one branch of & = k[(g) is associated with a sheet £„ , the label n of this sheet will be used as a quantum number for the S-matrix pole belonging to the corresponding sheet image £„ ' in the A;-plane and for the associated resonant (bound) state. This quantum number allows to label even the poles that do not become bound state poles as the depth of the potential well is increased. The label n of a Riemann sheet provides a unique quantum number for the resonant (bound) state pole that belongs to the corresponding Riemann sheet image. It does not change when the potential strength is changed taking values on the same Riemann sheet. The method has been used for various shapes of potentials: a rectangular or Woods-Saxon well (PI), a rectangular well followed by a rectangular barrier (P2), and a rectangular or Woods-Saxon well with Coulomb barrier (P3) 4 ' 5 . 2.

Properties of the exotic resonant poles and states

For all mentioned potential barrier shapes Vbarir), which also contain a centrifugal component resulted from partial waves decomposition, a new class of poles, with unusual properties, has been identified. The exotic resonant state poles have the following unusual properties: (i) Instead of becoming bound or virtual state poles when the strength of the potential well increases to infinity, the exotic poles remain in some bound regions of the &-plane, in the neighborhood of some attractors (stable points). The number and position of these bound regions depend on the shape and height of the barrier. They occur only if the absorptive potential strength Xm g > 0 belongs to a certain window (t\ > 11m g |< t^)- Exotic

63

poles exist only on some Riemann sheet images, depending on the shape of the potential barrier, as illustrated in fig. 2. In fig.2a and 2b the sheets and the aggregate of the sheet images for potential P2 are given; in fig.2c and 2d the sheets and the aggregate of the sheet images for the potential PI are given; in fig.2e and 2f the sheets and the aggregate of the sheet images for the potential P3 are given.

Figure 2. The first four sheets E n , n = 1,2,3,4 and the aggregates of their fc-plane images En for the three mentioned shapes of the potential. One can see that for a rectangular barrier there are exotic poles only for strong absorptive potentials. There is an infinite number of Riemann sheet images on which there are situated exotic poles. On each Riemann sheet image there is only one bound region for the exotic resonant pole. In the case of a rectangular or Woods-Saxon well with centrifugal barrier there are exotic poles on a finite number of Riemann sheet images, the number of these sheet images increasing as the orbital angular momentum I increases. The exotic poles occur for either weak or strong absorptive potentials. In the case of a rectangular or Woods-Saxon well with Coulomb plus centrifugal barrier there is an infinite number of Riemann sheet images where the exotic poles are situated, and the exotic poles occur for either strong or week absorption. (ii) The wave functions of the RS corresponding to poles situated in the neighborhood of the attractors are almost completely confined to the region of the barrier. The localization of the wave function in the case of potential P2 is illustrated in fig. 3. As a consequence of the localization of their wave functions the ERS are almost insensitive to the behavior of the potential

64

0

0.5

1

1.5

2

2.5

r/R

Figure 3. The moduli of the wave functions of an usual RS (a) and of an ERS (b) for the potential P2 with equal radii for well and barrier. The values of the potential well depth g and the corresponding poles in the fc-plane are given. inside the well, but almost totally determined by the potential in the barrier region. 3. Di-nuclear P Q M S - a particular case of ERS The ERS corresponding to poles at the first attractor kz form rotational bands. An approximation of the energy and width of these ERS has been obtained from the asymptotic expression of kz for large values of the Coulomb parameter c = ZiZ2e2M/h :

where kB = [2c + / ( / + 1)] 1 / 2 ; X = [k% + 1(1 + l ) ] 2 / 3 ; <*i = Re a and a2 = Im a, with a = (97r/8) ' exp(i7r/3). From the analysis of Eq. (1) it results that both di-nuclear PQMS and ERS at the first attractor form rotational bands of simple configuration states at high energies in nuclei, near the top of the total barrier Ti2k2B/2MR2. A good agreement was obtained in the comparison of the theoretical energies given by (1) with the experimental energies of the PQMS reported in literature, from 1 2 C+ 1 2 C up to 28 Si+ 28 Si by using the same prescription for the radius R = ro(A{3 + A\'3) with r 0 =1.3 fm for all nuclear systems. The experimentally observed deviation from the linear dependence of E on /(/ + 1) in the light systems, such as 12 C+ 1 2 C, 1 2 C + 1 6 0 and 1 6 0 + 1 6 0 , is reproduced by the dependence of the

65

slope of the tangent to the curve E vs 1(1 + 1) with respect to c and / from Eq. (1). The calculated energies are obtained with the same radius prescription, both below and above the Coulomb barrier. Other authors 6 ' 7 have been forced to use two rotational bands for light heavy-ions systems, separated by the Coulomb energy Ec0ui • J g 0

2 6 10 14

18 20 2 2 2 6

10 12 14 16

2 6

10 12 14 16

4)

.

40

UJ

20 L(L+1)

Figure 4. Comparison of the experimental excitation energies of QMS with the ERS energies given by eq. (1) (continuous curves). The dot line is the grazing line. The dashed lines are the E vs 1(1 + 1) lines for different configurations (two separate spheres below the Coulomb barrier and two partially overlapping spheres above the Coulomb barrier).

It is difficult to compare the PQMS widths and ERS widths due to the process of spreading of the single particle excitation represented by the PQMS on a large energy region. It would be necessary to identify and analyze all the QMS of the same J* that represent fragments of PQMS, spread on an energy interval of several MeV. For the available data a good agreement was found between the calculated widths of the ERS given by eq.(2) and the experimental widths of the PQRM obtained by the reconstruction from the the spread fragments 8 ' 9 . The small amplitude of the wave function of an ERS inside the well leads to a small overlap with the adjacent RS of the continuum that are mostly confined to the compound nucleus radius, which is smaller than the potential well radius. In other words < ipERs^CN > is small. This small overlap confers stability to ERS against the dissolution into the complex neighboring compound nuclear states. The ERS are a new kind of doorway states, whose stability is a consequence of the localization of the wave function, rather than of a symmetry. Eq. (2) provides information on the observability of QMS. For the light systems the width increases rapidly as / increases so that it becomes very

66 large for a relatively low I value and the corresponding resonance in the cross section is not observed. For heavier systems the widths of E R S increase slowly as / increases and consequently the states can be observed even at very large / values. For example, in the 1 2 C + 1 2 C system the highest /-value of the observed quasimolecular resonance is / = 1 8 , while in the 2 8 S i + 2 8 S i quasimolecular resonances with 1=42 could be observed 1 0 . Systematic heavy ions scattering studies 11 have shown t h a t an enhanced gross structure both in the angular distribution and excitation functions for light nucleus-nucleus systems is produced by a weakly absorbing four parameter optical potential of Woods-Saxon form. T h e absorption t h a t explains the scattering d a t a belongs to the absorption window t h a t ensures the occurrence of the E R S . As a conclusion, it was shown t h a t the di-nuclear parent quasimolecular state is an exotic resonant state t h a t corresponds to a S-matrix pole in the neighborhood of an attractor in the Ar-plane. T h e properties of the P Q R S ( excitation energies, deviation from the linear dependence of excitation energies on / ( / + 1 ) , widths, stability, observability) result naturally from the general properties of the ERS. T h e open problems mentioned in connection with the P Q R S are solved. T h e equations (1) and (2) have a predictive character, giving the energies and widths of the P Q M S .

References 1. H. Feshbach, J. Phys. (Paris) C 5 , Suppl 11, 177 (1976). 2. N. Cindro, in Nuclear Collective Dynamics, International Summer School of Nuclear Physics, Poiana Brasov, Romania, World Scientific, 1982, p.397. 3. R. G. Newton, Scattering Theory of Waves and Particles, 2nd ed., Springer Verlag, New York-Heidelberg-Berlin, 1982. 4. C. Grama, N. Grama and I. Zamfirescu, Ann. Phys. (N.Y.) 218, 346 (1992). 5. C. Grama, N. Grama and I. Zamfirescu, Ann. Phys. (N.Y.) 232, 243 (1994). 6. D. A. Bromley, in Proc. 4th Int. Conf. on Clustering Aspects of Nuclear Structure and Nuclear Reactions, eds. J. S. Lilley, M. A. Nagarajan, Reidel, Dordrecht, 1985, p. 1. 7. H. S. Khosha, S. S. Malik and R. K. Gupta, Nucl. Phys. A, 513, 115 (1990). 8. R. R. Betts, Nucl. Phys. A 447, 257c (1985). 9. H. Frohlich et al., in Lecture Notes in Physics 156, ed. Eberhardt K.A., (1982) p. 79. 10. R. R. Betts, S. B. Di Cenzo and J. F. Petersen, Phys. Lett. B 100, 117 (1981). 11. R. H. Siemssen, in Nuclear Molecular Phenomena, Proc. Int. Conf. on Resonances in Heavy Ions Reactions, Hvar, Yugoslavia, eds. N. Cindro, 1977, p.79.

FISSION INVESTIGATIONS AND EVALUATION ACTIVITIES AT IRMM F.-J. HAMBSCH AND S. OBERSTEDT EC-JRC-IRMM Retieseweg, B-2440 Geel, Belgium E-mail: [email protected] G. VLADUCA AND A. TUDORA Bucharest University. Faculty of Physics, R-76900 Bucharest, Romania E-mail: anabella @ Olimp.fiz. infim. ro

Fission fragment properties and cross-sections have been investigated for ' U(n,f), 239Pu(n,f), 237Np(n,f), 252Cf(SF) and 233Pa(n,f). Interpretation of the experimental results was done within the multi-modal fission model. The three most dominant fission modes were considered, the two asymmetric standard I (SI) and standard n (S2) modes and the symmetric superlong (SL) mode. For the evaluation the statistical model was extended to include the concept of multi-modality of the fission process. Fission mode deconvoluted fission cross-sections, neutron multiplicites and spectra for the SI, S2 and SL modes were calculated for the first time in the incident neutron energy range from 0.01 to 5.5 MeV for the isotopes mentioned above, except 252Cf and 233 Pa. Good agreement was found with the experimental data. Additionally, branching ratios were deduced for the different modes giving the possibility to calculate fission fragment mass yield distributions at incident neutron energies, where no experimental data exist. Last but not least, the first ever direct fission cross-section measurements of 233Pa were performed. The new evaluation resulted in reduced fission cross-sections as compared to evaluated libraries. 235 238

1.

Experimental investigations

The IRMM has a longstanding tradition in the field of neutron induced fission physics studies. It is especially well equipped with world-class facilities as the high resolution neutron time-of-flight spectrometer GELINA and the 7MV Van de Graaff accelerator for quasi-monoenergetic neutron production. During the past decade several neutron induced fission reactions have been studied in the energy range from eV up to 6 MeV and spontaneous fission. The reactions under investigation were 235 ' 238 U(n, f). 239 Pu(n, f), 237 Np(n, f),

67

68

Cf(SF) and Pa(n, f). For all isotopes but Pa, thefissionfragmentmassyield (Y(A)) and total kinetic energy (TKE) distributions were measured. 233Pa was only investigated for the fission cross-section, due to its very short half life of only 27 days. A double Frisch-gridded ionization chamber has been used as fission fragment detector. As neutron source from thermal up to 6 MeV both GELINA and the 7MV Van de Graaff accelerator were used. The isotopes 235U and 239Pu have been studied in the resolved resonance region (up to 200 eV), the others including 235U with quasi mono-energetic neutrons up to 6 MeV. For the unique measurements of the 233Pa(n,f) cross-section mono-energetic neutrons up to 8.5 MeV have been used. In Fig. 1 a typical Y(A, TKE) distribution is shown together with the position and FWHM of the SI, S2 and SL-modes. The results have been described within the multi-modal fission model [1]. Fig. 2 shows the different moments of such a distribution (upper left: mass yield, lower left,

[

I

I

I

I

BO

I

100

I

I

I

I

180

I

I

I

I

I

140

I

l_l

L

160

F r a g m e n t Mass Figure 1. Y(A, TKE) distribution of modes.

237

Np(n,f) with the position and shape of the dominant fission

TKE(A), upper right: Variance of the TKE(A) distribution and lower right: dissymmetry of the TKE(A) distribution, a measure of the skewness of this distribution) in comparison with a fit within the model of Ref. [1] (full line). In parallel calculations have been performed of the potential energy surfaces for 238 Np [2], 239U [3] and 252Cf [4] within this model. As a remarkable results it was found that the bifurcation point of the fission modes lies in the second minimum of the double humped fission barrier. As a consequence separated outer barriers for each of the fission modes exist. For the symmetric superlong mode, this was already established from experiments because the yield of symmetric masses increases with increasing incident neutron energy.

69

120

125

130

135

MO

A [amu] Ill

> \

s

•.J

m

120

125

130

13S

1*0

145

150

A [amu]

155

160

1S5

170

A [amu]

Figure 2. Comparison of experimental data for 239Pu(nu,,f) with the fission mode model. Also higher moments of the Y(A,TKE) distribution are shown.

2.

The statistical model

Since the theoretical interpretation of the experimental results was rather successful an attempt was made to include multi-modality into the evaluation of the corresponding fission cross-section as well as their neutron multiplicity and spectra. Based on experimental fission mode branching ratios deduced from the experiments mentioned in chapter 1 and the ENDF/B-VI fission cross-section [5], the mode separated fission cross-sections are obtained for the reactions n + 235 U, n + 238U and n + 237Np. In this energy range the neutron interaction with the target nucleus takes place through direct and compound nuclear mechanisms. For these deformed heavy nuclei, the elastic channel is strongly coupled with the other possible channels in the process and the direct mechanism has to be treated with the coupled channel method method (ECIS95 code [6] with the parameterization given in ref. [7]). For the compound nuclear mechanism a statistical treatment is used for fission, neutron elastic and inelastic scattering and radiative capture cross-section calculations. The statistical model [8] for fission cross-section evaluation was extended by including the multi-modality concept for fission.

70

The inner barriers and the isomeric wells were taken the same for all modes and the outer fission barrier for each fission mode was taken to be different. For each mode the sub-barrier effects, the direct, indirect and isomeric fission cross-sections are taken into account. The self-consistent calculations of the fission cross-section as well as total, capture, elastic and inelastic cross-sections were in good agreement with the experimental data and evaluated nuclear data libraries. As a side product, also fission fragment mass yield distributions have been deduced at incident neutron energies hitherto inaccessible to experiment. Concerning the neutron multiplicities and spectra, here the commonly used Los Alamos model [9] was modified to take into account the multi-modal fission, too. Additionally, it has been extended to a larger base of fissionfragment masses and takes into account the linear prompt y-ray energy dependence on prompt neutron multiplicity [10]. These aspects led to an improved agreement with experimental data.

E (MeV) Figure 3. Total fission cross-section in comparison with mode separated fission cross-sections for 237 Np(n,f).

3.

Results and discussions

The calculated fission cross-sections for the SI, S2 and SL modes and the total fission cross-section in comparison with the "experimental" modal crosssections (represented by different symbols) and available experimental data from EXFOR [11] (open circles) are given in Fig. 3 as an example for 237Np.

71 ioV

».--#• ~ ~ f f - » - » - * - - * - - * - " • « '

.-• 10' -

"""•-•-.. 237

10"-

•

1

\

Np(n,f)

\

IRMM branching ratios

si -

J" \

/

\

_

S2

\

SL

\

T

A T T T X 6 \.S

1 U-'l

v—Y"'l

1

10'-

•

10

'*

10'1

10°

E (MeV)

Figure 4. Branching ratios for 237Np(n,f).

For threshold reactions like 237Np and 238U, to get reliable barrier parameters, it is very important, that sufficient experimental data are available in the threshold region. Although some discrepancies are observed for the SI mode, especially in the threshold region, the overall agreement is convincingly good between calculations and experimental data. The branching ratios for 237Np(n,f) as calculated with the model and their comparison to the experimentally deduced branching ratios are given in Fig. 4. It is worth here to mention that using these total

S1

S2

SL

10"-

>

-1

70

80

90

1

100

Figure 5. Predicted mass distribution for

1

1

110

1 — !

120

1

1

130

1

1

140

Np(n,f) at E„=0.4 MeV.

1

"j

150

1

1—•"!-

160

170

72

branching ratios and extrapolating the IRMM modal data concerning the mass yield, standard deviations and mean masses, the fission fragment mass distribution can be estimated at any incident neutron energy in the studied energy range. 3.5

.9- 3.0-

' ' I ' ' • • I ' ' ' Experimental data from EXFOR {re-normallzed at Cf(SF)): • o Frehaut o Soleilhac and Frehaut A Boldeman v Prokhorova v Bljumkina O Savin * Fieldhouse x Meadows -?* Kaeppeler • D'Jachenko Evaluated exp.data(EXFOR): - Manero ••• Zhang

U(n,f) present evaluation

! 2.0

11 i i i i 11i i i i 1 1 i i i i i 11 11 i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i 11 i i i 111111

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

E„(MeV)

Figure 6. Total average prompt fission neutron multiplicity calculation for EXFOR data.

235

U(n,f) compared to

The important contribution of the SL mode in the sub-barrier energy region for 237Np(n,f) is remarkable. However, one must also be cautious, since the underlying experimental values for SL in the barrier region have large uncertainties. Hence slight changes could lead to different results for the branching ratios of the SL-mode. Nevertheless an example of a predicted mass distribution is shown in Fig. 5 for 237Np at En = 0.4 MeV, showing a maximum yield towards the position of the Sl-mode, as the calculations predict, that this mode is dominant at this incident energy (see Fig. 4). Examples for the evaluation of the total average prompt fission neutron multiplicity (Fig. 6) and the prompt fission neutron spectrum (Fig. 7) are given for 235U(n,f). In the latter case also the anisotropy of the neutron angular distribution has been taken into account. More details can be found in Ref. [10]. Last but not least Fig. 8 shows the evaluation of the 233Pa fission cross section up to 20 MeV. This was a real challenge, since for this isotope very little information is available in literature. A direct experiment was considered to be impossible due to the short half-life and hence very high activity of 233Pa. Nevertheless the experiment was done [12] resulting in cross-section values from E n =1.0 to 8.5 MeV [13]. For the evaluation up to 20 MeV [14], to render

73 i ' i ' i ' i

T

U(n,f) E„=0.5 M e V

'

i ' i

• i '

i ' i

• i •

r

exp.data EXFOR(2001) D En=0.53MeV o Ens0.52 MeV

Figure 7. Prompt fission neutron spectrum ratio with the anisotropy effect taken into account for 235 U(n,f).

—i—i—i—i—i—i—i Barreau et al. (Bruyeres p o t Barreau e t a l . (Perey-pot) IRMM

E (MeV)

Figure 8. Fission cross-section evaluation for 233Pa(n,f).

it even more difficult also the neighboring isotopes 231 ' 232 p a need to be taken into account in the evaluation process. Also for those isotopes very little information is available today. References 1.

U. Brosa, S. Grossmann, A. Miiller, Phys. Rep. 197, 167 (1990).

74

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

P. Siegler, F.-J. Hambsch, S. Oberstedt and J.P. Theobald, Nucl. Phys. A594, 45 (1995). S. Oberstedt, F.-J. Hambsch, F. Vives, Nucl. Phys. A644, 289 (1998). F.-J. Hambsch, S. Oberstedt,. J. Van Aarle, Proceedings on .Int. Conf. On Nuclear Data for Sci. and Tech., 1997, Trieste, Italy, Vol.59, Part II, 1239 ENDF/B-VI, ZA92235, ZA92238, ZA93237, MF=3 (2002) J. Raynal, 1994, Notes on ECIS94, CEA-N-2772, private communic.(1995) RIPL-1 (1998), RIPL-2(2003), segment IV, IREF=600 (G.Vladuca, A.Tudora, M.Sin). G. Vladuca, A. Tudora, F.-J. Hambsch, S. Oberstedt, Nucl. Phys. A707, 32 (2002). D. G. Madland and J. R. Nix, Nucl. Sci. Eng. 81, 213 (1982). F.-J. Hambsch, S. Oberstedt G. Vladuca, A. Tudora, Nucl. Phys. A709, 85 (2002). EXFOR Nuclear Data Library (2000), nucleus ZA93237, quantities CS, reactions (n,tot) (n,f) and (n,g). F. Tovesson, F.-J. Hambsch, A. Oberstedt, B. Fogelberg, E. Ramstrom, S. Oberstedt, Phys. Rev. Lett. 88, 062502 (2002). F. Tovesson et al., in preparation. G. Vladuca et al., in preparation.

INVESTIGATION OF GEV PROTON-INDUCED SPALLATION REACTIONS* D. HILSCHER, C.-M. HERBACH, U. JAHNKE AND V.G. TISHCHENKO Hahn-Meitner-lnstitut

Berlin, Glienickerstr.

100, D-14109 Berlin,

Germany

J. GALIN, B. LOTT, A. LETOURNEAU AND A. PEGHAIRE GAN1L (IN2P3-CNRS,

DSM-CEA) BP- 5027, F-14076 Caen-Cedex 5, France

D. FILGES, F. GOLDENBAUM, K. NUNIGHOFF, H. SCHAAL, G. STERZENBACH AND M. WOHLMUTHER Forschungszentrum

Jtilich, Institut fiir Kernphysik,

D-52428 JUlich,

Germany

L. PIENKOWSKI Heavy Ion Laboratory,

Warsaw University, 02-093 Warszawa,

Poland

W.U. SCHRODER AND J. TOKE University of Rochester, Rochester, NY 14627, USA

A reliable modeling of GeV proton-induced spallation reactions is indispensable for the design of the spallation module and the target station of future accelerator driven hybrid reactors (ADS) or spallation neutron sources (ESS), in particular, to provide precise predictions for the neutron production, the radiation damage of materials (window), and the production of radioactivity (3H, 7Be etc.) in the target medium. Detailed experimental nuclear data are needed for sensitive validations and improvements of the models, whose predictive power is strongly dependent on the correct physical description of the three main stages of a spallation reaction: (i) the Intra-Nuclear-Cascade (INC) with the fast heating of the target nucleus, (ii) the de-excitation due to pre-equilibrium emission including the possibility of multi-fragmentation, and (iii) the statistical decay of thermally excited nuclei by evaporation of light particles and fission in the case of heavy nuclei. Key experimental data for this endeavor are absolute production cross sections and energy spectra for neutrons and light charged-particles (LCPs), emission of composite particles prior and post to the attainment of an equilibrated system, distribution of excitation energies deposited in the nuclei after the INC, and fission probabilities. Systematic measurements of such data are furthermore needed over large ranges of target nuclei and incident proton energies. Such data has been measured with the NESSI detector. An overview of new and previous results will be given.

* This work was supported by the EU TMR-project ERB-FMRX-CT98-0244, the German Strategiefonds project "R&D for ESS" of the Helmholtzgesellschaft, and by the French GEDEON project. 75

76

1.

Motivation

The motivation for the present investigation of spallation reactions is twofold. First, the development of new high-flux spallation neutron sources necessitates an experimental validation of the underlying basic spallation reaction models in order to ensure that the present models and codes have reached an adequate precision which would allow to base the source concept reliably on calculations. Second, proton induced spallation reactions generate nuclei with high thermal excitation energy with a minimum of compression, deformation and spin. This property enables to study the decay of highly thermally excited nuclei, in particular fission at high excitation energies. For the validation of models/codes such as LAHET, HERMES, INCL, and FLUKA it might be sufficient to provide inclusive data such as production cross sections of neutrons, hydrogen, and helium. However for the detection of specific deficiencies in the models detailed and exclusive data is needed: correlation of neutron and light charged particle multiplicities, excitation energy distributions as well as energy spectra of charged particles. Isotopic Resolution of the Detector-Telescopes

Mass (ami)

Mass (amu)

Figure 1. NESSI detector consisting of the Berlin Neutron Ball (BNB) and the Berlin Silicon Ball (BSiB) with 162 detectors. The mass resolution for H, He, Li and Be obtained with the 6 ancillary telescopes are displayed in the right panels.

2.

Experiment

The NEutron Scintillator and Silicon detector NESSI (Fig.l) consists of two 4% detectors for neutrons (BNB) and charged particles (BSiB) supplemented by six AE-E-telescopes. The neutron ball BNB [1] measures eventwise the neutron multiplicity while the silicon ball BSiB [2] measures the multiplicity, energy spectra and spatial correlation of charged particles with sufficient particle identification to

77

separate hydrogen, helium, IMFs, and fission fragments. For more precise charge and mass resolution six ancillary detector telescopes are employed to measure light and medium mass isotopes with a considerable increased energy range up to about 200 MeV. The good mass resolution achieved with the fourmember telescopes is demonstrated in Fig. 1. For neutron multiplicity measurements with thick targets the silicon ball could be removed from the center of the BNB and be replaced by up to 35 cm long and 15 cm in diameter W, Hg, Pb cylinders. Measurements with such thick targets provided a systematic data set [3, 4] for bench mark testing [5] of the various codes including the transport part. p(1.2GeV)+Au,Tel.lat30° • NESSI

-D io

1 = 1 Evap.

INC.

Pre-Equilibrium Emission at E =1.2GeV

<mm* * * * * * r * * N « m ^ c h

* > 1 S io"1 1

©

10

* |

- INCL2-G for p

l/\r~~*~"H :

fy»%»**w^fc,l

10" 10

^e

I 50

e 40

30

1

y**vt»

10 "

20

,J

^He

i i

a *

40

60

$

*

i

••.•...••..•"•••..• •••... /... ^ 20

0

20

40

60

80

100

120

140

80

100

160

E kin (MeV) Figure 2. Left panel: Measured energy spectra of p, d, t, 3He, 4He from the reaction 1.2GeV p+Au at an angle of 30°. Right panel: relative yield of pre-equilibrium emission.

3.

Pre-equilibrium cluster emission

In fig. 2 the measured energy spectra of protons (p), deuterons (d), tritons (t), 3 He and 4He are shown for the reaction 1.2 GeV p+Au at a reaction angle of 30°. The shaded area indicates the evaporative part of the emission spectra of these particles. By inspecting these spectra it is obvious that a large fraction of the total production cross section is emitted prior to the attainment of a thermal equilibrium. From the spectra measured between 30° and 150° the relative angle-integrated contribution Opre/(opre+aeva) of pre-equilibrium (PE) emission can be deduced quantitatively. For targets between Al and Th about 40-60% of

78

all d, t, and He are emitted prior to the attainment of an equilibrium. The relative contribution of 4He PE emission is much smaller and amounts only to about 10%. This finding agrees quite well with our earlier data for the reaction of2.5GeVp+Au[6]. E as a Function of LP-Multiplicity for p(2500MeV)+Au YieldfromINCL+GEMINI

E* (MeV)fromINCL

Sim. E*-Distribution

| "Vj"

20

500

Ma

Yield from NESSI

E (Mn,M, ^Correlation from Simulation

1000

E* (MeV) Exp. E*-Distribution

25 ?!) 10

7 .•-

0

v

• .A •

15

>

Experimental Yield(M|l,M1 )

-J

••* __l i iA ki . _J 20 M„

500

1000

E* (MeV)

Figure 3. Method to determine the excitation energy from the measured multiplicities MLCP of light charge particles LCP and neutrons M„. The color code of the top middle panel is given in MeV.

The wider range of target nuclei covered with the present data, however, gives an astonishing result, that the ratio oCp-pre/oiNc-p of cross sections of PE composite-particles (cp) to INC protons depends only weakly on the target mass Ay [7]. The coalescence model discussed in ref. [6] would, instead, predict a stronger decrease of acp.pre/orNc-p with decreasing AT. For deuterons, for instance, the probability that an INC proton coalesce with an INC neutron should depend on the number of INC neutrons which can be shown [7] to be proportional to RT*Nj/AT, where RT and NT are the nuclear radius and the number of neutrons in the target nucleus, respectively. The present systematic data indicates that oCp-pre/o"iNc-p~NTMT- and not acp-pre/oiNc-p~KT*AV^T-

79 4.

Excitation energy distributions

From the measured multiplicities of evaporated light charged particles MLCP and neutrons Mn it is possible to deduce the excitation energy for each event [8]. This is shown schematically in Fig. 3. From a simulation calculation the matrix of the excitation energy E*(MB, M L C P) (middle top panel) is obtained. This correlation is folded with the experimental efficiencies and is then employed to look up the excitation energy E* for the measured M„ and MhCP. In Fig. 4 the thus deduced excitation energy distributions for the reactions 0.8, 1.2, and 2.5 GeV are compared with calculations with the ENCL [9] and LAFJET [10] codes. This figure shows that the INCL code reproduces quite well Distribution of Excitation-Energy E at p(GeV)+Au

0.8 GeV

1.2 GeV

2.5 GeV

I

E (MeV)

p(GeV) + Fe

p(GeV) + Au

Ep (GeV) Figure 4. Excitation energy distributions in the reactions 0.8, 1.2, 2.5 GeV p+Au, the lower panels displays the heating efficiencies of spallation reactions of Fe and Au nuclei as a function of proton energy.

80

the deduced experimental excitation energy distributions while the LAHET code predicts at higher bombarding energies considerable larger E* than experimentally observed. An interesting question one might ask is: how efficient is a spallation reaction in heating nuclei? This question is answered in the right panel of Fig. 4 where the ratio <E*>IEV of the mean value of E* and the incident bombarding energy is shown as a function of the proton energy Ep. The experimental data <E*>/EV for p+Au decrease rapidly from 21% at 0.8 GeV to only about 12% at 2.5 GeV, while <E*> would still increase slowly from 170 to 290 MeV. The INCL-prediction follows this decrease very closely, as does the calculation with the model of Golubeva et al. [11]. The LAHET-simulation, however, provides good agreement with the experiment only at low incident energy, while at high Ev Fig. 4 now reveals the full extend, i.e. a factor of 2, of the discrepancy between the INC models. 5.

Summary

It was demonstrated in this talk that detailed, exclusive, and systematic data is needed for the validation of and for identifying specific deficiencies in the modeling of the three stages of a spallation reaction: INC, pre-equilibrium, and evaporation. This was particularly demonstrated by the comparison of experimentally deduced and calculated excitation energy distributions. Similarly the deficiency of the LAHET code in describing the production cross sections of hydrogen and helium could be traced back [12,13] to the temperature dependent Coulomb barriers employed in this code. No satisfactory description of the pre-equilibrium cluster emission over a wide range of target nuclei is presently available. Though not directly mentioned in this short written contribution the systematic neutron production and in particular neutron multiplicities measured in thick targets of W, Hg, and W [3, 4] can be reasonably well described [5] by most of the models, including those which have deficiencies in describing the charged particle data. This latter finding is mainly due to an compensation effect [13, 14]. If in the first interaction less (more) excitation energy is transferred during the intra nuclear cascade to a nucleus more (less) energetic nucleons are emitted. In the secondary and tertiary reactions of the inter nuclear cascade these nucleons will then produce also more (less) neutrons. The obtained data was also exploited to investigate the lifetime of the window. For the same amount of neutron production in a typical target of a spallation neutron source the proton beam induced radiation damage in an Fe window could be shown to decrease almost linearly with the proton energy [15]. For heavier materials such as Ta a similar decrease of the radiation damage is found only for energies above about 3 GeV. Finally

81

preliminary results of measured fission probabilities in 2.5 GeV proton induced fission of U showed a very similar dependence on E*, MLCp, and Mn as in antiproton induced fission as investigated by the PS208 collaboration [16,17], References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

U. Jahnke et al, Nucl. Instr. andMeth. A508, 295 (2003). C.-M. Herbach et al, Nucl. Instr. andMeth. A508, 315 (2003). A. Letourneau et al, Nucl. Instr. Meth. B170, 299 (2000). D. Hilscher et al, Nucl. Instr. Meth. A414, 100 (1998). D. Filges et al., Eur. Phys. J. A l l , 467 (2001). A. Letourneau et al, Nucl. Phys. A712, 133 (2002). C.-M. Herbach et al., to be published. F. Goldenbaum etal, Phys. Rev. Lett. 77, 1230 (1996). J. Cugnon et al, Nucl. Phys. A620, 475 (1997). R.E. Prael, H. Lichtenstein, Rep. LA-UR-S9-30U, (1989). Ye.S. Golubeva et al, Nucl. Phys. A483, 539 (1988). M. Enke et al, Nucl. Phys. A657, 317 (1999). C.-M. Herbach et al., J. of Nucl. Science and Tech., Suppl. 2, 252 (2002). L. Pienkowski etal, Phys. Rev. C56, 1909 (1997). D. Hilscher et al. J. Nucl. Mater. 296, 83 (2001). U. Jahnke et al, Phys. Rev. Lett. 83, 4959 (1999). B. Lott et al, Phys. Rev. C63, 034616 (2001)

EVIDENCE FOR TRANSIENT EFFECTS IN FISSION B. JURADO*, K.-H. SCHMIDT, C. SCHMTTT, A. KELIC GSI, Planckstrafie

1, D-64291 Darmstadt,

Germany

J. BENLLIURE Facultad de Fisica, Univ. de Santiago de Compostela, Spain

E-15706 S. de

Compostela,

A. R. JUNGHANS Forschungszentrum

Rossendorf, Postfach 510119, 01314 Dresden,

Germany

The aim of this work is to experimentally investigate transient effects in fission. In order to simplify the theoretical description, we have chosen peripheral heavy-ion collisions at relativistic energies to reduce the side effects and to produce highly excited fissioning systems with well-defined initial properties. Thanks to an experimental setup specially conceived for fission studies in inverse kinematics, we could determine two new observables very sensitive to transient effects in fission. Quantitative values for transient effects are deduced from the comparison of these observables with a nuclear-reaction code where dissipation effects in fission are modeled in a highly realistic way.

1.

Introduction

The deexcitation process of a highly excited heavy nucleus requires a dynamical description that takes into account the time the system needs to populate the available deformation space and reach equilibrium. A dynamical description of the deexcitation process in terms of a purely microscopic theory is not possible to the present day due to the large number of degrees of freedom involved. For this reason, most of the current theoretical models are transport theories that try to portray the process using a small number of variables. In these theories one distinguishes between collective and intrinsic degrees of freedom, and the latter are not considered in detail but in some average sense as a heat bath. The collective degrees of freedom of the nucleus correspond to the coordinate motion of part or all the nucleons, e.g. vibrations and rotations. The intrinsic degrees of freedom are the individual states of the nucleons. The collective degrees of freedom and the heat bath are coupled, that is, excitation energy can be transferred between them. The process of transfer of energy between the collective degrees of freedom and the heat bath is denominated * Present address: GANIL, Blvd. H. Becquerel, B.P. 5027, 14076 Caen, France 82

83

dissipation. Dissipation is quantified by the reduced dissipation strength (5, which measures the relative rate with which the excitation energy is transferred between the collective and intrinsic degrees of freedom. In the frame of a transport theory, fission is the result of the evolution of the fission collective coordinates under the interaction with the heat bath and an external driving force given by the available phase space. This evolution can be obtained by solving the Langevin equation or its integral form, the Fokker-Planck equation (FPE). An important parameter in these two equations of motion is the dissipation strength /3. In spite of intensive theoretical and experimental studies, the strength of /? and its variation with deformation and temperature are still subject of intense debate [1]. In 1940 Kramers [2] developed the first transport theory to describe nuclear fission and found the stationary solution of the FPE. The idea of Kramers was recovered forty years later by Grange et al. [3], who theoretically investigated the influence of dissipation on the fission time scale by solving numerically the FPE. Their results showed that it takes a transient time z,rans until the current over the saddle point reaches its stationary value. The transient time originates from the time needed by the probability distribution of the particle to spread out in deformation space. Grange et al. [3] defined r,rans as the time that the fission width r/J) needs to reach 90% of its asymptotic value. A full dynamical calculation of the fission process should consider as well the emission particles. This can be done allowing for evaporation during the dynamical evolution of the system when solving the multidimensional FPE or Langevin equation. Another procedure widely used to study fission dynamics consists on introducing a time-dependent fission decay-width .T/0 in an evaporation code. Such a treatment is equivalent to solving the above mentioned equations of motion, under the condition that the time-dependent fission decay width /}(?) is obtained by solving the Fokker-Planck or Langevin equation at each evaporation step. Unfortunately, these three procedures require a very high computational effort. However, in an evaporation code one can get around this problem by using a suitable analytically calculable expression for r/jt). This allows incorporating realistic features of fission dynamics in complex model calculations for technical applications, e.g. the nuclide production in secondary-beam facilities, in spallation-neutron sources and in shielding calculations. 2.

Experiment

The experimental manifestation of transient effects is subject of controversy nowadays [4]. However, we will show that the experimental observation of

84

transient effects in fission is possible provided the appropriate reaction mechanism is used and adequate observables are considered. To observe transient effects a reaction mechanism is required that leads to excited nuclei with small deformation, so that the we can observe the equilibration of the probability distribution in deformation space. In addition, the reaction mechanism should lead to high enough excitation energies for the particle decay time to be smaller than the transient time. In this case, transient effects show up in a drastic way, since the system is forced to emit particles because fission is suppressed. These initial characteristics of the fissioning nucleus can be obtained by applying a projectile-fragmentation reaction, i.e. a very peripheral nuclear collision with relativistic heavy ions. Besides, this reaction mechanism induces a very small angular momentum 1 < 20h [5], which avoids additional influence on the fission process. Relativistic heavy-ion collisions can be investigated at GSI where a highly intense 238U beam is available. Concerning the observables, the analysis of particle multiplicities does not allow to explore the deformation range from the ground state to the saddle point independently. Total fission or evaporation-residue cross sections are the most used observables to investigate dissipation at low deformation. However, they are not sufficient to determine transient effects in an unambiguous way. To clearly define the characteristics of transient effects we need observables that allow selecting the fission events according to the excitation energy. This new type of observables could be measured thanks to an experimental set-up specially conceived for fission studies in inverse kinematics that was developed at GSI. This set-up is schematically illustrated in figure 1. When the projectile fragment fissions, the two fission fragments are focused in forward direction and detected simultaneously in a double ionization chamber that delivers a very accurate measurement of their nuclear charges. The velocity dependence of the energy-loss signals is corrected by means of the time of flight. The efficiency for fission of the set-up is of the order of 97%. The charge identification of both fission fragments enabled us to determine two new observables: the partial fission cross sections, that is, the cross section as a function of the fissioning element, and the charge distributions of the fission fragments that result from a given fissioning nucleus. In the next lines we will qualitatively explain why these observables are adequate to investigate transient effects on the way to the saddle point. The sum charge of the fission fragments is a very significative quantity, because it is directly related to the charge of the fissioning nucleus. Besides, the charge of the fissioning element goes linearly with the charge of the prefragment and hence, it gives an indication of the centrality of the collision. Low values of Zy+Z2 imply small impact parameters and large excitation energies induced by

85

the fragmentation process. Therefore, for the lightest fissioning nuclei (lowest values of Z/+Z2) transient effects will lead to a considerable reduction of the fission probability. According to empirical systematics, the width of the mass distribution of the fission fragments is a measure of the saddle-point temperature. This experimental result has been corroborated by twodimensional Langevin calculations [6]. Due to the strong correlation between the mass distribution of the fission fragments and the charge distribution, the same relation holds for the width of the charge distribution and the temperature at saddle. Thus, for the lower values of Z!+Z2 where the initial excitation energy is large and fission is suppressed with respect to particle evaporation, the nucleus will evaporate particles while it deforms, and the temperature at saddle will be smaller than the initial temperature. Consequently, transient effects will cause a narrowing of the corresponding charge distributions. - T0F,i2 s">7m Scinttttstor I Ionization chambers

/

AE,12

\

Beam

Figure 1. Experimental set-up for fission studies in inverse kinematics.

3.

Results

To deduce quantitative results on transient effects, the experimental observables introduced in the previous section need to be compared with a nuclear-reaction code. The code we use is an extended version of the abrasion-ablation MonteCarlo code ABRABLA [7]; it consists of three stages. In the first stage the characteristics of the projectile residue after the fragmentation are described according to the geometrical abrasion model. The second stage accounts for the simultaneous emission of nucleons and clusters (simultaneous break-up) that takes place due to thermal instabilities when the temperature of the projectile spectator exceeds 5 MeV [8]. After the break-up, the ablation stage models the sequential deexcitation of the system through an evaporation cascade. A reliable study of transient effects requires a realistic description of the timedependent fission decay-width. For this reason we have implemented in the third stage of ABRABLA a description of r/j) that is based on an approximate

86

solution of the FPE [9]. In table 1 the experimental total nuclear fission cross section of the reaction of 238U at 1 A GeV on lead obtained with the previous set-up is compared with the values obtained from several ABRABLA calculations performed with different shapes of the time-dependent fission width and different values of /3. Apart from a calculation performed with the new analytical approximation of [9], table 1 includes the two most widely used approximations for the time-dependence of the fission width. Compared to our analytical approximation these two approximations are rather crude. The calculation represented in the third row of table 1 uses a step function that sets in at a time equal to the transient time. This approximation underestimates the fission width during the initial time. The approximation used in the fourth row is an exponential-like in-growth function. This approximation overestimates the initial values of the fission width and starts with a very steep slope. The important difference between the initial behaviour of both descriptions leads to very different pictures of the relaxation process. As expected, the calculation without dynamical effects of the second row of table 1 overestimates the cross section. However, the other three approximations can reproduce the total fission cross sections although with different values of the dissipation strength. These results demonstrate that total fission cross sections allow to identify an overall reduction of the fission probability but are not sensitive to the shape of f/J). Table 1. Total nuclear fission cross section of comparison with different model calculations. Experiment [1]

U (1 A GeV) on Pb in

r/f) =step function, P = 2 x l 0 2 1 s"1 r / f ) ~ l-exp(-2.3t/r,„„), 0 = 4 x l 0 2 1 s"l

af""" = 2.16 ± 0.14 b a f nucl =3.33b afnud = 2.00 b a,nucl = 2.04 b

7 X 0 = FPE [9], P = 2 x l 0 2 1 s"1

Ofnucl = 2.09 b

No dissipation

Figure 2 represents the partial fission cross sections (figure 2a) and the widths of the charge distribution (figure 2b) for different fissioning nuclei measured in the reaction of 238U (1 A GeV) on (CH2)„. The experimental data (black dots) are compared with the same approximations for r/t) as in table 1. In the case of figure 2a) the three calculations agree quite well with each other and with the experimental data for the highest values of Zj+Z2, and start to differ for the lowest values of Z1+Z2. However, the deviations are not enough to decide which function r/t) gives the best description of the measured data. On the other side, figure 2b) shows a significant disagreement between the calculation done with the exponential-like description and the measured data. This disagreement suggests that the initial overestimation of the fission width

87

implied by the exponential-like approximation yields too large excitation energies at saddle. In figure 3 the same two observables of figure 2 are compared with a calculation that includes no dissipation (dashed line), with a calculation considering a constant fission decay-width equal to Kramers result (thick dashed

;

1

1

1

70

n

80

85

i„

90

Figure 2. Partial fission cross sections a) and partial widths of the charge distributions b) for the reaction of 238 U (1 A GeV) on (CH 2 ) n in comparison with several calculations. The dashed line is the result of using the exponential-like function and fi = 4-10 21 s"1, the dotted line is done with the step function and ft = 2-10 21 s"1, and the full line with t h e / # ) of [9] and )3= 2 1 0 2 1 s"1.

line), and with several calculations that include transient effects according to the fission width of [9] with different values of /?. As expected, both observables are visibly overrated by the transition-state model, confirming their sensitivity to dissipation. The calculation performed with the constant decay width of Kramers overestimates the observables as well, in contradiction with ref. [4]. For the two observables, the best description is given by the full line that corresponds to/3 = 2-1021s"' (full line). Such value of (3 corresponds to the critical damping and thus to the shortest transient time T,rtms~ (1.7±0.4)-10~21 s,.

n

es m Z, • Z,

9Q

Figure 3. The same observables as in figure 2 in comparison with several calculations. The dotted line and the dashed-dotted lines are calculations done using the function of [9] with/3= 0.5-10 21 s"1 and/3 = 5 1 0 2 1 s"1, respectively. For the rest of the curves see text.

88

4.

Conclusion

We have considered a reaction mechanism and have introduced new observables that allow the observation of transient effects in fission. We have developed an analytical approximation for the fission width that allows including realistic transient effects in an evaporation code without increasing the computing time. The comparison of the experimental observables with model calculations has lead to a value for rlrans ~ (1.7±0.4)10 21 s indicating that, for the range of temperatures considered, the motion up to the saddle point is critically damped.

References 1. 2. 3. 4. 5. 6. 7. 8. 9.

B. Jurado, PhD Thesis, Univ. Santiago de Compostela, Spain (2002). H. A. Kramers, Physika VII4, 284 (1940). P. Grange, et al., Phys. Rev. C27, 2063 (1983). H. Hofmann, et al., Phys. Rev. Lett. 90, 132701 (2003). M. de Jong, et al., Nucl. Phys. A613, 435 (1997). D. V. Vanin, et al., Phys. Rev. C59, 2114 (1999). J.-J. Gaimard, et al., Nucl. Phys. A531, 709 (1991). K.-H. Schmidt, et al., Nucl. Phys. A710, 157 (2002). B. Jurado, et al., Phys. Lett. B553, 186 (2003).

T R A P S FOR FISSION P R O D U C T IONS AT IGISOL

S. KOPECKY, T. ERONEN, U. HAGER, J. HAKALA, J. HUIKARI, A. JOKINEN, V. S. KOLHINEN, A. NIEMINEN, H. PENTTILA, S. RINTA-ANTILA, J. SZERYPO AND J. AYSTO Department of Physics, P.O. Box 35 (YFL), FIN-40014 University of Jyvaskyla, Finland

One of the main focus of the work at the K-130 cyclotron in Jyvaskyla has been the investigation of properties of neutron-rich nuclei, which are produced in fission reactions. As the production yields of nuclei far off the /3-stability become increasingly smaller new, more efficient techniques for producing and selecting these nuclei have to be employed. Therefore a triple-trap setup has been installed at the IGISOL facility in Jyvaskyla. This new facility not only improves the experimental condition for decay-spectroscopy and collinear laser spectroscopy it also enables mass-measurements as an additional tool for studying neutron-rich nuclei.

1. Introduction A variety of experimental methods are employed for studying the nuclear structure of neutron-rich nuclei. These investigations are an important first step for understanding the structure effects - and possibly new phenomena - for nuclei along the neutron drip-line. For producing these nuclei here in Jyvaskyla proton induced fission of 238 U and IGISOL - ion guide separator on-line - are employed. In the IGISOL method the ions are stopped and thermalized in a gas-cell1, and a fraction of these ions will survive as singly charged ions. By a differential pumping scheme and electrostatic fields the ions are extracted out of the stopping cell and are accelerated to typically 40 keV. Due to the chemical insensitivity of this technique and the short evacuation time of the gas cell, very short lived nuclei as well as all refractory elements are available for experiments. It has been determined that the yield for 112 Rh is approximately 1 0 - 3 - at a proton beam with 30 MeV and a beam intensity of 10 fiA this corresponds to approximately 10 5 ions/s. Two properties of IGISOL make further ion manipulation very difficult. IGISOL provides a quasi-continuous ion beam and the energy spread of the ion beam is rather large, it can be as high as 100 eV. To overcome these

89

90 problems a cooler trap has been designed and build 2 . The ion-cooler buncher at IGISOL is working on the principle of a segmented linear Paul trap, i.e. the confinement both in radial and axial direction is accomplished by electric fields. The device itself is placed on a high-voltage platform. This platform is adjusted that the ions enter the cooler with an energy of approximately 100 eV. The RFQ is filled with He buffer gas with a pressure up to 0.1 mbar. While passing through the cooler the ions loose their radial and axial energy by collisions with the buffer gas until they are finally stopped along the center of the trap inside the potential well. Finally they can be extracted by applying a suitable extraction potential. The extracted ion bunches can have a duration of 2-3 /us and an energy spread of less than 1 eV. The transmission through this device is typically in the order of 60 -70 %. This improved beam condition do not only allow the coupling of a Penning trap to the IGISOL facility it also provide strongly improved condition for collinear-laser spectroscopy3, enabling investigations of ions with yields less than 100 ions/s.

2. Penning-trap The beam extracted from the RFQ is injected into a Penning-trap system, which is situated at the same high-voltage platform as the cooler. In a Penning trap the confinement of the ions is accomplished by a combination of electric and magnetic fields. JYFLTRAP uses the concept of an open-end Penning trap, where the electric quadrupole field, necessary for confining the ions in axial direction, is produced by cylindrical electrodes 4 . The magnetic field at JYFLTRAP is provided by a 7 T super-conducting magnet. Two homogeneous regions are located 10 cm up- and downstream of the center of the magnet. The first region with a homogeneity better than 1 0 - 6 is used for the purification trap, whereas the second with a homogeneity of 1 0 - 7 is used for the precision trap. Between these two traps is a diaphragm with a length of approximately 5 cm and an opening of 2 mm, allowing for maintaining a pressure difference between the two traps and for extracting of the ions that are located close to the center axis of the first trap. More details about the construction of the Penning trap can be found elsewhere 5,6 . The transmission through the trap is 30%, and the capturing efficiency in the first trap is 60%, therefore the total efficiency of this device is approximately 20%. It also could be demonstrated that isobarically purified beam

91 can be extracted and implanted into a tape, therefore enabling /3-decay spectroscopy for nuclei with a weak production channel. For creating isobarically pure beam the mass selective buffer gas cooling technique 7 is employed in the purification trap. In this technique ions are manipulated by buffer gas pressure and azimuthally dipole and quadrupole fields. By choosing suitable combinations of buffer gas pressure, excitation duration and excitation amplitude it can be achieved that ions with a selected charge-over-mass ratio will be accumulated along the center axes of the trap. All the other ions will be located at a distance from the center. By extracting the ions through a diaphragm, an isobaric pure beam can be created. It is possible to find trapping schemes varying in total cycle time and in mass resolving power R = -^-. At JYFLTRAP aim was to find trapping schemes with mass resolving power better than 11=15000, a value that should allow for isobaric separation for a wide variety of nuclei. It could be established that this goal could be accomplished with total cycle times as short as 90 ms. In the reaction 58 Ni(p,n) 58 Cu within a total cycle time of 450 ms a value of R=150000 could be established. It could be concluded that such conditions allow for direct mass measurements with accuracies better than 50 keV. For the precision trap the time-of-flight method is employed. This method exploits the effect that ions with different radial energy inside the magnetic field will have a different time-of-flight to a detector position outside the magnetic field, this effect is caused by the conversion of radial energy into axial energy when the ions leave the magnetic field. By selectively increasing the cyclotron motion of ions inside the trap it will be possible to determine their cyclotron frequency and therefore their masses precisely. The way to achieve this selection is as follows. At first are the already isobarically purified ions carefully moved from the purification trap into the precision trap. The trap bottom of the second trap is 3 V lower than the purification trap. To avoid further, unnecessary increase of the axial energy - too high axial energies jeopardize the possibility of observing the time-of-flight effect - the capture time of the ions in the second trap has to be chosen very carefully. This can be done by observing the time-of-flight of trapped ions in the second trap and by adjusting the closing time. After capturing of the ions a azimuthally dipole-field is applied for 15 ms, for introducing some magnetron motion - a motion which has only a very small energy content. This is followed by an azimuthally quadrupole excitation. Such an applied RF field will couple the magnetron and cyclotron motion of the ions to each other. A periodic transfer from an initial magnetron

92 118-,

40Ar 116114112g» 1 1 0 -

«*-

O

0) 108-

E i-

106104102 2688790

2688800

2688810

2688820

~1 2688830

Frequency [Hz] Figure 1. Frequency scan for precision trap

to cyclotron and back to magnetron motion will occur. As the cyclotron frequency is approximately 104 times larger, the difference in their radial energy is large. By choosing the excitation duration and excitation amplitude accordingly, a full conversion of magnetron-motion into cyclotron motion can be achieved for the ion species which cyclotron frequency matches the applied RF-frequency. By measuring the time-of-flight as a function of the applied RF-frequency the precise cyclotron frequency of the ion species inside the trap can be determined. The width of this frequency distribution will be inverse proportional to the duration of the excitation. In Fig. 1 a frequency scan for Ar-40 is shown. This measurement was done with a excitation amplitude of 50 mV and excitation duration of 200 ms, the line shape of the experimental data can be well reproduced by calculations. With such a resolution it is expected that mass measurements with accuracies of a few keV can be achieved. At the final stage it is expected that measurements with accuracies of 1 keV - or even better - will be achievable.

93 1 — i — | — i — | — i — | — i

1—i—|—i—|-

600-

i I

Zirconium 400-

5? 03

;*, 200-

i i

UJ

< 2

0-

§

§

;

?

-200-

-400 ">

96

1

"""

97

i—•—r

98

99

T—•—i—•—i—•—r

100

101

102

103

-i

1

r-

104

Figure 2. Preliminary results for experimental determined Zr-masses compared to literature values 8

3. Mass measurements The aim with JYFLTRAP is to do mass measurements in the near future. As two traps are available, the trap suitable for the required accuracy can be chosen. Studies of e.g. the Q-values of super-allowed /?-decay need accuracies better than 1 keV, an accuracy that hopefully can be achieved in the precision trap in the future. On the other hand studies on global and local shell-effects and deformation on the mass surface only require accuracies between 10-100 keV, accuracies that can be achieved by using the purification trap alone. Neutron-rich Zirconium presents a case for possible studies in the purification trap. The occurrence of a shape transition between neutron numbers 56 and 60 is well established, but so far no reliable direct mass measurements have been performed for these nuclei. Zirconium is well available at IGISOL, with intensities ranging from 200 to 4000 ions/s. By using

94

the ion manipulation of the RFQ and the Penning trap, it was possible to measure the masses ranging from Zr-96 to Zr-104. The dominant source of uncertainty of these measurements are the statistical uncertainty and the uncertainty introduced by variation of the beam intensity, the combined uncertainty is typically 50 keV. It was estimated that systematic uncertainties - as caused by imperfection of the electric quadrupole field - are of minor concern at the present level of accuracy. In Fig. 2 a comparison of these preliminary experimental results with the mass values from the recent mass evaluation 8 is shown. It becomes clear, that for the isotopes with well established masses the present results agree nicely with the data from the literature. In case of all the neutron rich isotopes, all of which have only been determined by /3-endpoint measurements so far, a clear difference between the new values and the literature data becomes visible, emphasizing the importance of direct mass measurements. 4. S u m m a r y At the IGISOL facility of the University of Jyvaskyla a triple-trap setup has been designed and constructed for ion beam manipulation. This new facility opens the possibility of investigation the properties of neutron-rich nuclei with weak production channels by means of decay spectroscopy, collinear laser spectroscopy and direct mass measurements. Acknowledgments This work was supported by the Academy of Finland under the Centre of Excellence Program 2000-2005 (project no. 44875) and by the European Union within the NIPNET RTD project under the contract no. HPRI-CT2001-50034. References J. Aysto, Nucl. Phys. A693, 477 (2001). A. Nieminen, et al., Nucl. Instrum. Methods A469, 244 (2001). A. Nieminen, et al., Phys. Rev. Lett. 88, 094801 (2002). H. Raimbault-Hartmann, et al., Nucl. Instrum. Methods B126, 378 (1997). V.S. Kolhinen, et al., Nucl. Instrum. Methods B204, 502 (2003). Veli Kolhinen, Ph.D Thesis, University of Jyvaskyla, 2003. G. Savard, et al., Phys. Lett. A158, 242 (1991). G. Audi, et al., Nucl. Phys. A624, 1 (1997).

TRIPLE-HUMPED FISSION BARRIER AND CLUSTERIZATION IN THE ACTINIDE REGION

A. KRASZNAHORKAY, M. CSATLOS, J. GULYAs, M. HUNYADI, A. KRASZNAHORKAY JR. AND Z. MATE Inst, of Nucl. Res. of the Hung. Acad, of Sci., H-4001 Debrecen, P.O. Box 51, Hungary, E-mail: [email protected] P.G. THIROLF, D. HABS, Y. EISERMANN, G. GRAW, R. HERTENBERGER, H.J. MAIER, O. SCHAILE AND H.F. WIRTH Sektion Physik, Universitdt Miinchen, D-85748 Garching,

Germany

T. FAESTERMANN Technische Universitdt Miinchen, D-85748 Garching,

Germany

M.N. HARAKEH Kernfysisch

Versneller Instituut, 9747 A A Groningen, The Netherlands M. HEIL, F. KAEPPELER AND R. REIFARTH

Forschungszentrum

Karlsruhe, Inst f. Kernphysik, 760021,Karlsruhe,

Germany

The fission probability of 236 U has been measured as a function of the excitation energy with high energy resolution. Rotational band structures have been observed, with moments of inertia corresponding to hyperdeformed nuclear shapes. From the level density of the rotational bands the excitation energy of the ground state in the third minimum was determined. The excitation energy of the lowest hyperdeformed transmission gave an upper limit for the height of the inner fission barrier. The predicted effects of the clusterization in hyperdeformed states have been studied by measuring the mass and total kinetic energy distribution of the fission fragments in case of 232 Th.

1. Introduction The study of nuclei with exotic shapes is one of the most vital fields in modern nuclear structure physics. Superdeformed (SD) nuclei in the second minimum have shapes with an axis ratio {c/a) of about 2:1, whilst

95

96 hyperdeformed (HD) nuclei in the third minimum correspond to even more elongated shapes with axis ratio (c/a) of about 3:1 1. In a program aiming at studying the super- and hyperdeformed states in the actinides we have already studied the HD states in 234 U 2 and in 236 U 3 and the SD ones in 2 4 0 Pu 4 ' 5 using the resonance tunneling method. Here we present our latest results obtained for 236 U. The 236 U is exceptional, because it is the only isotope where hyperdeformed transmission resonances have been observed 3 and at the same time a superdeformed fission isomer is well-established 6 . The first aim of the present experiment was to increase the energy resolution we used before for studying the fission resonances in 236 U and resolve the structure of the vibrational resonances in the third minimum as well as to study the mass distribution from the HD resonances. Moreover, it is predicted 13 that the density distribution of 2 3 2 Th at the third minimum resembles a di-nucleus consisting of a nearly-spherical doubly-magic nucleus ( 132 Sn) and a well deformed one ( 100 Zr). Our second aim was to study the 232 Th(n,f) reaction around the En=1.6 MeV HD resonance and study the possible effects of the HD resonances on the total kinetic energy (TKE) distribution of the fragments and on their mass distribution.

2. Experimental method The experiment was carried out at the Munich Accelerator Laboratory to investigate the 235 U(d,pf) reaction with a deuteron beam of JE7d = 9.75 MeV, and using an enriched (99.89 %), 88 /jg/cm 2 thick target of 2 3 5 U 2 0 3 on a 22 /jg/cm 2 thick carbon backing. The energy of the proton ejectiles was analyzed with a Q3D magnetic spectrograph 7 . The Q3D spectrometer was placed at ©^ = 125° relative to the incident beam and the solid angle was 10 msr. The position of the analyzed particles in the focal plane was measured with a position-sensitive light-ion cathode-strip focal-plane detector 8 . Fission fragments were detected by two parallel plate avalanche counters. The active area of the detectors and their distance from the target was 16 x 16 cm 2 and 23 cm, respectively. The detectors were placed at 55° and 125° with respect to the direction of the beam. The mass - TKE correlations were studied in the 232 Th(n,f) reaction using mono-energetic fast neutrons produced in the 7 Li(p,n) reaction. The Van de Graaff accelerator at Forschungszentrum Karlsruhe produced the 50 /uA proton beam, which impinged on a 200 /jg/cm 2 metallic Li target. The average neutron flux at the Th target was ~ 1.8xlO 6 neutrons/cm 2 s.

97

The fission fragments were detected in a twin ionization chamber with parameters similar to the one published by Budtz-Jorgensen et al. 9 . We have used a large area (12.6 cm 2 ) and thin (100 /ug/cm2) 2 3 2 T h 0 2 target as a common cathode of the ionization chambers. 2.1. Hyperdeformed

states

in

236

(7

The resonances at 5.27, 5.34 and 5.43 MeV had been previously identified as hyperdeformed resonances 3 , however without resolving their rotational structure. For the first time, this was achieved in the present experiment. The measured high-resolution fission probability in terms of the excitation energy of the compound nucleus 236 U is shown in Fig. la,c). It was obtained by dividing the proton energy spectrum measured in coincidence with fission fragments by the smoothly varying proton spectrum from the (d,p) reaction. The excitation energy region containing HD resonances was analyzed in two steps, beginning with the resonance structure above 5.2 MeV. We fit our experimental results with overlapping rotational bands with the same moment of inertia and intensity ratio for the members in a band, as we did in our previous works 3,2 .

„- 0.16

-0.025

5.15 E* (MeV) Figure 1. (a, c) Fission probability (Pj) as a function of the excitation-energy. The superimposed solid line shows a fit to the data using rotational bands with K values indicated by the numbers (see text for details). The arrows indicate the positions of the band heads. The best fit has been obtained by using hyperdeformed rotational bands, (b, d) Consistent description of the angular-correlation coefficient Ai from Ref. 10 (data points) with the fit function from panel (a, c) based on the distribution of K values as indicated in (a, c).

98

In order to allow for a consistent description of the fission probability and the angular correlation coefficient A2 from Just et al. 10 , a distribution of K values rising from K = 1 to K = 4 had to be chosen. The arrows in Fig. la,c) mark the positions of the band heads with their respective K values marked as numbers. The resulting curve for the Ai angularcorrelation coefficient calculated based on the fit function derived from the fission probability in panel a) and c) is displayed in panel b) and d) of Fig. 1. We deduced a rotational parameter of R— 2.3 ± 0.4 keV and a moment of inertia of 0 = 217 ± 38 h2/MeV from the data. This agrees nicely with the rotational parameter we obtained previously for 236 U (R= 2.3 1^4 keV) 3 and also with the values calculated by Shneidman et al., 12 who assumed dinuclear systems, suggesting the possibility of an exotic heavy clustering as predicted also by Cwiok et al., 13 before. In the second step of the analysis, the proton energy spectrum below 5.2 MeV was investigated, where no conclusive high-resolution data were so far available. The result of the analysis in the excitation energy region between 5.05 MeV and 5.2 MeV is shown in Fig. lc), where the prompt fission probability is displayed together with the results of a fit by rotational bands similar to the procedure described above for the upper resonance region. Assuming overlapping rotational bands in the second well with a spin sequence of J* = 2 + - 4 + - 6 + - 8 + and a typical rotational parameter for superdeformed bands h2/20 fa 3.3 keV, the experimental data could not be reproduced. The best fit to the data was obtained in the case of h2/29 » 2.2 keV, which suggest a hyperdeformed nuclear shape also with this assumption. The rotational parameter derived from the best fit (Fig. lc) could be determined as h2/26 = 2.4 ± 0.7 keV, corresponding to a hyperdeformed configuration. This result is in contrast to the old assumption that the decaying vibrational excitations originate from the superdeformed second minimum. The occurrence of a transmission resonance in the third well at 5.1 MeV requires a rather complete damping and an inner-barrier height EA lower than 5.2 MeV. The depth of the third well has also been determined by comparing the experimentally obtained average level distances with the calculated ones using the back-shifted Fermi-gas description with parameters determined by Rauscher et al. in a similar way as we did in our previous work on 234 U 2 . We obtained a value of 3.1 ± 0.4 MeV for the energy of the ground

99 state in the third well in perfect agreement with our previous data obtained for 234 U, and also in a fair agreement with the theoretical results 13 ' 12 . 2.2. Fission characteristic 232 Th(n,f) reaction

of the 1.6 MeV resonance

in the

In order to study the possible effects of such a dinuclear system on the decay of the HD states, the mass distribution was determined using the double energy method 9 . The width (a) of the mass distribution is shown in Fig. 2(a) as a function of the neutron energy with conditions on the total kinetic energy. This condition was used to distinguish between hot and cold fission. In the case of a wide condition, the sigma is large and we can not see any effect of the HD state. When we require colder and colder fission the a gets smaller and the effect of the HD state becomes visible. In a small fraction of the fission processes, when the excitation of the fragments is small, we can observe the predicted sharpening of the mass distribution when we cross the HD resonances.

3.5 - T

2

1.5

HD resonances

1.55

1.6

1.65

1.7 1.75 E n (MeV)

1.5

1.55

1.6

1.65

1.7 1.75 E n (MeV)

Figure 2. (a) The width a of the mass distribution as a function of the bombarding neutron energy with different conditions applied to the TKE. (b) T K E of the fission fragments as a function of the neutron energy calculated for different mass-number cuts around A = 132.

We can investigate the effect also in a different way. Let us focus on the mass split of 100 + 132, gate on it and investigate the TKE distribution as a function of the neutron energy as shown in Fig. 2(b). When the gate is wide (A = 125-155), we cannot see any effect of the HD states, but when

100 it gets sharper (A = 132 ± 2), the effect gets larger. The 100 + 132 mass split is produced in a much less excited way (larger TKE) when we are at the HD resonance. 3. Summary We have measured the prompt fission probability of 236 U as a function of the excitation energy using the (d,pf) reaction with high resolution in order to study high-lying excited states in the third well. From the analysis of the rotational band structure the rotational parameter could be extracted as h2/26=2.3± 0.4 keV. The corresponding moment of inertia ( 0 = 217 ±38 7i2/MeV) agrees with the calculated value of Shneidman et al.. The hyperdeformed rotational-band structure observed in the rather low excitation energy region around 5.1 MeV independently supports our experimental finding of a rather deep third minimum, which is in agreement with theoretical predictions. We furthermore used the lowest transmission resonance in the third well to give an upper limit for the height of the inner barrier, which is also in agreement with theoretical predictions. Acknowledgement The work has been supported by DFG under HA 1101/6-3 and 436 UNG 113/129/0, the Hungarian Academy of Sciences under HA 1101/61, the Hungarian OTKA Foundation No.T038404, and the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO). References 1. 2. 3. 4. 5. 6. 7.

P.G. Thirolf and D. Habs, Prog. Part. Nucl. Phys. 49, 245 (2002). A. Krasznahorkay et ai., Phys. Lett. B461, 15 (1999). A. Krasznahorkay et ai., Phys. Rev. Lett. 80, 2073 (1998). D. Gassmann et ai., Phys. Lett. B497, 181 (2001). M. Hunyadi et ai., Phys. Lett. B505, 27 (2001). S.B. Bj0rnholm and J.E. Lynn, Rev. Mod. Phys. 52 (1980) 725. H.A. Enge and S.B. Kowalsky, in Proceedings of the 3rd International Conference on Magnet Technology, Hamburg (1970). 8. H.F. Wirth, PhD thesis, TU Munich (2001), unpublished. 9. C. Budtz-Jorgensen et ai., Nucl. Instr. Meth A285 (1987) 209. 10. M. Just et ai, Proc. Symp. Physics and Chemistry of Fission, IAEA, Jiilich, 71 (1979). 11. J. Blons et ai., Phys. Rev. Lett. 35, 1749 (1975). 12. T.M. Shneidman et ai., Nucl. Phys. A671, 119 (2000). 13. S. Cwiok et ai., Phys. Lett. B322, 304 (1994).

MICROSCOPIC ANALYSIS OF T H E Q - D E C A Y IN HEAVY A N D S U P E R H E A V Y NUCLEI

D. S. DELION National Institute of Physics and Nuclear Engineering, FOB MG-6, Bucharest-Magurele, Romania A. SANDULESCU Center for Advanced Studies in Physics, Galea Victoriei 125, Bucharest, Romania W. GREINER Institut fur Theoretische Physik, J.W.v.-Goethe Universitat, Robert-Mayer-Str. 8-10, 60325 Frankfurt am Main, Germany We analyze the a-decay along N — Z chains in heavy and superheavy nuclei. The a-particle preformation amplitude is estimated within the pairing model, while the penetration part by the deformed WKB approach. We show that for JV > 126 the plateau condition is not fulfilled along any a-chain, namely the logarithmic derivative of the Coulomb function changes much faster in comparison with that of the preformation factor. We correct this deficiency by considering an a-cluster factor in the preformation amplitude, depending upon the Coulomb parameter. For superheavy region an additional dependence upon the number of interacting a-particles indicates a clustering feature connected with a larger radial component.

1. Introduction and model The aim of this analysis is to show that the shell model estimate of the aparticle preformation factor is not consistent with the decreasing behaviour of Q-values along any neutron chain l'2. In Ref. 3 we analyzed this feature by treating the a-decaying state as a resonance built in a standard way, namely by using the matching between logarithmic derivatives of the preformation amplitude and Coulomb function. In this lecture we extend our analysis of the decay widths, by connecting the heavy with superheavy regions along a-like chains. Our purpose is not only to give a correct description of absolute decay widths. We will show that in order to fulfill the resonance condition it is necessary to use an additional a-cluster compo-

101

102 nent, depending upon the Q-value. Let us consider a transition connecting two axially deformed nuclei. The decay width can be estimated by using the following ansatz T = hv

gtt](R)

D(R) = T0(R)D(R)

G0{kR)

.

(1.1)

It is given by the product between the standard spherical width, given by the Thomas formula r 0 (-R) 4 , and the deformation factor D(R) 5 . It contains a ratio between the internal and external Coulomb solutions. The decay width does not depend upon the matching radius R within the local potential approach, because the internal and external wave functions satisfy the same equation and therefore are proportional. This is the socalled plateau condition. When the value of the internal wave function <7o {R) is given by an independent microscopic approach the internal and external functions do not a priori have the same derivatives and therefore we should investigate the dependence of the decay width (1.1) upon the matching radius. In this case the internal wave function is given by the amplitude to find the decaying a-daughter configuration for the initial mother wave function. For superfluid nuclei the final result is given by o ' ' " ' ' (R) fl — * 0(,P0> f^rnaxi

= e- 4 "° fl2 /2 £

"mini

"•)

WN(/30,nmM,Pmin)NiVo(4/3o)i]v/2(4/3o^2)

, (1-2) where L^' ' is the Laguerre polynomial normalized by N-factors and Wcoefncients are microscopically determined. Here single-particle (sp) parameter Po is connected with the standard harmonic oscillator (ho) parameter by using a scaling factor / 0 as follows w

ft - f R - f MNU Po - JOPN - fo-J—

~ & » -4TJ3 •

C\ v\ t1-3)

2. Analysis of data In order to understand the structure of the decay width it is necessary a careful analysis of all significant parameters. Let us first analyze the relevant parameters for the barrier penetration. It is already well known that the barrier penetration is sensitive with respect to the following two parameters 1) x '• the Coulomb parameter equal with twice the Sommerfeld parameter

103

The irregular Coulomb function Go{kR) depends exponentially on it. 2) /32 : the quadrupole deformation. The decay width has an exponential dependence upon the quadrupole deformation in D(R). This factor practically does not depend upon the matching radius. On the other hand the largest correction gives a factor of three for heavy nuclei and a factor of five in superheavy ones. Let us now analyze the important parameters for the preformation factor <7Q '(R) = RF0(R) in (1.1). The microscopic structure of the preformation amplitude is given by Eq. (1.2). It is very collective and therefore the transitions between ground states are not sensitive to the mean field parameters. Thus, in our analysis we used the universal parameterization of the Woods-Saxon potential 6 . The gap parameter was estimated by A r = 12/y/A 7 , because again the preformation amplitude is not sensitive upon its local fluctuation. It turns out that the approach is very sensitive with respect to the following three parameters, entering the preformation amplitude 1) nmax '• the maximal sp radial quantum number defined by Eq. (1.2), 2) /Jo : the sp ho parameter, depending upon / 0 denned by Eq. (1.3), 3) the amount of spherical configurations taken in the BCS calculation, given by Pmin, defined as the minimal considered pairing density. It turns out that beyond nmax = 9 the results saturate if one considers in the BCS basis sp states with P > Pmin = 0.02. Therefore we considered in our further calculations the value nmax = 9. We improved the description of the continuum by choosing a sp scale parameter / 0 < 1 in Eq. (1.3). Thus, by using a smaller ho parameter the sp wave function, and therefore the preformation amplitude, becomes flatter and it is better described at large distances. This parameter is not independent from the minimal pairing density Pmin- If' turns out that the common choice of f0 and Pmin ensures not only the right order of magnitude for the decay width, but also the above mentioned continuity of the derivative. The coefficients of the linear fit logw

T{R)

= 7o+7ii? ,

(2.2)

• exp

should vanish, i.e. 70 = 7i = 0, in order to have a proper description of the decay width. It turns out that they are very sensitive to the size parameter

104 /o and minimal paring density Pmin. We used the values of the parameters determined above, nmax = 9, /o=0.8 and P m j„=0.025, in order to analyze other a-decays. A correct theoretical description should give small fluctuations for 70 and 71, if the aclustering is entirely described within this approach. Indeed, this is the case for the region Z > 82, 82 < N < 126. Therefore the pairing description of a-decays in this region seems to be successful concerning both the ratio to the experimental width and the continuity of derivatives. The situation completely changes in the region above the magic neutron number N > 126. In Fig. 1 we investigated 12 even-even a-chains. The experimental decay widths are reproduced worse than in the previous interval, namely the quantity 70 Ri /o<7io(r/reXp) has a variation of one order of magnitude around 70 = 0 in Fig. 1(a). The reason for the variation of the slope parameter 71 in Fig. 1(b) is the relative strong dependence of the Coulomb parameter \ upon the neutron number along a-chains. It is well known that the derivative of the irregular Coulomb function strongly changes with respect to the parameter xTherefore the derivative of the microscopic preformation amplitude changes along a-chains much slower in comparison with that of the Coulomb function. Thus, the microscopic estimate of the preformation factor within the pairing model is not consistent with the external penetration factor if one uses a constant ho size factor / 0 = 0.8. In order to correct this deficiency let us define a variable size parameter / by a similar to (1.3) relation, namely

0 = ffa.

(2.3)

We use the following correction of the preformation factor R) = 40R2/2

e-

Y,

W

^rn,nmax,Pmin)^No(i0m)L^/o2)(Al3mR2)

(2.4) .

(2.5)

N

Therefore we decouple the ho parameter, entering the cluster-like exponential factor, from the fixed parameter sp ho parameter /3 m . We suppose a linear dependence of the size parameter / upon the Coulomb parameter P-Pm

= {f-

fm)PN = fl(X~

Xm)0N •

(2.6)

The above relation (2.4) can be written as follows ^ 0 \P j Pm; Tlmax > *min

j -*^ J

==

^

m

•*• 0\Pmi

^maxi

-*mini -^J

= F 0 (/3 — /3 m ,0,O;i?)F o (/3 R), (2.7)

105

Eeven—even i j 1 1 1 |i i 1 1

(a)

y^-

**TTTV > * - - - f 0 =0.80

=, I , , , i I i 130 135

i i i I i i i i I i i i i I i

140

145

150

M

I

M

155

M

I

M

160

1 I N

165

I I I I I M

170

I I I

175

0.4 0.3 (b)

0.2 0.1 0

1- . ^ d ? ^

-0.1 -0.2 -0.3 -0.4

~i

i

i

130

i

i

i

i

i

135

i

i

i

i

i

140

i

i

i

i

i

145

i

i

i

i

i

150

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [

155

160

165

170

175

Figure 1. (a) The parameter 70 versus the neutron number for different even-even enchains in Table 2. The preformation parameters are /o = 0.8, Pmin = 0.025. (b) The same as in (a), but for the slope parameter 71.

i.e. the usual preformation amplitude is multiplied by a cluster preformation amplitude with nmax = 0. Our calculations showed that indeed, this is the best choice for the slope correction of the preformation amplitude. If one uses a variable ho parameter for the second factor in the above relation one always obtains a linear decreasing trend of the slope parameter 71 along any a-chain. This is a strong argument in favour of the a-clustering nature of this correction.

106 We stress on the fact that the correction procedure has a relative character, depending upon the values /3m,Xm- We also remind that a similar technique, i.e. the use of a variable cluster ho parameter, was used in Ref. 8. The energy of the emitted particle can be splitted into two components, a pure shell model plus a cluster part, i.e. E = E0m+

E0_!3m .

(2.8)

Therefore the Q-value contains a smooth part and a fluctuation, given by four-body correlations not included in the pairing model. This representation is somehow similar to the standard Strutinsky procedure to split the binding energy into a smooth liquid drop term plus a shell-model fluctuation 9 , but of course the two terms in our case have different meanings. Let us point out that by using a constant ho parameter /3TO = 0.83 for all analyzed even-even emitters one obtains for the maximal value of the slope parameter ^(max) = 0. At this point the a-clustering is described only by the pairing correlations. It roughly corresponds to the maximal value of the Coulomb parameter Xm = 55. In this way the a-clustering process increases by decreasing the Coulomb parameter, because the ho parameter /3 in (2.6) is smaller and therefore the tail of the preformation factor increases. This is consistent with the physical meaning of the aclustering process, because a smaller Coulomb parameter correspond to a larger Q-value and consequently to a larger emission probability. Therefore in our calculations we used the parameters /3 m = 0.83, \m = 55. For the proportionality coefficient in Eq. (2.6) the regression analysis gives the value / i = 8.0 10~ 4 . From the analysis of Fig. 1 one remarks that in the superheavy region we still underestimated the slope parameter 71. The situation here can be improved by assuming a quadratic dependence of the coefficient /1 upon the number of clusters Na = (N — N0)/2 with iVo = 126, namely

h "»• h + hK •

(2-9)

We remind here that a quadratic in Na dependence of the Q-value was empirically found in Ref. 10 . We stress on the fact that this kind of dependence affects only the superheavy region, with large values of Na. In Figs. 2(a,b) we plotted the dependence of the parameters 70,71 upon the neutron number along the even-even a-chains. The improvement, especially for the slope 71, is obvious. Now the ratio to the experimental width is described within a factor of three for most of decays. We considered a correcting

107

term with / 2 = 1.28 10 6 . The mean value of the slope parameter and its standard deviation for even-even chains is 71 = —0.001 ± 0.034.

4 3 (a)

even—even

2 1 0

- / ^

-1 -2

f m = 0 . 8 3 , f, = 8.0 10" 4 f 2 =1 .28 1CT6

-3

II. I....

-4 130

135

I. I . .

140

I . . . _L

145

150

155

160

165

_L 170

J_ 175

Figure 2. (a) The parameter 70 versus the neutron number for different even-even achains in Table 2. The preformation parameters are fm = 0.83, f\ = 8.0 1 0 - 4 , j% — 1.28 10~ 6 , Pmin = 0.025. (b) The same as in (a), but for the slope parameter 71.

The quadratic dependence in Eq. (2.9) can be also interpreted in terms of the total number of interacting clustering pairs, namely N% m 2Na (Na —1)/2. Thus, our analysis based on the logarithmic derivative continuity, shows very clearly that the effect of the a-clusterisation becomes

108 much stronger for superheavy nuclei. Their half-lives are practically not influenced, but their radial tails should be significantly larger than those predicted by standard shell-model calculations.

3. Conclusions We analyzed in this lecture the a=clustering, using the decay widths for even-even a-emitters with Z > 82. We estimated the a-particle preformation amplitude within the pairing approach. We used the universal parametrization of the mean field and the empirical rule for the gap parameter A = Vl/s/A. Due to a coherent superposition of many spherical configuration the preformation factor is not sensitive to the the local fluctuation of these parameters. The penetration part was estimated within the deformed WKB approach. We showed that the decay width increases by a factor between three and five for /32 = 0.3, depending on the mass number. It turns out that the decay width is very sensitive to the sp ho parameter and the number of considered spherical configurations. They simultaneously determine the order of magnitude and the slope of the decay width with respect to the matching radius, giving the plateau condition. It is possible to describe all a-decay widths within a factor of two for Z > 82, 82 < N < 126, by using a constant, but smaller ho parameter fl = 0.8/?/v and a minimal pairing density P TO , n = 0.025. This shows that the relative amount of the a-clustering in this region can be entirely described within the pairing approach. It turns out that the slope of the decay width versus the matching radius has a strong variation for N > 126, in an obvious correlation with the Coulomb parameter. Thus, the relative amount of the a-clustering here cannot be described within the pairing approach and an additional mechanism is necessary. In order to restore the plateau condition and to improve the description of the decay widths we proposed a simple procedure. We supposed a cluster factor, multiplying the preformation amplitude. It contains exponentially an ho parameter, proportional to the Coulomb parameter. This ansatz is suggested by a similar exponential dependence of the Coulomb function upon this parameter. Therefore the energy of the emitted particle contains two terms, namely a smooth part and a cluster correction. The procedure improves simultaneously the ratio to the experimental width and the slope with respect to the matching radius, except for the

109

superheavy region. The relative increase of the a-clustering is related to the decrease of the Coulomb parameter. It is stronger for two regions, namely above N = 126 and in superheavy nuclei. It has a minimum around N = 152. An additional dependence upon the number of interacting a-particles improves the plateau condition for superheavy nuclei. This additional clustering, which seems to be very strong, may affect the stability of nuclei in this region. References 1. 2. 3. 4. 5. 6. 7. 8.

J.O. Rasmussen, Phys. Rev. 113, 1593 (1959). Y.A. Akovali, Nucl. Data Sheets 84, 1 (1998). D.S. Delion and A. Sandulescu, J. Phys. G: Nucl. Part. Phys. 28, 617 (2002). R. G. Thomas, Prog. Theor. Phys. 12, 253 (1954). P. O. Proman, Mat. Fys. Skr. Dan. Vid. Selsk. 1, no. 3 (1957). J. Dudek, Z. Szymanski, and T. Werner, Phys. Rev. C 23, 920 (1981). A.Bohr and Mottelson, Nuclear structure, vol. 1 (Benjamin, New York, 1975). P. Schuck, A. Tohsaki, H. Horiuchi, and G. Ropke, The Nuclear Many Body Problem 2001 Eds. W. Nazarewicz and D. Vretenar (Kluwer Academic Publishers, 2002) p. 271. 9. V.M. Strutinsky, Nucl. Phys. A 95, 420 (1967); Nucl. Phys. A 122, 1 (1968). 10. G. Dussel, E. Caurier, and A.P. Zuker, At. Data Nucl. Data Tables, 39, 205 (1988).

S E A R C H I N G FOR CRITICAL P O I N T N U C L E I I N FISSION PRODUCTS

N . V . Z A M F I R , E.A. M C C U T C H A N A N D R . F . C A S T E N WNSL,

Yale University, New Haven, Connecticut 06520-8124, E-mail: [email protected]

USA

The recently introduced critical point symmetries in the nuclear phase transition between spherical and deformed shapes have produced a large interest in t h e search for their empirical realizations. A review of this search in different regions of nuclear chart, including the neutron rich nuclei obtained in nuclear fission, is presented.

1. Introduction Low-lying collective nuclear structure is often understood and described in terms of shape paradigms of the harmonic vibrator, deformed symmetric rotor, and 7 - unstable models which constitute a set of idealized limits with analytical solutions. The range of structures between these benchmarks is large and complex and, until recently, the only way to describe transitional nuclei was by numerical diagonalizations of a multi-parameter Hamiltonian. A major breakthrough was made a few years ago with the discovery of new parameter free (except for scale) analytic solutions in the region of rapid change between spherical and deformed shapes. These new critical point symmetries describing nuclei close to a phase transitional point 1 - 2 ' 3 ' 4 ) defined in terms of the intrinsic state formalism of the Interacting Boson Model are called E(5) for 7-unstable nuclei 5 and X(5) for axially symmetric nuclei 6 . They were immediately supported by the discovery of empirical realizations 7 ' 8 . The idea of critical point symmetries has resulted in an intense search for new empirical examples 9 ' 10 ' 1:L > 12 ' 13 ' 14 ' 15 ' 16 . An interesting, but not yet fully explored, region of nuclei predicted to contain good candidates for the new type of symmetries is the medium mass neutron rich nuclei obtainable in nuclear fission. In fact, recently, the structure of the neutron rich Mo nuclei was discussed and compared with the X(5) symmetry 14.i5.!6 An overview of the present theoretical and experimental status of these new critical point symmetries will be presented. The predictions of new

110

111 possible critical point regions, based on a microscopic perspective related to the number of active particles, will be also discussed. 2. X(5) critical point symmetry Evidence for pronounced (3 softness in the phase/shape transition region led to the development of new symmetries, E(5) [ref. 5] for a spherical vibrator to a deformed 7-soft second order phase transition and X(5) [ref. 6] for a spherical vibrator to axially symmetric rotor first order phase transition. These symmetries consist of analytic solutions of the Bohr Hamiltonian with square well potentials in the quadrupole deformation. 1069-

Figure 1. Low-lying levels predicted by X(5) 6 . The excitation energies and the B(E2) values, indicated on the transition arrows, are given in relative units

Except for scale, the predictions for energies and electromagnetic transitions are parameter free. The low-lying spectrum and some characteristic B(E2) values are shown in Fig. 1 in units of E{2^) — E(0f) and B{E2;2f -» 0^)=100. Note that the ratio RA/2 = E(Af)/E(2f)=2.90, is indeed appropriate for a nucleus at the critical point of a vibrator to rotor phase transition 3 . Also, the yrast B(E2; J + 2 —* J ) values increase with J at a rate intermediate between that of a vibrator and a rotor. Particularly characteristic of the X(5) symmetry is that the energy of the Oj" state is fixed: Ro2 = E(02)/E(2^)=5.65. Finally, we note that the symmetry predicts inter-sequence B(E2) values. Since nuclei contain integer numbers of nucleons, their properties change discretely with N and Z and therefore, in any given transition region, there is no assurance that any specific nucleus will occur at the critical point. Nev-

112

ertheless, empirical manifestations of this symmetry were found in N=90 nuclei 152 Sm (ref. 8), 150 Nd (ref. 10), 154 Gd (ref. 12). 156 Dy (ref. 13). The Nd-Dy isotopic chains undergo a rapid transition from spherical to axially symmetric deformed structure. The two structural characteristic ratios R4/2 and Ro2 shown in Fig. 2 indicate that all four isotopic chains reach the same stage in their structural evolution, consistent with the X(5) type of structure, at precisely N=90. The energy spacings of the yrast band levels are also nearly identical to the X(5) predictions, as can be seen in fig. 3. The intraband B(E2) strengths also closely match the X(5) trend, except the B{E2; 6+ -> 4+) and B(E2; 10+ -» 8+) in 156 Dy. 3.5

3.0

If w W 2.0 J

•

I

1

I

1

1

1

L

15

ci" W 10

— o, i3"

•rs, 5

84

86

88

90

92

94

96

N Figure 2. Evolution of the 4]*" and 0^ energies, normalized to the 2+ energy across the N ~ 9 0 transition region, for the Nd, Sm, Gd, and Dy isotopic chains, compared with the X(5) predictions.

The experimental inter-sequence E2 transition strengths between the levels based on the 0 + level and the quasi-ground state band levels are in various degrees of agreement with the X(5) values. In general, the B(E2) branching ratios are close to the X(5) predictions, although the absolute values of individual B(E2) differ by an average factor of 3-4 8 ' 10 > 13 . As mentioned above, in the search for possible candidates for the X(5) symmetry, the simplest structural observable to consider is the R4/2 ratio, which reflects in general the position of that nucleus along the spherical-

113

Figure 3. Yrast band level energies and B(E2) values for the N=90 isotopes 1 5 2 S m (ref. 8), 1 5 0 Nd (ref. 10), 1 5 6 D y (ref. 13). The rotor, X(5), and vibrator predictions are shown for comparison.

deformed trajectory. Another useful and simple to use quantity that reflects the onset of deformation is the P factor 17 , given by P = NpNn/(Np + Nn), where Np(n) is the number of valence protons (neutrons) relative to the nearest closed shell. The onset of quadrupole deformation takes place in general at P ~ 5 (ref. 17). The candidates for a critical point structure in the vibrator-rotor shape/phase transition, i.e., X(5) candidates, should normally have P close to this value, as can be seen in fig. 4 . Both R4/2 and the P factor serve only as a guide to possible candidates for X(5) since R4/2 ~ 2.9 and P ~ 5 can also occur in 7-soft to axially symmetric rotor transition where the X(5) symmetry does not apply. Figure 5 illustrates the locus of P ~5 for several regions of nuclei. Of course, these contours serve only as guidelines since they ignore sub-shell closures (e.g., at Z=64) and their evolution with N and Z. An evolution of nuclear structure that is different relative to what it is expected on the basis of the standard magic numbers implies changes in shell structure, residual interactions, or both. Relative to their position to the stability line, there are two categories

114 i

i

1

1

1

1

1

i

i

— i — i — i

i — i

i

i

i

***-**

i.«*•

3 .

a*?

:**£ 0

i

Z=68-80

Z=54-66

Z=40-48

~m^ 2

4

6

8

0

2 4 6 8 0 P=N p N n /(N p +N n )

2

4

6

8

10

Figure 4. P-factor plots of R4/2 for the a) Z=52-66, b) Z=68-80 and c) Z = 40-48 regions. fl4/2=2.9 and P = 5 values are indivcated by dashed lines.

j

i :

::"

82

X

- •

-

50

1

1

^

•

..,

L" - J

28

»

28

50

U-"

1

.,

__

82

126

N Figure 5. Section of the nuclear chart showing the nuclei with P -^5 (shaded area) which give a guide to the locus of potential X(5) critical point nuclei.

of X(5) candidates: n-deficient nuclei which can be produced through (HI, xn) reactions and n-rich nuclei which can be obtained as fission products. We will discuss here only the neutron-deficient Nd-Yb nuclei in the N~90 region and the neutron-rich Kr- Mo in the N ~ 92 region. The former is precisely the region where X(5)-type nuclei were first found and the second is a region which can be extensively studied as fission products. Figure 6 shows these two regions expanded and includes empirical -R4/2 ratio for each nuclide. It can be easily seen that the P ~ 5 contour gives the locus of the X(5) candidates (i? 4 / 2 =2.90) very well. The curve in figure 6 (top) intersects all of the X(5) candidates with N=90 discussed above. The curve continues for higher Z away from N=90. At Yale we are currently studying 162 Yb and 166Hf which, from figure 6 (top) , are potential X(5)-like nuclei.

115 78

2.26 2.44 2.51 2.70 2.68 2 56 2 53 2 , i d 2.48 2.'V 2.4/

2.30

76 74

2 68

2 62 2,66

>**«93 m Sss,

1JT•595

3.07 315 3.22 3.2!

m

3.17 3.08 2.93

2.82J

3 . 3 p "'•> 3 27 3.24 3 09

3.11 3.19 3 25 3.2? 3,2* 3.29 3 3: 3 30 3 26 72 2.31 2,56 2.3? 3 12 3.23 3.27 3.29 3.3! 3.31 331 70 2.33 2.63

68 2 32 2/4|,3 10 3.23 3.28 3.29 3,31 3.31 3.3 21 3.25 3.29 3.30 3.31 66 ; A

' i H I 3-

—

64 2.1 \ Ma,24 329 3.30 3.30 62 2.32 60 1«

I I I 3322 5 3 29 • 3 0 3.30 ^H[ ° 3 29 3.32

58 2.59 2 . 8 ^ . 1 5 56 2.66 2,84 J2S9

R.»

88 90 92 94

48

1.79

46

1.79 2.13

2.11

96 98 100102 104 106 108 110 112 114 116

2.27 2.36

a.as

2.34

2.29 2.30 2,37 2.39 2,38 2,33

2.29 2.38 2.40 2,42 2.46 2,53 2 56 2.58

44 1,62 2,14 2,2? 2,33 2.48 2.65 2.75 2.76 2.73 42

1,81 2.09 1.92 2.12 2.51 2.9J,

4 0 1.60 1.60

1,5!

2.M? 3.15 3.23

38

1,99 2.06 2.56 2.20 3»1 3.22

36

2,12

2.28

—

34 32 R«

30 52

54

56

58

60

62

64

66

68

70

72

74

N Figure 6. Empirical R4/2 ratios for nuclei in the a) 54
The curve in Figure 6 (bottom) indicates that the best X(5) candidates in the A~ 100 region are 104,106,108 MO p i g u r e 7 s hows that, indeed, the evolution of the R4/2 ratio follow that for a transition from vibrational to X(5) structure along the Mo isotopic chain. The rotational limit is not reached. The RQ2 ratio in not known in all these nuclei but the value in 104 Mo is not unreasonably far from the X(5) prediction. In figure 8 the relative yrast energies and the B(E2) values with the X(5) predictions are compared. The interpretation is contradictory. While the energies are consistent with the X(5) predictions, the B(E2) values in the yrast bands of 104 Mo and 106 Mo follow a rotational behavior rather than the X(5) trend. These discrepancies point to the need for more work, experimentally and theoretically, on this issue.

116 3.2 3.0

f» a

2.4 2.2 2.0 7

6

X(5)

6* 5 4

sr

3 2

Figure 7.

Similar to figure 2 but for 104,l06,l08 Mo

nuc]ei.

§

© T

CQ

t

Figure 8. Relative yrast band level energies and B(E2) values for 1 0 4 , 1 0 6 , 1 0 8 M O i 6 rotor, X(5), and vibrator predictions are shown for comparison.

T h e

117 3.

Conclusion

Prior studies have shown t h a t the N = 9 0 nuclei from Nd-Dy exhibit m a n y similarities t o t h e predictions of the X(5) critical point symmetry. To ext e n d t h e search for "X(5)-like" nuclei, t h e P factor is a useful tool t o identify possible candidates. In the neutron deficient region t h e P factor suggests the previously studied N = 9 0 nuclei while in t h e neutron rich region, t h e P factor points t o t h e Sr and Mo isotopes, obtainable t h r o u g h nuclear fission.

Acknowledgments This work was supported by U.S. D O E G r a n t No. DE-FG02-91ER-40609.

References 1. A.E.L. Dieperink, O. Scholten, and F. Iachello, Phys. Rev. Lett 44, 1747 (1980); Nucl. Phys. A346, 125 (1980). 2. D.H. Feng, R. Gilmore, and S.R. Deans, Phys. Rev. C 23, 1254 (1981). 3. F. Iachello, N.V. Zamfir, and R.F. Casten, Phys. Rev. Lett. 8 1 , 1191 (1998). 4. F. Iachello, in Proc. Int. School of Physics "Enrico Fermi", Course CLIII, eds. A. Molinari et al., IOS Press, Amsterdam 2003. 5. F. Iachello, Phys. Rev. Lett. 85, 3580 (2000). 6. F. Iachello, Phys. Rev. Lett. 87, 052502 (2001). 7. R.F. Casten and N.V. Zamfir, Phys. Rev. Lett. 85, 3584 (2000). 8. R.F. Casten and N.V. Zamfir, Phys. Rev. Lett.87, 052503 (2001). 9. A. Frank, C.E. Alonso, and J.M. Arias, Phys. Rev. C 6 5 , 014301 (2001). 10. R. Kriicken et al., Phys. Rev. Lett. 88, 232501 (2002) 11. N.V. Zamfir et a l , Phys. Rev. C65, 044325 (2002). 12. A. Dewald et a l . Int. Conf. on Nuclear Structure with large Gamma arrays, Legnaro, Italy, 2002. 13. M.A. Caprio et a l , Phys. Rev. C66, 054310 (2002). 14. D.S. Brenner, in Mapping the Triangle, eds. A. Aprahamian, J.A. Cizewski, S. Pittel, and N.V. Zamfir, AIP Conf. Proc. No. 638 (AIP, Melville, NY, 2002), p. 223. 15. P.G. Bizzeti and A.M. Bizzeti-Sona, Phys. Rev. C66, 031301(R) (2002). 16. C. Hutter et a l , Phys. Rev. C67, 054315 (2003). 17. R.F. Casten, D.S. Brenner, and P.E. Haustein, Phys. Rev. Lett. 58, 658 (1987).

FISSION BARRIERS IN THE QUASI-MOLECULAR SHAPE PATH

G. R O Y E R , C. B O N I L L A A N D K. Z B I R I Laboratoire

Subatech,

UMR : 6457, 4 rue A. Kastler, 44307 Nantes, E-mail: royer@subatech. inZpS.fr

France

R. A. G H E R G H E S C U Horia Hulubei National Institute of Physics and Nuclear Engineering, P.O. Box MG-6, RO-76900, Bucharest, Romania E-mail: [email protected]

The fission barriers standing in the quasi-molecular shape path have been determined within a generalized liquid drop model taking into account the nuclear proximity energy, the mass and charge asymmetry and an accurate nuclear radius. The barrier heights agree with the experimental symmetric and asymmetric fission barrier heights. The half-lives of the alpha and light nucleus decay and cluster radioactivity are reproduced within a tunneling process through these barriers. Rotating highly deformed states exist in this path. The entrance and exit channels governing the superheavy nucleus formation and decay have been investigated.

1. Quasi-molecular shape path New observed phenomena like asymmetric fission of intermediate mass nuclei, nuclear molecules in light nuclei, super and hyperdeformations, cluster radioactivity, fast-fission of heavy systems and fragmentation have renewed interest in investigating the fusion-like fission valley and quasi-molecular shapes. Furthermore, rotating super and hyperdeformed nuclear states and superheavy nuclei can be formed only in heavy-ion collisions for which the initial configuration is two close quasi-spherical nuclei. The selected shape sequence, two joined elliptic lemniscatoids, is displayed in Fig. 1. Analytical formulae are available for the main shape-dependent functions. 2. Generalized liquid drop model For these shapes the balance between the Coulomb forces and surface tension forces does not allow to link the sheets of the potential energy surface

118

119

f *> ^

ii.-

<£**•

#?-

^ ^ - ^

^

»^-

Figure 1. Selected shape sequence to simulate the fission, the cluster and alpha decay paths. The nuclei are spherical when they are separated.

corresponding respectively to one-body shapes and to two separated fragments. It is necessary to add another term called proximity energy reproducing the finite-range effects of the nuclear force in the neck or the gap between the nascent fission fragments. A Generalized Liquid Drop Model has been developed to take into account both this nuclear proximity energy, the mass and charge asymmetry, an accurate nuclear radius and the temperature effects1. The initial value of the surface energy coefficient has been kept. Microscopic corrections have been determined within the asymmetric two center shell model or simpler algebraic approximations 2 . 3. Symmetric and asymmetric fission barriers In this deformation valley the barrier top corresponds to two separated fragments maintained in unstable equilibrium by the balance between the repulsive Coulomb forces and the attractive nuclear proximity forces. With increasing mass the proximity forces induce progressively an inflexion in the curve and double-humped barriers appear naturally for actinides (see Figs. 2 and 3). The heights of the potential barriers 3 agree with the experimental fission barrier heights, in particular for the asymmetric fission of 70,76 Se, 75

Br,

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4. Half-lives of the alpha decay and light nucleus emission The partial half-lives for the a and light nucleus emission have been determined from the WKB barrier penetration probability as for a spontaneous asymmetric fission, without adjustable preformation factor 4,5 . The barriers have been adjusted to reproduce the experimental Q value (see Figs. 4 and 5). The agreement between the theoretical and experimental data of log 1 0 pi/ 2 (s)] for 373 a emitters is very good as for the emission of 1 4 C, 2 0 O, 23F) 2 4 , 2 6 ^ 28,30Mg ^

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Figure 3. Potential barriers including shell effects for the symmetric fission of 260 NO] 260 Rf> 262 g g> 266 H g snd 270 n 0

268

Fm,

Analytic formulae are proposed for the partial half-lives and predictions for the a decay of superheavy elements have been proposed 6 . 5. Super and hyperdeformed rotating nuclei Within this GLDM, the two-center shell model and the Strutinsky method or the algebraic droplet model shell corrections, normal, super and highly deformed minima appear in different angular momentum ranges. The first minimum has a pure microscopic origin. At intermediate spins, both the shell corrections and the proximity energy contribute to form the second potential pocket while, for the highest angular momenta, the persistence of

121

Figure 4. Potential barrier including empirical microscopic corrections against emission of a from the 2 6 4 H s parent nucleus. The dashed and solid lines correspond respectively to the deformation energy without and with a nuclear proximity energy term.

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a highly deformed minimum is mainly due to the proximity forces that prevent the negotiating of the scission barrier. The results for the quadrupole moment, the moment of inertia and the excitation energy7 agree roughly with the data obtained recently on the superdeformed bands in 4 0 Ca, 4 4 Ti, 48 Cr, 56 Ni, 84 Zr, 132 Ce, 152 Dy and 192 Hg. Predictions are given for the 126 Ba nucleus presently under investigation (see Fig. 6). 6. Very heavy elements The heaviest elements decay via a emission and the predictions of the halflives given by the formulas derived from the GLDM agree well with the data when the selected theoretical Qa is the one proposed by a recent version

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of the Thomas-Fermi model 6 . The fission barriers are one-humped barriers since the nuclear proximity forces can no more compensate for the high repulsive Coulomb forces. Due only to shell effects the barrier height can still reach 5 MeV, the value of the next proton magic number playing a major role (see Fig. 7). 4 N

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The potential barriers governing the entrance channel leading possibly to superheavy elements have been investigated with this model. For moderately asymmetric reactions (cold fusion reactions : 64 Ni, 70 Zn, 76 Ge, 82 Se, 86 Kr on 2 0 8 Pb) double-hump potential barriers stand and fast fission of compact shapes in the outer well is the main exit channel. Very asymmetric reactions (warm fusion reactions : 4 8 Ca on 238 U, 2 4 4 Pu or 2 4 8 Cm ) lead to one hump barriers which can be passed only with an energy much higher

123

than the ground state energy of the superheavy element. Then, only emission of several neutrons or an a particle can stabilize the nuclear system and allows to reach a ground state. The formation of superheavy elements via almost symmetric reactions is hardly likely (see Fig. 8).

r(fm) Figure 8. Potential barriers for different reactions leading to the 2 7 0 110 nucleus, r is the distance between mass centres. The vertical bar corresponds to the contact point.

7. Conclusion The potential barriers appearing in the quasi-molecular shape path have been investigated within both a Generalized Liquid Drop Model taking into account the interaction energy between the close nucleons when a deep neck or a gap exists and the shell corrections. The main characteristics of the symmetric and asymmetric fission, the light nucleus and a emissions, the highly deformed rotating states and the superheavy formation and decay can be described in this fusion-like deformation path. References 1. 2. 3. 4. 5. 6. 7.

G. Royer and B. Remaud, J. Phys. G: Nucl. Phys 10, 1057 (1984). R. A. Gherghescu and G. Royer, Phys. Rev. C68, 014315 (2003). G. Royer and K. Zbiri, Nucl. Phys. A697, 630 (2002). G. Royer, J. Phys. G: Nucl. Part Phys 26, 1149 (2000). G. Royer and R. Moustabchir, Nucl. Phys. A683, 182 (2001). G. Royer and R. A. Gherghescu, Nucl. Phys. A699, 479 (2002). G. Royer, C. Bonilla and R. A. Gherghescu, Phys. Rev. C67, 34315 (2003).

PROBING THE "LI HALO STRUCTURE BY TWO-NEUTRON INTERFEROMETRY EXPERIMENTS M. PETRASCU, A. CONSTANTINESCU1,1. CRUCERU, M. GR7RGIU*, A. ISBASESCU AND H. PETRASCU Horia Hulubei National Institute for Physics and Nuclear Engineering, P. O.Box MG-6 Bucharest, Romania I. TANMATA, T. KOBAYASHI, K MORMOTO, K. KATORI, A. OZAWA, K. YOSHIDA, T. SUDA AND S. NISHMURA RIKEN, Hirosawa 2-1 Wako, Saitama, 351-0198, Japan

A recent experiment with a new array detector aiming the investigation of halo neutron pair pre-emission in Si( u Li, fusion) is described. A new approach for testing the true n-n coincidences against cross-talk has been worked out. An experimental evidence for residual correlation of the pre-emitted neutrons is presented. The results obtained in building the n-n correlation function by using the available denominators are discussed. A recent iterative method for calculation of the intrinsic correlation function was also applied. An experiment for precise measurement of the intrinsic correlation function is proposed.

1.

Introduction

The neutron halo nuclei were discovered by Tanihata and co-workers [1]. These nuclei are characterized by very large matter radii, small separation energies, and small internal momenta of valence neutrons. Recently was predicted [2] that, due to the very large dimension of n Li, one may expect that in a fusion process on a light target, the valence neutrons may not be absorbed together with the 9Li core, but may be emitted in the early stage of the reaction. Indeed, the experimental investigations of neutron pre-emission in the fusion of u Li halo nuclei with Si targets [3,4], have shown that a fair amount of fusions (40±12)% are preceded by one or two halo neutron pre-emission. It was also found that in the position distribution of the pre-emitted neutrons, a very narrow neutron peak, leading to transverse momentum distribution much narrower than that predicted by COSMA model [5], is present. Some indication based on preliminary n-n coincidence measurements, concerning the presence of neutron pairs within the narrow neutron peak, has been mentioned in [3,4]. In the light of this indication, the narrow neutron distribution could be caused by the final state interaction [6,7] between two pre-emitted neutrons. Therefore, Permanent address: Bucharest University, Romania Permanent address: Technical University, Bucharest, Romania 124

125 on the basis of these first results, was decided to perform a new experiment aiming to investigate the neutron pair pre-emission in conditions of much higher statistics, by means of a neutron array detector. This experiment has been performed at the RTKEN-RIPS facility. 2.

Experimental Results

2.1. The Experimental Setup The experimental setup is shown in Fig. 1[8]:

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In this setup, three main parts are present: The first part contains the detectors used for the beam control: a thin scintillator at the F2 focus of the RIPS, two parallel plate avalanche counters (PI, P2) and a Vl(Vetol) scintillator, provided with a 2x2 cm2 hole. The second part consists of a MUSIC Chamber [9], containing inside a 500 fim thick strip silicon detector-target (SiS) and a V2(Veto2) Si detector, 200 jum thick. MUSIC was used for the identification of the inclusive evaporation residues spectra produced in the detector-target, and for suppression of the energy degraded beam particles. The third part is the neutron array detector [10]. It consists of 81 detectors, made of 4x4x12 cm3 BC-400 crystals, mounted on XP2972 phototubes. This detector, placed in forward direction at 138 cm from the target, was used for the neutron energy determination by time of fight and for neutron position determination. The distance between adjacent detectors was 0.8 cm. The array

126

components were aligned to a threshold of 0.3 MeVee, by using the cosmic ray peak at 12 MeV (8 MeVee). The numbering of the detectors was performed in the following way: The central detector was labeled 1. The 8 detectors surrounding detector 1, were labeled counter clock wise 2-9. The 16 detectors of the second circle were labeled 10-25 and so on. In the present paper the coincidences between adjacent detectors are denoted as ""first order coincidences". Coincidences between two detectors separated by one detector are denoted as ""second order coincidences" and so on. With the trigger specified in Fig. 1 caption, one could investigate inclusively the 911 Li + Si fusion. The large 5x5 cm2 silicon Veto2 detector, placed behind the Si-strip target-detector, eliminated the elastic, inelastic, and breakup processes at forward angles. The measurements were performed with 13A MeV "Li and 9Li beams. 2.2. The Forward Neutron Peak The energy range corresponding to the neutron pre-emission process was established between ~8 and -15 MeV [11]. In Fig. 2, the position spectrum measured along the horizontal line connecting detectors 58-74 is shown [12]. The FWHM of this spectrum is ~ 13 cm and corresponds to a solid angle of ~9 msr. Within this narrow peak, a large number of n-n coincidences were observed for u Li [8], by comparing the data obtained with u Li and with 'Li beams.

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Figure 2. The position spectrum measured along the horizontal line connecting detectors 58-74, is shown. The neutron energy was selected between 6-16 MeV. The FWHM of this spectrum is -13 cm and corresponds to a solid angle: ~9 msr.

127

2.3. True Neutron-Neutron Coincidences and Cross-Talk Cross-talk (at.), is a spurious effect in which the same neutron is registered by two or more detectors. A complete simulation of the array detector performances by using MENATE program [13], was recently performed [12]. We have investigated in this way the c.t. distribution as a function of t=t2-tx for different coincidence (1 st to 4th) orders. The simulation was performed by firing the central detector 1 by neutrons of given energy and by extracting the crosstalk events corresponding to detectors 2-9 (first order), to detectors 10-25, (second order) and so on. For each event, the space and time coordinates and also the light output were available. In these simulations was found a notable suppression of short neutron trajectories between detectors 1 and 2 [12]. For example in 1000 c.t. events there are no trajectories shorter than 1.8 cm. The number of 1.8 cm trajectories is less than 5 in 1000 c.t. events. Due to this concentration of events caused by c.t., appears a remarkable improvement of oti time resolution of detector 1 [12]. In Fig. 3, the experimental n-n coincidence (true and c.t.) are denoted by open up-triangles with un-capped error bars. The distribution of simulated first order c.t. as a function of t2-t\ is indicated by solid squares with capped error bars. The simulations were performed by taking three different neutron energies: 8, 11, and 15 MeV, representing respectively, the lower limit, peak and upper limit of the neutron pre-emission spectrum. A number of 1000 c.t. were calculated in each case. One may see that in all three figures (a, b, c) there is a window, denoted by TC (true coincidences), in which the yield of c.t. is very low (near 0.1 counts). The width of TC window is the same (0.6 ns) for 11 and 15 MeV and is larger (0.8 ns), for 8 MeV neutrons. TC is separated by a vertical dotted line, from the CT (cross-talk) window in which c.t. yield is much larger. The first c.t. point in CT window is by a factor -10 higher than the c.t. points in TC window. This means that a change in the c.t. mechanism is taking place by passing from the CT to the TC window. A two-parameter (time-trajectory length) analysis shows that in the majority of events the trajectory length in TC window is larger than ~6 cm. Since a neutron cannot cover this distance in such a short time, it follows that c.t. is realized in TC window predominantly by y rays. This explains also why c.t. yield is so low in the TC window. The vertical arrows in Fig. 3, are indicating that the remaining 46 true coincidences after d^n rejection [14] are well inside the TC window. In Fig. 4, the c.t. simulation for second order coincidences is shown. One may see that the number of true coincidences (71) remaining after drain rejection is also well inside the TC window. In this Fig. the entire c.t. peak

128 is shown. It is remarkable that MENATE program is able to describe fairly well the experimental c.t. distribution.

Vt, (ns) Figure 3. Monte Carlo simulation of the first order c.t. The open up-triangles with uncapped error bars represent the experimentally measured coincidences. The solid squares with capped error bars represent the simulated c.t.

2.4. Experimental Evidence for Residual Correlation of Single Detected Halo Neutrons The two-neutron correlation function [15] is given by : C(q)=kNc(q)/Nnc(q), in which Nc(q) represents the yield of coincidence events and Nnc(q), the yield of uncorrelated events. The normalization constant k is obtained from the condition that C(q)=l at large relative momenta. The relative momentum q is given by: q=l/2 I p r p 2 1, p t and p 2 being the momenta of the two coincident neutrons. A crucial problem for getting the correlation function is the construction of denominator in the upper formula. A thorough analysis of this problem is presented in [16]. Two approaches are commonly used: one is the event mixing technique, the other is the single neutron product technique. In the event mixing approach the denominator is generated by randomly mixing the neutrons from the coincidence sample. This method has the advantage that the uncorrelated distribution corresponds to the same class of collisions and kinematic conditions as in the case of the numerator, but has the disadvantage

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that it may distort the correlation one wants to measure, because the event mixing technique may not succeed to de-correlate completely the events. In the single product technique the denominator is constructed by the product of single neutron distributions. This method is preferred in [16], by considering that the background in this case is truly uncorrelated, but this is not valid for the halo neutrons [17], because of residual correlation. In [17] was assumed that residual correlation in the case of halo neutrons should exist due to the large value of C{q) -10, and therefore an iterative calculation was applied in order to get reasonable value for C(q). We have found an experimental evidence for residual correlation of the halo neutrons pre-emitted in the fusion of "Li+Si. Essentially we have proven the existence of residual correlation by applying the single product technique in the following situations: (a) By coupling randomly single neutrons and by applying the rejection procedure afterwards [16]. (b) By replacing the neutrons in the coincidence sample by neutrons with closest energies from the single neutron sample, corresponding to the same detectors as in the coincidence sample [12]. In this way, both types of denominators: A and B, consist of single neutron products to which a rejection procedure has been applied. We have shown that denominator A presents large fluctuations and is significantly higher than denominator B,

130 when expressed as a function of q in steps of 0.5 MeV/c [12]. In the case when larger steps of q are used (2 MeV/c), denominator A remains significantly higher than B, but displays no more fluctuations. 2.5. Present Status of11 Li Halo Neutron Correlation Function. Conclusions By using denominator A, we obtained a correlation function corresponding to r0=5 fm close to the one (5.3 fm) obtained in [18]. Here r 0 represents the variance of Gaussian source assumed in the model of ref. [7]. The n-n separation r,,,, is a Gaussian distribution of variance -Jl r0 a n d r ^ =^6r0 . It follows that r0 ~5 leads to r™s -13 fm. This is an inflated value due to residual correlation that produces an increase of denominator A. By using denominator B, we obtained a correlation function corresponding to r0=4.2 fm, leading to r™ =10.2 fm which is not far from r™s = 8.3 fm predicted by COSMAj model [5]. One has to point out that the initial denominator obtained in ref. [17] corresponds to the same r0=4.2 fm value as in the case of our denominator B (see the insert in Fig.5 for u Li, ref. [17]). We have tried to understand why in ref. [17] was not obtained the same initial denominator as in ref. [18] or in our case (denominator A). We have found that in [18] and in our case the geometrical conditions of measurements were such that the angles subtended by one detector were nearly the same ~1.6°. In the case of ref. [17] this angle was about 1.7 times larger, and therefore a smoothing of residual correlation could take place, so that the correlation function corresponded not to r0=5 fm, but to r0=4.2 fm. A similar smoothing took place in our case for denominator B by taking a distribution of detectors not a random one, but a particular distribution corresponding to the measured sample of n-n coincidences. In ref. [17] an elegant iteration procedure was worked out for getting the intrinsic correlation function from the measured one. In this iterative procedure are implied all the measured C(qt) values with their experimental errors. Finally the reconstructed correlation function appears with substantially increased errors in comparison with the initial one. We have applied this method starting with the correlation function defined by r0= 4.2 fm. We have found a stable solution corresponding to r0=3.3±0.8 fm [12], in good agreement with the value obtained in [17] (2.7±0.6 fm). In Fig. 5(b) of ref [12] is represented by down triangles the shape of the denominator obtained by this calculation. We consider that at present a challenging task is to try to distinguish between the r 0 predicted by COSMA: and by COSMAn models [5]. An answer to this question will be an experiment aiming to determine the intrinsic correlation function by using "Li and "Be halo nuclei. The nucleus

131 n

Be will be an ideal uncorrelated background source, since it contains only one halo neutron. This experiment should be done by using a 12C instead Si target. A sharp cut-off estimation [19] has indicated that the n-n correlation peak will be about 2 times higher in the case of 12C than in the case of Si target. The experimentally observed signatures of residual correlation could be of use in the identification of new halo nuclei [20], References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

I. Tanihata et al., Phys. Lett. 160B, 380 (1985). M. Petrascu et al., Balkan Physics Letters 3(4), 214. (1995). M. Petrascu et al., Phys. Lett. B405, 224 (1997). M. Petrascu et al., Rom. J. Phys. 44, 83 (1999). M. V. Zhukov et al., Phys. Rep. 231, 151 (1993). S. Koonin et al., Phys. Lett. 70B, 43 (1977). R. Lednicky and L. Lyuboshits, Sov. J. Nucl. Phys. 35, 770 (1982). M. Petrascu et al., preprint RIKEN-AF-NP, 395, 2001. H. Petrascu et al., Rom. J. Phys. 44, 105 (1999). M. Petrascu et al., Rom. J. Phys, 44, 115 (1999). M. Petrascu, Proc. Int. Symp. Exotic Nuclei, Baikal Lake Russia 2001 (World Scientific Singapore, 2002) p 256. M. Petrascu et al., Phys. Rev. C69, in print (2004). P. Desesquelles, The program MENATE. M. Petrascu, Proc. Int. Sem. (HIPH'02, Dubna, Russia, edited by Yu.Ts.Oganessian, R. Kalpakchieva (Yad. Fiz- in press). G. I. Kopylov, Phys. Lett. 50 B, 472 (1974). R. Ghetti et al., Nucl. Phys. A660, 20 (1999). F. M. Marques et al. Phys. Lett. B 476, 219 (2000). K. Ieki et al., Phys. Rev. Lett. 70, 730 (1993). M. Petrascu et al. Proc. Int. Conf. Cluster03, Nara Japan, (Nucl. Phys. A, in print). M. Petrascu et al., (unpublished).

DISSIPATION IN A W I D E R A N G E OF MASS-ASYMMETRIES

M. M I R E A Institute of Physics and Nuclear Engineering, P.O. BOX MG-6, Bucharest-Magurele, Romania Email: [email protected]

In unitary manner, all kind of binary partitions, including the alpha- and clusterdecays, are treated as fission processes in a wide range of mass-asymmetries. In this spirit, the whole nuclear system is characterized by some collective coordinates which vary and manage the evolution of the system. The decaying system provides a time dependent single-particle potential in which the nucleons move independently. Investigations concerning the fine structure of alpha- and clusterdecay together with the dissipation in fission are realized.

The fine structure of alpha decay was discovered in 1929 by Rosemblum. This phenomenon was explained many years latter by Mang who considered that the preformation probabilities of the emitted nucleus in a given channel are proportional with the square overlaps between the parent and the daughter wave functions. In the case of cluster decay, a fine structure in the 14 C radioactivity of 2 2 3 Ra was first observed in 19891. Surprisingly, about 87% transitions were to the first excited state of the daughter and only 13% transitions to the ground state. This process being similar to the fine structure of the alpha decay, this analogy was emphasized in the theoretical investigations. It is however of interest to note that theoretically, the fine structure in the case of cluster decay was anticipated in different works 2,3 . This phenomenon was also interpreted reasonably by taking into account simple nuclear structure considerations 4,5 . Phenomenological approaches showed6 that the spectroscopic amplitudes to the first excited state must be 180 times higher than that to the ground state. These results are not consistent with those based on nuclear structure considerations. Invoking for the first time the effect of the specialization energy, a good agreement with experimental results was obtained in the frame of the superasymmetric analytical fission model 7 . Alternatively, in a competitive way, it was

132

133

(R-R.,)/(Rf-R,) Figure 1. Neutron level scheme for 1 4 C spontaneous emission from 2 2 3 R a versus the normalized elongation. The levels (with H=3/2) emerging from l i n / 2 , I715/2 a n d 3d 5 / 2 are represented with thick lines.

proposed that the fine structure can be explained appealing to the LandauZener promotion mechanism 8 . It is evidenced that the fine structure can be explained by investigating the modality in which the levels bunched initially in shells are reorganized during the decay to reach the final configuration, using fission-like models. A nuclear shape parameterization directed by elongation, necking and mass-asymmetry will be used. The neutron level scheme for the 14 C emission from 2 2 3 C obtained within the superasymmetric two-center shell model9 (STCSM) is presented in Fig. 1. The energy diagram for neutrons is plotted in this figures as function of the normalized elongation. In the initial ground-state, the Ra unpaired neutron is on the 3/2 level emerging from z 13 / 2 . Adiabatically, after the separation, this level reaches the #9/2 g.s. state of the daughter. It is possible that the unpaired neutron skip from one level to another region due to the Landau-Zener effect. We have four avoiding crossing regions where single particle excitations can take place 10 ' 11 . Using an appropriate internuclear distance velocity and solving the associated system of coupled differential equations, the single-particle occupation probabilities of the final orbital can be obtained. The internu-

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Figure 2. Theoretical and experimental values of the total and partial half-lives relative to cluster decay in a Geiger-Nutall plot. The experimental values of the total half-lives for the 1 4 C emission from 2 2 2 R a , 2 2 4 R a , 2 2 6 R a , 2 2 5 Ac and the partial values of the halflives from 2 2 3 R a are displayed with empty circles. The theoretical values for the 1 4 C emission from Ra are plotted with empty squares while the theoretical values concerning the 2 2 5 Ac parent are represented with empty triangles. A filled square and a filled triangle refer to the theoretical values obtained without taking into consideration the Landau-Zener effect.

clear velocity value is in accordance with that obtained in Ref. 12. A very good agreement between experimental and theoretical values was obtained. The emission of 14 C from 225 Ac was also treated because some experiments were planned to measure the kinetic energy of the emitted nucleus accurately enough to infer the levels of the daughter 13 . The theoretical and experimental hindrance factors for both reaction are plotted in Fig. 2. As a first conclusion it can be emphasized that the Landau-Zener effect can explain the fine structure in cluster decay. So the behaviors exhibited by the fine structure depend not only on the structure of the parent, the daughter and the emitted fragment but also on the dynamics of the process. The alpha-decay was also treated 14 in the same framework analyzing

135 the emission from 2 1 1 Po. In alpha-decay, apart the Landau Zener-effect, another effect competes strongly in determining the single particle probabilities, that is the Coriolis or rotational coupling. The system of coupled differential equations displays now terms due to radial coupling and terms due to rotational couplings. The STCSM provides again all the ingredients to calculate the single particle transitions. The ratio between intensities to first and second excited states on intensity of the g.s. were obtained. These results agree well with the theoretical ones. Using the previous method, it was assumed that the pairs reach the lowest levels during the disintegration. Without this assumption, it follows that the system can not end in its ground state due to the fact that nucleons can not jump between levels with different quantum numbers, then these levels cross. A way to bypass the problem is to use a solution of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations 15,16 where the Landau-Zener effect is introduced to replace the effect given by a part of the residual interactions. The response of the system is estimated when the nuclear shape is changed. Using the variational principle, the system of equations which determine quantities as pm (the single quasiparticle occupation probability of orbital m) and py. (the pairwise occupation probability of orbital k) is obtained 17 . Again, a very good agreement with the experimental results is obtained for the 14 C emission from 2 2 3 Ra. Three mass-partitions were studied 18 in the fission of 2 3 6 U, the light fragment being 1 1 8 Pd, 134 Te and 150 Ce, denoted sym channel, 102 channel and 86 channel, respectively. The path in the configuration space (spanned by elongation, necking and mass-asymmetry) followed by the fissioning system was obtained from the last action trajectory principle. So, the maximal value of the penetrability of the barrier is obtained. Now, having in mind that the penetrabilities are proportional with the mass-partition probabilities, that means with the experimental yields, we can compare our results with values of some compilations. The experimental yields are 1.3 x l O - 2 for sym-channel, 6 for 102-channel and 2 for 86-channel. These values (normalized to the sym-channel) are plotted in Fig. 3(a). Unfortunately, the theoretical trends of the penetrabilities, displayed in Fig. 3(b), show a different behavior. If we neglect the variations of the effective mass, a qualitative and quantitative agreement can be obtained, as displayed in Fig. 3(c). This agreement was invoked already 19 to obtain the optimization of a neutron rich nuclei source. So, the experimental distribution must be directed or ruled by other ingredients apart the deformation energy and effective masses. This effect can be the dissipation. The coupling of collective

136

100

105

110

120

AL (amu) Figure 3. Yields normalized to the sym-channel as function of the light fragment mass. (a) Experimental values, (b) Values obtained from the penetrabilities associated to the minimal action paths, (c) Values obtained from the penetrabilities associated to the minimal action paths by considering that the inertia equals the reduced mass of the system, (d) Values obtained from penetrabilities associated to the minimal action paths by modifying the potential barriers according with the dissipation effects.

degrees of freedom with the microscopic ones causes dissipation and a modification of the adiabatic potential. The dissipation along the trajectory of minimal action is calcuated as in Ref. 17 by solving the TDHFB equations. A very exciting behavior was found. The dissipated energy is larger for the sym-channel and decreases for the very asymmetric 86-channel. Another interesting finding is the fact that the dissipated energy is practically zero up to the second well and begins to increase when the second barrier is penetrated. Calculating again the yields with the dissipation included, a good agreement with the experimental data was found as displayed in Fig. 3(d). As a conclusion, the experimental distributions can be explained not only as a guided evolution of the nuclear system managed by potential energy

137 and inertia, but also by the effect of dissipation. An analogy with a previous treatment concerning the emission of light nuclei is striking. The TDHFB equations can be basically reduced to a serie of equations 15 reflecting the Landau-Zener effect for paired nucleons, the gap being the interaction matrix element. Basically, the same treatment was applied in the study of the fine structure emission of cluster 8 ' 13 ' 17 and alpha-decays 14 . In the study of the fine structure, the Landau-Zener promotion mechanism directs the probability to increase the potential barrier with a quantity called specialization energy. So, these treatment represents a step towards an unitary investigation of all kind of binary partitions, in a wide range of mass-asymmetries. It can be also emphasized that the same internuclear velocities, fitted in the case of cluster-decay 17 , succeed to reproduce also several observables in the case of fission. The dissipation is caused by the rearrangement of orbitals during the whole fission process, beginning from the ground state up the scission point. It was evidenced that the fine structure of particle emission can be explained by investigating the modality in which the levels bunched initially in shells are reorganized during the decay to reach the final configurations. References 1. 2. 3. 4. 5. 6. 7.

L. Brillard et al., C.R. Acad. Sci. Paris 309, 1405 (1989). M. Greiner and W. Scheid, J. Phys. G 12, 229 (1986). I. Silisteanu and M. Ivascu, J. Phys. G 15, 1405 (1989). R.K. Sheline and I. Ragnarsson, Phys. Rev. C 43, 1476 (1991). G. Ardisson and M. Hussonnois, Radiochimica Acta 70/71, 123 (1995). R.K. Gupta et al., J. Phys. G 19, 2063 (1993). D.N. Poenaru and W. Greiner, in Nuclear Decay Modes, Eds. D.N. Poenaru and M. Ivascu, IOP, p. 317, 1996. 8. M. Mirea, Phys. Rev. C 57, 2484 (1998). 9. M. Mirea, Phys. Rev. C 54, 302 (1996). 10. J.Y. Park, W. Greiner and W. Scheid, Phys. Rev. C21, 958 (1980). 11. Moon Hoe Cha, J.Y. Park and W. Scheid Phys. Rev. C36, 2341 (1987). 12. N. Carjan, O. Serot and D. Strottman, Z. Phys. A349, 353 (1994). 13. M. Mirea, Europ. Phys. J. A4, 335 (1999). 14. M. Mirea, Phys. Rev. C63 034406 (2001). 15. J. Blocki and H. Flocard, Nucl. Phys. A273, 45 (1976). 16. S.E. Koonin and J.R. Nix, Phys. Rev. C13, 209 (1976). 17. M. Mirea, Mod. Phys. Lett. A18, 1809 (2003). 18. M. Mirea, L. Tassan-Got, C. Stephan and C. O. Bacri, Nucl. Phys. A735, 21 (2004). 19. M. Mirea, O. Bajeat, F. Clapier, F. Ibrahim, A.C. Mueller, N. Pauwels and J. Proust, Europ. Phys. J. A l l , 59 (2001).

PHYSICS W I T H SPIRAL A N D SPIRAL 2

M. L E W I T O W I C Z Grand Accelerateur National d'lons Lourds, B.P. 55027, 14076 Caen Cedex, France E-mail: [email protected]

Several examples of recent results obtained with SPIRAL beams on the properties of nuclei in the vicinity of drip-lines and/or magic numbers are presented. The future plans of the GANIL/SPIRAL facility related to the SPIRAL 2 project are shortly described.

1. Physics with SPIRAL and SPIRAL 2 1.1.

Introduction

The nuclear structure, well established for nuclei close to the valley of stability, is expected to evolve significantly in the presence of important excess of neutrons or protons. Nuclei in the vicinity of the drip lines exhibit particularly important changes in the intrinsic structure related to the very low binding energy and the strong influence of the continuum states. In order to obtain the most complete information on these effects a use of radioactive beams in a wide range of isospin and energy is necessary. High energy beams produced by in-flight fragmentation and postaccelerated ISOL beams proved to be complementary with respect to their intensity, isotopic purity and optical quality. Both techniques currently in use at the GANIL/SPIRAL facility offer unique possibilities to make experiments with light radioactive beams (A<80) in the energy range from 30 keV/nucleon to about 80 MeV/nucleon. The successful experimental program of study of nuclei far from stability going on since about 15 years at GANIL using radioactive beams produced in-flight was extended recently towards new possibilities offered by highquality, low energy radioactive beams available at the SPIRAL facility. In the present paper only one example of the studies of nuclei far from stability with SPIRAL beams is described in detail.

138

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1.2. The SPIRAL

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The SPIRAL facility combines the ISOL production method, a universal and fast graphite target, an ECR source for ionization of radioactive atoms with high power (today 1.4 kW, up to 6 kW in the close future)

140 heavy ion stable beams from GANIL cyclotrons. The radioactive beams are accelerated and separated in the newly constructed CIME cyclotron. A construction of SPIRAL was accomplished in 2001 and first experiments performed with stable and radioactive beams have shown an excellent overall acceleration efficiency of the accelerating system (from the exit of the ion source to the secondary target) ranging from about 20 to 35%. During the first year and a half of operation SPIRAL was be able to deliver radioactive beams of noble gases (He, Ne, Ar and Kr) with an intensity of 104- 108 particles per second in the energy range from about 3 to 15 AMeV (see table 1). The high purity (in all cases better than 99%) of the radioactive beams was obtained combining a chemical selectivity of the target-ion source system (not heated transfer tube) and the high mass resolving power of the CIME cyclotron (up to 10000). Table 1. First radioactive nuclear beams of the SPIRAL facility. Ion 6

He1+ He1+ 8 He2+ 18 Ne 4 + 76Krii+ 74Krii+ 8

Energy A MeV 5 3.4 15.4 7 43 43

Intensity pps 3xl07 5xl04 1.3xl0 4 2xl06 5xl05 lxlO4

As intensities of low energy radioactive beams are often several orders of magnitude lower than typical intensities of stable beams the RNB experiments require detection devices of a very high efficiency. Two of them, namely a 411 7-array called EXOGAM and a high acceptance, variable mode magnetic spectrometers called VAMOS became operational recently at GANIL. These two spectrometers in combinations with charged particle detectors like MUST, TIARA and DIAMON are ideal tools for study nuclear structure as well as reaction mechanism in reactions with low energy stable and radioactive beams. 1.3. First experiments

with SPIRAL

beams

The first SPIRAL experiment was dedicated to a measurement of the excited states of 19 Na with the resonant elastic scattering method *. Other experiments deal with the following topics:

141

• Search for the 4n resonances with the 8 He beam; • Structure of halo nuclei in the elastic, inelastic scattering and transfer reactions with 8 He; • Sub-barrier fusion with halo nuclei studied via 7-ray spectroscopy with the 6 ' 8 He beams; • Study of K-isomers in the Po isotopes in fusion- evaporation reactions and in-beam 7-ray spectroscopy with the 8 He beam; • Structure of very neutron deficient A=130 nuclei in fusionevaporation reactions and in-beam 7-ray spectroscopy with the 76 Kr beam; • Low-energy Coulomb excitation of light Kr isotopes. In the following we will concentrate on the last item. On the proton rich side of the chart of nuclei, an observation of the 0 + isomeric states (see upper part of figure 3) through the 7-ray and conversion electron spectroscopy applied to the fast fragmentation products gives an opportunity to follow the shape evolution in the 7 2 _ 7 4 Kr region 2 . A simple analysis of these results in the framework of the two level mixing model suggests an oblate-prolate shape coexistence with equal amplitudes in 74 Kr. Similarly, the ground state of the N=Z nucleus 72 Kr was deduced to have almost pure oblate configuration. Further insight on the shape evolution in these nuclei can be obtained by means of the low energy Coulomb excitation experiments with SPIRAL beams. Two experiments of this kind were performed with 76 Kr and recently with 74 Kr in order to measure the transition probabilities B(E2) and the static quadrupole moments. The first of these quantities allows to deduce an absolute value of deformation, the second its sign. The use of the Coulomb excitation reactions gives an opportunity to excite both yrast and non-yrast states in the projectile. The experiments were performed at the beam energies of 4.3 A MeV on titanium and lead targets. The experimental set-up consisted of the EXOGAM gamma array (4 to 8 clover detectors) and a silicon-strip detector in order to detect an angle and energy of the projectile-like or target-like particles. A preliminary analysis of the 76 Kr data shows, for the first time experimentally, that the ground-state band of this nucleus is prolate. At the same time the second 2 + state seems to have an oblate deformation 3 . An excellent quality data, as shown in figure 3, were obtained recently for the Coulomb excitation of 74 Kr. Due to the high selectivity of the 7-ray-charged particle coincidences no pics corresponding to the /3-j decay of the radioactive beam are present in the

142

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1.4. The SPIRAL

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It is planned that in few years from now a relatively limited range of ions produced by the SPIRAL facility will be extended to heavier neutron-rich

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nuclei produced in a low energy fission of uranium in the proposed SPIRAL 2 facility 4 . A full description of the nuclear physics topics and interdisciplinary applications which might be covered with the SPIRAL 2 beams is beyond the scope of this contribution, but one can mention that both high-intensity stable and fission-fragment radioactive beams can be used to cover very broad range of nuclei very far from stability (Fig. 5). A use of these high-intensity beams at the GANIL low-energy ISOL facility or their acceleration to a few tens of MeV/nucleon opens new possibilities in nuclear structure physics, nuclear astrophysics, reaction dynamics studies as well as in atomic physics, condensed matter studies, radio-biology and radiochemistry (see Ref. 4). A layout of SPIRAL 2 is presented in figure 4. A new superconducting linear driver (LINAG) will deliver a high intensity, 40 MeV deuteron beam as well as a variety of heavy-ion beams with mass over charge ratio equals to 3 and energy up to 14.5 AMeV. Using a carbon converter and the 5 mA deuteron beam, a neutroninduced fission rate is expected be 1.3 x 10 13 fissions/s with a low density UCa; target, and up 5.3 x 10 13 fissions/s for high-density UC X . The expected intensities of RNBs after acceleration should reach, for example, 109 pps for 132 Sn and 10 10 pps for 92 Kr. Besides the method which uses a carbon converter, a direct irradiation of the UCX with beams of d, 3,4 He, e ' 7 Li, or

144

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12

C can be applied if a higher excitation energy leads to higher production rate for a nucleus of interest. The neutron-rich fission products could be complemented by nuclei near the proton drip line provided by fusion-evaporation reactions. For example, a production of up to 8 x 104 atoms of 80 Zr per second using a 200 //A 24 Mg 8 + beam on a 58 Ni target should be possible. The extracted ISOLtype RNBs will be subsequently accelerated to energies of up to about 7-8 AMeV in the existing CIME cyclotron. Regions of the chart of nuclei which will be accessible with both radioactive and stable SPIRAL 2 beams are shown in figure 5. One of the important feature of the future GANIL/SPIRAL/SPIRAL 2 facility will be a possibility to deliver up to five stable or radioactive beams simultaneously. For example, let's assume that using the LINAG accelerator and the adequate uranium target one produces high intensity radioactive beams of fission fragments. After ionization a beam of the given mass Ai can be used in the very low energy experimental area. At the same time mass separator will deliver another beam of mass A2 for the further acceleration in the CIME cyclotron. This beam, thanks to the dedicated beam line from CIME to the Gl and G2 caves, can be used for experiments with EXOGAM and VAMOS. Simultaneously, the standard GANIL beams can be accelerated and used in the IRRSUD facility (stable beams at about 1 AMeV), at the SME beam line (stable beams at 8-10 AMeV) and in the existing experimental area (50-100 AMeV stable or radioactive beams

145 produced in-flight). The full cost of the SPIRAL 2 facility is estimated to 80 MEuros. The detailed design study of the project will be complited next year. One might expect a decision of the construction of the facility to be taken in 2004, allowing a first beam to be delivered in 2008. Numerous international collaborations are currently under elaboration in order to construct and operate the facility on the fully European basis. 2. Conclusions The GANIL facility offers unique possibilities to study nuclei far from stability using both fragmentation-like (A<100, E<100 AMeV) and ISOL/SPIRAL RNBs (A<80, E<25 AMeV). Experiments performed recently with these beams, employing the large variety of spectrometers and high efficiency devices like EXOGAM, VAMOS, LISE, SPEG, TIARA and MUST have shown many spectacular results in the study of nuclear structure. Middle range plans of GANIL are based on the new RNB facility called SPIRAL 2 which should deliver in several years from now both high intensity ISOL beams of fission fragments and high intensity heavy-ion beams (E<14.5 AMeV, I(, eam = 1 pmA). Up to 5 stable/radioactive beams in the several tens of keV to 100 AMeV energy range will be delivered simultaneously for experiments on nuclear physics and interdisciplinary research. SPIRAL 2 might become in the future an integral part (as a part of the driver or the post-accelerator) of EURISOL. References 1. 2. 3. 4.

Nouvelles du GANIL, Hors Serie, GANIL, February 2002. E. Bouchez et al., Phys. Rev. Lett. 90 (2003) 082502. E. Bouchez PhD thesis 2003, Strasbourg University, to be published. SPIRAL II Web page, www.ganil.fr.

TWO-PROTON RADIOACTIVITY OF

45

FE

C. B O R C E A Institute of Physics Bucharest-Magurele,

Le Haut

and Nuclear Engineering, P.O. Box MG-6, Romania and CEN Bordeaux-Gradignan, Vigneau, F-33175 Gradignan-Cedex, France

The decay of the proton drip-line nucleus 4 5 Fe has been studied at the SISSILISE3 facility of GANIL, after projectile fragmentation of a 5 8 Ni primary beam. Fragment-implantation events have been correlated with radioactive decay events in silicon telescopes on an event-by-event basis. The decay-energy spectrum of 4 5 Fe implants shows a distinct peak consistent with a two-proton ground-state decay of 4 5 Fe. None of the events in the peak were found to be in coincidence with 7 radiation or with f) particles which were searched for in the telescope-surrounding detectors. The decay energy for 4 5 Fe agrees nicely with several theoretical predictions for two-proton emission. These predictions strongly support the observed decay to be a simultaneous two-proton ground-state decay.

1. I n t r o d u c t i o n The limits of particle stability, the drip lines, are reached if the nuclear forces are no longer able to bind an ensemble of nucleons with a too large neutron or proton excess. On the proton-rich side of the valley of stability, these unstable nuclei decay by emission of one proton for odd-Z nuclei or two protons for even-Z nuclei from their ground states. Two-proton (2p) radioactivity is predicted to occur for even-Z proton-rich nuclei beyond the proton drip line since 1960 1. Due to the pairing energy, the 2p candidates cannot decay by a sequential emission of two protons as the one-proton daughter is energetically not accessible. Therefore, only a simultaneous two-proton emission is possible which can take place in two different ways: i) by an isotropic emission of the two protons which then have no angular correlation, i.e. they fill the whole phase space available, but in order to easily penetrate through the Coulomb and centrifugal barrier of the daughter nucleus share most probably equally the decay energy available; ii) by a correlated emission where in the decay the 2 He resonance is formed

146

147 which decays either already under the Coulomb and centrifugal barrier or outside the nucleus. In both cases, the most probable energy difference between the two protons is close to zero. However, for a 2 He emission, a small relative angle between the two protons might be observable. Recent theoretical predictions 2,3'4>5 pointed out that 45 Fe, 48 Ni, and 54 Zn are the best candidates for two-proton ground-state decay as their 2p Q values are about 1.1-1.8 MeV, whereas the one-proton emission is either energetically forbidden or extremely disfavoured due to small oneproton decay energies and very narrow intermediate states as a consequence of the rather high combined Coulomb and centrifugal barrier. Therefore, half-lives in the 100/us to a few millisecond range were predicted for these medium-mass nuclei. With the advent of projectile-fragmentation facilities equipped with powerful separators for in-flight isotope separation, medium-mass proton drip-line nuclei came into experimental reach and two of the above mentioned most promising candidates, 45 Fe 6 and 48 Ni 7 , could be observed for the first time as quasi-stable isotopes with half-lives longer than a few hundred nanoseconds. In addition, part of the decay strength of 45 Fe was observed 8 in the experiment designed to observed for the first time 48 Ni 7 . However, due to the set-up of the electronics in this experiment, two-proton events triggered the data acquisition only with a very low probability.

2. E x p e r i m e n t a l p r o c e d u r e In the experiment at the SISSI-LISE3 facility of GANIL 10 , the projectile fragmentation of a 58 Ni primary beam at 75 MeV/nucleon has been used to produce proton-rich nuclei in the range Z=22-28. After production in the natural nickel target (240 fim in thickness) located in the SISSI device, the fragments of interest were selected by the Alpha spectrometer and the LISE3 separator equipped with an intermediate beryllium degrader (50/um in thickness). At the focus of the LISE3 separator, a set-up was mounted to identify and stop the fragments as well as to study their radioactive decays. This set-up consisted in two channel-plate detection systems for timing purposes mounted at a first LISE focal point 22.9 m upstream from the final focus, a sequence of four silicon detectors (300/jm, 300/zm, 300^im, 6mm in thickness, respectively) with the third one being a silicon-strip detector with 16x16 x-y strips with a pitch of 3 mm, and a Germanium array in close geometry. The silicon detectors were equipped with two parallel electronic chains with different gains, one for heavy-fragment identification and the

148 other for decay spectroscopy.

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The fragments of interest were stopped in the third silicon detector of the telescope and identified on an event-by-event basis by means of their flight times measured between the radio frequency of the GANIL cyclotrons and the first silicon detector as well as between the channel-plate detectors and the same silicon detector and by their energy loss in all detectors of the telescope (see Refs. 7 and 8 for details about the procedure). Figure 1 shows a two-dimensional identification spectrum of the energy loss in the first silicon detector as a function of the time of flight. Radioactive decay events were triggered either by the implantation detector E3 or by the adjacent silicon detectors E4. For any event triggering the data acquisition, all channels were read and written on tape. The efficiency to observe a p particle in the E4 detector for a j3 decay occurring in the implantation detector was about 30%. The 7 energy calibration and the detection efficiency was obtained with standard calibration sources. The efficiency was about 1.6% at 1.3 MeV.

149 All in all, 22 45 Fe implantations were identified. Due to a rather low total implantation rate of much less than one radioactive isotope per second in each pixel, an implantation-decay correlation could be performed on an event-by-event basis. 3. Results Figure 2a shows the decay-energy spectrum correlated with implants of 45 Fe where only decay events occurring less that 15 ms after a 4BFe implantation were analysed. The spectrum exhibits a pronounced peak at (1.14±0.05) MeV with only a very few other counts. In contrary, in the spectrum in Figure 2b conditioned by a decay time in the interval between 15 ms and 100 ms, the 1.14 MeV peak has almost completely disappeared and other events higher in decay energy show up. These counts are consistent with the decay-energy spectrum of 43 Cr 8 , the 2p daughter of 45 Fe. The 1.14 MeV peak, however, seems to originate only from the fast decay

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of 45 Fe. In addition, the events in this peak have no coincident /3-particle signals in the adjacent detector E4 (see Figure 3a) beyond the noise level, whereas these coincident j3 particles can be observed nicely for 46 Fe implants (Figure 3b) analysed with a similar condition in energy for the cen-

150

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(3 energy (keV) Figure 3. a) /3-particle spectrum from the 6mm-thick detector E4 in coincidence with events in the peak at 1.14 MeV. b) Similar spectrum obtained after 4 6 Fe implantation conditioned by a decay-energy range in the E3 detector of E = (0.875 - 1 . 3 ) MeV, which yields the same statistics as for the 1.14 MeV peak of 4 5 Fe. The insets show the decayenergy spectrum for the two nuclei with the dark area and the dotted lines indicating the decay-energy condition applied to generate the /? spectra as well as the full-statistics 46 Fe 0 spectrum. Counts below about 400 keV are most likely due to the intrinsic noise of this large-volume detector.

the same for 45 Fe and 46 Fe and therefore similar ^-detection efficiencies can be assumed, the non-observation of f3 particles in coincidence with the 1.14 MeV peak alone is a strong indication that this peak originates from a direct two-proton ground-state decay of 45 Fe. The probability to miss all P particles for the 12 events in the peak is as low as 1.4%. Although the 7-detection efficiency was rather low, it is worth mentioning that none of the 12 events in the 1.14 MeV peak is in coincidence with a 7 ray. The observation of only twelve events in the peak at 1.14 MeV indicates that the branching ratio for 2p decay of 45 Fe is not one hundred percent, in agreement with theoretical prediction of a /3-decay half-life of about 7 ms 3 . However, the data-acquisition dead-time of about 0.5 ms makes us lose about 3-4 events. The dead zone between two strips of the implantation detector is another possible source of losses. The events with an energy above 6 MeV (see Figure 2a) decay with a half-life compatible with the one of 45 Fe and are therefore most likely /3-delayed events. With this information, a branching ratio for 2p emission of 70-80% can be estimated.

151 The distinct difference between the decay spectrum of 45 Fe (Figure 2a) and of its neighbor 46 Fe 8 is another hint that we are not dealing with the same decay type. If 45 Fe would decay by a /3-delayed mode, it seems to be reasonable to expect a similar decay-energy spectrum for 46 Fe and for 45 Fe. The observation of one pronounced peak from the decay of 45 Fe is a strong hint that 45 Fe is not decaying by a /? decay as does 46 Fe. The decay-time spectrum of 45 Fe gated by the 1.14 MeV peak is shown in Fig. 4. A one-component fit with an exponential yields a half-life for 45 Fe of Tx/2 = (4.7J^;4) ms. The decay-time spectrum of events up to 100 ms after a 45 Fe implantation can be fitted by taking into account the decay of 45 Fe and its 2p daughter 43 Cr. The half-life then is (5.1±\\) ms.

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Figure 4. Decay-time spectrum of 4 5 Fe. The twelve events in the 1.14 MeV peak are fitted by a one-component exponential using the maximum likelihood procedure. The half-life thus obtained is (4.7±f44) ms. A fit, including the daughter decay, of all correlated event up to 100 ms after 4 5 Fe implantation (see inset) yields a half-life of (5-7±IA) ms for 4 5 Fe and a value of T 1 / 2 = (16.7± 7.0) ms for 4 3 Cr, consistent with literature s . The dark shaded counts originate from the 1.14 MeV peak.

4. Discussion Combining the results of the GANIL experiment with a similar experimant at GSI 9 with a smaller statistics but a faster acquisition system, the average decay energy is (1.14±0.05) MeV and the half-life from both experiments gives T 1 / 2 = 3 . 8 i ^ m s . The energy of the 45 Fe peak of about 1.14 MeV agrees nicely with Q2P value predictions from Brown 2 of 1.15(9) MeV, from

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Q value Q 2p (MeV) Figure 5. Barrier-penetration half-life as a function of the two-proton Q value, Qiv, for 45 Fe. The barrier penetration was calculated by assuming a spectroscopic factor of unity. Different model predictions 2,3,4,12,13,14,15,16,17 w e r e u s e d for Q2p- The experimentally observed Q value of Qp = 1.14 MeV of 4 5 Fe implies a di-proton barrier-penetration half-life of 0.024 ms.

Ormand 3 of 1.28(18) MeV, and from Cole 4 of 1.22(5) MeV. These models use the isobaric-multiplet mass equation and shell-model calculations as well as Coulomb-energy shifts to determine masses of proton-rich nuclei from their neutron-rich mirror partners. Q-value predictions from models aiming at predicting masses for the entire chart of nuclei are in less good agreement with our present result. All the 2p Q-value predictions are summarized in Figure 5, where they are used in barrier-penetration calculations using the simple di-proton model for two-proton emission (the model used in 2 with R = 4.2 fm). For Ep = (1.14±0.05) MeV, these calculations predict a di-proton barrier penetration half-life of (0.024+Q 017) ms, if one assumes a spectroscopic factor of unity. Brown 2 ' n calculated a spectroscopic factor of 0.195 for a direct 2p decay of 45 Fe which increases the barrier tunnel time to a predicted half-life of (0.12lo'o9) rns. This di-proton model yields, for a given Q value, a lower limit for the partial half-life for the two-proton emission 5 . An upper limit can be obtained by calculating the decay width as the product of the penetrability for the two individual protons with half the decay energy each. Using the same spectroscopic factor, this gives a half-life of

153 about 200 s. A sequential decay seems to be excluded for 45 Fe, as the intermediate state, the ground state of 44 Mn, is, depending on the prediction used, either not in the allowed region or at the very limit of the allowed region. The model predictions 2 ' 3 ' 4 range from Qip = -24 keV to +10 keV. As the intermediate state is most probably rather narrow (barrier-penetration calculations yield a value of about T = 50 meV), the first proton would have a very long half-life (hours or even days), which makes this decay mode very unlikely. 5. Summary and outlook The results of a GANIL experiment concerning the decay of 45 Fe have been presented. The measured decay energy yielded a peak at 1.14 MeV, the determined half-life was of 3.8 ms, and, in particular, no coincident f3 or 7 radiation was observed for the events in the decay-energy peak. In addition, strong indications were found for the decay of the 2p daughter, 43 Cr, after implantation of 45 Fe. Additional support comes from the width of the 45 Fe peak, which does not show any broadening due to /3-particle pile-up. The energy of the observed peak is in nice agreement with theoretical predictions for the 2p decay energy. A consistent picture arises, if one assumes that a two-proton ground-state emission occurs. 45 Fe is thus the first case of a nucleus which decays by two-proton ground-state radioactivity with a half-life longer than typical reaction times ( « 10 _ 2 1 s). Whereas the 2p ground-state decay of 45 Fe is established with the present data, future high-statistics data should definitively allow to conclude on the nature of the two-proton decay, 2 He emission or three-body decay. This question can be addressed by measuring the individual proton energies and the relative-angle distribution for the two protons emitted which should be either isotropic (three-body decay), forward-peaked (2He emission), or a mixture of both. For this purpose a time projection chamber with a spatial resolution of about 200 microns on all three dimensions has been built and is actually being tested together with its associated integrated electronics. Acknowledgments The experiment was the fruit of collaboraive efforts of research teams from CENBG-Bordeaux, GANIL-Caen, GSI-Darmstadt, Warsaw University and IFIN-HH-Bucharest. Their agreement to present the above results

154 is warmly acknowledged. References 1. V.I. Goldansky, Nucl. Phys. 19, 482 (1960). 2. B.A. Brown, Phys. Rev. C 4 3 , R1513 (1991). 3. W.E. Ormand, Phys. Rev. C 5 3 , 214 (1996). 4. B.J. Cole, Phys. Rev. C54, 1240 (1996). 5. L. Grigorenko et al, Phys. Rev. Lett. 85, 22 (2000). 6. B. Blank et al., Phys. Rev. Lett. 77, 2893 (1996). 7. B. Blank et al., Phys. Rev. Lett. 84, 1116 (2000). 8. J. Giovinazzo et al., Eur. Phys. J. A10, 73 (2001). 9. M. Pfiitzner et al., Eur. Phys. J. A14, 279 (2002). 10. J. Giovinazzo et al, Phys. Rev. Lett. 89, 102501 (2002). 11. B.A. Brown, Phys. Rev. C44, 924 (1991). 12. P. Haustein, At. Data Nucl. Data Tab. 39, 185 (1988). 13. P. Moller, J. R. Nix, W. D. Myers, and W. J. Swiatecki, At. Data Nucl. Data Tab. 59, 185 (1995). 14. J. Duflo and A. Zuker, Phys. Rev. C52, R23 (1995). 15. Y. Aboussir, J. Pearson, A. Dutta, and F. Tondeur, At. Data Nucl. Data Tab. 61, 127 (1995). 16. G. Audi and A. H. Wapstra, Nucl. Phys. A625, 1 (1997). 17. H. Koura, M. Uno, T. Tachibana, and M. Yamada, Nucl. Phys. A674, 47 (2000).

OPTIMIZATION OF ISOL UCX TARGETS FOR FISSION INDUCED BY FAST NEUTRONS OR ELECTRONS O. BAJEAT*, S. ESSABAA, F. IBRAHIM, C. LAU, Institut de Physique Nucleaire, 91406 Orsay,

France

Y. HUGUET, P. JARDIN, N. LECESNE, R. LEROY, F. PELLEMOINE, M.G. SAINT-LAURENT, A.C.C. VILLARI GANIL, Bd H. Becquerel 14076 Caen cedex 5, France F. NTZERY, A. PLUKIS, D. RIDIKAS DAPN1A, CEA Saclay, 91191 Gifsur

Yvette,

France

J.M. GAUTIER LPC, 6, Bd du Marechal Juin, 14050 Caen cedex,

France

M.MIREA NIPNE, P.O. Box, MG-6, Bucharest,

Romania

Two ways of production of radioactive beams using uranium carbide targets are taken into consideration: fission induced by fast neutrons and by bremsstrahlung radiation. For the SPIRAL 2 project, the fission of the uranium carbide target will be induced by a neutron flow created by bombarding a carbon converter with a 40 MeV high intensity primary deuteron beam. Calculations and design of the target in order to reach 1013 fission events per second with good release have been done. The second way is the photofission using an electron beam. In 2004 the ALTO project (Accelerateur Lineaire Aupres du Tandem d'Orsay) will give a 50 MeV/lOuA electron beam. This facility will allow more than 1011 fissions/s. In this case, the electron beam hits the target without converter. Calculations are realized in order to estimate the production and to choose the best target shape.

1. UCx targets For both projects: Spiral 2 with fast neutrons and Alto with electrons, the same kind of targets will be used. Targets are conceived in agreement with the ISOLDE method [1,2]. A such type of thick target is constructed by an assembly of disks (thickness of about 1 mm) composed from a mixing of Uranium carbide and graphite. The graphite allows to limit the carbide grain size for diffusion paths minimization. These pellets are obtained by * Corresponding author: [email protected] 155

156

compressing a mix of Uranium oxide and graphite powders. The carbonation is made by heating the pellets up to 2000 °C under vacuum. During irradiation, the targets are heated up to 2200 °C. 2.

Comparison between the two ways of production

Some experimental results are available for rare gas productions using fast neutrons and bremsstrahlung radiation [3]. In the case of neutrons, a deuteron beam hits a graphite converter. In the case of bremsstrahlung, an electron beam is focused on a tungsten converter or directly on the uranium carbide target itself. The experiments carried out in the frame of the PARRNE program described in the reference [3] showed that, with the same target of 14 mm diameter and 60 mm length, the production in atoms per microcoulomb is about two times higher with 50 MeV electrons without converter than with 80 MeV deuterons. For a high intensity primary beam, the main limitation of the photofission method is the energy deposited in the target which can produce failures. 3.

SPIRAL 2 target

For the SPIRAL 2 project the specification is to reach 1013 fission events per second using an UCx target, a 40 MeV / 5 mA deuteron beam and a rotating carbon converter. The production of a target irradiated by fast neutrons is estimated using the FICNER code [4]. This code offers the possibility to estimate the effects of geometrical parameters onto the production. The Fig. I Effect of the distance converter-target on the production target 80 mm diam, / 80 mm length CO

rt

111

s/s

2,b 2

c

beam diam, 30

<> /

beam diam, 60

fis

.2 1,i> 1

0) •o J2

0,5

c

0 10

30

50

70

90

dist, converter / target in mm

Figure 1. Effect of the converter-target distance on the production for two different sizes of the beam (diameter 30 mm and 60 mm). In this example, the distance is considered between the entrance of the converter and the target front.

157 emphasizes the importance to place the target as close as possible to the converter. The results obtained within the mentioned numeric code showed that a conical target would not be better for the production than a cylindrical one having the same volume. For the SPIRAL 2 project, it is planned to make a target of 80 mm diameter and of 80-mm length placed at about 40 mm from the entrance of the converter (Fig. 2). graphite container I

80

UCx pellets

"IgU

Figure 2. The SPIRAL 2 target: 19 series of about 60 pellets of 15mm diameter, 1 mm thickness and a spacing of about 0.3 mm between each pellet.

The target has to work at a temperature higher than 2000 °C in order to allow an efficient release of the produced radioactive elements. The power deposited inside the target by the fission reactions is about 500 Watt for 1.6 1013f/s. Then, an extra heating must be added in order to reach convenient temperatures. Moreover the transfer tube between the target and the ion source has to be heated at 2000°C too, for the ionization of non volatile nuclei. 4.

ALTO target

For this project the goal is to reach 1011 fission events per second using a 50 MeV/10 uA electron beam [5]. The production of the target is estimated using the FICEL code [6]. Due to the absorption of photons, the production does not increase proportionally with the target density. The case of a conical shape was also studied. The table 1 shows that a conical target 3 times larger would produce only 30 % more fission events than the cylindrical one.

158 Table 1. Comparison of a cylindrical and a conical target for photofission (target density = 3.6 g/cm3) 1st diameter mm 14 14

2nd diameter mm 14 34

Volume cm3 15 47

Length mm 100 100

No fission/s forlOuA 1.0 10" 1.3 10"

4.1. Example for a converter The production in the target by using a tungsten converter has been studied. In this case, a part of the fission events is due to the photons emitted from the converter. Another part is due to the bremsstrahlung radiations produced in the target by the electrons which hit the target if the converter thickness is lower than the electron range in the tungsten. target production with converter UCx target 14 mm diam, 100 mm length; tungsten converter irradiated by 50 MeV electron beam

without conv

1 mm

2 mm

4 mm

5 mm

8 mm

converter thickness

Figure 3. Fission yields produced in the target with different converter thicknesses. In black: fission induced by photons produced in the target. In gray: fission induced by photons produced in the converter. The converter is in direct contact with the target.

These results show that the production is better without converter. Nevertheless, a converter could be useful to reduce the energy deposited in the target. In fact if the converter thickness is equal to the range of electrons, no electrons will hit the target and only the energy due to photon absorption will be deposited in the target. The results given in the table 2 show that the converter would reduce the production by a factor 5 while the energy deposited would be reduced by a factor 10.

159 Table 2. Production and energy deposited in the target without converter and with a 10 mm tungsten converter.

Without converter Converter W 10 mm

No of fission per UC 1.3 1010 0.26 1010

Energy deposition inMeV 35 3.4

For the ALTO project, an assembly of about 90 pellets of 14 mm diameter, 1 mm thickness and within a small spacing between each pellets will be used. For such a combination, about 350 Watt of the 500 Watt incident beam will be absorbed in the target, 150 Watt being re-emitted out of the target as photon radiation. 5.

Release times (SPIRAL 2 and ALTO)

Some effusion calculations using the Monte-Carlo method are under way to find the best spacing between the pellets. A large spacing will decrease the mean number of collisions of radioactive atoms in their way to reach the entrance of the ion source but, in the same time, the production will be lower due to the lower effective density of the target. References 1. H.L. Ravn et al., Nucl. Instr. Meth. B 26, 183 (1987). 2. C. Lau et al., Nucl. Instr. Meth. B204, 246(2003). 3. F. Ibrahim et al., Europ. Phys. J A15, 357 (2002). 4. M. Mirea et al., Europ. Phys. J. A l l , 59 (2001). 5. O. Bajeat and al., Proceedings of the NANUF03 workshop, Bucharest, Sept. 2003, to be published at World Scientific. 6. M. Mirea et al., Nucl. Instr. Meth. B201, 433 (2003).

THE ALTO PROJECT: A 50 MEV ELECTRON BEAM AT IPN ORSAY O. BAJEAT*, J. ARIANER, P. AUSSET, J.M. BUHOUR, J.N. CAYLA, M. CHABOT, F. CLAPJER, J.L. COACOLO, M. DUCOURTEUX, S. ESSABAA, H. LEFORT, F. IBRAHIM, M. KAMINSKI, J.C. LESCORNET, J. LESREL, A. SAID, S. M'GARRECH, J.P. PRESTEL, B. WAAST Institut de Physique Nucleaire, F-91406 Orsay cedex, France G. BIENVENU Laboratoire de I' accelerateur lineaire, F-91406 Orsay cedex, France

The PARRNE 2 device allows the production of neutron-rich isotopes beams using the ISOL method on a thick 238U target. With fast neutrons produced by 26 MeV / 1 uA deuteron beam, 109 fission/s are induced in the UCx target. In order to improve this production, it has been decided to use the photofission method. A 50 MeV electron accelerator connected with the PARRNE 2 separator is now under construction at IPN.

1.

Specifications

Some calculation of production with electrons has been carried out [1, 2]. For the same uranium target used to produce exotic beams with the on line isotope separator PARRNE 2 through fast neutron induced reactions, it seems possible to induce up to 1011 fission events per second using a 50 MeV / 1 0 pA electron beam (against 109 with the 26 MeV / 1 pA deuteron beam obtained in the past). Using the PARRNE 2 separator, about 5 photofission experiments of 3 weeks of irradiation per year are expected to be feasible. Several ion sources will be adapted on this set up: ISOLDE FEB IAD type, surface ionization, laser... Moreover the electron beams can be used also for other applications: for example in biochemistry (irradiation of proteins, study of DNA under irradiation...) or for industrial applications (irradiation of electronic components). The exploitation is planned to start in 2005. The price of the device is rather low (about 1 M€ without manpower) due to the fact that some equipments have been supplied by other laboratories: the accelerating section was offered by CERN (the LEP injector), other RF equipments are obtained * Corresponding author: [email protected] 160

161 from the Laboratoire de l'Accelerateur LinSaire (LAL Orsay) and a substantial part of the infrastructure already exists [3]. 2.

Characteristics

The maximum energy is 50 MeV with a maximum average intensity of 10 uA. The repetition rate is 100 Hz with an impulsion current duration between 2 ns to 2 us. The maximum emitance is estimated at 6 n- mm- mrad at 50 MeV. 3.

Implantation

The Fig. 1 displays schematically the set up of the installation. The beam line is equipped by instruments for the beam diagnostic: measurement of current, beam position, energy and energy dispersion. The use of the deuteron beam will remain possible.

Figure 1: lay- out of ALTO and the PAR

/ Tandem accelerator of Orsay.

References 1.

2. 3.

M. Mirea, O. Bajeat, F. Clapier, S. Essabaa, L. Groza, F. Ibrahim, S. Kandry-Rody, A.C. Mueller, N. Pauwels and J. Proust, Nucl. Instr. Meth. B201, 433 (2003). O. Bajeat et al., Proceedings of the NANUF03 workshop, Bucharest, Sept. 2003, to be published at Word Scientific. S. Essabaa et al., IPNO report 02-01, 2002.

SENSIBILITY OF ISOMERIC RATIOS A N D EXCITATION F U N C T I O N S TO STATISTICAL MODEL P A R A M E T E R S FOR T H E ( 4 ' 6 ' 8 H E , N , 3 N ) - R E A C T I O N S

T. V. CHUVILSKAYA AND A. A. SHIROKOVA Institute of Nuclear Physics Moscow State University, Russia M. HERMAN IAEA Nuclear Data Section, Vienna, Austria The calculations of the isomeric ratios erm/<79 and excitation functions for the reactions 109 Ag(a,3n) 110m 9In, 107 Ag( 6 ' 4 He,n,3n) 110m 3In and 128 130 ' Te( 8 - 6 He,3n,n) 133m »Xe in the framework of the statistical theory of nuclear reactions were performed. The model of Hauser-Feshbach, the exciton Griffin model and the recently developed statistical model code EMPIRE-2.18 1 with full angular momentum coupling were used. For the reactions induced by a-particles we used the Gilbert-Cameron level densities and the Multi-Step Compound approach. The fusion cross sections of the reactions induced by 6 ' 8 He projectiles were calculated in terms of the simplified coupled channels method (CCFUS code). The new results of the calculations ICSR for the reactions 130 Te( 4 He,n) 133m9 Xe (1) and 128 Te( 6 He,n) 133 ™ 9 Xe (2) on the statistical code EMPIRE-18 are shown in the Table 1. The results for the reactions 128 Te( 8 He,3n) 133m »Xe (3) and 130 Te( 6 He,3n)- 133mfl Xe (4) are shown in Table 2. The results are in a good agreement with the experimental data for a-particles induced reactions obtained 2 at Moscow State University (INP). It was indicated by us the interest in the investigation with radioactive beams of 6 ' 8 He ions, the reactions producing the isomeric pairs. It was shown by the calculations 3 the important role of the reduction of the Coulomb barrier at the population of high spin low energy states.

162

163 Table 1. exp. 1/2/ E*, 15 17 20 23 24 25 27 28 29 31

calc.1/2/

0.1 0.2 0.4 0.4 0.4 0.5 0.4 0.4 0.4 0.4

E\ 17.8 19.7 22.6 25.5 26.5 28.5 30.2 31.2 32.2 34.2

0.1 0.2 0.4 0.4 0,4 0.5 0.4 0.4 0.4 0.4

calc.1/2/ E*, Cm/Cg 17.8 0.8 19.7 0.9 22.6 1.0 1.2 25.5 26.5 2.0 2.4 28.5 2.6 30.2 2.7 31.2 2.8 32.2 2.8 34.2

Cm/Cg

0.5 ± 1 ± 1.8 ± 1.8 ± 2.0 ± 2.4 ± 1.8 ± 2.4 ± 2.0 ± 2.0 ±

C m /(Tg

0.8 0.9 1.0 1.2 2.0 2.4 2.6 2.7 2.8 2.8

(2)

(1) E*,

Cm/o"s

E*,

Cm/o-g

22.6

9.8

22.1

98

26.8

Table 2. exp. 1/2/ E", 15 17 20 23 24 25 27 28 29 31

Cm/fg

0.5 ± 1 ± 1.8 ± 1.8 ± 2.0 ± 2.4 ± 1.8 ± 2.4 ± 2.0 ± 2.0 ±

(4)

(3) E*,

22.8 23.8 24.7 26.6

Cm/fg

0 2.3 1.76 5.3

E",


24.9 25.8 26.8 28.7

1.4 5.2 4.1 7.0

References 1. M. Herman, to be published. 2. N.K. Glebov, A.F. Tulinov, V.A. Khodyrev, T.V. Chuvilskaya et al., Izv. Ac. Nauk., Ser.Fiz. Russia 55, 141 (1991). 3. T.V. Chuvilskaya, in Abstract of International Conference "Nuclear Structure at the Limits", Argonne, July 22-26, ANL, Illinois, p.172, 1996.

F R A G M E N T M A S S D I S T R I B U T I O N OF T H E 2 3 9 P u ( d , p f ) R E A C T I O N VIA T H E S U P E R D E F O R M E D /3-VIBRATIONAL RESONANCE

K. NISHIO, H. IKEZOE, Y. NAGAME, S. MITSUOKA, I. NISHINAKA, L. DUANf K. SATOU, M. ASAI, H. HABA, K. TSUKADA, N. SHINOHARA, AND S. ICHIKAWA Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-1195, Japan In order to investigate the influence of the initial /?-vibrational motion of the fissioning nucleus on the scission configuration, we have measured the fragment mass distribution of the 2 4 0 Pu fission following the (3-vibrational resonance 1 . The /3-vibrational state {Kn = 0 + state 2 ) is formed on the second minimum ( superdeformed(SD) minimum ) of the double-humped fission barrier. This state is observed below the threshold energy in the form of an enhanced fission cross section due to a resonance tunneling induced when the excitation energy (Eex) of the compound nucleus matches the level. The reaction of 239 Pu(d,pf) was used to study the resonance fission of 240 Pu. The 13.5 MeV deuteron beams were supplied by the JAERI-tandem accelerator and irradiated the 2 3 9 Pu target. The excitation energy (Eex) of 2 4 0 Pu was determined by measuring the kinetic energy of the outgoing proton. Protons were detected by a AE-E telescope, which consists of two silicon detectors (300-^m thick for AE and 1500-/xm for E). The telescope was set at 135° relative to the beam direction having a solid angle of 45 msr. The energy resolution for protons was about 55 keV. Two fission fragments were coincidentally detected by two silicon PIN diodes, which were equipped on both sides of the target with a similar aperture. The center of the PIN diodes were set at 90° relative to the beam direction having a solid angle of 1.25 sr. The energy calibration of the PIN diode was obtained by using the Schmitt formula 3 . The fragment masses were determined from their kinetic energies by following the mass and momentum conservation law. *On leave from Institute of Modern Physics, Chinese Academy of Sciences, 730000 Lanzhou, China

164

165 In the spectrum of proton-fission coincidence events as function of excit a t i o n energy of 2 4 0 P u , the resonance peak associated with the /?-vibrational state is observed at 5.05 MeV, which agrees well with t h a t of Ref. 2. By gating this resonance (4.78 < Eex < 5.30 MeV), we constructed t h e mass distribution as shown in Fig. 1(b). Also shown in Fig. 1(a) is t h e mass distribution for 5.30< E e x < 6.00 MeV, which corresponds t o t h e fission barrier height. Solid curves are the distribution for 2 3 9 Pu(n t h,f) taken from Ref. 4. T h e fission following the /3-vibrational state show the asymmetric mass distribution similar to 2 3 9 Pu(n t h,f) within statistical error. T h e 2 4 0 P u system following the /^-vibrational resonance descends into a fission valley which is identical t o the fission valley of 2 3 9 Pu(n t h,f)It would be interesting t o investigate the mass distribution following t h e vibrational states formed on t h e hyperdeformation minimum 5 , where cluster configuration of 1 3 2 Sn is predicted 6 .

(E ex =5.30-6.00MeV)

(E ex =4.78 - 5.30 MeV )

Fragment Mass [u]

Figure 1. Fission fragment mass distribution for the data for 239 Pu(n th ,f) 4 .

239

Pu(d,pf) reaction. Solid curves are

References 1. K. Nishio et a l , Phys. Rev. C67, 014604 (2003). 2. P. Glassel et a l , Nucl. Phys. A256, 220 (1976). 3. H.W. Schmitt et al., Proc. of the Symp. on Physics and Chemistry of Fission, Salzburg, (IAEA, Vienna, 1965), Vol. 1, p.531. 4. C. Wagemans et a l , Phys. Rev. C30, 218 (1984). 5. A. Krasznahorkay et al., Phys. Rev. Lett. 80, 2073 (1998). 6. S. Cwiok et al., Phys. Lett. B322, 304 (1994).

F I N G E R P R I N T S OF FINITE SIZE EFFECTS IN N U C L E A R MULTIFRAGMENTATION

A D . R. R A D U T A A N D A L . H. R A D U T A National

Institute of Physics and Nuclear Engineering, Bucharest, POB-MG 6, Romania

A microcanonical multifragmentation model is used to investigate different aspects related to a possible liquid-gas phase transition taking place in excited nuclei. It is shown that due to the finite size of the system properties generally specific to the critical point manifest is a wide region of the phase diagram. Is is shown that the scaling of isotopic yields is affected by finite size effects. Using a simplified one component Lennard-Jones fluid phase diagrams of different size systems are calculated. The result is that the critical point of the system is size dependent.

The connection between multifragmentation as decay mechanism of excited nuclei and a possible liquid-gas (LG) phase transition taking place in nuclear matter is a subject of hot debate in the last two decades and was initially motivated by the strong resemblance between the van der Waals potential and the nucleon-nucleon interaction potential. From principle the difficulty of any study was related to whether or not the well-known criteria of evidencing a phase transition taking place in thermodynamical systems can be applied to atomic nuclei which are supposed to be highly non-extensive. The non-extensivity is obviously due to the finite size and to the presence of the long-range Coulomb interaction. The present talk aims to discuss whether or not data obtained from multifragmentation experiments can be used to infer information concerning a possible LG phase transition. Three different aspects will be presented. The first item regards the scaling property of fragment size distributions which is known to happen in the critical point of the system. In order to study whether this effect is present in a small system, like the atomic nucleus, we used the microcanonical multifragmentation model from Ref. 1 to produce charge distributions corresponding to equilibrated sources having different masses and we analyzed them as experimental data are usually analyzed. The analysis was done over a wide energy range (2-22 MeV/nucleon

166

167

excitation energy), in both primary and asymptotic stages of the decay, with and without Coulomb interaction, at different freeze-out densities. The result was that a rather good quality scaling is obtained in all cases and the quality is improving with the decreasing of the freeze-out volume (by approaching the real critical point), as one can see in Fig. 1. In what regards the values of the critical exponents, one may say that they depend on the source size, freeze-out density, change from the primary to the asymptotic stage of the decay and from the case in which the Coulomb interaction is present to the one in which it is switched off 2 . The conclusion is that the apparent scaling is a spreading effect of the critical point due to the finite size of the system.

/ * " * * * * « ! ^?¥>».

asymptotic V=2V 0

r\ f

primary V=3V„

r

primary V=4V„ A'(E-E.)

%,

asymptotic V=3V„

A asymptotic V=4V„ A' (E-Ec)

Figure 1. Scaling function / from Eq. (N {A,p) — A~T f(A"(p — pc))) from primary (left side) and asymptotic (right side) size distributions at three different volumes with the inclusion of the Coulomb interaction. Black symbols: energies ranging from 2 to 12 MeV/u. Grey open symbols: energies ranging from 12 to 22 MeV/u.

168 The second item regards a very interesting property of the isotopic yields, recently evidenced in multifragmentation experiments. It was shown that the ratio of isotopic yields of the fragments emitted from the decay of two equilibrated sources having the same size, same excitation energy, same temperature but different isospin values is an exponential function of the neutron and proton numbers of the emitted fragment. R21{Z,N)

= Y2{Z,N)/Y1(Z,N)

= Cexp{aN

+ f3Z).

(1)

1

Using the microcanonical multifragmentation model we studied the dependence of the slope parameters a and /? on the mass, excitation energy and freeze-out volume of the considered pair of sources. The slope of the yield ratio depend on mass, excitation energy, considered pair of sources and differ from the primary to the asymptotic stages of the decay. The dependence on the freeze-out volume was negligible in the considered range (V = 3Vb to lOVo) 3 . Moreover, for large emitted fragments or small sources, the slope of the yield ratio depend also on the mass of the emitted fragment, as one can see from Fig. 2. This result was interpreted as a finite size effect.

Figure 2. Isotopic yield ratios for the primary decay of (50, 20) and (40, 20) at Eex = 5 MeV/nucleon and V = 6Vb as a function of neutron (left panel) and proton (right panel) numbers. Lower panels: Dependence of the slope parameters a and f) on the size of the considered emitted cluster. Here a (/3) represents the slope of log R.2i(Z, N) versus N (Z) for each considered value of Z (N).

169 1.4 1.3 1.2

3l.1 I— 1 0.9

"• u 0

0.1

0.2

0.3

P

0.4

0.5

0.6

0.7

0.8

(O

Figure 3. Phase diagrams corresponding to the truncated and long range corrected Lennard-Jones fluid, corresponding to different sizes of the system. The system's size is specified on top of each diagram. Points calculated via Maxwell constructions are represented with symbols. Full lines are fits of Guggenheim scaling relation for the coexistence curve on the calculated points.

The third item concerns the phase diagram of a finite system versus the phase diagram of an infinite system having the same interaction potential. The problem was solved in the framework of a one-component LennardJones fluid and the conclusion was that the shape of the phase diagram is strongly dependent of the size of the considered system 4 , as results from Fig. 3. More precisely, the critical density is increasing and the critical temperature is decreasing with decreasing the system size. A remarkable result is that not even a 1000-component system is a good approximation of the infinite system. The general conclusion of the performed studies is that much precaution should be taken before comparing the results of a multifragmentation experiment concerning a possible LG phase transition in atomic nuclei with the results of a LG phase transition taking place in infinite fluids. References 1. Al. H. Raduta and Ad. R. Raduta, Phys. Rev. C55, 1344 (1997). 2. Al. H. Raduta, Ad. R. Raduta, Ph. Chomaz and F. Gulminelli, Phys. Rev. C65, 034606 (2002). 3. Ad. R. Raduta and Al. H. Raduta, In Proc. of the "International Workshop on Multifragmentation and Related Areas", Caen, France, November 2003. 4. Al. H. Raduta and Ad. R. Raduta, Nucl. Phys. A724, 233 (2003).

SYSTEMATICS OF THE ALPHA-DECAY TO VIBRATIONAL 2 + STATES* S. PELTONEN AND J. SUHONEN Department of Physics, University of Jyvaskyld, POB 35, FIN-40351, Jyvaskyld, Finland D.S. DELION National Institute of Physics and Nuclear Engineering Bucharest-Magurele, POB MG-6, Romania

We have done a systematic analysis of a-decays to excited 2+ states. Collective excitations were considered within the Quasiparticle Random-Phase Approximation. As a residual twobody force we used the surface-delta interaction. The only free parameter is the ratio of the isovector and isoscalar strengths. This approach is able to explain the general features of electromagnetic and a-transitions along isotope chains. We conclude that the a-decay to excited 2+-state is induced mainly by the effective residual interaction between proton and neutron systems. We also predicted a-decay hindrance factors of 2+-states with respect to the ground state and B(E2) values for even-even nuclei.

1.

Introduction and our model

Recent experimental papers suggested that the a-decay fine structure can be a powerful tool to investigate nuclear structure (for example [1]). In this work we use the QRPA formalism developed in our previous works [2,3] to make a systematic prediction about fine structure a-decay to lowest excited 2 + state. The aim of our present work was to perform a systematic analysis of the adecay fine structure for the lowest 2 + states in even-even nuclei with relatively small quadrupole deformation, where N and Z are not magic numbers. We computed the HF within the QRPA formalism. The single-particle spectrum is given by a diagonalisation procedure of the Woods-Saxon mean field with the universal parametrisation[6]. In our QRPA calculation we considered 19 proton and 19 neutron sp states around the Fermi surfaces. In this way we obtain an appropriate representation of radial wave functions beyond the nuclear radius, which is the most important one for a correct calculation of the a-decay process. The QRPA amplitudes contain the information about the nuclear * This work has been supported by the Academy of Finland under the Finnish Centre of Excellence Programme 2000-2005 (Project No. 44875, Nuclear and Condensed Matter Programme at JYFL). 170

171 structure in the HF and B(£2)-values. We will characterize the "collectivity" of the first excited state by the ratio of the sums of the squared QRPA amplitudes. As a residual force we had the surface-delta interaction with equal strengths in proton-proton and neutron-neutron channels. The only free parameter was the ratio of the isovector to the isoscalar strength, Iv/ls. Value Iv/Is=0 corresponds to a pure isoscalar interaction with a common nucleonnucleon interaction strength. In Ref. [3] we investigated this case for a-decay from the Rn isotopes. Now we extended our analysis to the interval -\
Conclusions

We performed a systematic analysis of the HF and B(E2) values versus die ratio Iv/ls and die energy of the first collective state E2+. It turns out mat mis formalism is able to explain the main trends seen in the systematics of experimental data, namely the decrease of the B(E2) value and the increase of the HF with increasing energy E2+ along any neutron chain. Finally, we showed that the minimal values of the HF best fit die experimental data for vibrational and transitional nuclei [4,5]. This gives the general physical picture of the a-decay to collective 2+ states. It is mainly induced by the effective residual interaction between proton and neutron systems. Based on this conclusion, we performed a prediction of HFs for all spherical and transitional nuclei for which the half-lives were measured. References 1. J. Wauters et. ah, Z. Phys. A342, 277 (1992); Z Phys. A344, 29 (1992); Z. Phys. A345, 21 (1993); Phys. Rev. C47, 1447 (1993); Phys. Rev. C50, 2768 (1994); Phys. Rev. Lett. 72, 1329 (1994). 2. D.S. Delion andRJ. Liotta, Phys. Rev. C56, 1782 (1997). 3. D.S. Delion and J. Suhonen, Phys. Rev. C64, 064302 (2001). 4. S. Raman, C.W. Nestor jr., and P. Tikkanen, At. Data Nucl. Data Tables 78, 1 (2001). 5. Y.A. Akovali, Nucl. Data Sheets 84, 1 (1998). 6. J. Dudek, Z. Szymanski, and T. Werner, Phys. Rev. C23, 920 (1981).

ANALYSIS OF A N E U T R O N - R I C H NUCLEI S O U R C E B A S E D ON PHOTO-FISSON

M. MIREA AND L. GROZA Institute of Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania O. BAJEAT, F. CLAPIER, S. ESSABAA, F. IBRAHIM, A. C. MUELLER, AND J. PROUST Institut de Physique Nucleaire, 91406 Orsay Cedex, France N. PAUWELS Laboratoire d'Utilisation du Rayonement Electromagnetique, BP34, 91898, Orsay Cedex, France S. KANDRY-RODY Universite Chouaib Doukkali, BP 20 El Jadida, Maroc

Nuclear fission of heavy nuclei is a process which allows the production of neutron rich isotopes. Exploiting this property, a source of intermediate energy nuclei near the stability limit can be conceived using the ISOL (Isotope Separation On-Line) technique and the photo-fission process. In a first step, an electron beam of 30-60 MeV is focused onto a W converter or onto the uranium carbide target (UCx) itself to deliver a bremsstrahlung radiation. In the second step, the gamma rays induce the fission of the 238 U. Large fission events yields are expected due to the huge photo-fission cross section traduced by a broad peak of about 160 mb height for 15 MeV gamma rays. Motivated by a succesfull experiment 1 in the frame of the ongoing ALTO project, a theoretical exploratory study of such a source of neutron-rich elements is realized. A survey of the radiative electron energy loss theory is reported in order to estimate numerically the bremsstrahlung production of thick targets. The resulted bremsstrahlung angular and energy theoreti-

172

173 cal distributions delivered from W and UCx thick converters are presented a n d compared with previous results. An acceptable agreement is obtained with t h e d a t a of Ref. 2. Some quantities as t h e number of fission events produced in t h e fissionable source and the energy loss in the converters are also reported as function of t h e geometry of the combination and the incident electron energy. An a t t e m p t of comparison with experimental d a t a shows a quantitative agreement. This study is focused on initial kinetic energies of the electron beam included in the range 30-60 MeV, suitable for the production of large radiative 7-ray yields able t o induce t h e 2 3 8 U fission through the giant dipole resonance. A confrontation with t h e number of fission events produced in the frame of the fast neutron induced fission method indicates t h a t the photo-fission can be a competitive concept 3 . T h e number of neutrons together with g a m m a radiation doses were estimated as function of the electron beam energy and intensity 4 . A design for the geometry of the W-converter and the UCx-source combination was also provided in order to obtain high fission yields avoiding a high energy deposition in the uranium t a r g e t 5 . This theoretical study gives evidence for the advantages obtained by eliminating the intermediate converter and offers the possibility to estim a t e the required radiative shield of our combination. Furthermore, the numerical code developed will permit the evaluation the efficiency dependence for different quantities of the neutron rich ion source (such as the number of fission events) in order to optimize the yields.

References 1. F. Ibrahim, J. Obert, O. Bajeat, J.M. Buhour, D. Carminati, F. Clapi er, C. Donzaud, M. Ducourtieux, J.M. Dufour, S. Essabaa, S. Gals, D. GuillemaudMueller, F. Hosni, O. Hubert, A. Joinet, U. Kster, C. Lau, H. Lefort, G. Le Scornet, J. Lettry, A.C. Mueller, M. Mirea, N. Pauwels, O. Perru, J.C. Potier, J. Proust, F. Pougheon, H. Ravn, L. Rinolfi, G. Rossat, H. Safa, M.G. Saint Laurent, M. Santana-Leitner, O. Sorlin and D. Verney, Europ. Phys. J. A 1 5 , 357 (2002). 2. M.J. Berger and S.M. Seltzer, Phys. Rev. C2, 621 (1970). 3. M. Mirea O. Bajeat, F. Clapier, S. Essabaa, L. Groza, F. Ibrahim, S. KandriRody, A.C. Mueller, N. Pauwels and J. Proust, Nucl. Instr. Meth. B201, 433 (2003). 4. M. Mirea, O. Bajeat, F. Clapier, M. Hassaine, F. Ibrahim, A.C. Mueller, N. Pauwels, J. Proust, D. Verney, R. Antoni, L. Bourgois and S. Kand ri-Rody, Radioprotection 37, 503 (2002). 5. O. Bajeat and M. Mirea, Rom. J. Phys. 47, 725 (2002).

N U M E R I C A L CODE FOR S Y M M E T R I C T W O - C E N T E R SHELL MODEL

P. STOICA Institute of Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania The theoretical analysis of fission processes is limited by the use of onecenter shell models. The simplest way to generalize the Nilsson model for such purposes is to use a two-center shell model. A numerical code 1 for a superasymmetric two-center shell model was developed recently in our Institute in order to study axially-symmetric disintegration processes in a wide range of mass-asymmetries, including the alpha-decay 2 . This work was based on the Frankfurt model3 for the two-center oscillator potential. However, the formalism used in this context is not appropriate for the study of near-symmetric fission. The main difference lies in the fact that the system of eigenvectors of the basic two-center oscillator for reflection symmetric systems is characterized by two good quantum numbers, the parity and the projection of the intrinsic spin Q. In the case of mass-asymmetries, the levels are characterized by only one good quantum number, that is Q. Accordingly, the mathematical formalism differs between the two kinds of parameterization. The analytical formulas are based on the formalism described in Ref. 4. The code was developed for a nuclear shape parameterization given by two spheres of equal radii smoothed joined by a neck given by the rotation of a circle around the axial axis of symmetry. Accordingly, the potential is corrected by various terms which take into account the influence of the neck, the spin terms and the depths of the potentials. The eigenvalues system is obtained by solving the two-center harmonic potential in cylindrical coordinates. As an example, the neutron single-particle levels for 238 U fission are displayed in Fig. 1 as function of the distance between the centers of the nascent fragments. The numerical code is ready for applications and was successfully used for fission studies 5 . The input parameters are the elongation, the A and Z

174

175

D (fm) Figure 1. Neutron level scheme for the symmetric fission of of 1 fm as function of the elongation.

238

U with a necking radius

parent values and the spin constants. The single particle levels behave as Nilsson levels for small deformations in order to reach finally the levels of the two separated fragments when the elongation tends to infinity. References 1. 2. 3. 4. 5.

M. Mirea, Phys. Rev. C54, 302 (1996). M. Mirea, Phys. Rev. C63, 034603 (2001). J. Maruhn and W. Greiner, Z. Phys. 251, (1972). E. Badralexe, M. Rizea and A. Sandulescu, Rev. Roum. Phys. 19, 63 (1974). M. Mirea and al, Europ. Phys. J. A l l , 59 (2001).

DEFORMED OPEN QUANTUM SYSTEMS

A. ISAR Department of Theoretical Physics, Institute of Physics and Nuclear Engineering, Bucharest-Magurele, POB MG-6, Romania E-mail: [email protected]

A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is obtained in the microscopic model, using perturbation theory. The coefficients of the master equation depend on the deformation function. The steady state solution of the equation for the density matrix in the number representation is derived and the equilibrium energy of the deformed harmonic oscillator is calculated in the approximation of small deformation.

We derive 1 in the Born-Markov approximation the following master equation for the density operator which describes the quantum dynamics of the /-deformed oscillator interacting with a dissipative environment: % = -\\H,P]

+ {[[D+(Sl)a,p],ai] -

+ ±Dpq(n)),p],a1]-±[tJ,{a,p}]

[[a\D-{il) + H.c.}.

The /-deformed oscillator is defined1'2 by the operators A = af(N) = f(N + l)a, At = f(N)at = a*f{N + 1), N = rfa and its Hamiltonian is "H = huj(AA^ + A^A)/2. Here a) and a are the ordinary creation and annihilation operators, / is the deformation function and the following notation are used (m and w are the mass and, respectively, ordinary frequency):

i. | m j D „ ( f l ) + ags,. D . ( n ) = L [ m u D t t { a ) _ fees, where ft = ft(iV) = [{N + 2)f2(N + 2) - Nf2(N)]/2 and £>pp(ft), Dqq(Q), Dpq(Q) and A(ft) play the role of deformed diffusion and, respectively, dissipation coefficients. The /-oscillator (in particular, (/-oscillator) is a nonlinear quantum oscillator and, consequently, the diffusion and dissipation coefficients which model the influence of the environment on the deformed

176

177 oscillator strongly depend on the introduced nonlinearities. In the limit / -» 1 (fi -> 1), the deformation disappears and the evolution equation becomes the Markovian master equation for the damped harmonic oscillator obtained in the Lindblad theory for open quantum systems, based on completely positive dynamical semigroups. In the particular case of a thermal equilibrium of the bath at temperature T, we take the diffusion coefficients of the form muDqq{Sl) = - ^ -

= -Acoth — ,

Dpq(Cl) = 0,

with A = const, function. The steady state solution of the equation for the density matrix in the number representation is 1

For the case of a thermal state, the stationary solution takes the form P i » = ZJ1 exp{-^-[(n 2kT

+ l ) / 2 ( n + 1) + n/ 2 (n)]},

,,-=P,0)eXp^m, Zf being the partition function. This expression has the form of the Boltzmann distribution. In the limit / -> 1 the probability P s '^(n) becomes the usual Boltzmann distribution and Zf tends to the partition function for the ordinary harmonic oscillator. In the case of the gr-deformation we obtain the following expression for the equilibrium energy of the damped harmonic oscillator in the approximation of a small deformation parameter 2 T(Q(N) = 1 + T2(N + l) /2) U. £ ( 0 0 ) = —(CQth ^ c

~

e0 e0 + l (e/3_i)2le/3_1

e2fi+4eP + l P ( e /3_ 1 )2 J'

+T2C),

_ hu_ P~kT-

When there is no deformation (r -» 0), one recovers the energy of the ordinary harmonic oscillator in a thermal bath. In the limit T —> 0, one has c -> 0 and E(oo) = hu/2. References 1. A. Isar and W. Scheid, Physica A310, 364 (2002). 2. A. Isar, A. Sandulescu and W. Scheid, Physica A322, 233 (2003).

DECOMMISSIONING THE RESEARCH NUCLEAR REACTOR VVR-S MAGURELE -BUCHAREST: ANALYZE, JUSTIFICATION AND SELECTION OF DECOMMISSIONING STRATEGY M. DRAGUSIN, V. POP A, A. BOICU, C. TUCA, I. IORGA, C. MUSTATA National Institute of Physics and Nuclear Engineering, -P.O.BoxMG-6, Magurele, Romania The decommissioning of Research Nuclear Reactor VVR-S Magurele Bucharest involves the removal of the radioactive and hazardous materials to permit the facility to be released without representing a further risk to human health and the environment [1-3]. A very important aspect of decommissioning is the analyze, justification and selection of the decommissioning strategy. Two strategies: DECON (Immediate Dismantling) and SAFSTOR (Safe Enclosure) are in study (see Table 1). The site is placed in "Campia Romana" between rivers Sabar and Dambovita at about 3 km South - West from built limit of the Bucharest city and 8 km right line from town center, at distances 0.8 km, 1.2 km, and 5 km from rivers Ciorogarla, Sabar and Arges, respectively, in South-South-West direction. Group I, part of the National Institute for Physic and Nuclear Engineering, where the "VVR-S Nuclear Reactor" is located at about 1km from Magurele village. The Group I precincts are connected to highway Bucharest Magurele by a lateral asphalt road of 1 km length and a joint of 0.8 km of belt railway. Around Group I, precincts of radius of about 800 m there is an affronted zone, constituting an exclusion and sanitary protection zone. The site is provided with facilities and installations, including service ducts (2.20m X 1.80m) which in their turn, contain the cool water piping, service cooling water piping, thermal piping, compressed air piping and the power cable routes. In accordance with IAEA documents, the decommissioning of the VVR-S nuclear reactor, will be realized by a process which contains three successive stages. This process corresponds to the method described by NRC as DECON immediate decommissioning after the end of the authorized preservation period. We notice that: the shut-down moment of WWR-S Nuclear Reactor was in 1997; the decommissioning period for completing 1 and 2 stages is estimated at 5 years; the beginning of the stage 3 of decommissioning activities will take

178

179

place after a minimum 12 years period after the shut-down of the reactor, a similar effect with the maintaining period. The DECON stage 1 (2004- half 2006) will preserve the operationally of all reactor buildings and systems and is focussed on the evacuation from the site of the materials, equipment and non-nuclear structures having a foreseen minor effect on the subsequent DECON stages. Table 1. Several elements for comparation between option 1 and 2. Factor Waste quantities Future use of site and facilities. Waste routes

Defueling, draining and maintenance Minimum decommisioning waste.

Immediate dismantling Large quantities of decom. Waste.

Building and site environmental restoration.

Plant knowledge and exposure.

Maintenance team needed and relevant knowledge experience should be retained, relating to the wide range of remaining systems for future decommissioning planning and implementation.

Building and site Ecological restoration and their reutilization in short time. Generally available but additional facilities would be needed for size reduction and for packaging of large individual component Use personnel with experience from Reactor, we expect high exposure (collective dose) which implies an appropriate radioprotection system.

Regulatory Aspects

No additional regulatory framework required.

Appropriate regulatory framework needed, but is not yet in plane.

Technology

Part of necessary tasks can be performed with existing staff, working under existing operational methods and procedures.

Hazards

The reactor building should not withstand a sessions plane crash, explosion or fire. Major damage from earthquakes can not be excluded. The reactor building can not be considered as an effective long term secondary containment. Consequently the speed of significant quantities of radioactivity must be regard as possible hazard..

Decontamination and dismantling technologies must be applied. More waste packaging and transport technologies are needed, composed with normal operations. Robotics and new storage technologies are needed,too. Subject to confirmation by structural specialists the reactor block is likely to be adequately resistant to external events. Since all significant radioactivity is safely enclosed inside the reactor block, a possible collapse of the reactor building would not lead to a spent of radioactivity. Hazards can happen from accidental mistakes of the workers, a very good training will minimize them. Possible accidents or incidents will be analyzed and required measures will be taken, as well as other protection measures for preventing possible hazards.

Available

180

The DECON Stage 2 (half 2006-2008) includes the bulk of the substantive decommissioning operations - decontamination, dismantling, demolition, treatment, conditioning, off-site evacuation and disposal of radioactive waste and the erection of the Secured Containment Volume for the coming hold-up period. A basic prerequisite for the initiation of Stage 2 is that all nuclear fuel is completely evacuated from the reactor house. Requisite conditions regard the full operability of the decom-related working facilities, especially the Radioactive Waste Treatment Station, Spent Fuel Storage Facility, and Hot Cells for possible recanting of spent fuel. At the end of the hold-up time, the stage 3 DECON (2009 - 2019) can be initiated in accordance with a specific authorization of the Regulatory Authority. The basic prerequisite for proceeding to Decommissioning Stage 3 is that a full radiological characterization of the site ascertains that the procedure is safe, and feasible in conformity with the norms in effect at that time. Finally, as a completion of the ecological reconstruction, what may eventually remain from the current reactor compound is the laboratory building that may be retrofit into a "clean" research facility. In consideration of the demolition work-taking place in the area as described (v. the reactor house), an appropriate architectural and structural engineering solution should be identified and implemented. References 1. Decommissioning Handbook, DOE/EM-383, DOE/EM-0142P, USA. 2. Legea nr. lll/96/rep98, legea 193/2003, Norme CNCAN in domeniul nuclear. 3. Decommissioning Plan of VVR-S Reactor, 2002-2003.

K-SHELL VACANCY PRODUCTION AND SHARING IN (0.2-1.75) MEV/u Fe, Co + Cr COLLISIONS C. CIORTEA, I. P1TICU, D. FLUERA§U, D.E. DUMITRIU, A. ENULESCU, M.M. GUGIU, A.T. RADU Nuclear Physics Department, National Institute for Physics and Nuclear Engineering "Horia Hulubei", P.O.Box MG-6Mdgurele, 76900Bucharest, Romania

K-shell ionization cross sections and mean vacancy sharing probabilities measured in the near-symmetric collision systems Fe and Co + Cr at 0.2 -1.75 MeV/u energies are reported. The cross section values have been corrected for multiple ionization in the outer (L, M) shells by using the energy and yield shift method. Mean ionization probabilities per electron in the outer shells have been estimated. Calculations in the Briggs model, using SCA with relativistic hydrogenic wave functions and binding correction, could explain the 2pO molecular orbital ionization cross sections at higher energies (SI MeV/u). The vacancy sharing results show that predictions of a two-state coupling Meyerhof-Demkov model is less fulfilled at higher energies (SI .5 MeV/u).

In slow collisions, where projectile velocity is small compared with the orbital velocity of the active electron, in the near of K-K level matching, a large enhancement of inner-shell ionization over the predictions of the Coulomb excitation theory is explained in the electron promotion model. The dominant process of K-shell vacancy production is the ionization of the 2pa molecular orbital (MO) at small inter-nuclear distances followed by sharing of the primary vacancies among the K-shells of the partners [1,2]. In the present paper, K-shell ionization cross sections in the collision systems Fe, Co + Cr at 0.2-1.75 MeV/u bombarding energy are reported. Beams of 56Fe, 59Coq+ ions (3
182

shell is comparable with that of Cr L-shell in both collision systems, in contrast with the results for the projectile. This result could be qualitatively explained by a rapid partially filling of the M-shell vacancies within the solid target. Cross sections for the K-shell and 2pcrMO ionization, as well as 2pa-ha MO vacancy sharing probabilities, were determined. In Fig. 1 the results for Fe+Cr are given. Typical experimental errors are in the range of 10% - 30%. Fe + Cr

L 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1 Collision energy (MeV/u)

Fe + Cr

\ •

Con.m.i. Mayerhof

(b)

O.tO 0.15 0.20 025 0.30 0.35 0.40 Reciprooal collision velocity (a.u.)

Figure 1. (a) K-shell and 2pa MO ionization cross sections in the collision systems Fe + Cr in dependence of collision energy; (b) 2po-lsa MO vacancy sharing probabilities in function of the reciprocal collision velocity. The lines in the figures give model calculations (see the text).

The one-step direct ionization of 2pa molecular orbital has been estimated by using the Briggs united-atom (UA) model [4], in an approximation due to Meyerhof [5], and doing UA semi-classical calculations with relativistic hydrogenic wave functions [6]. The lines in Figure 1(a) correspond to calculations with tabulated \JA-2p binding energies, without (dash-dot line) and with (straight line) binding energy corrections [7], respectively. As can be seen, the latter predictions are fairly good with experiment at higher (>1 MeV/u) energies, but increasingly lower for decreasing energy. Qualitative consideration of rotational 2pn-2pa MO promotion, by one-collision two-step or multiple-collisions processes [1], could not explain this disagreement. For 2po-lscrMO vacancy sharing, the Meyerhof-Demkov prediction [2], shown by the straight line in Fig. 1(b), is less fulfilled.

References 1. W.E. Meyerhof and R. Anholt, T.K. Saylor, Phys. Rev. A16, 169 (1977). 2. W.E. Meyerhof, Phys. Rev. Lett. 31, 1341 (1973). 3. A. Berinde et al., in "Atomic and Nuclear Heavy Ion Interactions", eds. A. Berinde et al. (CIP Press, Bucharest, 1986), Vol. I, pp.453, 461. 4. J.S. Briggs, J. Phys. B8, L488 (1975). 5. W.E. Meyerhof, Phys. Rev. A18, 414 (1978). 6. D. Trautmann and F. Rosel, Nucl. Instrum. Meth. 214, 21 (1983). 7. S.S. Gershtein and V.D. Krivchenkov, Zh. Eksp. Teor. Fiz. 40, 1481 (1961) (in Russian).

SOME FISSION YIELDS FOR 235U (N,F), 239PU (N,F), 238U (N,F) REACTIONS IN £E NEUTRON SPECTRUM CRISTINA GARLEA Institute of Physics and Nuclear Engineering, P. O. Box MG-6, Bucharest, Romania ION GARLEA SENDRA- Nuclear Technology. Ltd., Bucharest, Romania

In the reference neutron spectrum EE [1,2,3], some yields for fission reactions of 235U, 239Pu and 238U have been measured. The exposures have been made in the centre of LE-ITN facility, using detectors of: 235 U (Al alloys with 10% and 20% ^ U ) , 239 • Pu (Al alloys with 5% and 10% 239Pu), • 238U (metallic detectors), delivered by ORNL-USA. The irradiations were performed in the VVRSRomania research reactor, at a nominal power of 2 MW thermal [4]. The exposure fluences were more than 1014 n/cm2. The neutron flux monitoring was performed by two monitors - fission chambers fabricated by CEA France. The fissionable detectors were packed in Aluminium. After irradiation, the radioactivity of the fission products was measured by high resolution y spectrometry, using a Ge crystal, absolutely calibrated in efficiency [5]. For the counting of the fission events there were considered the ratios between cross sections of the reactions 239Pu (n,f) and 238U (n,f) versus the one of the reaction 235U (n,f), obtained in the frame of the intercomparison program on the reference systems SS-ITN Romania and EE-Mol Belgium [6]. The measured fission yields are displayed in Table 1. Table 1. Fission yields Reaction 95

235

U (n,f)

^Pufof) 238

U (n,f)

Zr 6.71 ±3.2% 5.11 ±4.2% 5.29 ±4.1%

Fission products ,31 Rh I 3.17 ±3.2% 3.46 ±5.6% 7.18 + 4.0% 3.41 ±5.4% 5.79 ± 3.7%

103

183

140

Ba 6.13 ±3.1% 5.73 ±8.0% 6.06 ±4.1%

184 The measured fission yields have been compared with those determined in the CFRMF spectrum as well as with those recommended by ENDF/B library. The uncertainties in the reported values include: • errors in the determination of the fissionable detector mass, • statistical uncertainty, • errors in the absolute efficiency spectrometer calibration. Acknowledgments The authors gratefully recognized the contribution of their colleagues from CEN/SCK Mol Belgium to the development of the EE-ITN facility. References 1. I. Garlea, C. Miron, M. Lupu, P. Hie, A. Thurzo, N. Stanica, F. Popa and G. Fodor, Rev. Roum. Phys. 23, 409 (1978). 2. I. Garlea, C. Miron and F. Popa, Rev. Roum. Phys. 25, 107 (1980). 3. D. Albert, W. Hansen, W. Vogel, I. Garlea, C. Miron and C. Roth, Rep RPP-16/80 Zfk Rossendorf, Germany, 1980; Proc. IV ASTMEURATOM Symposium on Nuclear Dosimetry, NBS, Washington, USA, March 1982. 4. I. Garlea, C. Miron-Garlea, C. Roth, D. Dobrea and T. Musat, Proc. V Symp. ASTM-EURATOM Neutron Dosimetry for Fuel, Cladding and Structural Materials, Eds. J.P. Genthon, H. Rotger, Reidl. Publ. House, Dordrech, Oland 1983. 5. C. Garlea, I. Garlea, A. Rodna and C. Kelerman, Int. Conf. On Safe Decomissioning for Nuclear Activities, IAEA CN-93[50], Berlin, Germany 2002. 6. I. Garlea, C. Miron and A. Fabry, Preprint BLG/ITN 106, Belgium 1976; Rev. Roum. Phys. 22, 627 (1977).

RECALIBRATION OF SOME SEALED FISSION CHAMBERS FRANCE - IN MARK III, MOL, BELGIUM FACILITY HAMID AIT ABDERAHM1, ION GARLEA2, C. KELERMAN2 AND CRISTINA GARLEA3 l

SCK>CEN, Mol, Belgium

SENDRA- Nuclear Technology. Ltd, Bucharest, Romania Laboratory 2

institute of Physics and Nuclear Engineering, Bucharest, Romania

The selection of neutron fields allowing the integral neutron data validation as well as the calibration of the instrumentation used in the absolute measurements, was a continuous task of the experts in the area. The choosing of the neutron spectrum is based on the hypothesis of correct description of the spectral shape by calculation methods as well as integral and differential measurements. Several standards were proposed to cover the energy range between 0 and 18 MeV. The fundamental requirement to qualify a neutron field as standard is its accurate description in terms of the neutron flux distributions (space, angles and energy). 252Cf point sources are recognized by scientific community as standards for the energy range 0.5 - 8 MeV, with standard deviation less than 2% and the source strength being measured with uncertainties less than 1.5%. The 235U fission thermal neutron spectrum in Mol cavity may be considered as a standard taking into account the followings: •

• •

The uncertainties in spectral shape of 235U fission spectrum theoretically estimated are less than 2.5% (in terms of standard deviation) in the range 0.5 - 8 MeV; The fission spectrum distributions in 1-m cavity versus ideal spectrum are manageable and precisely established; The strength function can be obtained by flux transfer from the NIST 252C source.

The 235U fission spectrum implemented at SCK/CEN (Mol) is less known than the NIST 252Cf standard field. This means that its utilization involves the use of several corrections that increase the uncertainties. On the other hand, the

185

186

use of • •

U fission spectrum has two main advantages:

better representation of the actual source term in nuclear reactors, even for mixed plutonium-uranium systems; capability to deliver high neutron fluxes, of the order of 109 cm'Y 1 (Mol) and even larger (NIST Cavity Fission Spectrum) [1].

The 235 U fission thermal neutron spectrum is generated in an 1-m diameter cavity located in the vertical thermal column of BR1 reactor in Mol, Belgium. The fast neutron source has a cylindrical shape. It is made from metallic Uranium, 93% enriched in 235U. The thermal neutron flux in the thermal column produces a fission spectrum in the uranium converter, the thermal neutron being absorbed in a Cd tube (1-mm thickness) placed just behind the U-converter. Cd tube is sealed at the lower part, its upper part passing through the concrete shielding outside the reactor. This experimental arrangement allows the exposure of the detectors in fission spectrum without the shut down of the reactor. The neutron flux generated in the center of system for MARK III configuration is 3.1xl0 8 neutron/cm2s at 1 MW of BR1 reactor power. A high precision monitoring system (with uncertainties less than 0.5%) was installed in cavity in order to determine the power level (neutron flux). The thermal neutron flux in position selected for monitoring is not dependent by the absorbers loaded in the cavity. Consequently, the central neutron flux %25 is just proportional with the monitor response, specified as MON (cps). The linearity of this response (corrected for electronic pile-up) is better than 0.2% in a wide range, from some W up to 1 MW. Characterization of the thermal neutron 235U fission spectrum obtained in the SCK/CEN 1-m diameter cavity by mean of MARK III fission source was promoted by A. Fabry's works [1]. In a common program with NIST-USA, the calculations and measurements which define the corrections necessary to simulate a pure fission spectrum from a real spectrum were performed. The final results were obtained by taking into account several corrections, including the correction due to the geometry factor, the wall return correction and the correction due to the perturbation introduced by the fission chamber. The ratio SyCF/SuMON between the counting rate for the fission chamber upper discrimination threshold and the same quantity for monitor was obtained. The registration method of fission fragments and applied corrections are accordingly with Ref. [2]. The 20-mm diameter plate fission chambers (delivered by CEA France) have been exposed in the center of MARK III system, at an operation power of

187

the reactor BR1 - Mol of 700 kW. The ratio SuCF/SuMON was determined for each exposed fission chamber. The reaction rates obtained by measurements have been corrected. Finally, a determination of the absolute masses for the fission chambers under calibration was realized. For the determination of the absolute masses of the exposed fissionable deposits there was used the value of the flux transferred from 252Cf standard source (/MON), as well as the value of central unperturbed reaction rate, in pure field of fission source, value obtained by fission chambers containing the same isotope, in NBS geometry. The deposits of NBS fission chambers were objects of the international inter-comparisons, in MASURCA reactor as well as in MARK III facility. The absolute mass, as well as the associated uncertainty, were determined for each main isotope of fission chamber. Table 1. Mass Data for the Fission Chambers Mass of main isotope in fissionable deposit, 2S-Mol (xE17 nuclei)

Mass of main isotope in fissionable deposit, MARK III (xE17 nuclei)

Mass of main isotope in fissionable deposit, Thermal Spectrum (xE17 nuclei)

Recommended mass (xE17 nuclei)

Ratio of 1973/2003 calibration

Romanian Fis sion Chambers 2 "U 23 2.281(11.6%) 239 Pu 24 2.367 (±1.8%) 237 Np 25 2.123(±2.4%) 238 U 27 1.768(12.4%) 232Th 17 1.700(13.0%)

2.198(12.7%) 2.376(12.5%) 2.015(12.0%) 1.739(11.6%) 1.582(12.8%)

2.201(11.8%) 2.415(11.6%)

2.200(+2.2%) 2.396(12.2%)

-

-

1.037 0.988 1.053 1.017 1.075

Chamber identification and main isotope

In Table 1, the absolute masses measured for the five fission chambers FC23 - 235U, FC24 - 239Pu, FC25 - 237Np, FC27 - 238U and FC17 - 232Th are presented. For each fission chamber, a certificate containing two parts was prepared. The first part refers to the quality of the central unperturbed signal, in pure field of MARK HI source. The second part gives the data used to obtain the absolute mass of the main fissionable isotope in fission chamber deposit. In Table 2, the calibration certificate of the fission chamber having 239Pu as main fissionable isotope is presented. The neutron flux (reported to monitor indications) was measured with Au foils. Its value was used for the determination of the absolute masses using the cross sections at 2200 m/s, Westcott factor g(T) and the ratio SuCF/SuMON measured in the center of the cavity. The reaction rates have been corrected for the exposure in thermal flux.

188 Table 2. Mol MARK III Cavity Spectrum Calibration Certificate for Pu239 Fission Chamber No.24. Vertical distance to cavity midplane Z(cm)

Observed signal Su/MON

0.0 -24.3 +25.7

7.29E-3

-

Derivation of Central Unperturbed Free-Field Signal Field Signal corrected Structural for background & background scatter correctcorrection wall-return ion (Su-Bu-WuVMON (Su-Bu)/Su P(Z) 0.9901 0.9740 0.9795

5.94E-3

1.040

Genuine flux geometry attenuation G(Z) 0.9982

Central unperturbed signal

S.71E-3

The fission chambers have been calibrated in the intermediate energy reference spectrum, in 1973 in EE-Mol facility [3] as well as in 1974 in ££ITN [4] in the frame of the international inter-comparison program. Fissionable deposits of the Grundl type fission chambers were absolutely calibrated and certified by NIST-USA. The results from SCK/CEN obtained in this program are given in Table 1. Masses of the main isotopes are compared with the values obtained in the 1973 calibration program. Mass values obtained for 235U in this program differs from the mass obtained in 1973, namely the actual recommended mass is less with 3.6%. The masses obtained in MARK i n and thermal spectra differ with 0.1%. FC24 - 239Pu presents a variation of 1.2% in actual mass compared with that in 1973. The actual measurements in fast and thermal fluxes have consistent results, in the range of experimental errors. For 237Np, the discrepancies between the mass value obtained in 1973 and that measured in 2003 is 5.3%. Examining the value of ratio between the data for 237Np and 235U obtained in 1973 for NIST chambers and those delivered by CEA France one can see a discrepancy of 4.5%, in favor of the first. This difference of calibration in 1973 can explain partially the actual discrepancy. In the IRMA program there was found a similar discrepancy of 3.5% between the results of measurements performed at SCK/CEN using IRMM deposits of 237Np and previous measurement. These discrepancies can be explained by the 239Pu contamination in the old 237Np fission chambers. FC27 - 238U presents a good agreement between previous and actual measuring results. FC17 - 232Th was measured versus various NIST fissionable deposits. The values obtained for both chambers (No. 17 as well as No. 1381) being net lower than obtained in 1973. In the IRMA measurements it was established that 232Th

189

mass obtained by SCK/CEN calibration was less with 5.4% versus that obtained in other labs. This can explain the discrepancy of 7.5% of our measurements. The same situation is for FC1381 - 232Th used in the both measuring program. References 1. 2. 3. 4.

A. Fabry, "Neutronic Characterization of the TAPIRO Fast-Neutron Source Reactor", Final Report, Vol. 1. SCK-CEN, Mol., Belgium (1988). J. Grundl, D. M. Gilliam, N. Dudek and R. J. Popek, Nucl. Techol. 25, 237 (1975). A. Fabry and I. Garlea, Proc. IAEA-208, Vol. II, 291-308, (1978). I. Garlea, C. Miron and A. Fabry, BLG 512/ITN 106, Belgium (1976); Rev. Roum. Phys. 22, 627 (1977).

MUON DECAY, A POSSIBILITY FOR PRECISE MEASUREMENTS OF MUON CHARGE RATIO IN THE LOW ENERGY RANGE ( < 1 GEV/C ) B. MITRICA 1 , A. BERCUCI 1 ' 2 'IFIN-HH,

2

Forschungszentrum

RO-76900 Bucharest, POB MG-6,

Romania

Karlsruhe, POB 3640, 76021 Karlsruhe,

Germany

I.M. BRANCUS 1 , J. WENTZ 1 ' 2 , M. PETCU 1 , H. REBEL 2 ' 3 , C. AIFTIMEI 1 , M. DUMA 1 , G. TOMA 1 ' IFIN-HH, RO-76900 Bucharest, POB MG-6,

2

Forschungszentrum

Romania

Karlsruhe, POB 3640, 76021 Karlsruhe,

University of Heidelberg, 69120 Heidelberg,

Germany

Germany

The atmospheric flux of muons and neutrinos originates from the decay of charged pions and kaons produced by cosmic rays in the atmosphere. Muons have a relatively large lifetime and they decay in electrons and neutrinos [1]. The muon charge ratio represents the ratio of positive to negative atmospheric muons. The measurements are performed using a small compact device, WILLI (Weakly Ionizing Lepton Lead Interactions), by detecting the lifetime of the muons in different materials [2], Avoiding the difficulties of measurements with magnetic spectrometers, this method gives precise results on muon charge ratio especially in the low energy where the influence of magnetic field is stronger. In the present configuration the detector is construct as a rotatable device which permits measurements on different inclinations and azimuthal directions [3,4]. Measurements of the muon charge ratio performed in the East - West directions with the detector inclined at 45° shows a pronounced Eas-West effect for the muon momentum range 0.35-0.50 GeV/c.

1. Introduction The cosmic rays are bombarding the Earth's atmosphere with an intensity of about 1000 particles/s/m2, containing mainly protons and alpha particles, but also heavier elements up to iron. The energy spectrum involves more than 11 orders of magnitude, reaching 1020 eV and decreasing with the energy as an exponential E"2,7. At an altitude around 15 - 25 km, a primary cosmic particle interacts with atmospheric nuclei and produces an avalanche of secondary particles in a disk shape, containing millions of particles, such phenomena being 190

191 WILLI 1998

Trigger modules

-BB'Ji^>.. '_„}i

*1

Aiui-countm

Active modules

(a) 1.8 wiu.mil

1.6

I

WILU-01

WILLI-02

West *=+==•. 1.4

I + -

, , f

1.2

WILLI-03

} i\

Ii

_+_

1 j

0.8

'-

0.6

-

*

!

'=¥="

East

Llli I

0.3

0.4

0.5

0.6 0.7 0.8 0.9 1 p(| [GeV/c]

(b) Figure 1. The WILLI detector (a) and muon charge ratio (b) with the associated East-West effect.

called Extensive Air Showers (EAS). The EAS are composed by three important components: -the electromagnetic component, including electrons, positrons and gamma rays,

192 -the hadronic component, the central one, -the muonic component, originating from the decay of pions and kaons. 7T > [f + V^Vp)

K*

(1)

> \r + v^Vn)

Thus atmospheric flux of secondary cosmic rays, consists overwhelmingly of muons from decay of charged pions and kaons. 2.

The WILLI experiment

In the initial configuration, the electromagnetic calorimeter WILLI-97 has been built from 20 modules of 90 x 90 cm2, where each module contains a Pb layer (1 cm thickness) and a scintillator layer NE174 (3 cm thickness) fixed in Al support (1 cm thickness). Using such calorimeter measurements have been performed of the muon energy in the range 1-10 TeV and of the muon charge ratio for muons with vertical incidence and a mean impulse =0,87[GeV/c]. In a next configuration the detector has been optimized for muon charge ratio investigation by eliminating the Pb layers and improving the detection efficiency, by rejecting the background noise with an anticoincidence system. In this configuration 2 sets of measurements have been performed, one having the detector placed in the underground of Tandem building, under 60 cm concrete, (WTLLI-98) and another one, moving WILLI in a building with less absorbing ceiling, (WTLLI-99), measuring muon charge ratio in the low energy range = 0,20 - 0,28 [GeV/c]. The results have been included in the Cosmic Rays Reference Book. Recently, the detector has been modified and transformed in a compact rigid detector with rotating facilities in zenithal and azimuthal direction. Such rotatable system, WILLI-2001, allows measurements of the charge ratio of muons with different angles of incidence, being possible to determine the East West effect of the Earth magnetic field, which deflects the trajectories of the charged particles in the atmosphere. References 1. 2. 3. 3.

I.M. Brancus, J. Wentz, B. Mitrica et al., Nucl. Phys. A721, 1044c (2003). B. Vulpescu et al., J. Phys G: Nucl. Part. Phys. 27, 1167 (2001). I.M. Brancus et al., Report WP17 IDRANAP 18-02 (2002). B. Mitrica, Diploma Thesis (2002).

RESEARCH AND DEVELOPMENT ACTIVITIES AS SUPPORT FOR DECOMMISSIONING OF THE RESEARCH REACTOR W R - S MAGURELE M. DRAGUSIN Institute of Physics and Nuclear Engineering, P.O. BoxMG-6, Bucharest,

1.

Guidelines

The Research Reactor VVR-S Magurele was start-up the 27th July 1957. From 23 December 1997 the reactor is in a permanent shutdown. The official announcement for decommissioning was given in April 2002. The main purposes for its utilization were: research, radioisotope production and material exposure. The main characteristics can be listed as follow: 1. Reactor type: tank, water moderated and cooled, water reflector; 2. Equipment and nuclear fuel made in Former Soviet Union; 3. Built and started by Russian-Romanian team; 4. Thermal power of 2 MWth; 5. Average flux of thermal neutron: 1013 n/cm2s; 6. Number of horizontal experimental 9; 7. Number of vertical exposure channels 16; 8. Number of biologic channels 3; 9. Graphite thermal column 1; 10. Number of pumps in primary circuit 5; 11. Number of heating exchangers 2; 12. Number of distilled water tanks 4; 13. Nuclear fuel assemblies: 16 rods for EK-10, 15 rods for C-36; 14. Number of fuel assemblies within core: at fueling start 36 and at fueling end 50; 15. Total number of control and shut off rods: compensation rods 5 and shut-off rods 3. For the decommissioning activity, our national and international partners are the IAEA for elaborating of the detailed decommissioning plan, DOE-USA for an enhancement of the nuclear safety, the EC by two Phare projects related especially to the Radwaste National Repository, the Romanian govern through the Education, Research Ministry, the Nuclear Agency, the Industry and

193

194 Commerce Ministry, RAAN, SITON, ANDRAD and the National Commission for Nuclear Activities Control. In order to remove the radioactive and hazardous materials to avoid risks to human health and environment, the project involves four phases: 1. Assessment; 2. Development; 3. Operations; 4. Closeout. Several engineering steps must be fulfilled: 1. Determination of the radiological inventory (contamination and activation) 2. Identification of options, determination of needed resources taking into account the local conditions and requirements; 3. Evaluation of strategies and scenarios, assessment of human and technical resources, definition of the waste management, design special equipment and development of the project management organization; 4. Identification of potential hazards and necessary protective measures; 5. Computer modeling using certified codes in criticality and health physics, safety analyses aiming to enhance the safety of personnel; 6. Selection of decommissioning process to reduce contamination and to comply with storage, disposal and public reuse requirements; 7. Waste volume reduction, optimum treatment and conditioning; 8. Robotics for dismantling, demolition, maintenance and recycling; 9. Documentation and records keeping. The actual D&D for VVR-S is the first Romanian project in decommissioning of nuclear facilities. It is a complex project, which requires a very intensive exchange of information, cooperation in many aspects as scientific, technological and managerial.

LIGHT HEAVY-ION DISSIPATIVE COLLISIONS AT LOW ENERGY

A. POP, A. ANDRONIC, I. BERCEANU, M. DUMA, D. MOISA, M. PETROVICI, V. SIMION National

Institute for Physics and Nuclear Engineering PoB MG6, RO-76 900, Bucharest-Magurele, E-mail: [email protected]

- "Horia Hulubei" ROMANIA

G. I M M E , G. L A N Z A N O , A. P A G A N O , G. R A C I T I , R. C O N I G L I O N E , A. D E L Z O P P O , P. P I A T E L L I , P. S A P I E N Z A I.N.F.N.

- Laboratori

Nazionali del Sud and Universita I-951&9 Catania, ITALY

di

Catania,

N . C O L O N N A , G. D ' E R A S M O , A. P A N T A L E O I.N.F.N.

Sezione

di Bari , Italy and Dipartimento ITALY

di Fisica,

Universita

di

Bari,

Dissipative processes have been investigated experimentally in several light heavyion systems, using a complex detector which has as main components two position sensitive ionization chambers. Experimental evidence and comparison with theoretical calculations suggest a mechanism similar to deep inelastic processes in heavy and medium systems, even in the case of completely damped events.

The study of dissipative processes in light heavy ion collisions was concentrated on optimum Q value systematics for moderate energy damping and on the challenging point of view of the competition between the deep inelastic orbiting mechanism and the fusion-fission one in the energy domain of complete damping. A systematic experimental study of dissipative processes in light heavyion systems l has been undertaken aiming to follow: detailed correlations and systematic behaviour of experimental observables at variance with medium and heavy systems, properties of the dinuclear system by the analysis of the fluctuations in various excitation functions, charge equilibration process, angular momentum transfer by gamma multiplicity measurements. The isospin relaxation mode was experimentally evidenced in the case of

195

196 light systems too and described with a model for the damped quantum oscillator in the charge asymmetry degree of freedom, using the same parameters already found for heavier systems. Detailed correlations of experimental observables, namely: velocity distributions, TKE-# c m , TKE-Z plots, angular distributions and a detailed systematics of the interaction times as a function of TKE, suggested that a dynamics from quasielastic to completely damped events is present even in the case of light systems. The experimentally measured charge distributions allowed to establish model independent and model dependent systematics for light, medium and heavy systems. Theoretical calculations for the 1 9 F+ 2 7 A1 reaction at 111.4 MeV incident energy have been done using the BNV transport model and the FMD model. The calculations are in good agreement with the experimental data and predict the dissipative character of the reaction even in the case of light systems. The surface friction model (SFM) with deformation has been developed by taking into account the coupling with the mass/charge asymmetry degree of freedom and has been applied to the 1 9 F+ 2 7 A1 reaction at 111.4 and 136.9 MeV incident energy. The experimental data are reasonably well reproduced for the TKE-# c m (Fig. 1) and diffusion TKE-Z plots although the ridge corresponding to complete dissipation overestimates the experiment. Explicit treatment of angular momenta of the interacting

80 100 ° 2° 40 60 80 10° 0 cmO V0) . Figure 1. Comparison between experimental data (left) and SFM calculations (right) for the 1 9 F(111.4 MeV) + 2 7 A 1 reaction. On the left are also drawn DONA code predictions (full points), and BNV calculations (open squares). 0

20

40

60

fragments and further development of this model could improve the agreement with the experimental data. Thus it can be used for comparison with the experimental information on angular momentum transfer. References 1. A. Pop et al., Nucl. Phys. A679, 793 (2001) and references therein.

ESTIMATES OF T H E a RATES FOR D E F O R M E D S U P E R H E A V Y NUCLEI

I. SILI§TEANU, W. SCHEID1, M. RIZEA AND A.O. SILI§TEANU Institute of Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest-Magurele, Romania Institut fur Theoretische Physik der Justus-Liebig-Universitat, Giessen, Germany In present work we propose an approach to reduce the problem of particle emission rates of spheroidal nuclei to the solution of homogeneous and inhomogeneous systems of coupled differential equations arising from the Schrodinger equation. We show that some of the previous development in the question carried out so far in the Wigner R-matrix formalism can be restated in a slightly different form within the Feshbach formalism of resonance nuclear reactions which has advantages of unified treatment of the structure and nuclear dynamics and of emphasis on the more essential mathematical steps. Additionally, the treatment of the decay rates for radioactive states associated with resonances in deformed field is more general and inherently less dependent on arbitrary assumptions than other available R-matrix treatments. New theoretical and computing methods are developed in order to describe the particle emission rates taking into the account of non-sphericity of interaction which complicates the solution of the differential equations describing the "fine structure" intensity patterns in multichannel decay. First of all, we develop a procedure to iterate the nuclear interaction directly in equations of motion in order to obtain the solution for resonant multichannel decay of ground or excited radioactive states. We calculate the emission rates and "fine structure" intensity patterns and confront these to data and results of other models. Some predictions are made for the ahalf-lives of possible new deformed superheavy elements (SHE) [ 1 - 4 ] . The procedure may be useful for designing the resonant particle decay spectroscopy technique in next experimental studies of clustering and decaying phenomena involving the radioactive states. In the case of a-decay of a single resonance

197

198

state v into a channel of angular momentum /, the partial decay width is given in Refs. [5,6]. Table 1. Summary of the a-decay data and calculated a-decay half-lives for 268Mt. The decay chain assignments have been obtained in experiments at GSI-Darmstadt (Hofman et al [1]) using the reaction of 6 4 JVi+ 209Bi — • 2 7 2 111 + I n . The deformation parameters /3 are taken from [7]. Alpha

P aren t

Qeaxp-

rrp- (s)

chain

nucleus

MeV

Experiment

I - a.2

I I -CC2

268

268

Mt

Aft

10.259

0.710 1 0 -

10.097

rptheOT.

1

0.171

268

M t

0.720 1 0 - 1

10.221

rptheOT.

no coupling 1

(g)

with coupling

(1=3)

0.19010- 1

0.157 1 0 " 1 (1=0)

0.49210 - 2

0.452 1 0 "

2

0.950 10- (1=3) 2

0.49710" 2

(1=0)

0.14710" 2

0.556 10~ 1 (1=3)

0.28810- 1

0.41110III - a 2

(g)

0.197 1 0 -

1

(1=0)

0.52810- 2

The experimental signatures of radioactive states in nuclei have traditionally been strong and can be supported by selective excitation in atransfer reactions, vibrationally or rotationally spaced energy levels, enhanced electromagnetic moments and transition strengths, and appreciable cluster particle width for resonant states above the decay treshold. The experimental observation of a-particle groups with similar energies suggests that the parent and daughter nuclei are deformed. This may reveal important information on interplay between nuclear structure and dynamics and provides in many cases a powerful basis for extending the spin-parity information from the daughter nuclide to the unknown parent. Let us consider the case when exist appreciable interactions between the emitted particle waves with different final states. For the particle emission from a decaying state of the total spin / into a set of decay channels c (defined the total spin of residual nucleus R and the orbital momentum / of particle, c = {R,l}), the following two systems of coupled differential equations is obtained: [fr + *&(r)-H^1-^V(«»(r)]«SB(r)-

^(J)(r)

£

WRlRll,u°Rll,{r)=Q

(1)

£+*k(r)-^-^V<°>(r)]u£,(r)1m

f}VW(r)

E

WRlRll,uRll,(r)

=

^IRl(r)

(2)

199 where, kRl = Ei - ER Ei, I = R + l, and Ei En — Ei.are the total energies of initial (Ei) and final nuclei (ER,Ei). We restrict attention to the case in which all decay channels are open so that the boundary conditions are l

m

(r = 0) = 0,

u

uRl(r = 0)=0.

Rl(r > °°) ~ <W/kR)1/2SJ(Rl,R'l')exp

ex

k

(3)

r l7

P .-i( RR' - r/2)}+i(kRR>r-l'ir/2)

«£,(»•—• oo) = 0.

(4) (5)

where 5 is the scattering matrix. If the matrix elements of the interaction potential have no singularities of order two or higher at the origin, then for small r the solutions of (1) with that satisfy (3) are given by uRl(r ) = dRirl+1 where a is a matrix of constants. The solutions thus obtained will not, in general, satisfy the asymptotic boundary conditions (4). Thus, N linearly independent solutions of (1) must be found and a suitable linear combination of them matched to the correct asymptotic form. The solutions u°Rl(r )may be matched to the boundary conditions at two values of r large enough so the terms VRim'a.re negligible. A special type of eigenvalue solution will be considered here for which the behaviour of solution in each separate channel is similar to that of Gi in the one channel problem. In each channel the absolute value of u°Rl{r )decreases to the of small fraction of its value inside of nucleus and only after that enters the region within which it has an oscillatory character (a condition similar to that of resonances in central field). Such a solution can be modified by introduction of potential barrier extending to large r in order to convert the decaying state into a discrete level with a single decay channel. The solution inside the nucleus can be expected to be unaffected by the removal of the barriers and its amplitude to decreases approximately with the time as in the case of one channel problem. The partial width in the channel (Rl) is Tm =

2TT

s;:: wuRiir)dr2 C:;

^m(r)^m(r)dr

(6)

Assuming that the formation amplitude can be simply factorized [6] as: Ihir)

= (Svm)x,2Gl{r)

(7)

(SRlis the spectroscopic factor), the width (5) can be rewritten as: Rl —

JR Rl;L 1

o.b. Rl

(8)

200

where the "one-body" resonance width is:

Tti- =

2TT

irr::;Gi(r)u%(r)dr

(9)

ujjf-being a solution of (2) in which the inhomogeneity is merely G;(r). Estimations of the a-rates of SHE 268 109 [1] are presented in Table I. We can conclude that the a-halflives of ground and excited states of 268 M i depend on the sensible interplay between penetration and very low hindrance (structure) factors and also on the strength of coupling of decay channels with very similar energies. Experimental observation of the fine structure in a-decay and our theoretical analysis of emission halflives may provide in many cases a powerful method of extending spin-parity information from daughter nucleus to parent, determining excitation energies of the daughter and deducing some information on single particle states in superheavy nuclei . In the future work, our group plan to apply this method to: investigate the effects of nuclear deformation on the decay rates in long a-decay chains of SHE, study the dependence of fission barriers on angular momentum and deformation, explore in detail the radioactive ground and excited states of new SHE [1 — 4], estimate electromagnetic moments,emission rates and branching ratios and compare the results with the ones of [7 — 12]. The methods presented here may be also useful for designing the resonant particle decay spectroscopy techniques in next experimental studies of clustering and decaying phenomena involving the radioactive states of deformed SHE. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. II. 12.

S. Hofmann and G. Miinzenberg, Rev. Mod. Phys. 72, 733 (2000). S. Hofmann et al., Eur. Phys. J. A10, 5 (2001). Yu. Ts. Oganessian et al., Phys. Rev. Lett. 83, 3154 (1999). Yu.Ts. Oganessian et al., Phys. Rev. C63, 011301 (2001). I. Sili§teanu, W. Scheid, Phys.Rev. C51, 2023 (1995). I. Silisteanu, W. Scheid and A. Sandulescu, Nucl. Phys A679, 317 (2001). P. Moller, J.R. Nix and K.-L. Kratz, At. Data and Nucl. Data Tab. 66, 131 (1997). Z. Patyk and A. Sobiczewski, Nucl. Phys. A354, 229(1996). K. Rutz, M. Bender, T. Burvenich, T. Schilling, P.-G. Reinhardt, J.A. Maruhn, W. Greiner, Phys. Rev. C56, 238 (1997). M. Ivascu and I. Silisteanu, Nucl. Phys. A485, 93 (1988). I. Silisteanu and M. Ivascu, J. Phys. G: Nucl. Part. Phys. 15, 1405 (1989). M. Ivascu and I. Silisteanu, Sov.J. Part.Nucl. 21, 589 (1990).

LIST OF PARTICIPANTS

H.A. ABDERRAHIM

D. BUCURESCU

SCKCEN, Boeterang 200, B-2400 Mol, Belgium

Institute for Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania

Y.ABE

I. BULBOACA

Yukawa Institute for Theoretical Physics, Kyoto University, 606-8505, Kyoto, Japan

Institute for Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania

M. APOSTOL

F. BUZATU

Institute for Physics and Nuclear Engineering, Institute for Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania P.O. Box MG-6, Bucharest, Romania

Marilena AVRIGEANU

N. CARJAN

Institute for Physics and Nuclear Engineering, Centre d'Etudes Nucleaires de Bordeaux, 33175 Cradignan Cedex, France P.O. Box MG-6, Bucharest, Romania

V. AVRIGEANU

M. CHIS

Institute for Physics and Nuclear Engineering, Romanian Nuclear Agency, Mendeleev Street, P.O. Box MG-6, Bucharest, Romania Bucharest, Romania

O. BAJEAT

Tatjana V. CHUVILSKAYA

Institut de Physique Nuceaire, F-91406, OrsayCedex, France

Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119899 Moscow, Russia

L. BIRO National Commission for Nuclear Activities Control, Libertatii 14, Bucharest, Romania

R. BOBULESCU Faculty of Physics, University of Bucharest, P.O. Box MG 11, Bucharest, Romania

C. BORCEA Centre d'Etudes Nucleaires de Bordeaux, 33175 Cradignan Cedex, France

C. CIORTEA Institute for Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania

Anisoara CONSTANTINESCU Faculty of Physics, University of Bucharest, P.O. Box MG 11, Bucharest, Romania

A. DANIEL Flerov Laboratory of Nuclear Reactions, JINR 141980, Dubna, Moscow region, Russia

201

202 S. DOBRESCU

A. ISAR

Institute for Physics and Nuclear Engineering, Institute for Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania P.O. Box MG-6, Bucharest, Romania

E. DRAGULESCU

F.-J. HAMBSH

Institute for Physics and Nuclear Engineering, EC-JRC-IRMM, Retieseweg, B-2440, Geel, P.O. Box MG-6, Bucharest, Romania Belgium

M. DRAGUSIN

D. HILSCHER

Institute for Physics and Nuclear Engineering, Hahn-Meitner-lnstitut, Glienickerstr. 100, D14109 Berlin, Germany P.O. Box MG-6, Bucharest, Romania

Daniela FLUERASU

C. KELERMAN

Institute for Physics and Nuclear Engineering, SENDRA Nuclear Technology. Ltd., Lahovary P.O. Box MG-6, Bucharest, Romania Place 1A, Bucharest Romania

Cristina GARLEA

Alina ISBASESCU

Institute for Physics and Nuclear Engineering, Institute for Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania P.O. Box MG-6, Bucharest, Romania

I. GARLEA

Beatrice JURADO

SENDRA Nuclear Technology. Ltd., Lahovary Grand Accelerateur d'lons Lours, P.O.Box Place 1A, Bucharest, Romania 5027, F 14021 Caen Cedex, France

R.A. GHERGHESCU

A. KRASZNAHORKAY

Institute for Physics and Nuclear Engineering, Institute of Nuclear Research (ATOMKI), H4001 Debrecen Pf. 51, Hungary P.O. Box MG-6, Bucharest, Romania

Cornelia GRAMA

S. KOPECKY

Institute for Physics and Nuclear Engineering, University of Jyvaskyla, Department of P.O. Box MG-6, Bucharest, Romania Physics, P.O. Box 35 (YFL), FIN-40014, Finland

N. GRAMA M. LEWITOWICZ

Institute for Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania Grand Accelerateur d'lons Lours, P.O.Box 5027, F 14021 Caen Cedex, France

Yu.P. GANGRSKY

N. MARINESCU

Flerov Laboratory of Nuclear Reactions, JINR Faculty of Physics, University of Bucharest, 141980, Dubna, Moscow region, Russia P.O. Box MG 11, Bucharest, Romania

203 M. MIREA

H. PETRASCU

Institute for Physics and Nuclear Engineering, Institute for Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania P.O. Box MG-6, Bucharest, Romania

B. MITR1CA

Adriana RADUTA

Institute for Physics and Nuclear Engineering, Institute for Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania P.O. Box MG-6, Bucharest, Romania

A.C. MUELLER

G. ROYER

Institut de Physique Nuceaire, F-91406, Orsay Cedex, France

Laboratoire Subatech, UMR 6457, A. Kastler 4, 44307 Nantes, France

Carmen MUST ATA

A. SANDULESCU

Institute for Physics and Nuclear Engineering, Romanian Academy, Advanced Research Institute, Victoriei Street, Bucharest, Romania P.O. Box MG-6, Bucharest, Romania

F. NEGOITA

I. SILISTEANU

Institute for Physics and Nuclear Engineering, Institute for Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania P.O. Box MG-6, Bucharest, Romania

K. NISHIO

W. SCHEID

Atomic Energy Research Institute, Ibaraki 319- Institut fur theoretische Physik der JustusLiebig-Universitat Giessen, Germany 1195, Japan

S. PELTONEN

P. STOICA

University of Jyvaskyla, Department of Physics, P.O. Box 35 (YFL), FIN-40014, Finland

Institute for Physics and Nuclear Engineering, P.O. Box M G - 6 , Bucharest, Romania

D.N. POENARU

G. STRATAN

Institute for Physics and Nuclear Engineering, Institute for Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania P.O. Box MG-6, Bucharest, Romania

Amalia POP

A. SEZGIN

Department og Physics, University of Nidge, Institute for Physics and Nuclear Engineering, Nidge, Turkey P.O. Box MG-6, Bucharest, Romania

M. PETRASCU

G. TOMA

Institute for Physics and Nuclear Engineering, Institute for Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania P.O. Box MG-6, Bucharest, Romania

204

Carmen TUCA N. ZAMFIR

Institute for Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania WNSL, Yale University, New Haven, P.O. Box 208121, Connectitut, USA

Anabella TUDORA Faculty of Physics, University of Bucharest, P.O. Box MG 11, Bucharest, Romania

I. ZAMFIRESCU Institute for Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest, Romania

New Applications of

NLJCL- EAR FISSION This book covers new experimental and theoretical studies that focus on the modern developments o f nuclear fission, aiming at various applications in a wide range of fields and bringing together scientists working in different fields related to nuclear fission. The following topics are dealt with: radioactive beam facilities based on nuclear fission; nuclear waste transmutations and the future accelerator-driven system; fission and spallation nuclear data and modeling; experimental and theoretical advances in the study of nuclear fission; fusion reactions and decay modes of superheavy nuclei; stability against fission and manybody systems; superasymmetric and multicluster fission.

World Scientific www.worldscientific.com 5600 he