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4bohr a . This is an indication that the adiabatic potential can be used for interpretation of features of the dynamics for which this range of R is responsible. would show flat distribution. The present results are clearly not the case. At present, number of the (C, C, S, S) coincidence events is quite limited and the results are considerably scattered, however, the histogram of 9 shows clear preference to around n/2, being consistent with known dihedral angle. This means the dissociation of highly ionized DMDS would be reasonably approximated to the Coulombic scheme. The histogram of 9 shows preference to around q>= 0 and n, which correspond to the P- and M-DMDS in fig. 3, respectively. The results show that the CEI technique would give distinguishable images for enantiomers. Acknowledgments JU
R / a.u.
R / a.u.
Figure 1. Potential energy curves (including centrifugal term J ( J + l ) / 2 / x R 2 ) for angular momentum J = 0 (left) and for J = 20, 25, 30 (right).
The dependence of the shape of Vad(R) and Vo(R) on the angular momentum J is shown in the right hand part of Fig. 1 for J = 20, 25 and 30. It demonstrates how the outer potential well is build and disappears with growing J. From the previous discussion it is also obvious that the outer well is located in the region where adiabatic potential curve describes satisfactorily the dynamics of the system. 2.2. Extraction
of metastable-state
parameters
To determine the lifetime of the resonances in the H^" system we calculate the cross sections for vibrational excitation(VE) and dissociative attachment (DA) processes e-+H3(t;i)->e--r-Ha(t;/)>
(5)
e - + H 2 ( 0 - ^ H + H-,
(6)
and preform the least squares fit to the famous Fano formula in the vicinity of resonance. The best fit gives values of the resonance energy Er and the width T r from which we find the lifetime r = h/Tr. It turns out that the resonances are very narrow. Sampling the cross section with the constant a Imaginary part of A and norm of vector p are smaller then the difference between Vj oc and Vad
348
energy step we can easily miss the resonance. The discussion above shows that the resonances in the scattering cross section have to be located close to bound states in the outer well in the potential Vad- Although we do not use this potential in calculation of the cross sections, we employ it as an auxiliary tool to localise the resonances. Once we know the approximate position of the resonance we can calculate the cross section in a narrow energy interval on a very fine grid and use the Fano formula to find the properties of the respective metastable state. It is interesting to compare values of the parameters for the states got from this procedure and from the same procedure but using cross sections calculated within LCP approximation. As an example we give parameters for lowest resonance in J = 23 Er = -75.294meV, LCP) E^ = -75.362meV,
Tr = 6.020 x 10- 6 meV, r ^ c p = 1.662 x 10- 5 meV.
The agreement in the position of the resonance is very good in accordance with previous discussion of validity of the LCP potential. On the other hand the decay width is almost factor of three off. This is understood if we remember that the autodetachment responsible for the decay happens at small R where LCP approximation is not very good. We developed also an alternative strategy to calculate the lifetime of the resonance directly using nonlocal potential given by Eq. (2) and wavefunction obtained for outer well in Vad as the (vibrational) discrete state interacting with H2 + e~ and H + H - continua. The decay width is then found using projection-operator formalism. Detailed description of this procedure is beyond the scope of this brief progress report and will be given elsewhere. Another possibility, to find the resonance parameters, would be the direct calculation of the poles of the scattering S-matrix as has been done for J = 0 within LCP approximation by Narevicius and Moyseyev10. 3. Meta-stable states — summary The dissociative attachment cross sections with the narrow resonances are also shown in the paper of Houfek et al.5 The complete summary of potential energy curves Vo and Vad for J — 21,22, ...,28 with location of the states in outer potential wells has been given in ECAMP conference in Rennes last year 2 including some VE cross sections in resonance region and values of autodetachment widths. The details will be given elsewhere. It is interesting to remind some details.
349 The VE cross sections for J = 21,22 are very similar to VE cross sections for J = 0 with prominent boomerang oscillations. The shape of the lowest "oscillations" is different, they become narrow and well separated. Such behaviour is known for VE cross section for HC1 and was confirmed experimentally by Allan 11 . Looking at Fig. 1 we find that Vad for J ~ 20 has a similar shape to the potential for H + C l - system. The appearance of boomerang resonances is allowed by low height of the inner barrier which does not shield the autodetachment region for energies close to DA threshold. As the alternative (and equivalent) interpretation, the narrowing of the lowest boomerang oscillations can be understood as an interference effect for multiply reflected waves from the inner barrier in similar way as in optical interferometers. There is thus smooth transition between boomerang oscillations and the outer well resonances. Both can also be understood as the states located in the outer part of the adiabatic potential or as an interference of the wave-packet multiply scattered back by the same potential. For higher J the VE cross sections are smooth and it is difficult to find resonances without knowing their location. The size of cross section at resonances exceeds 200A2 for elastic electron scattering from H2 molecule with J = 25. It goes high above smooth background which is below lA 2 . 3.1. Energies
and
lifetimes
The summary of all narrow resonances for both H^" and D^" is given in Fig. 2. The characteristic features can be understood in terms the shape of the adiabatic potential. For each J the width of resonances grows with the energy b which is clearly the quantum tunnelling effect. The decrease of the width and increase of energy with J is associated with the strengthening of the inner barrier and rising of the bottom of the well. Anomalous behaviour for positive energies is due to changes of the shape of the outer well with J. The isotopic effect is more-less trivial. The widths are lower for Dl^ since it is more difficult to tunnel through the barriers for heavier particles and the states are less separated in the energy.
b
W i t h exception of high resonances for lower J which are better understandable as boomerang oscillations (the inner barrier is too low).
350
10"'
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State energy (meV) Figure 2. Summary of energies and decay widths/lifetimes of narrow resonances in H 2 and D J . Energies are given relative to H + H - ( D + D ~ ) threshold.
351 4. Conclusions We have found strong theoretical evidence for the existence of the metastable states of molecular hydrogen anion with lifetimes reaching (is order. The long lifetime can be understood in terms of orbiting H + H - , with angular momentum of J — 21 — 27, protected by potential barrier form autodetachment at small R. Local complex potential approximation can not be used to get correct lifetime. The creation of the states in e - + H 2 or H + H - collisions is difficult although cross sections exceed 200A 2 . With the widths of 10~ 6 — 10 - 9 eV the production rates with any realistic experimental energy resolution would be very small. This could explain mixed success in experimental efforts to detect such species 12 . Recently the HJ with lifetimes of /is order have unambiguously been detected 1 . The species have been produced by sputtering of T1H2 and TiD2 surfaces with Cs + ions. More experimental evidence is needed to confirm that the anions produced in the experiments are identical with the ones proposed here. Acknowledgments We would like to thank prof. Xuefeng Yang (Dalian University of Technology, PR China) for bringing the problem of the existence of the metastable molecular hydrogen anion to our attention. This work has been supported by Grant Agency of Czech Republic as project no. GACR 202/03/D112. References 1. R. Golser, H. Gnaser, W. Kutschera, A. Priller, P. Steier, A. Wallner, M. Cizek, J. Horacek and W. Domcke, Phys. Rev. Lett. 94, 223003 (2005). 2. M. Cizek, J. Horacek and W. Domcke, ECAMP 2004 in Rennes, poster available on http://utf.mff.cuni.cz/~cizek/publications.html 3. P. L. Gertitschke and W. Domcke, Phys. Rev. A47, 1031 (1993). 4. M. Cizek, J. Horacek and W. Domcke, J. Phys. B31, 2571 (1998). 5. J. Horacek, M. Cizek, K. Houfek, P. Kolorenc and W. Domcke, Phys. Rev. A70, 052712 (2004). 6. J. Horacek, M. Cizek, K. Houfek, P. Kolorenc and W. Domcke, to be published. 7. W. Domcke, Phys. Rep. 208, 97 (1991). 8. M. Berman, C. Mundel and W. Domcke, Phys: Rev. A31, 641 (1985). 9. R. J. Bieniek, Phys. Rev. A18, 392 (1978). 10. E. Narevicius and N. Moiseyev, Phys. Rev. Lett. 84, 1681 (2000). 11. M. Allan, M. Cizek, J. Horacek and W. Domcke, J. Phys. B33, L209 (2000). 12. R. E. Hurley, Nucl. Instrum. MethodsllS, 307 (1974). W. Aberth, R. Schnitzer and M. Anbar, Phys. Rev. Lett. 34, 1600 (1975). Y. K. Bae, M. J. Coggiola and J. R. Peterson, Phys. Rev. A 29, 2888 (1984).
(E,2E) EXPERIMENTS WITH RANDOMLY ORIENTED AND FIXED-IN-SPACE HYDROGEN MOLECULES MASAHIKO TAKAHASHI1 Institute of Multidisciplinary Research for Advanced Materials, Tohoku University Sendai, 980-8577, Japan Institute for Molecular Science Okazaki, 444-8585, Japan This report aims to introduce our recent studies on ionization-excitation processes of the hydrogen molecule by means of the (e,2e) and (e,2e+M) methods. Following a description of the spectrometers employed, the experimental results will be presented to show how electron-molecule collision dynamics depends on each ionization process. The results involve the first observation of molecular frame (e,2e) cross section, demonstrating a geometry effect of molecular orientation on the (e,2e) scattering amplitude.
1. Introduction Through the last three decades of studies of binary (e,2e) spectroscopy or electron momentum spectroscopy [1], it has been demonstrated that the electron-impact ionization reaction at large momentum transfer is a sensitive probe for investigating the electronic structure of matter. The method involves detection of the two outgoing electrons in coincidence. Hence recoil momentum of the residual ion q and binding energy of the ejected electron £bmd can be determined with the help of the laws of conservation of energy and linear momentum. 9 = P0-P1-P2 £
bind =E0~E\-E2
(!) (2)
Here them's and £j's (j=0,l,2) are momenta and kinetic energies of the incident and two outgoing electrons, respectively. Under the high-energy Bethe ridge conditions [1-4], the collision kinematics can be described by the so-called electron Compton scattering that most nearly corresponds to collision of two free electrons with the residual ion acting as a spectator [5]. Then the E-mail address: [email protected]
352
353
momentum of the target electron before ionization p is equal in magnitude but opposite in sign to the ion recoil momentum q. P = -q = Pi+P2-Po
(3)
In this way (e,2e) cross section can be measured as a function of binding energy and target electron momentum, allowing one to look at individual molecular orbitals in momentum space. In spite of the remarkable feature of the method, however, binary (e,2e) spectroscopy has not yet reached the stage of full use of its ability for molecules. The reason for this may be twofold; (1) a more complete knowledge of the binary (e,2e) reaction dynamics is an ever-increasing necessity as sophistication of experiments increases, and (2) the present (e,2e) experiments measure averages over all orientations of gaseous molecules, resulting in enormous loss of information on electronic structure, anisotropy of the target wavefunction in particular. However, small cross section involved has been hindering one from developing (e,2e) spectroscopy satisfactorily. Under these circumstances, we have constructed two types of multichannel spectrometers [6,7]. The first spectrometer [6] enables one to measure binary (e,2e) cross sections of randomly oriented gaseous molecules with remarkably high sensitivity. The second spectrometer [7] has been developed for (e,2e) experiments with oriented molecules to discuss scattering in the molecular frame. In the present report, a brief account of the spectrometers will be given, followed by our recent collision dynamics studies on ionization-excitation processes of randomly oriented and fixed-in-space hydrogen molecules. 2. Multichannel (e,2e) and (e,2e+M) Spectrometers In Figure 1(a) we show a schematic diagram of the (e,2e) spectrometer [6]. Here the symmetric noncoplanar geometry is employed in which two outgoing electrons having equal scattering angles of 45° (#1=02=45°) and equal energies (Ei=E2) are detected in coincidence. In short, electron impact ionization occurs where an incident electron beam collides with a gaseous target from eight gasnozzles. Two outgoing electrons emerging at #i=$=45° are selected by a pair of entrance apertures extending over the electron azimuthal angle $\ and fc ranges from 70 to 110° and from 250 to 290°. Then the electrons are energy analyzed and detected by means of a spherical analyzer followed by a pair of positionsensitive detectors. Since a spherical analyzer maintains the azimuthal angles of the electrons, both energies and angles can be determined from their arrival positions at the detectors. Thus it is possible to sample (e,2e) cross section over
354
a wide range of binding energy and momentum simultaneously. This extensively improves coincidence count rates and statistical precision.
Figure 1. Schematic diagrams of (a) (e,2e) and (b) (e,2e+M) spectrometers.
Figure 1(b) shows a schematic drawing of the second spectrometer developed for (e,2e) experiments with fixed-in-space molecules [7]. The difference between the first and second spectrometers lies in the employment of seven channeltrons to detect fragment ions, which are placed at ion azimuthal angles ^,'s of 0, 45, 90, 150, 195, 240, and 285° in the perpendicular plane with respect to the incident electron momentum vector po- There are two key concepts behind this experimental setup. Firstly, in the symmetric noncoplanar scattering kinematics, the ion recoil momentum vector q is dominated by its component perpendicular to p0 when incident electron energy is sufficiently high. Secondly, if the molecular ion dissociates much faster than it rotates, the direction of fragment ion departure coincides with the molecular orientation at the moment of the ionization [8]. Thus, by detecting dissociation of molecular ion in the perpendicular plane, the angle of q from the molecular axis can be determined; molecular frame (e,2e) spectroscopy becomes possible in this manner, which can be designated by the (e,2e+M) method. Although the experimental setup limits the study on molecular orientation perpendicular to po. it enables one to look at molecular orbitals of linear targets in the three dimensional form if the experiment is performed at the high-energy limit where the plane-wave impulse approximation (PWIA) is valid [1-4].
355
3. Results and Discussion 3.1. (e,2e) Experiments on the Hydrogen Molecule In Figure 2 we show experimental momentum profiles or spherically averaged (e,2e) cross sections as a function of ion recoil momentum, which were obtained for the hydrogen molecule at impact energies of 1200, 1600 and 2000 eV [9]. Also included in the figure are associated PWIA calculations of Lermer et al. [10], which were digitized from the literature and folded with the momentum resolution of the spectrometer used in the present study. To make comparison between experiment and theory the experimental and theoretical momentum profiles for the primary ionization transition to the lsa g ground ion state are independently normalized so that their area becomes unity. The scaling factors obtained at individual impact energies are subsequently applied to the corresponding experimental and theoretical momentum profiles for the transitions to the 2sag and 2prju excited ion states. Thus all the momentum profiles in Figure 2 share a common intensity scale.
T—i—i—i—|—i—i—i—i—(—I
Momentum fa.u]
0.015
I—i—i—i—i—|—i—i—i—i—|—I—i—i—i—i—|—i—i—i—i—p
Momentum fa.u.l
Figure 2. Experimental momentum profiles of the hydrogen molecule for the transitions to the (a) lsag, (b) 2sag, and (c) 2po\, ion states, obtained at impact energies of 1200 (A), 1600 (O), and 2000 (•) eV. The lines are associated PWIA calculations by Lermer et al. [10].
356 It is evident from Figure 2(a) that shape of the lscrg experimental momentum profile does not vary with impact energy except for slight changes due to the finite momentum resolution effects and that agreement between experiment and PWIA is always satisfactory. This means that the primary ionization transition reaches the high-energy limit, where PWIA is valid, at impact energy of 1200 eV. On the other hand, for the 2sag and 2pau transitions that accompany a joint change of state of the two target electrons, it can be seen from Figures 2(b) and (c) that the experiments are substantially different from theory. The most striking feature of the results may be the shape of the 2pcfu momentum profile. While PWIA strictly requires the 2pau momentum profile to exhibit ungerade symmetry with no intensity at the momentum origin, the experiment shows gerade symmetry with a maximum near the momentum origin at every impactenergy examined. Difference in symmetry between experiment and PWIA is thus clear for the 2pau channel. In addition, difference in intensity between experiment and PWIA can be seen and it is considerably larger for the 2pc?u channel than 2sag. These observations are consistent with the previous studies of Lermer et al. [10,11] at impact energy of 1200 eV. To seek for the origin of the symmetry and intensity differences, second-order terms of the plane-wave Born series model were examined and the two-step (TS) mechanism [12,13] has been eventually identified as the principal source of the observations in the following manner [9]. The TS mechanism describes two sequential collisions of the projectile with different target electrons; the ionization-excitation can occur, for example, through the primary ionization process followed by a single excitation process to an excited ion state from the lsa g ground ion state. Since the excitation process involved should be dominated by forward scattering or pseudo photonimpact, symmetry property of contributions of the TS mechanism is essentially determined by the primary ionization process and would be always gerade, showing little dependence upon the final ion state produced. However, difference must appear in intensity, because the forward-scattering excitation transition to the 2pcru state from the lsa g state is optically allowed whereas that to the 2sag state is optically forbidden. Thus for the 2pau channel the experimental (e,2e) cross section can be remarkably enhanced by the TS mechanism and the symmetry difference would arise. These findings strongly suggest that a more complete knowledge of the range of validity of PWIA would be required for studies on satellite structures of atoms and molecules, those with small pole strengths in particular.
357 3.2. (e,2e+M) Experiment on the Hydrogen Molecule An (e,2e+M) experiment on the hydrogen molecule was performed under experimental conditions where impact energy of 1200 eV and a retarding voltage of 2.5 V were employed [14]. The use of the 2.5 V retarding voltage ensures that axial recoil fragments H+ from all the excited ion states are detected but fragments from the lsa g ground ion state with up to 1 eV kinetic energy are entirely removed from the detection. Molecular frame (e,2e) cross sections obtained for the 2sag and 2pau transitions are shown in Figure 3, where they are presented so that distance from the origin to each data point represents the relative magnitude of the cross section with the molecular axis drawn in the vertical direction. Here, by taking advantage of the inversion and rotation symmetry of the molecular frame (e,2e) cross section about the molecular axis for the homonuclear target, the results are plotted so as to give the 24 data points whereas the measurement was performed at only seven ion azimuthal angles. To our best knowledge this is the first observation of molecular frame (e,2e) cross section [14].
Figure 3. Molecular frame (e,2e) cross sections of the hydrogen molecule for the transitions to the (a) 2sag and (b) 2pa„ ion states, obtained at impact energy of 1200 eV. The arrows represent the direction of the molecular axis. The solid lines are theoretical predictions of PWIA calculations.
Although the statistics of the data leave much to be desired, one can see transition specific anisotropy of molecular frame (e,2e) cross section. Geometry effects of molecular orientation on the (e,2e) amplitudes are evident and the 2sCTg and 2pau experiments are strikingly different from each other. The angular distribution of the former experiment is relatively isotropic, while that of the latter shows maxima along the molecular axis. This can be understood by considering the role of the first-order PWIA mechanism that probes electron
358
momentum densities of the 2sag and 2pau excited components of the target wavefunction. Indeed, PWIA calculations, shown by solid lines in the figure, predict such angular distributions which reproduce qualitatively the shapes experimentally observed. However, difference in intensity between experiment and PWIA can be seen, especially in the 2pou channel. This is consistent with the (e,2e) studies on the hydrogen molecule [9,10]. Since the intensity difference between experiment and PWIA is a rough measure of contributions of the TS mechanism, the 2pau result of the (e,2e+M) experiment could be used for studying geometry effects of molecular orientation in the mechanism. In this respect, one may take notice of a tendency that the two outgoing electrons seem to escape preferentially so as to leave the ion recoil momentum vector q near the direction parallel to the molecular axis rather than perpendicular. Unfortunately, poor statistics of the present data make it difficult to discuss such geometry effects and hence we leave the issue for later experiments with improved data. 4. Summary Our spectrometers have demonstrated that the capability to measure energy and angular correlations among the charged particles simultaneously is a useful advance for (e,2e), together with the show case experiments on the hydrogen molecule. Furthermore, molecular frame (e,2e) spectroscopy has been proposed based on the (e,2e+M) method. In this report it has been used to explore a geometry effect of molecular orientation on the (e,2e) scattering amplitude of the hydrogen molecule and how it depends on nature of the final ion state. Another promising direction would be to perform similar experiments for various linear molecules at the high-energy limit, in order to look at molecular orbitals in the three-dimensional form. We believe that further attempts along this line would develop unexploited possibilities of (e,2e), opening the door for detailed studies of bound electronic wavefunctions of molecules as well as of stereodynamics of electron-molecule collisions. Acknowledgments The author gratefully acknowledges his colleagues in the (e,2e) and (e,2e+M) studies on the hydrogen molecule; Prof. Y. Udagawa and Dr. N. Watanabe at the Tohoku University, Prof. Y. Khajuria at the IIT Madras, and Prof. J.H.D. Eland at the Oxford University. The author thanks the organizing committee for giving him the opportunity to be involved in ICPEAC at Rosario. This research was partially supported by the Ministry of Education, Science, Sports and
359
Culture, Grant-in-Aid's for Scientific Research (B), 13440170, 2001 and for Exploratory Research, 14654069, 2002. References 1. I. E. McCarthy and E. Weigold, Phys. Rep. C27, 275 (1976). 2. C. E. Brion, Int. J. Quantum Chem. 29, 1397 (1986). 3. M. A. Coplan, J. H. Moore and J. P. Doering, Rev. Mod. Phys. 66, 985 (1994). 4. E. Weigold and I. E. McCarthy, Electron Momentum Spectroscopy (Kluwer Academic/Plenum Publishers, New York, 1999). 5. R. A. Bonham and H. F. Wellenstein, in: B. Williams (Ed.), Compton Scattering (McGraw-Hill, New York, 1977). 6. M. Takahashi, T. Saito, M. Matsuo and Y. Udagawa, Rev. Sci. Instrum. 73, 2242 (2002). 7. M. Takahashi, N. Watanabe, Y. Khajuria, K. Nakayama, Y. Udagawa and J.H.D. Eland, J. Electron Spectrosc. Related Phenom. 141, 83 (2004) 8. R. N. Zare, Mol. Photochem. 4, 1 (1972). 9. M. Takahashi, Y. Khajuria and Y. Udagawa, Phys. Rev. A68, 042710 (2003). 10. N. Lermer, B. R. Todd, N. M. Cann, Y. Zheng, C. E. Brion, Z. Yang and E. R. Davidson, Phys. Rev. A56, 1393 (1997). 11. N. Lermer, B. R. Todd, N. M. Cann, C. E. Brion, Y. Zheng, S. Chakravorty and E. R. Davidson, Can. J. Phys. 74, 748 (1996). 12. T. A. Carlson and M. O. Krause, Phys. Rev. 140, A1057 (1965). 13. R. J. Tweed, Z. Phys. D23, 309 (1992). 14. M. Takahashi, N. Watanabe, Y. Khajuria, Y. Udagawa and J.H.D. Eland, Phys. Rev. Lett. 94, 213202 (2005).
INITIAL AND FINAL STATE CORRELATION EFFECTS IN (E,3E) PROCESSES G. QASANEO Departamento de Fisica, UNS and CONICET, 8000 Bahia Blanca, Argentina S. OTRANTO Physics Department, University of Missouri-Rolla,Rolla MO 65401, USA Departamento de Fisica UNS, 8000 Bahia Blanca, Argentina K. V. RODRIGUEZ Departamento de Fisica, UNS and CONICET, 8000 Bahia Blanca, Argentina In this work we investigate the process of double ionization of He by electron impact. The four-body continuum is described by a product of three Coulomb functions and the electron-electron correlation is included through distortion factors and effective charges. The initial state of the system is described by a product of a plane wave for the projectile and Hylleraas-//te functions for the bound electrons. The Hylleraas-/iie functions here used satisfy the Kato cusp conditions at all the two-body coalescence. The fivefold differential cross section for double ionization of He is evaluated with the functions introduced. The effect of the correlation both in the initial as well as in the final channel are studied.
1. Introduction The ionization of atoms by charged particle impact is one of the most important processes studied in atomic physics. The development of new experimental techniques has lead to what is known as kinematically complete experiments, where the momenta of all the ejected particles after a collision process are detected. In the (e,3e) experiments, the momenta of the two emitted and the scattered electrons are detected in coincidence (see e.g. [1]). A proper theoretical description of such experiment implies the definition of adequate wave functions for the initial and final collision channels as well as the formalism defining the cross sections [2]. The purpose of our work is to partially contribute on these issues. In section 2 we introduce a set of functions both for the initial and final channels and in section 3 we apply the models of section 2 to the double ionization of He
360
361 by electron impact. Calculations at high and intermediate energies are performed and compared with recent experimental data. Some conclusions are drawn at the end of section 3.
2. Theory The FDCS for the double ionization of He is given by u
=
dQ.]d0.1dQ.idE1dEl
/ _ \ 4 /CJ/CT/C ^yK 1K1KL, ' kQ
,2
(1)
v
Here ko and kj are the momenta of the incoming and outgoing projectile, k2 and k3 are the momenta of the ejected electrons after the collision. dQi, dfi 2 and dfi 3 denote, respectively, the solid angle elements for the scattered and the two ejected electrons. The transition matrix Tp is given by Z 1 1 7>=(«F- • — + — + — r
1
n r,3
(2*r
(2)
-e"°>.\
Here *F" is defined by the product of three Coulomb wave functions (one per each electron-nucleus interaction) and a Coulomb distortion function for the ejected electrons dynamics, that we shall call C4W. The Sommerfeld parameters included in the functions are defined using the following set of charges Z,=-Z+ Z,=-Z +
/'
,+ / '
Z„-l + (l--^W)cM* B --i^coi*„, l ,
vn(v, +v 2 ) v„(v,+vjv ."'
"12 ( v l + V 2 )
+
^ v„+va)
(i-7a)-J^ "
, Z,=-Z+
V2,(v2+V,)
'
v,j+v12
"'
(3)
, + (l-Z 2 1 )
V„(v, + V j )
"
V23(v2+V,)
The function a(E23) is defined in terms of the sum of ejected electrons energies, E23 and the He ground state energy EHeby a(E23)=EHe/(E23+EHe). These charges are designed to fulfill the three- and four-body Wannier limits and are an extension of the work of Berakdar [3]. For the He ground state
+ ^e-°M">
<pa„ = 1.396 e z ( ' "•' ^ ^ f lfj^ X
(4)
+0.0\4e-°'""-] + cM+'lVcM+rlVvlrl
+cm,ri]
where c2oo=0.127, c002=0.000487, c22o=-0.209, cm=0.023. The mean energy given by
362
These functions satisfy the Kato cusp conditions at all the two-body coalescences. 3. Results and conclusions The FDCS of Eq. (1) for the double ionization of He by incoming electrons with an initial energy of 5599 eV and ejected electrons at 10 eV [1] is shown in Fig. 1. We use our C4W model for the final channel and the functions of Eq. (4) for the initial state. The results obtained are compared with two cases of the set of absolute data of Lahmam-Bennani [2]. We choose the cases where one of the electrons is ejected at 291° and 319° respectively. As we can see the results obtained with C4W-^// are in good agreement with the experimental data. On the other hand, the FDCS obtained with the C4W-^GS5 model disagree in magnitude with those obtained with
?°'.
li
UJ
/ \ 240
300
Figure I. FDCS for the double ionization of He. The projectile energy is 5599 eV and the scattering angle 0.45°. [1]. The ejected electrons are emitted with 10 eV each. The dots represent the absolute experimental data of Ref. [1]; full line: C4W-
In Fig. 2 we show our calculations for the double ionization of He by electrons with an energy of 601 eV [6]. The projectile scattering angle is 1.5° and the ejected electrons have an energy of 11 eV. [6]. The results obtained with the C4W-^// are compared with the experimental data of Lahmam-Bennani [6] for the cases where one of the electrons is ejected at 200° and 280°. As we can see from the figure the C4W model shows a strong departure from the First Born
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approach and improves the description as compared with the Born-C3. A similar description is found for all the other cases discussed in Ref [6].
Figure 2. FDCS for the double ionization of He. The projectile energy is 601 eV and the scattering angle 1.5°. [6]. The ejected electrons are emitted with 11 eV each. The dots represent the relative experimental data of Ref. [6]; full line: C4W-ipn; dashed line: C3-
In conclusion, we introduced a set of functions to describe both the initial and final channel for the double ionization of He by electron impact. For the initial channel a function with similar characteristics to the Pluvinage proposal and a Hylleraas-//£e function were given. For the final channel a product of three Coulomb functions times a distortion factor all of them with effective charges was defined. The C4W model has the proper three- and four-body Wannier limits. We applied these functions to the evaluation of FDCS for the (e,3e) process. According to the results obtained for the case of high energy projectiles, the lack of symmetry between the initial and final channels Hamiltonians is responsible for the magnitude disagreement between the calculation and the experimental data. On the other hand, for intermediate energies, where deviations from the Born approximation should be expected and are clearly obtained, the C4W model here introduced partially describes the structure presented by the experimental data of Ref. [6]. Acknowledgments This work has been supported by PICTR 2003/00437 of the ANPCYT (Argentina) and PGI 24/F027 Universidad Nacional del Sur (Argentina). References 1. 2. 3. 4. 5. 6.
A. Lahmam-Bennani et al, Phys. Rev. A 59, 3548 (1999). J. Berakdar et al, Phys. Rep. 374, 91 (2003). J. Berakdar, Phys. Rev. A 55,1994 (1997) K. V. Rodriguez and G. Gasaneo, in press to J. Phys. B (2005). G. Gasaneo et al, to be published Lahmam-Bennani, et al., Phys. Rev. A 67, 010701 (2003); S. Elazzouzi et al J. Phys. B 38, 1391(2005)
AN (e,y2e) EXPERIMENT FOR SIMULTANEOUS IONIZATIONEXCITATION OF HELIUM TO THE He+(2P)2P STATES BY ELECTRON IMPACT A. DORN, G. SAKHELASHVILI, t C. HOHR, AND J. ULLRICH Max-Planck-lnstitut fur Kemphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany A.S. KHEIFETS, J. LOWER Research School for Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia K. BARTSCHAT Department of Physics and Astronomy, Drake University, Des Moines, 1A 50311, USA Simultaneous ionization and excitation of helium atoms by 500 eV electron impact is observed by a triple coincidence of an ionized slow electron, the recoiling He* ion, and the radiated vacuum ultraviolet (VUV) photon (X = 30.4 nm). Kinematically complete differential cross sections are presented for the He+(2p)2P final ionic state, demonstrating the feasibility of a quantum mechanically complete experiment. The experimental data are compared to predictions from state-of-the-art numerical calculations. For large momentum transfers, a first-order treatment of the projectile-target interaction can reproduce the experimental angular dependence, but a second-order treatment is required to obtain consistent magnitude.
1. Introduction Fundamental atomic four-body reactions as they occur in electron helium collisions where both target electrons change their state are benchmark systems for state-of-the-art theories. The dynamics of this process is governed by electronic correlation in the initial and final states and/or by higher order contributions in the projectile target interaction. For low projectile velocities approaching the threshold of the process under consideration three strongly interacting electrons move in the nuclear Coulomb potential, a situation which presently can not be handled by any theory in full detail. Double excitation of both helium electrons [1] or, the process discussed here, simultaneous ionization of one electron and excitation of the second electron, are particularly interesting. Present address: Tbilisi State University, Chavchavadze Ave. 3, 0179 Tbilisi, Georgia.
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This is because the number of continuum electrons in the final state is reduced with respect to double ionization which makes the treatment tractable for many theoretical models. Here we present an experimental investigation for ionization and simultaneous excitation, e-0(kt>) + He-+He+(2p)2P(kR) + e;(ka) + e;(kb)<
(1)
where we demonstrate the feasibility of a so called "perfect experiment" [2, 3] for this process, meaning that both, the kinematics of the collision and the quantum mechanical state vector of the excited ion are fully determined [4]. For a given momentum ICQ of the projectile the kinematics of the collision is fixed by measuring at least two momentum vectors of the final state particles, be it the electron momenta ka and h or one electron momentum and the recoiling ion momentum kR. The quantum mechanical state vector of the excited ion can be determined by measuring either the angular emission pattern of the fluorescence radiation emitted in the decay He*(2p) 2P^>He+(\s) 2S + y (A = 30.4nm),
(2)
or by measuring its Stokes parameters. Thus a triple coincidence experiment is required which was not feasible to date due to the discouragingly low detection efficiencies of traditional multi-coincidence techniques. Pioneering double-coincidence studies performed for He+(n = 2) states can be grouped into (e,2e) and (e,ye) investigations, either summing the contributions from the 2s and 2p states of He+ or leaving the collision kinematics undefined by not detecting the second electron. 2. Experiment The experiment was performed at the Max-Planck-Institute fur Kernphysik in Heidelberg using a reaction microscope, a combined electron and recoil ion momentum spectrometer which has been extended by two large-area (80 mm diameter) multi-channel plate detectors for detection of the emitted vacuum ultraviolet radiation [4]. Measuring in coincidence the momentum vectors of a low energy electron (Eb < 12.5 eV), kb, and the recoiling ion, kR, the collision kinematics was determined by momentum conservation: ka = k0 - &t>- kR. The main experimental challenge is posed by huge background signal rates. In this respect the decisive step forward of the present set-up is the relatively large triple coincidence efficiency of 0,16 % (the product of the detector solid angles and their detection efficiencies) which allows for projectile beam currents as small as I = 60 pA, strongly reducing the background signal. In addition, we can
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use energy and momentum conservation to further discriminate against random coincidences.
3. Results In Figure 1 experimental triple differential cross sections are shown for electron emission (Eb = 5 eV ± 2 eV) into the scattering plane for two different values of the momentum transfer q = 0.6 a.u. and q = 1.2 a.u.. In addition the results of two different theoretical models are shown in which the interaction between the fast projectile and the target is treated perturbatively, while the ejected-electron - residual-ion interaction (effectively electron scattering from He+ with appropriate boundary conditions for ionization) is handled via convergent multi-channel expansions using momentum-space close-coupling (CCC) or a configuration-space R-matrix with pseudo-states (RMPS) approach. These methods yield nearly identical first-order results [5], but they differ in the
TDCS
Figure 1. Triple differential cross sections (TDCS), d3a/(dn,d£2bdEb), for Eo = 500 eV as a function of the slow-electron emission angle 8b, measured with respect to the projectile beam forward direction. The energies Eb and the momentum transfers |q| are indicated in the diagrams. Continuous lines: second-Bora RMPS calculation. Dashed line in (a): second-Born CCC calculation. Dotted line in (b): first-Born CCC calculation, multiplied by 2.5.
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extent to which second-order effects in the projectile-target interaction are incorporated. So far the CCC method only accounts for dipole interactions in second order [6], while the RMPS implementation includes monopole, dipole, and quadrupole terms [7]. Consequently, the second-order CCC approach is currently limited to small momentum transfers. The experimental data are not absolute but the data for different momentum transfers are cross normalized. Therefore the experimental data are scaled with one common factor giving the best agreement of the overall magnitude of the second order theories at q = 0.6 a.u.. While for this case neither of the theory curves is in perfect agreement with the experimental cross section, both are very similar in absolute magnitude and both reproduce the rough course of the measured data. Interestingly for large momentum transfer of q = 1.2 a.u., where only the first order CCC result is available, again the shape of the measurement is reproduced by both theories but now the 1. Bom CCC curve has to be multiplied by 2.5 in order to fit the magnitude of both, the 2. Bom RMPS calculation and the experimental values. From this observation and from comparison with the 1. Bom RMPS result (not shown here) the conclusion can be drawn, that the second order contribution is relatively strong. Surprisingly it manifests itself mainly in the magnitude, but not in the shape of the cross section. In future experiments the angular distribution of the emitted fluorescence radiation will be analysed. In this way the excitation amplitudes and their relative phases will be accessible with the final goal to perform a "perfect experiment".
Acknowledgments This work was supported, in part by the Australian Research Council (JK, ASK), and the United States National Science Foundation (KB). References 2. V.V. Balashov and I.V. Bodrenko, J. Phys. B 32, L687 (1999). 3. N. Andersen and K. Bartschat, Polarization, Alignment, and Orientation in Atomic Collisions, (Springer, New York 2001). 3. N. Andersen and K. Bartschat, J. Phys. B 37, 3809 4. G. Sakhelashvili et al., Phys. Rev. Lett. 95,033201, (2005) 5. A.S. Kheifets, I. Bray and K. Bartschat, J. Phys. B 33, L433. 6. A.S. Kheifets, Phys. Rev. A 69, 32712 (2004). 7. Y. Fang and K. Bartschat, J. Phys. B 34, 2747 (2001).
COLLISIONS INVOLVING EXOTIC PARTICLES
ANTIHYDROGEN IN THE LABORATORY Michael Charlton Department of Physics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, UK We review progress in the synthesis of antihydrogen, starting with the first experiments that created relativistic anti-atoms via pair production with positron capture in antiproton-atom collisions. More recent work has seen antihydrogen formed under controlled conditions by the merger of cold antiprotons with positron plasmas in a Penning trap environment. These studies have allowed some information to be extracted on the states of antihydrogen which are formed and the formation mechanism(s), the (positron) temperature dependence of the antihydrogen reaction and the spatial and speed/energy distributions of the emergent anti-atoms. This work will be discussed here. A newly tested method of antihydrogen formation based upon interactions of antiprotons with excited state positronium atoms will also be described. We attempt to anticipate the near future for antihydrogen research, with the main goal being to perform spectroscopy on trapped anti-atoms for precision comparison with transitions in hydrogen. The physics motivations for undertaking these challenging experiments will be briefly recalled.
1 Introduction and Motivation The recent creation of low energy antihydrogen in the laboratory [1,2] was a landmark in atomic physics research. This achievement has already spawned an explosion of theoretical activity in cognate areas of atomic and plasma physics, which has been fuelled by further experimental advances by the ATHENA [3-7] and ATRAP [8-10] collaborations. In this article we can only attempt a selective review of this fast-evolving literature. More comprehensive reviews have been given elsewhere recently [11,12]. The main physics motivations for antihydrogen production lie in the promise for tests of CPT symmetry and antimatter gravity. CPT is a theorem in local quantum field theory in which the three quantum mechanical transformations of C (charge conjugation), P (parity) and T (time reversal) are combined. There are no known violations of this symmetry (see e.g. [13] for a summary of limits), but expectations are that modern theories of particle physics, that treat particles as extended objects rather than points, will naturally contain CPT violation. In this respect, precise hydrogen-antihydrogen comparisons may provide an important testing ground for new physics. Gravity remains the "odd one out" in terms of Grand Unification. Indeed, as is well known, there is currently no acceptable quantum theory of gravity. Furthermore, we have no information on the gravitational interaction of antimatter. For instance, all we can glean from CPT is that antihydrogen will fall as fast towards a hypothetical anti-Earth as hydrogen does towards Earth. Given the current state of affairs either quantum mechanics or general relativity (or both of them) are incomplete. At the very least this makes gravity on antimatter an interesting phenomenon to study.
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2 High Energy Antihydrogen The first demonstration of antihydrogen in the laboratory was forthcoming in 1996 from the PS210 experiment which was undertaken at the (now-defunct) Low Energy Antiproton Ring (LEAR) at CERN [14], following an earlier suggestion [15]. In this work a circulating antiproton beam at an energy of 1.2 GeV intersected a gas jet target of xenon atoms. In rare events, the interaction of the antiproton with the xenon nucleus lead to pair creation, but with the positron emerging bound to the antiproton. (At the chosen interaction energy this process has a cross section of around 1 nb or 10"33 cm2 for the xenon target.) Once formed, the antihydrogen atoms were separated from the antiproton beam at the first bending magnet after the interaction region and various detectors were used to register its presence and separate it from background signals. In all, a total of 9 antihydrogen atoms were unambiguously identified. This experiment was followed by another at Fermilab [16] in which a background-free sample of about 60 antihydrogen atoms were detected following antiproton-hydrogen collisions at various energies between 5.2 and 6.2 GeV. Both of these experiments produced tiny quantities of antihydrogen per antiproton interaction, and resulted in the anti-atoms being spaced from one another by large and unpredictable intervals and formed at kinetic energies (and with energy/momentum spreads) too high to be useful for further experimentation. The stage was set for cold antihydrogen. 3 Production of Cold Antihydrogen This field has had a long gestation period. Initial efforts and aspirations can be traced back to the mid-to-late 1980's. That decade saw great strides in understanding the physics behind the creation of low energy positron beams and in their applications (see e.g. [17, 18]). Crucially, rapid progress was also made around this time by Gabrielse and co-workers in trapping antiprotons and then cooling them to cryogenic temperatures [19, 20]. These advances facilitated beautiful experiments that measured the charge-to-mass ratio of the antiproton [e.g. 21, 22] and also paved the way for antihydrogen formation. Parallel experiments at LEAR were undertaken in the early 1990's in which large antiproton clouds were assembled [23, 24]; this effort was eventually to result in the ATHENA venture. It was also early in this era when much effort was expended in devising antihydrogen production schemes. These included the nested Penning trap approach [25] (used by both ATRAP and ATHENA) and the antiproton-positronium method (e.g. [26-28]); see below. The nested Penning trap system used by ATHENA is illustrated in Fig. 1. (Recall that, in a Penning trap, the particles are confined axially by the applied electric field and radially by a magnetic field, typically of several Tesla in strength, applied along the axis of the system.) The on-axis electric potential, provided by the voltages applied to the cylindrically symmetric electrode system was used to simultaneously confine the positrons and antiprotons. (Details of the
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K ^ * * ^ * ? ^ . ^-^"?f%>'.^ ^
\
\. J \m$& fast
Figure 1: (a) Schematic illustration of the ATHENA nested well apparatus with pion and y-ray detectors included, (b) On-axis nested well potential showing the antiproton well (dashed line) before mixing,
capture, cooling and manipulation of the antiproton and positron swarms can be found elsewhere [1, 2, 11, 12, 29, 30].) In ATHENA around 104 antiprotons were released into a positron plasma containing about 108 positrons at a density of - 2 x 108 cm"3. The nested well system used (Fig. 1) meant that they entered the positron cloud at a kinetic energy of about 30 eV, whereupon cooling occurred and antihydrogen formation ensued [5]. The relevant particle parameters for ATRAP are typically 4 x 105 positrons at a density of ~ 2 x 107 cm"3 [31] and 2 x 105 antiprotons. The two experiments used quite different, though complementary, methods to identify antihydrogen production. Once formed, any antihydrogen that survives the plasma electric fields, and collision processes therein, will migrate out of the charged particle traps. Most antihydrogen atoms will drift to the electrode walls of the traps in the immediate vicinity of their point of creation and annihilate on contact. However, some will, presumably mainly due to solid angle considerations, travel along the axis of the apparatus. These anti-atoms can, depending upon their binding energies, be field ionized by appropriate electric fields associated with potential wells that can also be used to re-trap any liberated antiprotons. The latter can be ejected as required and used as a proxy for antihydrogen formation.
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ATHENA used the annihilation of antihydrogen to generate their signature. Put simply, such events produced a few charged pions from the annihilation of the antiproton and a pair of back-to-back 511 keV y-rays following the annihilation of the positron (see Fig. 1). A purpose-built imaging detector [32, 33] able to locate the antiproton vertex (i.e. the point of annihilation) was deployed, and the demand made that this event be accompanied by the characteristic y-ray signal emanating from the same point at the same time. Later, ATHENA found that other, less stringent, proxies could be used to pinpoint antihydrogen via a capability to spatially distinguish between annihilations due to antihydrogen and to bare antiprotons [3 4]. In essence the ATHENA detection technique was a global technique in the sense that all emitted antihydrogen could be detected, more-or-less independently of its binding energy. This to be contrasted with the method developed by ATRAP that relied upon field ionization of suitably weakly bound states. The disadvantage of (presumably) only sampling a small fraction of the antihydrogen produced was mitigated by the degree of state- (or more properly, binding energy) selectivity offered by this technique. (Recall that the binding energy, Eb, (in meV) and stripping electric field, F, (in Vcm1) are related by Eb = (0.38)(F)"2 [34].) In the ATRAP case antihydrogen was formed in a nested trap arrangement by repeatedly driving the antiproton cloud through the positron plasma; thus some axial emission preference may have ensued. 4
Physics with Cold Antihydrogen
In the period since the creation of cold antihydrogen, a number of important studies have been undertaken using the nested Penning trap approach. We describe these briefly, taking the ATHENA and ATRAP results separately for ease of presentation. In an important study, ATHENA showed that around 65% of antiproton annihilations it observed during positron-antiproton mixing at 15 K (the positron base temperature) were due to antihydrogen [4]. In 2003, instantaneous antihydrogen formation rates of over 400 s"1 were observed; see Fig. 2. ATHENA has made the most complete study to date of cooling of antiprotons immersed in a positron plasma, correlated with antihydrogen formation [5]. By analyzing the time-dependence of the energy distribution of the antiproton swarm once it had been released from its holding well (see figure 1), and comparing changes in this distribution with the behaviour of the antihydrogen signal, a number of important conclusions were forthcoming. (Note that in this work the positron plasma typically has a radius of 3 mm, a length of 30 mm and a density of just over 10s cm"3 [35, 36].) When the positrons are cold (typically 15 K) the antiprotons which have good physical overlap with the
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0
2
4
6
8
10
12
14
Interaction time (s) Figure 2: Antihydrogen formation rates from ATHENA; see text.
positron plasma cool within about 10-20 ms to energies where antihydrogen formation proceeds efficiently; see the inset of Fig. 2. On a longer timescale (> 1 s) a slower cooling of antiprotons occurs leading to a continued, though diminishing, production of antihydrogen. This behaviour is most likely associated, as detailed in [5], with the cooling of antiprotons initially radially separated from the antiproton cloud. This is probably caused by the slow radial expansion of the positron plasma. A further effect is observed after about 500 ms when some of the antiprotons become axially separated from the positrons and occupy the lateral wells on either side of the plasma. This is thought to be due to ield ionization of Rydberg antihydrogen at the longitudinal extremes of the nested potential; see [5] for further details and discussion. Given the capability of ATHENA to manipulate the temperature of their positron plasma, Tm and to record the change in temperature [35, 36], a study of the rate of antihydrogen production versus Te was undertaken [7]. This was motivated by a desire to try to isolate the mechanism(s) responsible for antihydrogen formation since it is well known (see e.g. [11] and references therein) that the two main reactions have quite distinct dependencies upon Fe. In particular, direct radiative capture, which is expected to lead to more tightly bound antihydrogen atoms, should vary as Fe"0,63, whilst the three-body reaction (two positrons, plus an antiproton), which predominantly populates high-lying states, should display a steep TJ4'5 behaviour and dominate at low temperatures. ATHENA derived antihydrogen production rates using three different proxies [7]. The sharp increase at low temperatures expected for the three-body reaction was not observed in any of the data and a i t to their trigger rate data yielded a power law of T^"im'2 [7]. The apparent accord with predictions for radiative combination is, however, shattered when the absolute rate of antihydrogen formation in ATHENA (see Fig. 2) is compared with expectations* which turn out to be about an order of magnitude lower [7]. This puzzle needs to be
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resolved, but clues lie, as pointed out by Robicheaux [37], in the nature of the experiments wherein the antiprotons pass in and out of the positron plasma such that the three-body process is periodically arrested. The characteristic 7V4'5 behaviour is that expected for an antiproton in thermal equilibrium with a positron plasma of infinite extent - clearly this situation is not mirrored experimentally. Further experimental and theoretical work in this area is anticipated. ATHENA has recently published a study of the spatial distribution of cold antihydrogen formation [6]. They find that the distribution is independent of Te and is axially enhanced. This has indicated that antihydrogen is formed before the antiprotons reach thermal equilibrium with the positron plasma. A careful analysis of the data [6] provided a lower limit on the temperature of the antihydrogen along the axis of the trap of 150 K, with clear retrograde implications for prospects for trapping (section 6).
i I I 0.2 0,0 0.0
\
n
ZOO meV
0.2
0.4
OS
0,8
t.O
frequency of osculating prsirtnpping field in MHz
Figure 3. The ratio of signals between normalization and ionization wells (see text) at various frequencies of the oscillating pre-stripping field. Unity corresponds to no pre-field. The quoted energies correspond to ATRAP fits [9] for the kinetic energy of the emitted antihydrogen.
The ATHENA study [6] is in broad accord with results from ATRAP [9] who produced a first measurement of the velocity of antihydrogen atoms emitted in their driven production technique. Weakly bound states were field ionized in detection wells and counted following ejection onto an annihilation target. Clear evidence, based upon observed signals and solid angle considerations, that this production technique resulted in preferential axial emission of antihydrogen has been given [9]. In essence the ATRAP velocity measurement was achieved by superimposing an a.c. field onto a d.c. analyzing field located between the antihydrogen production region and the detection well. As the frequency of the a.c. field was increased, fewer of the weakly bound atoms travelled quickly enough to avoid ionization. Gabrielse et al. [9] developed a simple model to relate the number of antihydrogen atoms they detected at various r.f. frequencies to their kinetic energy. Results are summarized in Fig. 3 where a best fit is found with a kinetic energy of around 200 meV. We do not have the space here to discuss the implications of this result (the interested reader should consult the original publication [9]), but further work is clearly motivated.
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As previously indicated, the ATRAP field ionization method can be used to derive information on the state-distribution (at least of the weakly bound states), or more properly perhaps on their binding energies. This was first done by Gabrielse et al. [8], who compared the ratio, R, of the signals between so-called normalization and ionization wells. The state analysis was performed by varying the electric field, F, encountered by antihydrogen on its way to the ionization well, whilst keeping the conditions the same with respect to the normalization well. Figure 4 shows their data indicating a linear drop-off with electric field. This implies a flat distribution for dR/dF which, together with the (magnetic field free) result that F and the principal quantum number, n, are related by F = l/16n4, suggests that the shape of the w-distribution, dR/dn, is proportional to n'5. Further work is needed to interpret this result, but the production rate and the observed states firmly point to the importance of the three-body reaction in promoting antihydrogen formation. 1,6
(a)
k
1.2 0.8 0.4
§ u
0.0 0.02
_+l, ^
20 40 60 80 state-analysis sleclric field in Wcm
|c) class.cal
0,10
,. h|ttpcl blue-sNfted
I
•- !
0.05 0,00 40
rpd
\ 1 ,1
50
60
70
80
90
n
Figure 4. First state-distribution information for weakly bound antihydrogen atoms [8].
Most recently, ATRAP have extended their field ionization technique to allow identification of more deeply bound antihydrogen atoms [10]. The binding energies derived (though given in terms of an effective radius of the anti-atoms) were sufficiently high (radii, concomitantly low) to identify these as antihydrogen atoms beyond the guiding centre atom regime [38]. The main implication here is that such bound states are expected to decay rapidly, radiatively, to the ground state. Again, following this first observation [10] further work is necessary. Antihydrogen from Antiproton-Positronium Interactions The utility of charge exchange in interactions of antiprotons with positronium as a source of antihydrogen was first suggested by Deutch and co-workers [26, 27].
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An experimental demonstration of the feasibility of the reaction was confirmed in the charge-conjugate proton-positronium system [39]. Important extensions to the ideas relating to this scheme were forthcoming when it was realized that reaction rates were dramatically enhanced if excited states of positronium could be used [40], and that for sufficiently high-lying states antihydrogen recoil (and thus kinetic energy) would be minimal [41]. An ingenious method to implement interactions of excited state positronium with antiprotons was suggested some time later by Hessels et al [42]. It involved a double Rydberg charge exchange scheme. First, laser-prepared caesium atoms, typically in a nominal state of principal quantum number around n = 50, would be allowed to interact with a trapped 4 K positron cloud. Positronium formation by charge exchange into bound states with zero energy defect (i.e. binding energies similar to the n = 50 caesium atoms corresponding to about n = 35) would then occur. A further interaction of the Rydberg positronium with a nearby antiproton cloud could lead to antihydrogen formation in states around n = 45. This weakly bound state could then be field ionized in a nearby well. This sequence is illustrated schematically in figure 5.
?**« \ . 5 ' positron **&
Ps* P®* w* v
'
' >#. * \JV
*' >A-i H
Vp
;1 \ J
^P
• detection trap
cesium oven Figure 5. Schematic of the ATRAP laser-controlled antihydrogen experiment [43].
Very recently, ATRAP have observed this reaction sequence [43]. In a proof-ofprinciple experiment, 14 ± 4 antihydrogen atoms were detected when lasers were tuned to produce caesium in the 37D (without magnetic field) state (equivalent binding energy around 10 meV). No signal was observed with the lasers detuned or without positrons present. The importance of this reaction in promoting the creation of truly cold antihydrogen (suitable for capture in magnetic gradient traps) was alluded to earlier in this section and experimental verification will be an important next step.
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Open Questions and the Future
It is clear that to perform spectroscopy on antihydrogen to rival current precisions with hydrogen (around 1 part in 1014 [44]) a trapped ensemble of anti-atoms will need to be created. If gravity measurements on antihydrogen are to be contemplated very low temperatures for the anti-atom (~ mK) are necessary. How to achieve the latter is by no means clear (though some interesting, but very challenging, suggestions are beginning to emerge; see e.g. [45]), but it is likely that trapped antihydrogen will be involved. Thus, a major challenge for the future of the field is to trap antihydrogen. This will probably involve a magnetic gradient device employing a quadrupole [46] or higher-order pole configuration. The main question here is compatibility of the inherent magnet gradients of the neutral trapping fields with the stability of the charged particle clouds and plasmas [47-50]: work and debate are ongoing. However, assuming these problems will be solved, it is still unclear which production technique will produce the highest yield of trappable antihydrogen; current technology means that trap depths are likely to be limited to around 1 K. There are manifest uncertainties in the nested trap scenario regarding velocityand state-distributions on production (section 4) and whether any relaxation towards lower speeds/states is occurring. Nonetheless, this method is efficient and can likely be refined. The antiproton-excited state positronium method (section 5) is also promising, but needs development. At the time of writing the CERN Antiproton Decelerator facility [51] is dormant while CERN undertakes infrastructure changes for the LHC era. We look forward to this, but also to the resumption, in the late Spring of 2006, of the unique 5.3 MeV beams for the low energy antiproton/antihydrogen experiments. Ackowiedgements The author is grateful to the ATHENA and ATRAP teams for permission to use their data. He thanks his co-authors in [11] for many years of fruitful interaction. He is also grateful to the UK Engineering and Physical Sciences Research Council for funding his antihydrogen work over the years and for the excellent support provided by CERN via the AD facility. References 1. M. Amoretti et al., Nature 419, 456 (2002) 2. G. Gabrielse et al, Phys. Rev. Lett. 89, 21301 (2002) 3. M.C. Fujiwara et al., Phys. Rev. Lett. 92, 065005 (2004) 4. M. Amoretti et al, Phys. Lett. B 578, 23 (2004) 5. M. Amoretti et al, Phys. Lett. B 590, 133 (2004) 6. N. Madsen et al, Phys. Rev. Lett. 94, 033403 (2005) 7. M. Amoretti et al, Phys. Lett. B 583, 59 (2004) 8. G. Gabrielse et al, Phys. Rev. Lett. 89, 233401 (2002)
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9. G. Gabrielse et al, Phys. Rev. Lett. 93, 073401 (2004) 10. G. Gabrielse et al, 'First evidence for atoms of antihydrogen too deeply bound to be guiding centre atoms' submitted for publication (2004) 11. M.H. Holzschieter, M. Charlton and M.M. Nieto, Phys. Rep., 402, 1 (2004) 12. G. Gabrielse, Adv. At. Mol Phys. SO, 155 (2005) 13. Particle Data Group Phys. Lett. B 592,84 (2004) 14. G. Baur et al, Phys. Lett. B 368, 251 (1996) 15. C.T. Munger, S.J. Brodsky and I. Schmidt, Phys. Rev. D 49, 3228 (1994) 16. G. Blanford et al, Phys. Rev. Lett. 80, 30307 (1998) 17. A.P.Mills Jr., in A. Dupasquier and W. Brandt (eds.) Positron Solid State Physics, Proc. Int. School of Physics "Enrico Fermi" (Course CXXV) IOSHolland 432 (1983) 18. P.J. Schultz and K.G. Lynn, Rev. Mod. Phys. 60, 701 (1988) 19. G. Gabrielse et al, Phys. Rev. Lett. 57, 2504 (1986) 20. G. Gabrielse et al, Phys. Rev. Lett. 63,1360 (1989) 21. G. Gabrielse et al, Phys. Rev. Lett. 65, 1317 (1990) 22. G. Gabrielse et al, Phys. Rev. Lett. 82, 3198 (1999) 23. X. Feng et al, Hyperflne Interactions 100, 103 (1996) 24. M.H. Holzscheiter et al, Phys. Letts A 1U, 279 (1996) 25. G. Gabrielse et al, Phys. Letts. A 129, 38 (1988) 26. B.I. Deutch et al, in B.E. Bonner and L.S. Pinsky (eds.) Proc. 1st Workshop on Antimatter Physics at Low Energies, Fermilab Batavia IL 371 (1986) 27. J.W. Humberston et al, J. Phys. B. At. Mol Phys. 20, L25 (1987) 28. B. I. Deutch et al, Physica Scripta T22, 248 (1988) 29. J. Estrada et al, Phys. Rev. Lett. 84, 859 (2000) 30. L.V. J0rgensen et al, Phys. Rev. Lett, in press (2005) 31. P. Oxley et al, Phys. Lett. B 595, 60 (2004) 32. C. Regenfus, NIMA 501, 65 (2003) 33. M. Amoretti et al, NIMA 518, 679 (2004) 34. T.F. Gallagher, Rydberg Atoms (Cambridge University Press) (1994) 35. M. Amoretti et al, Phys. Rev. Lett. 91, 055001 (2003) 36. M. Amoretti et al, Phys. Plasmas 10, 3056 (2003) 37. F. Robicheaux, Phys. Rev. A 70, 022510 (2004) 38. S.G. Kuzmin, T.M. O'Niel and M. Glinsky, Phys. Plasmas 11, 2382 (2004) 39. J.P. Merrison et al, Phys. Rev. Lett. 78,2728 (1997) 40. M. Charlton, Phys. Lett. A 143,143 (1990) 41. B. I. Deutch et al, Hyperflne Interactions 76, 153 (1993) 42. E.A. Hessels, D. Homan and M. Cavagnero, Phys. Rev. A 57, 1668 (1998) 43. C.H. Stony et al, Phys. Rev. Lett. 93, 263401 (2004) 44. M. Niering et al, Phys. Rev. Lett. 84, 5496 (2000) 45. J. Walz and T.W. Hansch, Gen. Rel. Grav. 36, 561 (2004) 46. D.E. Pritchard, Phys. Rev. Lett. 51, 1336 (1983) 47. E.P. Gilson and J. Fajans, Phys. Rev. Lett. 90, 015001 (2003) 48. J. Fajans and A. Schmidt. NIMA 521, 318 (2004) 49. J. Fajans et al.Phys. Rev. Lett, submitted (2004) 50. T. Squires, P. Yelsey and G. Gabrielse, Phys. Rev. Lett. 86, 5266 (2001) 51. S. Maury, Hyperflne Interactions 109,43 (1997)
ATOMIC COLLISIONS INVOLVING POSITRONS
H. Ft. J. WALTERS AND C. STARRETT Deptartment or Applied Mathematics and Theoretical Physics, Queen's University, Belfast, BT7 INN, United Kingdom In this report we present a short overview of some areas of interest in positronic atomic physics. The areas include: bound states; positron-atom scattering; positronium-atom scattering; positronium-positronium scattering; annihilation; cold antihydrogen.
1. Introduction Atomic systems involving positrons are very correlated. As such, they present a considerable challenge to theory. The positron, being light, is exquisitely sensitive to the atomic enviroment and so the opportunities for correlated behaviour greatly outweigh those available to "ordinary" atomic systems consisting only of electrons and nuclei. That the correlation problem is formidable is evidenced by the fact that, after many years of searching for bound states of positrons with atoms, it is only in the last eight years that some such states have definitely been shown to exist 1,2 . In this report we shall give a short overview, of necessity somewhat selective, of activities within the subject. The areas we shall touch upon are: bound states; positron-atom scattering; positronium-atom scattering; positronium-positronium scattering; annihilation; and cold antihydrogen. In our formalism we shall use atomic units (au) in which h = me = e = 1, the symbol CLQ will denote the Bohr radius. 2. Bound States The simplest bound state is positronium (Ps). It consists of a single electron bound to a single positron and is like a light hydrogen atom. Like all positronic bound states, the positron eventually annihilates with the electron into 7 rays, so the state has a finite lifetime. This lifetime depends upon the total spin of the Ps. Positronium in the spin single state is called para-positronium (p-Ps), in the triplet state ortho-positronium (o - Ps).
381
382
p-Ps(ls) (o-Ps(ls)) annihilates predominately into two (three) 7 rays with a lifetime of 0.125ns (142ns) 3 . In the late 1940s/early 1950s it was demonstrated that Ps*, PS2 and PsH were bound 4 ' 5 ' 6 . Until 1997 only eight bound states had been convincingly shown to exist, these included the four already mentioned together with PsF, PsCl, PsBr and PsOH 7 . In 1997, the proof that the positron could bind to the Li atom l'2 radically changed the picture. Since then, more than 50 bound states have been positively identified. A much fuller discussion of bound states may be found in the article by M. Bromley in this volume. 3. Positron-Atom Scattering In positron-atom scattering the following processes are possible: e++A
Elastic Scattering
(la)
e++A*
Excitation
(lb)
n+
Ionization
(lc)
Ps Formation
(Id)
e+ + A
+ ne~
Vs(nlm) + A+ _
P s + A++ s + A(n+1)+
+
- + ,4(n+2)+ +
Ps ne-
ne- "
-
Formation
(le)
Transfer Ionization
(If)
Transfer Ionization
(lg)
with P s +
A
+ 7 rays
-
Formation
Annihilation
(lh)
Only (la) to (lc) apply to electron-atom scattering and so positron-atom scattering provides a much more interesting set of possibilities. The most powerful theoretical method presently in use to treat positronatom scattering is the coupled-pseudostate approach. To illustrate the idea let us look at e + + H scattering. In this approach the collisional wave function # is expanded in atom states, tpa, and Ps states,
Fa(rp)Mre)
+£
G 6 (R)&(t)
(2)
b
where r p (r e ) is the position vector of the positron (electron) relative to the proton, R = (r p + r e ) / 2 , and t = r p — r e . If the states ipa and fa are eigenstates then, to get a complete representation, not only bound states but continuum states would have to be included in (2). Pseudostates are a way of discretizing the continuum into a finite number of bound-like states 8 ' 9 .
383
They are constructed by diagonalizing the atomic/Ps Hamiltonian in some suitable basis. In the coupled-pseudostate approximation the eigenstate continuum in (2) is replaced by discrete pseudostates. Substitution of (2) into the Schrodinger equation and projection with <j>a and ipb leads to coupled equations for the functions Fa(rp) and Gb(R). To illustrate the power of the pseudostate method, we show in figure 1 results for e + + H ( l s ) scattering 9 . Figures 1(a), (b), (c) illustrate very good agreement with experiment while figure 1(d) demonstrates the universality of the approach in that it gives a complete, and internally consistent, picture of all the main processes. Coupled-state calculations have also been
Energy (eV)
Figure 1. Positron scattering by H(ls). Curves are 33-state approximation of reference 9 . Experimental data are from 10<11, (a) total Ps formation; (b) ionization; (c) total cross section, (d) upper solid curve, total cross section; long-dashed curve, total Ps formation; short-dashed curve, elastic scattering; dash-dot curve, H(2p) excitation; lower solid curve, ionization.
performed on Li, Na, K, Rb, Cs, He, Mg, Ca, and Zn
12,13
.
4. Positronium-Atom Scattering The treatment of Ps-atom collisions presents a substantial challenge to theory. It is complicated by the fact that both projectile and target have internal structure. However, the advent of o-Ps(ls) beams 14 ' 15 - 16 has made
384
such a theoretical undertaking worthwhile. Again, the coupled-pseudostate approximation is the most powerful instrument for this kind of study. To see what is involved, let us look at the simplest case of Ps+H scattering. Here the collisional wave function can be expanded as
* = J2\G°b(RMh)Mr2)
+ (-l)SeGai,(R2)
(3)
a,b
where r p (rj) is the position of the positron (ith electron) relative to the proton, Rj = (r p + rj)/2, tj = (r p — rj), Se (= 0,1) is the total electronic spin, and the sum is over Ps (H) eigenstates/pseudostates
385
100
10
20 30 Energy (eV)
40
Figure 2. Ps(ls)+H(ls) total cross section in a 22-Ps state frozen target approximation 17 . Curves: lower solid, frozen target total cross section; upper solid, frozen target total cross section with first Born estimate 19 for H target excitation/ionization added; short-dashed, Ps(ls) elastic scattering; long-dashed, Ps(n=2) excitation; dash-dotted, Ps ionization.
~ 50
1
2 3 4 Energy (eV)
5
6
Figure 3. Ps(ls)+H(ls) total cross section: (a) solid curve, calculation including excitation/ionization channels of H (9Ps9H approximation of 2 0 ) ; dashed curves, frozen target calculations 20 ; (b) 9Ps9H approximation of (a) with the H - channel added 2 2 . except at 10 eV, the calculated cross section slightly underestimates the measured values while the down-turn in the measurements at 10 eV is not reproduced by the theory. However, the experiments are very difficult and the frozen target approximation is not the final say. A very interesting new development has been the first measurement of Ps fragmentation and the longitudinal energy distribution of the resulting positrons 16>24>25. Figure 4(b) shows the measured total Ps fragmentation cross section compared
386
with the frozen target calculation of figure 4(a). The agreement between theory and experiment is encouragingly good.
16
1
i
1
i
I
i
00 —
B
'
1i-H
l"«M
B" "' S5" "l" 3D ' "
1C
20
,(*V) ^ 3° Enetgy
Figure 4. Ps(ls)+He(l 1 S) cross sections in the 22-state frozen target approximation of 18 : (a) total cross sections compared with experimental data from 14 ' 15 ; (b) Ps fragmentation cross section compared with experimental data from 24 .
Further frozen target calculations on Ne, Ar, Kr and Xe may be found in 26 while a calculation of Ps-Li scattering including excitation of the Li and excitation/ionization of the Ps may be seen in 27 . 5. Positronium-Positronium Scattering This may seem an esoteric topic but it has two interesting areas of application. The first concerns a suggestion of Platzman and Mills 28 for producing a Bose-Enstein condensate (BEC) of Ps. The idea is to create a dense gas of Ps in a submicron cavity located very near the surface in a solid. The gas is to be formed by injection of positrons into the cavity. Initially both p-Ps and o-Ps will be present but the decay of the shortlived p-Ps will leave only o-Ps. To ensure that the o-Ps is not quickly destroyed by ortho to para conversion collisions between the o-Ps atoms, or with the cavity walls, it is essential that the o-Ps be spin polarized, which requires that the injected positrons be spin polarized, and that the solid be an insulator with paired electron spins. Calculations of the scattering lenght of spin polarized o-Ps(ls) atom in collision with each other 2 9 , 3 0 give the positive value +3.0 ao which means that a stable BEC of spin polarized o-Ps(ls) seems to be possible. The second application is to exciton-exciton processes in solids, 29 - 31 . Exciton-exciton systems bear a similarity to the Ps-Ps system and BoseEinstein condensation of excitons is also of considerable interest 29>31.
387 6. Annihilation In-flight annihilation of positrons in collision with atoms and molecules gives "pin-point" information on correlation. Annihilation results are normally expressed in terms of the parameter Z e / / defined as Z
Zeff
f
= ] P / | * ( r p , x i , x 2 , . . . , x z ) | 2 8(rp - ri)drpdx.idx.2 • • • dx.z
(4)
where ty is the collisional wave function for the system, r p is the positron coordinate, Xj = (r,, Si) are the space and spin coordinates of the ith electron, and Z is the number of electrons in the atom/molecule. Zeff measures the "effective" number of electrons seen by the positron in the target. Since the positron attracts electrons we might expect Z e / / > Z. Suprisingly, experiments with trapped thermal positrons in the presence of large organic molecules have uncovered values of Z e / / grossly in excess of Z, in fact as high as ~ 5 x 10 4 Z 32 . Various ideas were put forward to explain these unexpected results, in particular the suggestion of resonance formation. An analysis by Gribakin 33 has shown that such high values of Z e / / would be possible if the positron were trapped in a vibrational Feshbach resonance. It has now become feasible to produce positron beams with sufficiently narrow energy width to test this explanation. Figure 5 shows measurements on ethane 34 which demonstrate that the high thermal values of Zeff come from large enhancements associated with vibrational thresholds, as would be expected from vibrational resonances. 7. Cold Antihydrogen The first production of cold (< 15K) antihydrogen (H) was announced in 2002 35>36. The motivation for creating cold H is that it offers the opportunity for making very high precision tests of the weak equivalence principle of general relativity for antimatter and of the CPT theorem of relativistic quantum mechanics 37 . To undertake these tests the H is required to be very cold and in its Is ground state. The present method of production mixes positrons and antiprotons in a nested Penning trap. Unfortunately, this seems to result in most of the H ending up in Rydberg states 38 . How to de-excite these states to the ground state in sufficient numbers remains to be solved. Nevertheless, let us assume that H(ls) has been obtained and trapped. In the trap there will inevitably be some trace amounts of impurities, most likely He and H2. In addition, the trapped H(ls) will very probably need to be further cooled (a temperature <1K is desired). One
388
0.0
0.1
0.2
05
0.4
05
energy (eV) Figure 5. Zeff f° r ethane as a function of positron energy 3 4 . Vertical bars along the abscissae indicate the strongest infrared-active vibrational modes. The arrow on the ordinate indicates Z e / / for a Maxwellian distribution of positrons at 300K
way to achieve this would be to introduce a cold background gas. The question therefore arises, what is the probability of the H(ls) being destroyed by trace gases or cold background gas? Calculations to explore this question have been undertaken on the simplest system, H(ls)+H(ls). In H(ls)+H(ls) collisions, the H may be destroyed either through rearrangement into Ps and protonium (Pn), H(ls) + H(ls) -» Ps(nlm) + Pn(NLM)
(5)
or through in-flight e + — e~ or p-p annihilation. In the first instance calculations have focused upon a Born-Oppenheimer treatment. Using this approach calculations of elastic scattering have been made from which the p-p in-flight annihilation can be evaluated 39 . In addition, by employing the distorted-wave approximation, cross sections for the rearrangement process (5) have been obtained 3 9 ' 4 0 . More recent work 4 1 employs an optical potential to try to consistently handle the effect of the rearrangement channel (5). A more dynamical treatment has been given by Armour and Chamberlain 42 who have used the Kohn variational method with four open channels, viz, H(ls)+H(ls) and Ps(ls)+Pn(Ns), N=22, 23, 24. While there are differences beween results 4 0 ' 4 1 ' 4 2 ) a typical set of cross sections in the cold collision regime would be: aei = 908 a2, 42 , ^r-eor- = 0 . 6 7 £ - 1 / 2 a2, 42 , <7pp - 0.14E _ 1 / 2 a2, 39 , where aeU <Jrear, and opp are the elastic, rearrangement (5), and in-flight pp annihilation cross sections respectively, and E is the impact energy in the centre-of-mass frame.
389 In-flight electron-positron annihilation is neglegible in comparison to that of p — p 43 . While aei is effectively constant at low energies, arear and <7pp diverge as E~1/2, consequently, as the temperature falls, the destruction processes begin to dominate the cooling from elastic scattering. Using
390 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47.
G. Laricchia et al, Nucl. Instr. and Meth. B 2 2 1 , 60 (2004). C.P. Campbell et al, Phys. Rev. Lett. 80, 5097 (1998). J.E. Blackwood et al, Phys. Rev. A60, 4454 (1999). M.T. McAlinden et al, Can. J. Phys. 74, 434 (1996) J.E. Blackwood et al, Phys. Rev. A65, 032517 (2002) J.E. Blackwood et al, Phys. Rev. A 6 5 030502 (2002) H.R.J. Walters et al, Nucl. Instr. and Meth. B 2 2 1 , 149 (2004). R.J. Drachman, Phys. Rev. A19, 1900 (1979). S. Armitage et al, Phys. Rev. lett. 89, 173402 (2002). C. Starrett et al, Phys. Rev. A72, 012508 (2005). J.E. Blackwood et al, J. Phys. B 35, 2661 (2002); B36, 797 (2003). S. Sahoo et al, Nucl. Instr. Meth. B233, 312 (2005). P.M. Platzman and A.P. Mills Jr., Phys. Rev. B49, 454 (1994). J. Shumway and D.M. Cepsley, Phys. Rev. B 6 4 , 165209 (2001). I.A. Ivanov et al, Phys. Rev. A65, 022704 (2002). L.V. Butov, Solid State Commun. 127, 89 (2003). K. Iwata et al, Phys. Rev. A 5 1 , 473 (1995). G.F. Gribakin, Phys. Rev. A 61, 022720 (2000). S.J. Gilbert et al, Phys. Rev. Lett. 88, 043201 (2002). ATHENA collaboration, M. Amoretti et al, Nature 419, 456 (2002). ATRAP collaboration, G. Gabrelse et al, Phys. Rev. Lett. 89, 213401 (2002). M. Charlton et al, Phys. Repts. 241, 65 (1994). G. Gabrelse et al, Phys. Rev. Lett. 89, 233401 (2002). S. Jonsell et al, Phys. Rev. A64, 052712 (2001). P. Proelich et al, Phys. Rev. Lett. 84, 4577 (2000); J. Phys. B 37 1195 (2004). B. Zygelman et al, Phys. Rev A69 042715 (2004). E.A.G. Armour and C.W. Chamberlain, J. Phys. B 35, L489 (2002). P. Froelich et al, Phys. Rev. A70, 022509 (2004). P.K. Sinha and A.S. Ghosh, Phys. Rev. A68, 022504 (2003). E.A.G. Armour et al, Nucl. Instr. and Meth. B 2 2 1 , 1 (2004). S. Jonsell et al, Phys. Rev. A70, 062708 (2004). Nucl. Instr. and Meth. B vol 221 (2004), vol 192 (2002), vol 171 (2000), vol 143 (1998); Can. J. Phys vol 74 (1996); Hyperfine interactions vol 89 (1994). 48. New Directions in Antimatter Chemistry and Physics, eds., C M . Surko and F.A. Gianturco (Kluwer, Dordrecht, 2001).
IONIZATION AND POSITRONIUM FORMATION IN NOBLE GASES
J. P. MARLER, J. P. SULLIVAN+ AND C. M. SURKO University of California, San Diego 9500 Gilman Dr., La Jolla, CA, 92093, USA Present address: RSPhysSE, Australian National University Canberra, Australia E-mail: [email protected]
This paper reviews key results of our recent study [Marler et at, Phys. Rev. A 71, 022701 (2005)] of direct ionization and positronium formation in the noble gases from the thresholds for these processes to 90 eV. Results for argon and xenon are emphasized. The original study also reports similar results for neon and krypton. The experiment uses a cold, trap-based positron beam and scattering in a strong magnetic field to make absolute cross section measurements. Comparison with a detailed set of previous measurements yields reasonably good absolute agreement. A third, independent analysis was used to resolve the remaining discrepancies to a < 5% level in argon, krypton and xenon. Key aspects of the work, comparison with available theory, and open questions for future research are discussed.
1. Introduction While positron interactions with matter play important roles in many physical processes, the study of positron interactions is much less well advanced, particularly at low energies than that of the analogous electron-matter interactions [1]. In part, this has been due to the relative unavailability of good sources of low-energy positrons. The advent of trap-based positron beams has provided new opportunities to study a variety of processes. In this paper, we describe the results of a recent study of ionization in noble gases [2]. These targets were chosen because they are relatively simple atoms for theoretical calculation, and because they are also among the simplest atoms to study experimentally. Positrons can ionize atoms and molecules through three processes, direct ionization, positronium (Ps) formation, and direct annihilation. The first two have cross sections on the order of OQ, where ao is the Bohr radius, whereas direct annihilation has a cross section that is orders of magnitude
391
392 smaller[l]. Consequently, it is neglected in the present study. Comparison of the measured direct ionization cross sections with available theoretical calculations yields quantitative agreement at the 20% level[2]. However comparison of the measured positronium formation cross sections with available theoretical predictions yields only modest and qualitative agreement [2]. The lack of quantitative agreement between theory and experiment highlights the need for further consideration of this important and fundamental process. 2. Experimental Techniques The experimental technique for forming a cold, trap-based positron beam using a 22 Na source, frozen neon moderator and buffer-gas trap is described in detail elsewhere[3, 4]. The scattering technique and further details of the experimental procedures are described in detail in Ref. [2]. Due to limited space, we refer the reader to these references for additional details. Accumulator
Scattering cell
RPA
Annihilation /plate
•
Bs
BA
Nal detector
Figure 1. Schematic diagram of the electrode structure (above) and the electric potentials (below) used to study scattering with a trap-based positron beam.
The beam formation and scattering apparatus are illustrated schematically in Fig. 1. The positron beam is magnetically guided through a scattering cell and retarding potential analyzer (RPA). The positron beam energy in the scattering cell, e = e(V — Vs), where Vs is the potential of the scattering cell, can be varied from ~ 0.05 eV to 100 eV. The apertures on the gas cell are sufficiently small so there is a well denned interaction region in which the pressure and the potential are constant, and the path length can be accurately determined. The electrical potential, VA, on the RPA can be
393 varied to analyze the energy distribution of the positrons that pass through the scattering cell. The energy resolution of the positron beam used in the experiments described here is ~ 25 meV (FWHM). The ionization and positronium formation cross section measurements presented here were done using a technique that relies on the fact that the positron orbits are strongly magnetized[5, 6]. For the experiments described here, the magnetic field in the scattering region, Bs, and in the analyzing region, BA, can be adjusted independently. When Bs » BA, the invariance of the quantity, £ = E±/B (where E±\s the energy in the particles gyromotion in the plane perpendicular to the magnetic field) allows us to measure the total positron energy using the RPA [5, 6]. For direct ionization measurements, the RPA is set to exclude positrons that have lost an amount of energy corresponding to the ionization energy or greater. The absolute direct ionization cross section is then calculated from the number of positrons rejected by the RPA and the intensity of the positron beam [5, 6]. Since positronium is a neutral atom that is not guided by the magnetic field, positrons that form positronium in the scattering cell either annihilate in the cell or drift to the cell walls and annihilate there. Thus positronium formation results in a loss of positron beam current. This loss in intensity and the intensity of the incident positron beam is used to obtain the absolute Ps formation cross section [6].
3. Experimental Results Shown in Fig. 2 are measurements of the direct ionization cross sections for argon and xenon. Also shown is a comparison with the experimental results of Refs. [7, 8] renormalized as described in Ref. [9]. The data from Refs. [7, 8] are derived from relative cross section measurements made in a crossed beam experiment using a coincidence technique and then normalized to the analogous electron cross sections at higher energies. The two data sets shown in Fig. 2 agree reasonably well. The only qualitative difference is that, generally, the cross section values presented here are somewhat larger than those of previous measurements, ranging from ~ 15% in argon and xenon to ~ 30% in krypton[2]. The present measurements of positronium formation cross sections for argon and xenon are shown in Fig. 3. The data are generally featureless, reaching a maximum and then decreasing monotonically at higher energies. The only exception is a possible "shoulder" in the data for xenon that
394
10
20
30
40
50
60
70
80
90
Incident positron energy (eV)
Figure 2. Direct ionization cross sections (•) as a function of positron energy for argon and xenon from Ref. [2]. These data are compared with two other determinations of these cross sections: (D) the direct ionization measurements from Refs. [7, 8]; and (—) using the total ionization from Ref. [9] minus the present measurements for the positronium formation. Also shown for comparison for argon are (A)the experimental data from Ref. [10].
10 t7£ JO, 8
"Ss^v3
. 2 f, \J «n 4
U
argon
\ SK,
I
J
10
^£ 20
30
40
50
60
70
80
90
10
20
30
40
50
60
70
80
90
Incident positron energy (eV)
Figure 3. The present direct measurements (•) of the positronium formation cross sections for argon and xenon as a function of incident positron energy from Ref. [2]. These data are compared with two other determinations of these cross sections: ( D ) the method of Ref. [9] using the total ionization of Ref. [9] minus the direct ionization measurements from Refs. [7, 8]j and (—) using the total ionization from Ref. [9] minus the present measurements for the direct ionization. The inset shows a "shoulder" observed in the present data for xenon on an expanded scale.
is shown on an expanded scale in the inset. Also shown in Fig. 3 is a comparison with the results of Ref. [9]. The experiment of Ref. [9] measured total ionization and direct ionization, and then used the difference to obtain an indirect measure of the Ps formation cross section. The two sets of measurements of positronium formation cross sections shown in Fig. 3 are in fairly good, quantitative agreement. There are, how-
395 ever systematic discrepancies, most notably in argon and krypton (i.e., see Ref. [2]) at energies greater than the peak in the cross sections. Since the differences begin at approximately the energy threshold for direct ionization, and the direct ionization cross section was used in Ref. [9] to obtain their positronium formation cross sections, this led us to consider a possible resolution of the remaining discrepancies.
4. Total Ionization and Further Analysis As discussed in Ref. [2], when the present, direct measurements of the direct ionization and positronium formation cross sections are combined to calculate the total ionization cross sections, the resulting total cross sections are in extremely good absolute agreement with those reported in Ref. [9] (i.e., +/- a few percent over most of the range studied). Thus we concluded that we could use the total ionization cross sections of Ref. [9] and our direct measurements for direct ionization to obtain an independent measurement of the Ps formation cross sections. The results of this analysis, shown by the solid lines in Fig. 3 agree well with the present, direct measurements (i.e., an independent measurement). We conjecture that the remaining difference between these two determinations of the cross section and the determination from Ref. [9] (open squares in Fig. 3) could be due to an under counting of ions in the (coincidence-technique based) direct ionization measurements reported in Ref. [9]. While the data sets are in reasonably good absolute agreement over most of the energy range studied, there are, for example, significant differences in argon. In argon, the data of Ref. [9] show a second peak in the cross section at energies beyond the main peak,i.e., at e ~ 25 eV, tentatively attributed to excited-state positronium, that is not seen in the present measurements. Similar but less pronounced peaks in the cross sections for krypton and xenon were reported in Ref. [9]. They are not seen in the present measurements, with the exception of a shoulder in the cross section in xenon beginning at ~15 eV (see inset, Fig. 3). For the direct ionization cross sections, we subtracted our positronium formation cross sections from the total ionization cross sections of Ref. [9] to obtain another, independent measurement of the direct ionization cross sections. The results (solid lines in Fig. 2) show excellent agreement between these two independent measurements for argon, krypton and xenon [2]. For neon, the additional analysis does not improve the situation [2].
396 5. Comparison with Theory In Fig. 4, we compare the direct ionization cross section measurements presented here with available theoretical calculations. The agreement between the measurements and theory is reasonably good. For further discussion, seeRef. [2].
0
1O20
3 O 4 0 W 6 O 7 0 M 9 0
0
10
2 0 3 0 W S 0 6 O 7 O 8 0 9 0
Incident positron energy (eV) Figure 4. Comparison of the present measurements of the direct ionization cross sections (•) as a function of positron energy for argon and xenon [2] with the theoretical predictions of (- -)CPE model of Ref. [11, 12], (—) CPE4 model of Ref. [11, 12], and (- • -) Ref.[13].
In Fig. 5, the present results for Ps formation are compared with the calculations of Refs. [14] using a coupled static-exchange approximation. Also shown are the results of a distorted-wave Born approximation (DWBA) calculation [15], that includes positronium formation in higher excited states. The static exchange model [14] agrees fairly well with the absolute magnitudes of the maxima of the measured cross sections, but the predicted dependence of the cross sections on positron energy are not in such good agreement with the measurements [2]. The predictions rise too quickly near threshold then fall more quickly, and finally, with the exception of neon, they are larger than the measured cross sections at higher values of energy (i.e., e > 50 eV). As shown in Fig. 5, sizable scale factors are required to match the magnitudes of the DWBA calculations [15] to the measurements, but the shapes of the cross sections as a function of positron energy are in reasonably good agreement with the present measurements [2]. We note that neither of the calculations predict a second maximum similar to those reported in Ref. [9] and most pronounced in the argon data (c.f., Fig. 3 above, open squares).
397
Incident positron energy (eV) Figure 5. Comparison of the present measurements (•) of the positronium formation cross section for argon and xenon [2] with the theory of (—) Ref. [14]. Also shown is the theory of (- -) Ref. [15], scaled by factors of 0.51 (argon) and 0.31 (xenon), so that the maximum values are equal to the maximum values of the experimental data.
6. Summary and Concluding Remarks We review here the highlights of recent absolute measurements of the positronium formation and direct ionization cross sections in the noble gases for positron energies from the thresholds to 90 eV. Comparison of the present measurements of the cross sections for direct ionization and positronium formation with those of Ref. [9] show good quantitative agreement for many features but some systematic differences. In order to resolve these remaining discrepancies, a third, independent analysis for both cross sections was performed that agrees very well with the present measurements over most of the range of energies studied for argon, krypton and xenon. In the case of neon, some discrepancies remain between the different data sets at the ±15% level. Previous data for positronium formation cross sections in argon, krypton and xenon [9] showed some evidence of a second peak in the cross section at energies 20 - 30 eV, with this feature being most prominent in argon. The present data show no evidence of these features. We conjecture that these peaks could be due to an undercounting of ions produced by direct ionization in the previous experiment. There is a remaining feature in the present data for Xe, perhaps best described as a "shoulder" in the cross section (see inset of Fig. 3). The onset at ~15 eV is somewhat below the threshold for positronium formation from the 5s shell electrons at 16.7 eV. Comparison of the direct ionization cross section measurements with available theoretical predictions indicates reasonable absolute agreement over most of the range of energies studied. The exception is near threshold where the predicted cross sections of Refs. [12, 16] in argon, krypton and
398 xenon are significantly larger than those observed. Comparison of the measured positronium formation cross sections with theoretical predictions yields qualitative, but not quantitative agreement. More theoretical work to understand this unique and very important process would be most welcome. Acknowledgments The authors thank K. Bartschat, S. Buckman, R. I. Campeanu, S. Gilmore, G. F. Gribakin, G. Laricchia, and H. R. J. Walters for helpful conversations, and E. A. Jerzewski for his expert technical assistance. This work is supported by the National Science Foundation, grant PHY 02-44653. References 1. M. Charlton and J. Humberston, Positron Physics Cambridge University Press, New York (2001). 2. J. P. Marler, J. P. Sullivan and CM. Surko, Phys. Rev. A 71, 022701 (2005). 3. S. J. Gilbert et al., App. Phys. Letts. 70, 1944 (1997). 4. C. Kurz et al., NIM B 143, 188 (1998). 5. S. J. Gilbert, R. G. Greaves and C. M. Surko, Phys. Rev. Letts. 82, 5032 (1999). 6. J. P. Sullivan et al, Phys. Rev. A. 66, 042708 (2002). 7. V. Kara et al., J. Phys. B. 30, 3933 (1997). 8. J. Moxom, P. Ashley and G. Laricchia, Can. J. Phys. 74, 367 (1996). 9. G. Laricchia et al., J. Phys. B. 35, 2525 (2002). 10. F. M. Jacobsen et al., J. Phys. B 28, 4691 (1995). 11. R.I. Campeanu, R. P. McEachran, and A. D. Stauffer, NIM B 192, 146 (2002). 12. R.I. Campeanu, L. Nagy, and A. D. Stauffer, Can. J. Phys. 81, 919 (2003). 13. K. Bartschat, Phys. Rev. A. 71, 032718 (2005). 14. M. T. McAlinden and H. R. J. Walters, Hyperfine Interactions 73, 65 (1992). 15. S. Gilmore, J. E. Blackwood and H. R. J. Walters, NIM B 221, 129 (2004). 16. R.I. Campeanu, R. P. McEachran, and A. D. Stauffer, Can. J. Phys. 79, 1231 (2001).
S T U D Y OF INNER-SHELL IONIZATION B Y L O W - E N E R G Y POSITRON IMPACT
Y. NAGASHIMA* AND W. SHIGETA Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan * E-mail: [email protected]. tus.ac.jp T. HYODO AND F. SAITO Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan Y. ITOH, A. GOTO AND M. IWAKI The Institute of Physical and Chemical Research (RIKEN), Hirosawa, Wako-shi, Saitama 351-0198, Japan
Inner shell ionization by low-energy positron impact has been studied. Development of an x-ray detector with thin Si(Li) crystals has enabled the measurement of absolute cross sections for positron impact ionization in the energy range below 30 keV. Threshold behavior of the cross sections for Cu K-shell and Ag, In and Sn L-shell ionization has been compared with the theoretical results calculated using the binary encounter formalism. The values for Cu if-shell and Ag L-shell ionization have also been compared with the results from the plane-wave Born approximation with Coulomb and relativistic corrections. The measured cross sections for Cu K-she\\ ionization are in good agreement with the theoretical values. The results for Ag, In, and Sn L-shell ionization are, however, smaller than the theoretical calculations.
1. Introduction When electrons or positrons with energies higher than the threshold energy are incident on a target, characteristic x-rays are emitted by inner-shell ionization 1 ' 2 ' 3 . The ionization process for positron (e + ) impact differs from that for electron impact because of the change in the sign of the Coulomb interaction and the absence of the exchange interaction. These effects are more pronounced near threshold. The study of threshold behavior 399
400
for positron impact in the energy range below tens of keV will provide information on both the Coulomb interaction and exchange interaction. It may also provide useful insight into the large discrepancies observed between experimental results and theoretical calculations for L x-ray production cross sections by electron impact 4 . For e + impact ionization, the absolute values of cross section measured to date are restricted to incident energies above 30 keV 5 . Measurements of the cross section ratios are also limited to above 20 keV 6 ' 7 . This is because the 7-rays emitted from positron annihilation in the targets deposit part of their energy in the x-ray detector crystal and produce a high background in the spectra 8 . Even in the case where the target thickness is comparable to or smaller than the mean-free path of the incident positrons such that most of the positrons pass through the target, a small number of positrons annihilate whilst in flight through the target thus producing a significant background. At lower impact energies, more positrons annihilate in the target and so the background increases. In this paper, we describe the development of a low-background x-ray detector 8 . We also describe the recent measurements of positron impact ionization cross sections for if-shell of Cu and L-shells of Ag 9 , In and Sn at low energies using this detector.
2. Development of Low-Background X-ray Detector The thickness of the Si(Li) crystals used in conventional x-ray detectors is 2—5 mm. The cross section of the photoelectric effect in the crystal material decreases rapidly with increasing photon energy; for x-rays of the energies below 10 keV, the half-value layer is less than 0.1 mm whilst that of 7-rays from positron annihilation is about 3 cm. Therefore, the background due to the 7-rays can be suppressed without any loss of x-ray detection efficiency if thin crystals are used. In the present work, we have fabricated an x-ray detector employing Si(Li) crystals of 0.25 mm in thickness 8 . The effective area of the crystals was limited to 20 mm 2 to optimize the energy resolution of the detector, which is dependent on the capacitance of the crystal. In order to obtain high efficiency, two crystals of 20 mm 2 were used and each crystal was connected to a separate pre-amplifler. The crystals were placed inside a Be window of 12.5 /zm thickness and cooled to 77 K using liquid nitrogen. The energy resolution was measured to be 300 eV at 5.9 keV. The background observed by the newly developed detector resulting
401
from positron annihilation 7-rays was tested by measuring the 4.5 keV K x-rays induced by 7-rays from a sample of Ti. The 7-rays were produced by a standard source ( 22 Na) attached to a Ti plate. Positrons were confined to and annihilated in the source because the 22 Na was encapsulated in a lucite plate of 2 mm thickness. The spectra obtained using the newly developed detector and also a conventional Si(Li) detector with a crystal of 3 mm thickness are shown in Figure 1 (a) and (b), respectively. The i
(a) Crystal thickness : 0.25 mm Effective area : 20 mm2+ 20mm'
2000
o U
1000
20000
0
n
2
4
6
8
10
Energy (keV)
i
'
i
'
i
'
\
10000
0
'
1(b) Crystal thickness : 3 mm I Effective area : 28 mm2
>
2
4
,
i
.
i
6
;
.
10
Energy (keV)
Figure 1. Spectra of K x-rays from Ti induced by 7-rays from a 22 Na standard source using (a) the low-background Si(Li) detector and (b) the conventional detector.
characteristic x-ray peak in (a) is isolated clearly, while the peak in (b) is obscured by the background. In this work, the low-background x-ray detector developed has been employed to measure the inner-shell ionization cross sections by positron impact as described in the following sections. 3. Measurements of Inner-Shell Ionization Cross Sections by Positron Impact 3.1. Experimental
Procedure
3.1.1. Slow Positron Beam Apparatus The experimental system used to measure the inner shell ionization cross sections consisted of a magnetically guided slow positron beam apparatus with a trochoidal ExB filter as shown in Figure 2. The magnetic transport system was composed of seven split solenoid coils which provided an axial field of about 0.01 T. A 22 Na positron source of activity 2 mCi was used for the measurements of Cu if-shell and Ag L-shell ionization whilst for In and Sn i^shell ionization, measurements were performed using a 22 Na
402
Coils
Positron Source y-ray shield
•CEMA
\
Turboraolecular Pir'ip
Figure 2. Schematic diagram of the slow positron beam apparatus.
source of activity 20 mCi. Positrons from the sources were moderated in an electro-polished tungsten mesh moderator 10 or a tungsten wire moderator 11 , which was placed 1 mm away from the window of the source capsule. The slow positrons emitted from the moderator followed helical paths down the line of travel of the beam in the magnetic field. They were transported to the ExB filter where unmoderated positrons were removed from the beam. After leaving the ExB filter, the beam entered an accelerator composed of an insulating tube and inner electrode tubes. The positrons were accelerated by floating the source end up to 30 keV. After leaving the accelerator, the positron beam goes in and out of focus repeatedly, as shown in Figure 2 1 2 . The positron helices have a period of 2-rrrn/eB, where m is the positron mass, e is the charge of positrons and B is the magnetic flux density. Hence the distance between two nodes, L, is given by 27ry/2m-E eB '
(1)
where E is the positron energy. By changing B, the beam could be focused on the target. The beam diameter at the target was less than 3 mm. The beam intensity during these investigations was 3.2 x 10 4 e + /s for the
403
Cu and Ag measurements and 2 x 10 5 e + /s for the In and Sn measurements. The low-background x-ray detector was placed in the target chamber at 90° to the beam line. The base pressure of the target chamber was 1 x 10~ 7 Pa. 3.1.2. Targets The targets were Cu, Ag, In and Sn thin films, deposited onto 10 /ig/cm 2 (40 nm) carbon films which were supported by aluminum holders with an aperture of 8 mm in diameter. The thicknesses of the deposited films were 6.7/ig/cm 2 (7.5 nm) for Cu, 7.6^g/cm 2 (7.2 nm) for Ag, 5.8/ug/cm2 (8.0 nm) for In and 5.8/ig/cm 2 (8.0 nm) for Sn. The average energy loss of the 10 keV positrons while passing through the targets was less than 1 % and the fraction of positrons annihilating in the films was less than 3 %. The targets were mounted at an angle of 30° to the incident beam direction. Using steering coils, the positron beam was directed only onto the film and not onto the aluminum holder. The x-ray signals from thick Cu, Ag, In and Sn thick targets (0.1 - 0.5 mm thickness) were also measured. 3.2. Results
and
Discussion
Typical x-ray spectra obtained are shown in Figure 3. Each spectrum from a thin film target was acquired over a period of about (1 — 2) x 105 s. The background signals of the spectra at 15 keV are higher than those at 30 keV due to a larger fraction of the positrons annihilating in the film target at the lower energy. While the Cu spectra have isolated peaks corresponding to Ka and Kp x-rays, only one peak, which includes all the signals due to all the L subshells, exists in the Ag spectra. If we assume that the emission of the characteristic x-rays is isotropic, the inner-shell ionization cross section, Q, is obtained from Nx = nlQNoeu,
(2)
where Nx is the x-ray count rate, n is the number density of the target atoms, / is the target thickness, No is the e + beam intensity, e is the x-ray detection efficiency and UJ is the fluorescence yield. The values of Nx were obtained by fitting the shapes of the peaks from the thick target data to the thin film data. The value of e was determined by counting the x-rays from a 55 Fe standard source which was placed at the target position.
404 'I""!""!""!""!""!
1
(b-1) Ag thin film target
4
6
X-ray Energy (keV)
X-ray Energy (keV)
Figure 3. X-ray spectra at positron impact energies of 15 keV and 30 keV for (a-1) Cu and (b-1) Ag thin films. The spectra for (a-2) Cu and (b-2) Ag thick targets at 30 keV are also shown.
The if-shell fluorescence yields for various elements have been measured by many authors and reliable values have been obtained. The value for the Cu if-shell fluorescence yield used in this study was 0.443 13 . Mean values for the Ag, In and Sn L-shell fluorescence yield were obtained by fitting a polynomial to a set of selected values for the various elements 14 : w£ g = 0.062 ± 0.009, tf£ = 0.071 ± 0.011,u7fn = 0.077 ± 0.012. The values of Q thus determined are plotted in Figure 4 against the positron impact energy. Theoretical values in relative units of inner-shell ionization cross sections for positron impact have been calculated using the binary encounter formalism by Gryzinski and Kowalski 15 ; these values are plotted in Figure 4. Khare and Wadehra 16 also calculated the ionization cross sections for Cu if-shell and Ag L-shell using the plane-wave Born approximation with Coulomb and relativistic corrections 16 . Their results are also plotted in the same figure. It can be seen that there is good agreement between the experimental data and the theoretical results for Cu iif-shell ionization. However, the experimental results for L-shell ionization for all the elements investigated
405 6
— i
(a) Cu K'-shell ionization 5
15
•
Present results Gryzinski and Kowalski 15 - - KharcandWadchra 16
S 4 o
1
1
1
1
—
(b) A g L-shell ionization •
Present results Gryzinski and Kowalski 15 - -KhareandWadchra 1 6
a °0
1"0
20
30
Positron Impact Energy (keV) — •
1
'
1
•
r
(c) In L-shell ionization •
Present results GryzinskiandKowalski 15
°0 10 20 30 Positron Impact Energy (keV) ,
1
,
1
,
(d) Sn L-shell ionization •
Present results Gryzinski and Kowalski 15
S o
CI
'S, 5
a °0 10 20 30 Positron Impact Energy (keV)
"0 10 20 30 Positron Impact Energy (keV)
Figure 4. Inner shell ionization cross sections plotted against positron impact energy. Theoretical values calculated using the binary encounter formalism 15 are also plotted. Theoretical predictions in the plane-wave Born approximation with Coulomb and relativistic corrections 1 6 are also shown for Cu if-shell and Ag L-shell. The arrows refer to the threshold energy, Eth.
are smaller than the theoretical results of Gryzinski and Kowalski 15 using binary encounter formalism. The values for Ag L-shell ionization are also smaller than theoretical values of Khare and Wadehra 16 . The discrepancies between the experimentally and theoretically determined values for In and Sn L-shell ionization cross sections are also observed in the corresponding electron impact cross sections measured by Tang et al 4 . 4. Conclusion A low-background x-ray detector has been developed. The use of this detector has enabled the measurement of the absolute cross section for e + impact ionization for various elements at energies from threshold to 30 keV. The cross sections obtained for Cu if-shell ionization are in good agreement with
406
the theoretical results calculated using the binary encounter formalism and those using the plane-wave Born approximation with Coulomb and relativistic corrections. The results for Ag, In and Sn L-shell ionization are, however, smaller than theoretical results. Further investigations are necessary for a better understanding of the inner-shell ionization processes by low-energy lepton impacts. Acknowledgments This work was supported by Grant-in-Aid for Scientific Researches (No. 12490006 and No. 14540371) from the Ministry of Education, Science and Culture of Japan, the Nuclear Cross-Over Research Funds and Matsuo Foundation, Japan. References 1. C.J. Powell, Rev. Mod. Phys. 48, 33 (1976). 2. H. Hansen, H. Weigmann and A. Flammersfeld, Nucl. Phys. 58, 241 (1964). 3. H. Knudsen and J.F. Reading, Phys. Rep. 212, 107 (1992) and references therein. 4. C. Tang, Z. Luo, Z. An, F. He, X. Peng and X. Long, Phys. Rev. A 65, 052707 (2002). 5. H. Schneider, I. Tobehn, F. Ebel and R. Hippler, Phys. Rev. Lett. 71, 2707 (1993). 6. P.J. Schultz and J.L. Campbell, Phys. Lett. 112A, 316 (1985). 7. W.N. Lennard, P.J. Schultz, G.R. Massoumi and L.R. Logan, Phys. Rev. Lett. 61, 2428 (1988). 8. Y. Nagashima, F. Saito, Y. Itoh, A. Goto and T. Hyodo, Materials Science Forum 445-446, 440 (2004). 9. Y. Nagashima, F. Saito, Y. Itoh, A. Goto and T. Hyodo, Phys. Rev. Lett. 92, 223201 (2004). 10. F. Saito, Y. Nagashima, L. Wei, Y. Itoh, A. Goto and T. Hyodo, Appl. Surf. Sci. 194, 13 (2002). 11. F. Saito, Y. Nagashima, T. Hyodo and M. Iwaki, in preparation. 12. N.B. Chilton and P.G. Coleman, Meas. Sci. Technol. 6, 53 (1995). 13. W. Bambynek, B. Crasemann, R.W. Fink, H.-U. Freund, H. Mark, CD. Swift, R.E. Price and P.V. Rao, Rev. Mod. Phys. 44, 716 (1972). 14. D.H.H. Hoffmann, C. Brendel, H. Genz, W. Low, S. Miiller and A. Richter, Z. Phys. A 293, 187 (1979). 15. M. Gryzinski and M. Kowalski, Phys. Lett. A183, 196 (1993). 16. S.P. Khare and J.M. Wadehra, Can. J. Phys. 74, 376 (1996).
POSITRON—ATOM B O U N D STATES A N D I N T E R A C T I O N S
M. W. J. BROMLEY ** Department
of Physics, San Diego State San Diego CA 92182, USA
University
J. MITROY, S. A. NOVIKOV Faculty of Technology, Charles Darwin University Darwin N. T. 0909, Australia A. T. LE, C. D. LIN Department
of Physics, Kansas State University Manhattan KS 66506, USA
Some recent progress in theoretical investigations of the interactions of low-energy positrons with atoms is presented. The emphasis being on studies of the positronic atoms, ie. atoms that are known to form electronically stable bound states with a positron. A variety of computational methods, configuration interaction, a hybrid configuration-interaction-Kohn, and hyperspherical close-coupling methods have been used to investigate a variety of phenomena. These include the structure of positron-atom bound states, elastic positron-atom scattering, in-flight annihilation and positronium formation during positron-atom scattering.
1. Introduction The interactions of low-energy positrons with atoms provides a host of problems for both experimentalists and theorists alike 1. Even for one of the most fundamental problems in positron physics, whether a positron can form an electronically stable bound state with a neutral atom, the first universally accepted calculation of positron binding to a neutral atom (lithium) was only performed in 1997 2 ' 3 . This paper reviews some of our theoretical progress in understanding low-energy positron-atom physics post-2002 when two of the present au* E-mail: [email protected] tThe presenting author attended ICPEAC due to the Sheldon Datz memorial fund.
407
408
thors published a review 4 of the known positronic atoms (e+He(3£>e), e + Li, e + Be, e + Mg, e + Ca, e + Cu, e + Zn, e + Sr, e + Ag and e + Cd). A 'positronic atom' has still not been demonstrated experimentally, but this research is partly motivated by the concurrent experimental progress due to the "Surko" positron trap, which is able to produce pulsed cold positron beams with Energies < 500 meV and widths < 25 meV l. A number of computational methods have been applied to study positronic atoms 4 , such as stochastic variational methods (SVM) 5 , manybody perturbation theory 6 ' 7 ' 8 , and quantum Monte-Carlo 9 methods. The configuration-interaction (CI) method has become one of the more successful approaches, despite its particular challenges, and we report here on some improved CI calculations of the structures of various positronic atoms 1 0 ' n . We also report on studies of positron-atom annihilation using a hybrid CI-Kohn variational scattering method 12>13. Finally, we discuss the results of multi-channel hyperspherical close-coupling (HSCC) calculations for positron scattering from sodium in the low-energy range 14. 2. CI calculations of positron-atom interactions The presence of localised electron-positron pairing means that all positronatom calculations are extremely demanding. The L5-coupled CI wavefunction looks like Nci
^LS = J2Cl ^«(ro) ( M r i) • • • <Mriv) ,
(1)
7=1
where ro is the positron, and r>o are the electron/s co-ordinates. Antisymmetry for the electron orbitals and the Clebsch-Gordan coefficients are both implied. The fundamental problem facing CI methods is that, when expanding a wavefunction with single-particle orbitals, viz. 4>i(*) = Pul(r)Yti,mi(t),
(2)
to accurately represent the CI wavefunction requires the inclusion of a large number of radial functions and partial-waves. Predominantly Laguerre type orbitals (LTOs) are employed to ensure radial basis orthogonality. The CI calculations are performed in the frozen-core approximation, where the valence-frozen core electron interactions are treated exactly. This is based on Hartree-Fock core orbitals with additional core polarisation potentials; a Vpi(ri) is semi-empirically tuned to reproduce the l e - spectrum, and a di-electronic term V^r*. *j) is also included. The CI method requires
409 the diagonalisation of large matrices, towards 10,000 for e+/e~ systems, and towards 500,000 for the sparse matrices of the e+/2e~ systems. These procedures are covered in detail elsewhere 15 . The CI-Kohn method is a natural extension of the CI method 12 , requiring the addition of long-range Bessel and Neumann orbitals which are orthogonalised against the short-range CI basis. The CI-Kohn method, in the end, requires solving a large set of linear equations. Table 1 shows the convergence of the s-wave phase shifts and annihilation parameter, Zes (k) from a series of CI-Kohn calculations of low-energy positron-hydrogen scattering at fc = 0.4 Og"1 with the inclusion of orbitals up to a maxiumum angular momentum J, and including a minimum of 25 LTOs per t. Table 1. Results of CI-Kohn calculations of low-energy elastic e + -H scattering k = 0.4 O.Q1 « 2.2 eV. The s-wave phase shifts {So) and annihilation parameter (Z°ff) are given for a series of calculations J. J 0
Net 1010
(So) -0.19921
(Z%) 0.453
J 10
Net 8786
<<5o> 0.11660
< Z p U ff>
1
2954
-0.01003
1.017
11
9411
0.11730
2.749
2
3786
0.05338
1.465
12
10036
0.11781
2.792
16 17
0.1201
3.327
3
4411
0.08173
1.796
Variational
'
2.699
The convergence of both the phase shifts and Zefi is currently being examined in detail elsewhere 10 for both CI and CI-Kohn calculations. The slow-convergence with J in Table 1 towards the variational limit is typical of partial-wave expansions, and is seen to be quite severe for even simple systems (e+-H scattering). There are a variety of extrapolation methods to estimate the partialwave increments to any expectation value AXJ where J > Jmax 18'10- Some of these methods follow Gribakin and Ludlow 19 who used perturbation theory to show that the asymptotic forms scale as AXJ oc (J + | ) _ p , where for energy P E = 4 and annihilation rates scale even slower {pz — 2). For a given CI calculation, the asymptotic region is not reached, and alternate methods are required. One of the best methods 18, labelled in Figure 1, is based on the two-term form: LZJ
^ = XJTW
+
TTTW'
(3)
the results of this and four other methods are shown in Figure 1. Reliable estimates can be obtained of positron-atom systems using large-scale CI calculations when combined with careful extrapolation.
410
v
3.8 3.6
Two-term,.
3.4
' \
e + -H
'
^ ^ 2 ^ gf
3K"
T^„—«
3.2
^
3.0 2.8
( /
/
^ ^ .
2.6 2.4
/
--''^^'max
/
10
12
Figure 1. Five different CI extrapolation methods of extrapolating the positronhydrogen scattering Zea data of Table 1. The explicit CI calculations are marked as Jmax- The method marked as two-term corresponds to Eqn.3.
3. CI calculations of positron-atom bound states The positronic atom system which has had the most number of estimates computed for its binding energy is e + Mg, some of which are seen in Table 2. The extrapolated CI results are in good agreement with the older fixed-core SVM results. New calculations of the alkaline-earth metal positronic atoms Table 2.
Results of various calculations of e+Mg. (r p ) (oo)
r „ (10 9 s e c - 1 )
3.405
7.040
0.6127
3.443
6.957
0.9267
0.01561
3.437
7.018
0.943
DMC 9
0.0168(14)
MBPT 6
0.0362
— —
— —
— —
Method
£ (hartree)
(r e ) (oo)
CI J = 12
0.01542
CI J = oo
0.01667
FCSVM 4
are underway u with parallelised code allowing for an order of magnitude more configurations than our previous calculations 20 . Interim results of positron binding to the alkaline-earth metal atoms Ca and Sr n are shown here graphically in Figure 2 alongside the present best estimates of the known positronic atom binding energies. Figure 3 shows the known positronic atom annihilation rates. The dotted lines are from calculations of positron binding to a model alkali atom 4 .
411
0.025
• SVM • cl pol T Other
0.020 ^
•
\
• Mg
f 0.015 Sr
to
,
Ps.
-0.010
.
3
0.005 0.000
He( Se) Li
A8--M
/
Cu
Be •*"Zn
. ....£r~ Na 0.2
0.15
0.25
..<*
0.35
0.3
LP. (Hartree)
Figure 2. Positronic atom binding energies against dissociation as a function of the atomic ionisation potential.
2.00
„1.50 'o CD
>"••«.
r P s =2.008x 10 9 sec" 1
Na
if-,.. •
o
"•••-.
sr
3
He( Se)
F::: Ca
•••
........
Mg
y)
°> 1.00 0.50 Be* 0.00 0.15
0.2
0.25
0.3
Zn
0.35
LP. (Hartree)
Figure 3. Spin-averaged annihilation rates r „ as a function of ionisation potential.
4. CI calculations of positron-atom annihilation The CI-Kohn method was implemented to investigate low-energy elastic positron scattering from the one-electron atoms, H and Cu 12 , and the oneelectron ions, He + , Li 2+ , B 4 + and F 8 + 13. The crucial parameter obtained from the CI-Kohn wavefunctions is the annihilation parameter, Zef[(k), at energies below the first inelastic threshold. The threshold behaviour of e + -Cu scattering was of primary interest to show that the presence of a bound state does not imply a massive Zeff. The CI-Kohn method found Zeff = 73 at threshold, and the behaviour with k is shown in Figure 4. A secondary consideration was that for some systems; the noble gases, alkanes, and F/Cl/Br substituted alkanes, a semi-
412 empirical scaling exists 21 . This scaling implies a huge Zeg for the Group II metal vapours, which is not the case for Cu. Figure 4 also shows a p-wave interaction on the verge of forming a shape resonance, resulting in a p-wave Zgff that can exceed that of the s-wave. 200 175 150 125
75 50 25 0 0
0.05 0.1 /c (units of aQ1)
0.15
0.2
Figure 4. Annihilation parameter Zeg for e+-Cu scattering. The p-wave contribution has a significant extrapolated component, hence three estimates are plotted.
Elastic positron-positive ion scattering was performed partly because of suggestions to use positive ions to cool positrons 13. Whilst previous calculations have looked at the phase shifts, these are the first annihilation calculations. Figure 5 shows that Zeff is generally negligible. In particular, for a 300K thermal e+ swarm (k « 0.05 a^1) with He+ Z$ « 10 - 5 1 . This means that e + - Atom n+ cooling schemes can effectively ignore annihilation.
5. Ps-formation during e + - N a scattering Our HSCC calculations were motivated by a recent experiment that measured the positronium (Ps) formation cross sections 22 (ie. of an electron undergoing charge transfer from the atom to the positron during the collision). This experiment found strong disagreement with close-coupling (CC) calculations 23,24 for energies near and below 1 eV. Speculation arose in Ref. 22 that the calculations were not converged as sodium was later shown to be a positronic atom. Our Ps-formation results for sodium, as shown in Figure 6, find broad
413
10 u 10"
1
•
1
•
1
1
1
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1
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• • ! ' • •
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:=
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/'
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/
fl+ -R
4+
. ••<
// •'
0.6 0.8 1 k (units of ajj1)
1.2
1.4
Figure 5. Annihilation parameter Zeff for e+ - Atom n + scattering, note that the lines are drawn through the computed data points to give the general trend.
agreement with previous CC calculations 23 ' 24 and disagreement with the experimental data below 2 eV 22 . The accurately-known Ps-Na + scattering length is reproduced by our calculations, and hence, our low-energy results are reliable. Experiment needs to revisit the sub E = 2 eV region.
0.01
Figure 6.
0.1
1 Energy (eV)
Ps-formation cross sections during e + -Na scattering.
414 6. Conclusions The difficulties in computing positron-atom interactions are enough to have any sensible-minded theorist running in the other direction. We, instead, have employed a variety of methods to tackle specific problems, in the process gaining an improved understanding of the nature of the few-body interactions involving positrons and atoms. Acknowledgments Funding provided by the Australian Research Council, U.S.A. Department of Energy, and U.S.A. Department of the Navy (Office of Naval Research). References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.
C. M. Surko, G. F. Gribakin, and S. J. Buckman, J. Phys. B 38, R57 (2005). G. G. Ryzhikh and J. Mitroy, Phys. Rev. Lett. 79, 4124 (1997). K. Strasburger and H. Chojnacki, J. Chem. Phys. 108, 3218 (1998). J. Mitroy, M. W. J. Bromley, and G. G. Ryzhikh, J. Phys. B 35, R81 (2002). G. G. Ryzhikh, J. Mitroy, and K. Varga, J. Phys. B 31, 3965 (1998). V. A. Dzuba, V. V. Flambaum, G. F. Gribakin, and W. A. King, Phys. Rev. A 52, 4541 (1995). V. A. Dzuba, V. V. Flambaum, G. F. Gribakin, and C. Harabati, Phys. Rev. A 60, 3641 (1999). G. F. Gribakin and J. Ludlow, Phys. Rev. A 70, 032720 (2004). M. Mella, M. Casalegno, and G. Morosi, J. Chem. Phys 117, 1450 (2002). M. W. J. Bromley and J. Mitroy, in preparation. M. W. J. Bromley and J. Mitroy, in preparation. M. W. J. Bromley and J. Mitroy, Phys. Rev. A 67, 062709 (2003). S. A. Novikov, M. W. J. Bromley, and J. Mitroy, Phys. Rev. A 69, 052702 (2004). A. T. Le, M. W. J. Bromley, and C. D. Lin, Phys. Rev. A 71, 032713 (2005). M. W. J. Bromley and J. Mitroy, Phys. Rev. A 65, 012505 (2002). A. K. Bhatia, A. Temkin, R. J. Drachman, and H. Eiserike, Phys. Rev. A 3, 1328 (1971). A. K. Bhatia, R. J. Drachman, and A. Temkin, Phys. Rev. A 9, 223 (1974). M. W. J. Bromley and J. Mitroy, in preparation. G. F. Gribakin and J. Ludlow, J. Phys. B 35, 339 (2002). M. W. J. Bromley and J. Mitroy, Phys. Rev. A 65, 062505 (2002). T. J. Murphy and C. M. Surko, Phys. Rev. Lett 67, 2954 (1991). E. Surdutovich, J. M. Johnson, W. E. Kauppila, C. K. Kwan, and T. S. Stein, Phys. Rev. A 65, 032713 (2002). G. G. Ryzhikh and J. Mitroy, J. Phys. B 30, 5545 (1997). C. P. Campbell, M. T. McAlinden, A. A. Kernoghan, and H. R. J. Walters, Nucl. Instrum. Methods Phys. Res. B 143, 41 (1998).
EXTRACTION OF ULTRA-SLOW ANTIPROTON BEAMS FOR SINGLE COLLISION EXPERIMENTS^
HIROYUKI A. TORI!*. N. KURD-DA*, M. SHIBATAt, Y. NAGATA*, D. BARNA*, M. HORI§, J. EADES§, A. MOHRI*, K. KOMAKI* AND Y. YAMAZAKI** 'Institute
of Physics, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan ' Atomic Physics Lab., RIKEN, Wako, Saitama, Japan X KFKI, Budapest, Hungary, §CERN, Geneve, CH-1211, Switzerland E-mail: [email protected]
The Trap group of ASACUSA collaboration has decelerated and confined millions of cooled antiprotons in an electromagnetic trap, 50 times more efficiently than conventional methods. They were then extracted out of the magnetic field of 2.5 T and transported at 10-500 eV. This unique ultra-slow antiproton beam from our apparatus named MUSASHI enables antiprotonic single collision experiments to reveal ionization and capture processes between an "antiparticle" and an atom.
1. Introduction Antiproton is the antiparticle counterpart of proton, having the same mass but with opposite charge. As an exotic particle with infinite lifetime, not only is it essential as an ingredient of antiprotonic atoms for precise test of CPT invariance between matter and antimatter 1 , but it provides an ideal probe for studies of atomic collision dynamics. Antiproton is a "theoreticians' ideal probe" which does not capture electrons but instead, acting as a "heavy electron" or as a "negative nucleus", itself gets captured in an atomic orbit, forming a highly excited Rydberg atom. Ionization or atomic formation processes at low antiproton energies are, however, still very poorly understood. With the aim of experimental realization of mono-energetic antiproton beams for collision experiments at low energies comparable to the Ryd^This work was supported by the Grant-in-Aid (10P0101) from the Japanese Ministry of MonbuKagaku-sho, Special Research Projects for Basic Science of RIKEN, and the Hungarian National Science Foundation (OTKA T033079).
415
416 berg energy, we developed a system consisting of a RFQ Decelerator, an electromagnetic trap and an extraction beamline. 2. Deceleration of antiproton beam At CERN, antiprotons produced at GeV energies were cooled and decelerated to 5.3 MeV in the Antiproton Decelerator (AD) ring, before being extracted to experimental zones as a pulsed beam of typically 3 x 107 antiprotons in a bunch of 100-200 ns. Thus produced antiproton beam needs further deceleration for them to be captured in vacuo electrostatically. A conventional method using thick degrader foils inevitably caused considerable energy spread, limiting the capture efficiency to only 0.01%-0.1%2,3. In order to decelerate antiprotons efficiently, the ASACUSA collaboration4 developed a Radio Frequency Quadrupole Decelerator (RFQD)5. RF wave was applied to the cavities in such a way as to decelerate microbunches of the antiproton beam at 5.3 MeV down to 63 keV with an efficiency of 30%. Since the RF cavities can be biased ± 60 keV, the output antiproton energy can be varied 10-120 keV. The output beam from the RFQD was injected into an eletromagnetic trap in a strong magnetic field of 2.5 T. The beam was focused on a thin PET (Mylar) double-layered foil of 90 /ig/cm2 each, used to isolate ultrahigh vacuum inside the trap. This foil had ten strips of silver electrodes evaporatively plated on it and served also as a highly sensitive beam profile monitor for the antiproton beam. Taking into account the energy loss in the foil, we set the bias voltage of the RFQD to 110 kV so as to maximize the number of antiprotons captured at less than 10 keV. 3. Confinement and cooling Antiprotons were then confined in the trap. We used a Multi-Ring Trap (MRT)6 consisting of 14 cylindrical electrodes placed coaxially along the magnetic field line. Figure 1 shows sequential steps for antiproton capture, cooling and extraction. The pulse of incident antiprotons were reflected backward at the DCE electrode floated at —10 kV. By the time the pulse returned after its round trip of typically 500 ns back to the UCE, the trap was closed by a fast switch which biased the UCE to —10 kV, confining a major part of the antiprotons. The antiprotons were then cooled by a plasma of typically 3 x 108 electrons preloaded in the harmonic potential, while the heated electrons cooled by themselves by emission of synchrotron radiation, until the antiprotons were trapped in the bottom of the harmonic
417
0.5
10
1.5
2.0 Z(m)
2.5
3.0
3.5
X-Y deflector
_ I mijMim ,n=c^3cniaDn]rziDrnmMCP1
•A1
VA2
"extractor electrodes
FIGURE 1. Sequential procedures of antiproton capture, cooling and extraction.
VA3
MCP2
FIGURE 2. Schematic of the extraction beamline and calculated trajectories of ultra-slow antiproton beams, together with a graph of magnetic field strength.
potential of 50 V depth. After selective release of electrons by opening one side of the potential for 550 ns, the remaining antiproton cloud was given torque by a rotating electric field to be compressed radially. For this purpose, one of the electrodes was segmented azimuthally into four parts, for application of RF voltages at sequentially shifted phases. With this trap, we successfully confined 1.2 x 106 cooled antiprotons until the end of our trap cycle of 1-5 minutes. We then accumulated antiprotons for 5 AD shots, trapping 4.8 x 106 antiprotons simultaneously, the largest number of antiprotons ever accumulated. 4. Extraction and beam transport The antiprotons were then released from the trapping potential as it was gradually shallowed, and were extracted as an ultra-slow continuous beam of 10-500 eV. Since the antiprotons tend to expand in radial direction when they follow the strongly diverging magnetic field line, it was essential that the antiproton cloud be well compressed radially in the trap. The extraction beamline was designed to transport antiproton beams over a length of 3 m. The antiproton beams were refocused three times by
418 sets of Einzel lenses at the position of apertures, as shown in Fig. 2. These variable apertures allow differential pumping of 6 orders of magnitude along the beamline 7 , which is necessary to keep the trap region at an extremely high vacuum better than 10~ 12 Torr to avoid antiproton annihilation, while the end of the beamline will be exposed to a background gas pressure of upto 10~ 6 Torr when a gas jet is crossed. The MRT, the superconducting solenoid and the transport line for the ultra-slow beam are jointly known as "MUSASHI", or the Monoenergetic Ultra-Slow Antiproton Source for High-precision Investigations. MUSASHI opens a new research field ranging from atomic physics to nuclear physics 8,9 , including our near-future project of antihydrogen synthesis in a cusp trap 1 0 . Especially, atomic formation and ionization processes by low-energy antiprotons can be studied under single collision conditions for the first time. We are now preparing a supersonic gas-jet target 1 1 for atomic collision experiments planned in the next years. The target is aimed to achieve a density of 3 x 10 13 c m - 3 , which will be crossed with the ultra-slow antiproton beams to produce antiprotonic atoms. 5. S u m m a r y With the conbination of a RFQD and a MRT, we have successfully decelerated antiprotons from 5 MeV to less than 10 keV, confined them and cooled them down to sub-eV energies. Out of 30 million antiprotons from the AD, 1.2 million antiprotons were trapped stably every few minutes. They were extracted at energies of 10-500 eV, and this ultra-slow antiproton beam will be a powerful tool for the study of atomic collision dynamics. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
M. Hori et al.., Phys. Rev. Lett., 91, 123401 (2003). G. Gabrielse et al., Phys. Lett. B 548, 140 (2002). M. Amoretti et al., Nucl. Instrum. Methods in Phys. Res. A 518, 679 (2004). ASACUSA collaboration web page, http://cern.ch/ASACUSA A. M. Lombardi, W. Pirkl, and Y. Bylinsky, in Proceedings of the 2001 Particle Accelerator Conference, Chicago, 2001 (IEEE), pp. 585-587. A. Mohri, H. Higaki, et al.., Jpn. J. Appl. Phys. 37, 664 (1998). K. Yoshiki Franzen, et al.., Rev. Sci. Instrum. 74, 3305 (2003). Y. Yamazaki, Nucl. Instrum. Methods in Phys. Res. B 154, 174 (1999). M. Wada and Y. Yamazaki, Nucl. Instr. Meth. B, 214, 196 (2004). A. Mohri and Y. Yamazaki, Europhys. Lett., 63, 207 (2003). V. L. Varentsov et al., in Proceedings of the Workshop on Physics with Ultra Slow Antiproton Beams, RIKEN, Japan, March 2005 (AIP, to be published).
POSITRONIUM FORMATION FROM VALENCE AND INNER SHELLS IN NOBLE GAS ATOMS
L. J. M. D U N L O P AND G. F. GRIBAKIN Department
of Applied Mathematics and Theoretical Physics, Queen's University Belfast, Belfast BT7 INN, UK E-mail: [email protected], [email protected]
When recent experimental positronium (Ps) formation cross sections have been compared with the most up-to date theoretical studies, the agreement is qualitative, but not quantitative. In this paper we re-examine this process and show that at low energies Ps formation must be treated non-perturbatively. We also look at Ps formation with inner shell electrons.
Positronium (Ps) represents a bound state between a positron and an electron. It is formed in positron-atom collisions, A + e+ —• A+ + Ps,
(1)
when the positron energy, e = k?/2, is above the Ps formation threshold, e>\en\-\Eu\
(2)
where en is the energy of orbital n and E\a = —6.8 eV is the energy of the ground-state Ps. In this work we will only consider Ps formation in the ground-state. Noble gas atoms have tightly bound electrons, making excited-state Ps formation much less probable. Recently positronium formation in Ne, Ar, Kr and Xe has been determined by two experimental groups, in London1 (UCL) and San Diego2 (UCSD). The two sets of data are in fairly good agreement. However, recent distorted-wave Born approximation (DWBA) calculations3 overestimate the cross sections by as much as three times (for Xe), although their overall energy dependence is reasonable. This is in contrast with earlier coupled-static calculations4, which yield better magnitudes of the cross section maxima, but disagree on the energy dependence. In this paper we perform lst-order and all-order calculations of Ps formation from valence and subvalence subshells. We also consider Ps formation from inner
419
420
shells. It produces inner-shell vacancies and can be important for positronannihilation-induced Auger-electron spectroscopy. In the lowest order of the many-body perturbation theory, the Ps formation amplitude is given by5 (*i.,K|V|n,e> = - / * i . , K ( r i , r 2 ) | r^foVcMdridra, (3) J Fi - r 2 | where y>e(ri) is the incident positron wavefunction, ipn{*2) is the HartreeFock wavefunction of the initial electron state ("hole"), and \&IS,K = (1 - £ n , \n'){n'\) ^ I S , K is obtained from the wavefunction of the groundstate Ps with momentum K, * i s , K ( r i , r 2 ) = e iK -( r ' +r *>/ 2 <Mr 1 - r a ),
(4)
by orthogonalising it to all electron orbitals n' occupied in the target ground state. The positron wavefunction is calculated in the field of the target. The Ps center-of-mass motion is described by a plane wave. The Ps formation cross section is found by integration over the directions of K,
(5)
This approximation is equivalent to DWBA for a rearrangement collision. The cross sections are found by summing over the positron partial waves from / = 0 to 10. Figure 1 shows the Ps formation cross sections for the valence np and subvalence ns orbitals in Ne, Ar, Kr and Xe. The present results for the np subshell agree with the Ps(ls) formation cross section from DWBA3. Both calculations progressively overestimate the cross section near the maximum, compared to the experimental results1,2 which were obtained by different methods. For Ne, Ar and Kr experiment and theory converge at higher energies, while in Xe the discrepancy persists. Ps formation thresholds for the inner shells lie at much higher energies, e.g., at 242 and 320 eV for the 2p and 2s orbitals in Ar. Ps formation from inner shells is suppressed due to the positron repulsion from the nucleus. Figure 2 shows that Ps formation by the outer shells dominate near the inner-shell thresholds. At higher positron energies in Ar the various contributions become comparable, with 2p dominant above 550 eV. Analysis of the lower partial-wave contributions which dominate near the cross section maximum (/ = 0-3), shows that they become close to and even violate (for Kr and Xe) the unitarity limit for the inelastic processes, °Ps < T(2Z + l)/fc2- This means that Ps formation cannot be treated perturbatively. In other words, one must take into account the effect of Ps
421
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40 60 Positron energy (eV)
100
Figure 1. Total Ps-formation cross sections from Eq. (5) for the valence and subvalence subshells; DWBA 3 is only for the np subshell; experiment, UCL 1 and UCSD 2 .
Ne
'
1
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d
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-
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500
61
Positron energy (eV)
Inner-shell Ps formation cross sections in Ne and Ar.
formation on the positron scattering. We achieve this by considering the Ps formation contribution to the positron-atom correlation potential5,
(£'i4Ps)k> = /
(e / ,n|y|tti., K )(*i.,K|y|n,g) E + en - Eu
2
- K /4
+ iO
d3K (2TT)3 '
(6)
The potential is complex above the Ps-formation threshold. The corre-
422
Figure 3. Ps formation cross sections obtained nonperturbatively using E' P s '. Vertical lines show ns Ps formation thresholds. sponding scattering phaseshifts, 5i = 5[ + id" are used to determine the cross section as <rps = ir/k2 2i°^o(2' + 1)(1 — e~4Sl )• This leads to noticeable reduction of the cross sections, especially for Kr and Xe, Fig. 3. Figure 3 shows that the subvalence ns subshell gives a small but detectable contribution. The cross section maximum is still overestimated. A better calculation must include a more accurate positron-atom correlation potential, and account for the interaction between the Ps and residual ion. References 1. G. Laricchia, P. Van Reeth, M. Szluinska and J. Moxom J. Phys. B: At. Mol. Opt. Phys. 35, 2525 (2002). 2. J. P. Marler, J. P. Sullivan and C. M. Surko, Phys. Rev. A 71, 022701 (2005). 3. S. Gilmore, J. E. Blackwood and H. R. J. Walters Nucl. lustrum. Methods B 221, 129 (2004). 4. M. T. McAlinden and H. R. J. Walters, Hyperfine Interactions 73, 65 (1992). 5. V. A. Dzuba, V. V. Flambaum, G. F. Gribakin and W. A. King, J. Phys. B: At. Mol. Opt. Phys. 29, 3151 (1996).
MOLECULAR EFFECTS IN N E U T R I N O M A S S MEASUREMENTS
N. DOSS AND J. TENNYSON Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK A. SAENZ AG Moderne Optik, Institut fiir Physik, Humboldt-Universitat zu Berlin, Hausvogteiplatz 5-7, D - 10117 Berlin, Germany S. JONSELL Department of Physics, Umea University, SE - 90187 Umea, Sweden The molecular physics issues facing the future tritium beta decay neutrino mass measurement experiment, KATRIN, are discussed. Results from investigations of these issues are presented.
1. Neutrino Mass Measurements - Tritium Beta Decay Experiments It is commonly accepted that the neutrino is not a massless particle as predicted by the Standard Model. There exists several experiments, within both particle physics and cosmology, designed to investigate this. The most direct measurements of the neutrino mass to date have been provided by laboratory-based tritium molecule beta decay experiments. The future KATRIN experiment is designed to measure the mass of the electron anti-neutrino to a precision of 0.2 eV.* The idea of the experiment is to detect the energies of the electrons created in the beta decay of molecular tritium: 3
HeT+(f)+e-+I7e,
423
(1)
424
and deduce the mass of the electron anti-neutrino, m,vc, by comparing the experimental beta spectrum to theoretical spectra close to the endpoint energy, the maximum beta electron energy. Some of the molecular physics issues facing the KATRIN experiment that we have been investigating are: 3 (1) HeT+ state distributions (0 - 240 eV) (2) T2 rotational excitation effects (3) Isotope (DT, HT) source contamination effects (4) Decays of other tritium species e.g. T_, T, T + , T3" and TjJ". 2. Final State Distributions The shape of the beta spectrum is dependant on the distribution of energy released in the excitation of the daughter molecule. The final state distribution (FSD) of 3 HeT + and 3 HeH + was calculated in the 1990's, 2,3 to meet the needs of the contemporaneous experiments. Due to the increased sensitivity and changes in requirements of the KATRIN experiment, the FSD of the six lowest electronic states of 3 HeT + and 3 HeD + has been calculated and the results presented in Ref. 4. The calculations is so far limited to electronically bound states as the aim of KATRIN is to obtain the neutrino mass by analysing the beta spectrum in an energy interval with a lower limit of 30 eV below the endpoint. The experiment will be performed with a T2 source at a temperature of 27 K. At this temperature the T2 molecules may be thermally excited and distributed across the first four rotational states of the electronic and vibrational ground state. Therefore separate FSD's have been calculated for T 2 in states J = 0, 1, 2 and 3, and DT/HT in states J = 0 and 1. Figure 1 shows the probability distribution's of the three isotopomers, for the first five electronically excited states for T2 in its ground rotational state. The energies and transition probabilities were calculated using Le Roy's programs LEVEL 5 and BCONT 6 . The theory and procedure used to calculate the FSD is also detailed in Ref. 4. 3. Sensitivity Error Estimates The emphasis of the new FSD calculations was to investigate the effect on the deduced value of the neutrino mass obtained from fitting, due to uncertainties in: (i) T2 source temperature for a thermal source.
425 1
'
1
1
i
1
1
1
1
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'
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-
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-
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-
3
l
ij '7 i]
1 0.015 — 2 a. 0.01
1
i
30
,
1
35 Energy (eV)
1
40
45
Figure 1. Final State Distribution for transitions to the first five electronically excited states of 3 H e T + , 3 HeD+ and 3 HeH+
(ii) ortho-para ratio of T2 for a non thermal source, (iii) isotope contamination in the source. It was found4 that the expected experimental uncertainties in temperature and ortho-para ratio have a small effect on the value of rriue deduced. However, for a neutrino mass of 0.2 eV, an expected uncertainty in the amount of DT molecules in the source between 0 and 10 % results an error in mj7e of about 19 %, which suggests that careful monitoring of the deuterium content of the source will be neccesary. 4. Beta Decay of other Tritium Species The molecular tritium source may also be contaminated with small amounts of other tritium species such as T~, T, T + , T j and T5". If the endpoint energies of the decay of these species lies within the KATRIN measuring interval and there is a significant amount of these species in the source, their final state distributions will also need to be taken into account. Some preliminary calculations of the endpoint energies of various tritium species was performed and given in Table 1. Electronic structure
426 calculations were performed using M O L P R O . 7 T h e range of energies given for T j is to account for zero point energy effects. Conversely the Tjj" calculations allow for the fact t h a t there are three symmetry distinct locations of T in a T j ion. T h e energies are given relative to the endpoint energy of T 2 decay ( E 0 = 18.6 keV). Table 1. Endpoint energies for the beta decay of various tritium species, relative to the endpoint energy Eo of T2 decay (Eo = 18.6 keV) Decay T - -> 3He + e~ +Ve T -> 3 He+ + e~ + ue T+ - • 3 He++ +e~ +ue
Endpoint energy (relative to Eo) + 15.42 eV - 8.43 eV - 49.23 eV
T j - • ( 3 HeT 2 ) + + + e~ + Ve
- 19.78 eV < E < - 15.62 eV
T+ -+ ( 3 HeT 4 ) + + + e~ + Ve
- 15.17 eV - 13.18 eV - 8.79 eV
Acknowledgments We t h a n k Klaus Eitel and other members of the K A T R I N collaboration for helpful discussions, and the Enginnering and Physical Sciences Research Council ( E P S R C ) for funding.
References 1. 2. 3. 4. 5.
J. Angrik et al., Design Report, FZKA scientific report 7090 (2005) S. Jonsell, A. Saenz and P. Froelich, Phys. Rev. C 60, 034601 (1999) A. Saenz, S. Jonsell and P. Froelich, Phys. Rev. Lett. 84, 242 (2000) N.Doss, J. Tennyson, A. Saenz and S. Jonsell, Phys. Rev. A, submitted R. J. Le Roy, University of Waterloo Chemical Physics Research Report C P 555R (1996) 6. R. J. Le Roy, Comput. Phys. Commun. 52, 383 (1989) 7. H. J. Werner, P. J. Knowles, R. Lindh, M. Schiitz et al., MOLPRO, a package of ab initio programs, see http://www.molpro.net
COLLISIONS INVOLVING HEAVY PROJECTILES
PROBING THE SOLAR WIND WITH COMETARY X-RAY AND FAR-ULTRAVIOLET EMISSION.
R. HOEKSTRA, D. B O D E W I T S AND R. M O R G E N S T E R N KVI Atomic Physics, Rijksuniversiteit Groningen, Zernikelaan 25, 9747 A A Groningen, the Netherlands E-mail:[email protected] CM.
LISSE
Planetary Exploration Group, Space Department, Johns Hopkins University, Applied Physics Laboratory, 11100 Johns Hopkins Rd, Laurel, MD 20723, USA A.G.G.M. TIELENS SRON, Kapteyn Astronomical Institute, Rijksuniversiteit Groningen, Landleven 12, 9747 AD Groningen, the Netherlands In this contribution the key role of charge transfer processes in modelling and understanding the fax-ultraviolet and X-ray emission induced by interaction of solar wind minor ions with cometary atmospheres is treated. The most relevant collision partners and energies are identified. In addition, the existence or lack of fundamental data is addressed.
1. Introduction Whenever multiply charged solar wind minor ions collide with neutrals in cometary or planetary atmospheres, charge exchange into excited states occurs. The excited projectiles subsequently decay to the ground state through the emission of one or more photons. Therefore, charge-transfer processes are a very strong source of energetic photons. For a highly charged ion Aq+ colliding on a neutral target B this can be summarized as follows: A«+ + B -* A(*-V+(nl) + B+ and A(«-1)+(n/) -» A(«-1)+(n'Z') + hi/
429
430
solar wind
T j ^ B ,v*MIHF
m
tow
shodk
Figure 1. Schematic representation of the interaction of the solar wind with comets. Scales vary in the figure: for example the bow shock is situated at ~ 10 5 — 106 km from the nucleus which is approximately 1-10 km in size.
Present-day satellite observatories such as XMM-Newton and Chandra have indeed found X-ray and far-ultraviolet (FUV) line emission following electron capture by solar wind minor ions on a variety of solar system objects, such as comets, Jupiter, Mars etc. 1 ' 2,3,4 ' 5,6 . As state selective capture cross sections and thus line emission intensities depend on the specifics of the interactions7,8, the line emission can be regarded as a fingerprint of the underlying charge exchange processes. Cometary FUV and x-ray emission can thus be used to probe the interaction between comets and solar wjn(j9,io,n,i2,i3,i4,i5,i6# r p ^ ^m motivated many renewed efforts in the ield of charge exchange research e.g. refs.13'17«18»19»20'21'22. Comets are considered to be dusty snowballs which were formed in the outer parts of the solar nebula some 4.5 billion years ago and have been in cold storage ever since23. They may have been essential in delivering volatiles to the terrestrial planets in the inner Solar system. Understanding their composition and evolution is therefore of key importance. This is one of the prime motivations for the Deep Impact mission24 to comet Tempel 1. When entering the inner parts of the solar system, a comet will heat up and different gases sublimate of its nucleus creating a coma. The atoms and molecules in the cometary atmosphere act as electron donors to solar wind ions penetrating the cometary atmosphere, until the ions are neutralized. The interaction is very schematically depicted in figure 1. The solar wind consists of protons, 5% helium and small fractions of heavier species (oxygen, carbon, nitrogen, neon, etc). The high coronal
431 temperatures (over 106 K) of the Sun imply that all ions in the solar wind are highly ionized. When the wind flows out into the solar system, their velocity and ionic composition remain nearly the same due to its low density and magnetic field. A rough distinction between two types of solar wind can be made: fast winds with velocities around 1,000 km/s and slow winds with velocities below 400 km/s 25 . Space-borne mass spectrometry has shown clear differences in their elemental and charge-state distributions26. Each wind type lasts for several days to weeks, but properties of the wind may vary within hours, reflecting changing solar conditions. The interaction of the solar wind with, for example, our Earth's magnetic field is best known for the Northern Light, sometimes it leads to geomagnetic storms that cause communication problems or electric utility blackouts.
2. Properties of cometary atmospheres In the inner solar system comets get heated by solar light such that large amounts of gases, mainly H2O and CO, are sublimated off the nucleus. All these molecules flow into space with velocities on the order of 1 km/s until they are dissociated and/or ionized by sun light 27,28,29 . The amount of CO is significantly different for different comets, e.g. Hyakutake (5%30), Halley (10%31) and Hale-Bopp (30%3). CO2 may be present on the percent level, while carbon and nitrogen compounds occur on the level of tenths of a percent. Molecular dissociation and ionization scale lengths depend on the distance to the Sun and vary greatly amongst species typical for cometary atmospheres29. Generally, water molecules are confined to the inner regions of the coma, while the outer regions are populated by atomic dissociation products H and O and molecules that are more stable in sun light, such as CO. To illustrate this figure 2 shows the neutral density profiles for a Hyakutake type comet with a low CO concentration (5%) and a total gas production rate of Q=2xl0 29 molecules/s at 1.07 A.U. from the Sun30, and for a Hale-Bopp (Q=6xl0 29 molecules/s, 30% CO and 10% C0 2 ) 3 2 type comet at 3.07 A.U. from the Sun. The density distribution of different cometary species and their dissociation products is calculated with a standard Haser model33'34 that assumes a spherical outflow. The distance to the Sun (R) determines the outflow velocity of the molecules (~0.85 R - 0 , 5 (km/s)) and the dissociation and/or ionization length scales29. The spatial extent and elemental distribution of
432
6
10
S
4
10 10 distance to nucleus (km)
3
10
,V
I
10
l
4
10 10 distance to nucleus (km)
1
10
Figure 2. Neutral density distributions as a function of the distance from the cometary nucleus for comets Hyakutake (left) and Hale-Bopp (right), at distances from the Sun of 1 and 3 AU, respectively.
the cometary cloud of neutrals is determined primarily by the solar radiation field. Water molecules and OH have short lifetimes as compared to CO, H and O. In both cases, the inner regions of the cometary gas cloud are dominated by molecules, in particular H2O, while at distances beyond 105 km from the nucleus atomic H and O dominate. As Hale-Bopp is a carbon rich comet very considerable CO and CO2 fractions are observed throughout the cometary atmosphere. Hyakutake is carbon poor and the outer regions of its coma can be seen to be fully dominated by the atomic dissociation products of water, H and O. Although at distances of > 106 km from the cometary nucleus, the neutral particle densities in the outflowing cometary gas are low, they are still significantly higher than interplanetary densities. 3. Solar wind properties Apart from protons and alpha particles, the solar wind consists mainly of multiply charged C, O, N and Ne ions. In addition smaller fractions of intermediately charged Mg, Si, S and Fe ions are present in the solar wind. As an example table 1 presents some typical compositions for slow and fast solar winds26. For slow winds on average higher charge states are populated. The velocities of slow and fast solar winds are ~ 200 - 400 km/s and ~ 500 - 1000 km/s. The full velocity range encompassed by the incoming slow and fast winds corresponds to a collision energy range of approximately 0.2 - 7 keV/amu. Lower energies are also of relevance because when the solar wind first interacts with a cometary atmosphere, the solar wind is decelerated and a
433 Table 1. Typical elemental fractions of fast and slow solar winds as measured by the Ulysses spacecraft 26 , normalized to the total oxygen ion abundance. ion
H+ C6+ C6+
8
0 + 7
o+ o6+
fast wind
slow wind
ion
fast wind
2
slow wind
1550
1780
He +
68
78
0.085
0.32
N7+
-
0.006
0.44
0.21
N6+
0.011
0.058
0.07
N5+
0.127
0.065
-
8
0.03
0.20
Ne +
0.102
0.084
0.97
0.73
Ne 7 +
0.005
0.004
bow shock occurs. The position of this shock depends on quantities such as solar wind densities and velocities, average ionization rates, and gas production rates 11 . Typical stand off distances are on the order of 105 106 km. Due to the shock, the wind is decelerated and heated but its ionic charge state distribution is not affected. Assuming a strong shock, the wind velocity in the forward direction is reduced to 1/4 of its initial velocity11, v i n . At the same time the shock heats up the wind. After the shock the Maxwellian averaged velocity amounts to ~ 0.77vj n u . Ion pick-up in the cometary atmosphere will lead to a cooling and further slow down of the solar wind. 4. Interaction of the solar wind with cometary atmospheres When penetrating the cometary atmospheres the solar wind ions initially encounter atomic hydrogen and atomic oxygen as collision partners while deeper in the atmosphere water molecules dominate, cf. figure 2. To determine where most of the charge exchange interactions occur we did a simple estimation of the distribution of oxygen ions along the central Sun-comet axis. As initial charge state distribution, the distribution of a slow solar wind as given in table 1 was used. In addition it was assumed that the ions move with a constant velocity of 400 km/s, i.e., no slowing-down or heating was included. The total charge transfer cross sections were estimated conservatively by half of the over-the-barrier cross section35 for one-electron capture, which is given by:
434 0.8 0.7
0.6 c
0.5
o
fo.4 LL
0.3 0.2 0.1 10*
10s
104
Distance to the Nucleus (km)
Figure 3. Oxygen charge state distribution along the comet-Sun axis for a slow solar wind interacting with a Hyakutake like comet at 1.07 A.U.
with q the charge state of the solar wind ion and IP the ionization potential of the neutral atom or molecule. The results for oxygen ions are presented in figure 3. Note that the line emission in the X-ray spectral range is due to K-line transitions in hydrogen- and helium-like ions of oxygen, carbon, neon and nitrogen36. Therefore, for the present example of oxygen ions most of the X-ray emission occurs at distances larger than 105 km from the nucleus. At these distances the outflowing cometary gas mainly consists of atomic hydrogen, atomic oxygen and CO, see figure 2, which are therefore the electron donors of interest. They are the neutral species to be incorporated in model simulations of FUV and X-ray emission by hydrogen- and heliumlike ions. As most of the charge transfer occurs at distances far outside the cometopause, straigth-line trajectory approximations may be used for the solar wind ion trajectories. At shorter distances to the nucleus, water molecules dominate the neutral gas, but here the charge state of the solar wind is already lowered such that the associated line emission is restricted to the FUV or visible spectral range. The situation is similar for carbon, nitrogen, and neon ions. For smaller comets, of which the atmospheres are collisionally thin, the inner regions which are H 2 0 dominated are of importance as X-ray source39. The emission is consequently fainter and the emission pattern changes from crescent shaped to circular centered around the nucleus. Also for large comets such as Hale-Bopp at large solar distances the molecular atmospheric constituents (see figure 2) need to be considered. Again, but
435
now because of the large distance to the Sun the X-ray emission is likely to be weak, Prom the above it is concluded that X-ray emission from comets is mainly driven by the interaction of fully-stripped and hydrogen-like oxygen, carbon, neon and nitrogen ions with H, O, CO, H2O and maybe CO2. As the interest is in line emission, n, I selective cross sections are needed and the whole subsequent decay cascade needs to be included to model the Lyman or K-line series of the different ions12. The FUV emission from the initial cascade steps and the higher K lines are likely to be more sensitive to the n, I distributions than the K-a line which is cascade driven. In collisions on multi-electron targets the modelling is complicated by the fact that twoor more-electron capture followed by autoionization may add substantially to the Lyman emission and in particular to the K-a line emission37,38. The question arises whether at present the fundamental data needed to model and interpret cometary x-ray spectra does exist. Collisions of fully-stripped low-Z ions on atomic hydrogen are the benchmark systems for atomic collision theory. In general there is a very good agreement between theory and experiment, see e.g. 8 . After the fully stripped ions, the He-like ions have been studied with similar success. For hydrogen-like ions the data is fragmented. In part this is due to the fact that one needs to consider two spin systems, singlet and triplet, of which the different n, I states are not easily separable. In principle there is no problem to generate the relevant cross sections. In first instance cross sections from fully-stripped ions of the same charge state as the hydrogen-like ions may be used to model cometary spectra. An actual determination of the singlet and triplet cross sections and their ratios remains of importance. In particular, at the lower energies, singlet-triplet ratios may differ from a statistical 1:3 ratio as e.g. observed in collisions of N 4 + and 0 3 + on H 43 ' 44 . The "forbidden" triplet K-a transitions, which are not observed in crossed-beam laboratory experiments19, dominate in cometary environments45 where time scales for decay are that long that the forbidden transition can be observed. The forbidden line emission is accessible in EBIT trap experiments13 and seen to deviate from 1:3. The experiments are restricted to low collision energies. For highly charged ions colliding on atomic oxygen no experimental data is available because producing dense atomic oxygen targets is very difficult. Only experiments with protons and He 2+ ions 4 °. 41 . 42 have been performed. For such complex many-electron targets as O, theory is still lacking too. Calculations of single-, and multiple electron capture for the interaction of multiply or highly charged ions with atomic oxygen with its four equivalent
436
0.2
300
400
500 600 700 800 Photon Energy (eV)
900
1000
Figure 4. Synthetic spectrum for a comet with an outgassing rate Q = 10 29 and 10% CO at a distance of 1 A.U. to the Sun. Spectra were modeled for three different types of solar wind. The solid black line indicates a spectrum due to slow wind, the dashed grey line is for fast wind and the dotted line is for a decellerated wind.
2p electrons and open shell structure will be very involved. While experiments on atomic oxygen require the development of intense atomic oxygen beams, investigations on CO and many other molecules can be done without serious experimental difficulties. First experiments on highly charged ion - CO, H2O, and CO2 collisions have been done (see e.g. refe
13,19,46,47)
a n d
more data is expected to become available soon. On the theory side, cross sectional data is basically lacking. To illustrate the impact of cross sectional data on X ray emission, figure 4 shows a synthetic X-ray line emission spectrum for a comet with an outgassing rate Q = 1029 and 10% CO at 1 A.U. from the Sun. The cometary atmosphere is therefore very similar to the Hyakutake one shown in figure 2. It is seen that for such a comet the outer regions are fully dominated by atomic hydrogen, therefore we used atomic hydrogen cross sections for all neutrals. Spectra were calculated for three different types of solar wind, a slow solar wind, a fast solar wind and a "decelerated" wind (a slow wind with the composition of a fast wind) using carbon and oxygen ion fractions given in table 1. The strongest and most easily resolved emission is due to the OVII charge exchange line at 566 eV, the OVIII at 660 eV, and the CVI and CV charge exchange lines at 368 and 308 eV, respectively, as was observed in the spectra of Linear S4 and McNaught-Hartley36,48. Spectra due to a fast wind are dominated by carbon emission, regardless whether the interaction with the cometary atmosphere decelerates the wind or not.
437
The slow wind contains more ions of higher charge states than the fast wind, resulting in a 'harder' X-ray spectrum. The most important features of a slow wind spectra are therefore the OVII and OVIII features above 500 eV. This implies that changes in cometary spectra are strongly linked to solar wind properties. To fully exploit the anticipated high-resolution spectra 4 7 of future missions such as ASTRO-E2 new detailed state selective charge transfer data is needed in particular for highly charged carbon and oxygen ions colliding on O, H2O and CO.
References 1. CM. Lisse, K. Dennerl, J. Engelhauser, M. Harden, F.E. Marshall, M.J. Mumma, R. Petre, J.P. Pye, M.J. Rickets, J. Schmitt, J. Trumper, and R.G. West, Science, 274, 205 (1996) 2. K. Dennerl, J. Englhauser, and J. Truemper, Science, 277, 1625 (1997) 3. V.A. Krasnapolsky, M.J. Mumma, M. Abbott, B.C. Flynn, K.J. Meech, D.K. Yeomans, P.D. Feldman, and C.B. Cosmovici, Science, 277, 1488 (1997) 4. R.M. Haeberli, T.I. Gombosi, D.L. DeZeeuw, M.R. Combi, and K.G. Powell, Science, 276, 939 (1997) 5. K. Dennerl, Astron. Astrophys, 394, 1119 (2002) 6. McCammon, D., et al., Ap. J., 576, 188 (2002) 7. R.K. Janev and HP. Winter, Phys. Rep., 117, 265 (1985) 8. W. Fritsch and C D . Lin, Phys. Rep., 202, 1 (1991) 9. V. Kharchenko and A. Dalgarno, J. Geophys. Res., 105, 18351 (2000) 10. T.E. Cravens, Science, 296, 1042 (2002) 11. R. Wegmann, K. Dennerl, and CM. Lisse, 2004, Astron. Astrophys, 428, 647 (2004) 12. V. Kharchenko, M. Rigazio, A. Dalgarno, and V.A. Krasnopolsky, Ap. J. Lett, 585, L73 (2003) 13. P. Beiersdorfer, K.R. Boyce, G.V. Brown, H. Chen, S.M. Kami, R.L. Kelley, M. May, R.E. Olson, F.S. Porter, C.K. Stahle, and W.A. Tillotson, Science, 300, 1558 (2003) 14. D. Bodewits, Z. Juhasz, R. Hoekstra, and A.G.G.M. Tielens, Ap. J. Lett, 606, 81 (2004) 15. R. Pepino, V. Kharchenko, A. Dalgarno, and R. Lallement, Ap. J., 617, 1347 (2004) 16. D. Bodewits, A.G.G.M. Tielens, R. Morgenstern, and R. Hoekstra, NucLInstrum.Meth.B., 235, 358 (2005) 17. G. Lubinski, Z. Juhasz, R. Morgenstern, and R. Hoekstra, J. Phys. B: At. Mol. Opt. Phys., 33, 5275 (2000) 18. G. Lubinski, Z. Juhasz, R. Morgenstern, and R. Hoekstra, Phys. Rev. Lett., 86, 616 (2001) 19. J.B. Greenwood, I.D. Williams, S.J. Smith, and A. Chutjian, Ap. J. Lett, 533, 175 (2000)
438 20. D.M. Kearns, R.W. McCuUough, and H.B. Gilbody, Int. J. Mol. Sci., 3, 162 (2002) 21. L.F. Errea, A. Marias, L. Mendez, B. Pons, and A. Riera, J. Phys. B: At. Mol. Opt. Phys., 36, L135 (2003) 22. M. Albu, F. Aumayr, and HP. Winter, Int. J. Mass. Spec, 233, 239 (2004) 23. S.A. Stern, Nature, 424, 639 (2003) 24. http://deepimpact.jpl.nasa.gov/ 25. M. Neugebauer et al. J. Geophys. Res., 103,14587 (1998) 26. N.A. Schwadron and T.E. Cravens, Ap. J., 544, 558 (2000) 27. W.-H. Ip, Astron. Astrophys., 92, 95 (1982) 28. I. de Pater and J.J. Lissauer, Planetary sciences (Cambridge University Press) (2001) 29. W.F. Huebner, J.J. Keady, and S.P. Lyon, Astroph. Sp. S. , 195,1 (1992) 30. V.A. Krasnapolsky and M.J. Mumma, Ap. J., 549, 629 (2001) 31. S.A. Fuselier, E.G. Shelley, B.E. Goldstein, M. Neugebauer, W.-H. Ip, H. Balsiger, and H. Reme, Ap. J., 379, 734 (1991) 32. N. Biver, et al., Science 275, 1595 (1997) 33. L. Haser, Bull. Acad. Roy. Sci. Liege, 43, 740 (1957) 34. M.C. Festou, Astron. Astrophys., 95, 69 (1981) 35. A. Niehaus, J. Phys. B: At. Mol. Phys., 19, 2925 (1986) 36. C M . Lisse, D.J. Christian, K. Dennerl, K.J. Meech, R. Petre, H. Weaver, and S.J. Wolk, Science., 292, 1343 (2001) 37. R. Hoekstra, D. Ciric, F.J. de Heer, and R. Morgenstern, Phys. Scr. T., 28, 81 (1989) 38. A.A. Hassan, F. Eissa, R. Ali, D.R. Schultz, and P.C. Standi, Ap. J. Lett, 560, 201 (2001) 39. C M . Lisse, D.J. Christian, K. Dennerl, S.J. Wolk, D. Bodewits, R. Hoekstra, M.R. Combi, T. Makinen, M. Dryer, C D . Fry, and H. Weaver, Astron. Astrophys., submitted (2005) 40. R.W. McCuUough, T.K. McLaughlin, T. Koizumi, and H.B. Gilbody, J. Phys. B: At. Mol. Opt. Phys., 25, L193 (1992) 41. W.R. Thompson, M.B. Shah, and H.B. Gilbody, J. Phys. B: At. Mol. Opt. Phys., 29, 725 (1996) 42. W.R. Thompson, M.B. Shah, and H.B. Gilbody, J. Phys. B: At. Mol. Opt. Phys., 29, 2847 (1996) 43. F.W. Bliek, G.R. Woestenenk, R. Hoekstra, and R. Morgenstern, Phys. Rev. A., 57, 221 (1998) 44. J.G. Wang, P.C. Standi, A.R. Turner, and D.L. Cooper,P/i3/s. Rev. A., 567, 012710 (2003) 45. V. Kharchenko and A. Dalgarno, Ap. J. Lett, 554, L102 (2001) 46. J.B. Greenwood, I.D. Williams, S.J. Smith, and A. Chutjian, Phys. Rev. A., 63, 062707 (2001) 47. P. Beiersdorfer, H. Chen, K.R. Boyce, G.V. Brown, R.L. Kelley, C.A. Kilbourne, F.S. Porter, and S.M. Kahn, Nucl. Instrum. Meth. B., 235, 116 (2005) 48. V.A. Krasnapolsky, D.J. Christian, V. Kharchenko, A. Dalgarno, S.J. Wolk, CM. Lisse, S.A. Stern, Icarus, 160, 437 (2002)
P R O D U C T I O N OF 0 2 + + N E U T R A L S F R O M T H E COLLISION OF C 3 + W I T H WATER.
H. LUNA * NCPST and School of Physical Science, Dublin City University, Dublin 9, Republic of Ireland.
Glasnevin,
P. M. Y. GARCIA AND G. M. SIGAUD Departamento de Fisica, Pontificia Universidade Catdlica do Rio de Janeiro, RJ 22452-970, Brazil. M. B. SHAH Department of Pure and Applied Physics, Queens University Belfast, BT7 INN, UK.
Belfast
E. C. MONTENEGRO Instituto de Fisica, Universidade Federal do Rio de Janeiro, Cx. Postal 68528, Rio de Janeiro, RJ 21941-972, Brazil
Water double ionisation by heavy ions, in the energy range where the Bragg peak maximizes, is of key importance for heavy ion therapy. Because double ionised water molecule is not stable, it will dissociate, leading to different channels involving the formation of two single charged fragments or one double charged fragment. In this work we have measured the production of 0 2 + (plus neutrals) by C 3 + from 1 to 3.5 MeV energy range. Three different channels will contribute for the O z + production, namely: transfer ionisation, direct ionisation and single electron loss. Our results were compared to an atomic case, neon, where a recent experimentaltheoretical work has been done 26 .
1. Introduction. T h e interest on the interaction of atoms, ions, electrons and photons with water molecule is of key interest for many fields in science, ranging from the fundamental understanding of the molecular dissociation to its applica* email: [email protected]. ie
439
440
tion in bio and medical physics. In most of the cases, the need of accurate absolute cross sections and information about the fragmentation products became important. Two examples in vogue are: first, modelling of astrophysical systems such as the UV and x-ray emission from comets *. Second, the use of heavy energy ions in the treatment of tumours as an alternative (less aggressive and more effective) to the x-ray treatment 2 . To date, several works have been done concerning the study of water dissociation in the gas phase state. The first atomic data on ionisation date from 1968 of Toburen et al 3 where single electron capture and loss were measured for proton and neutral hydrogen in the energy range of 100 to 2500 keV. In 1978, K. H. Tan and co-workers 4 measured the absolute oscillator strengths (10-60 eV) for photoabsorption and break-up of water, using the electron impact coincidence techniques, often referred as the dipole (e,2e) method. The study of the water dissociation by electron impact was extended and partial cross sections were measured to electron energies impact up to 1 keV 5 , e . Recently, using synchrotron radiation, the resonant photofragmentation of water near the oxygen K edge was studied by Piancastelli et al7,s and Stolte et al9. Prom 1985 to 1988 Rudd and co-workers 10-15 published extensive data of total cross sections for proton impact ionisation 10 and electron capture, ionisation and electron loss by He + n followed by the study of angular and energy dependence of the cross sections for ejection of electrons from the water molecule induced by electrons 12>13, protons 14 and atomic hydrogen 15
In 1995 Werner et al16 studied the multiple ionisation and fragmentation of water by protons from 100 to 350 keV, obtaining partial cross sections for the production of positive ions and fragmentation cross-sections involving the multiple ionisation channels H + + H + + Oq+ (q = —1,0,1 and 2). Later, Gobet et al17,18 and Seredyuk et al19 extended the study of single electron capture in the collision of proton and He 2 + with water to the lower keV range. Concerning heavy ion projectiles, Greenwood et al 2 0 , Pesic et al 21 , Olivera et al22, and Luna and Montenegro 23 studied the water dissociation with different foci. Greenwood et al was interested in obtaining absolute total single and double electron capture cross sections of highly charged Carbon, Nitrogen and Oxygen ions with molecules of interest on cometary atmospheres in order to obtain absolute line-emission intensities. In this case, the ion energy studied was compatible with the solar wind range (few keV/u). Pesic et al studied the energy and angular distribution of fragment
441
ions from the collisions of 2-90 keV Ne 9 + ions (q = 1,3,5,7 and 9). Olivera et al, on the other hand, focused on tumour cancer ion therapy using a heavy ion beam of Xe 4 4 + at 6.7 MeV/u. In our previous work 23 , we have studied the water dissociation by C 3 + over energies near the Bragg peak. In this collision regime the production of 09+ was found to be bigger than the H 2 0 + . This result has a direct implication in the subsequent fast chemistry near an ionisation site, in particular on the oxygen production in the first stage of the water radiolysis. In this work, we make a closer look into the water dissociation for a particular multiple ionisation reaction, the production of 0 2 + + neutrals. We have measured absolute cross sections for the following collision channels: transfer ionisation, H20 + C 3 + - > 0 2 + + H + H + e + C2+
(1)
direct double ionisation, H 2 0 + C 3 + -> 0 2 + + H + H + 2e + C 3 +
(2)
single electron loss, H 2 0 + C 3 + ^ 0 2 + + H + H + 3e + C 4 +
(3)
2. E x p e r i m e n t . The experimental set-up used in this work has been described previously 24 and detailed description on the experimental apparatus will not be given here. Shortly, a collimated mono-energetic C + beam delivered by the 4MV Van de Graaff accelerator of the Catholic University of Rio de Janeiro is primarily analysed by a 90 degree magnet. The monoenergetic beam crosses a stripper where the highly charged components C 3 + are produced. The desired beam charge state component is selected and directed onto the experiment beam line by a subsequent switching magnet. After coUimation, the beam is cleaned from the spurious components just before the collision chamber by a third small magnet. After crossing the collision chamber where the gas cell is placed, the main and the product beams are separated by a forth magnet and detected by a position sensitive MCP detector placed at the end of the beam line 4 m downstream.
442
~-> I
coincidence 1o pump <)ZZD
3
Ilk..
MCP position-sensitive MCP
0 5 + ,0 4 + ,0 3 +
L;^
analyzing magnet
slits Figure 1. Schematic diagram of the apparatus, used in the Van de Graaff laboratory, PUC-Rio.
The target is formed by an effusive water vapour set-up, formed by a manifold system welded to a Pyrex bottle containing de-ionized water. The system is primary pumped by an external rough pump until the pressure inside the bottle decreases to the point where the water turns into ice. At this stage, all the gases (N2 and O2) have been pumped out. The pump is then valved off and the iced water is warmed up. In order to assure a pure H2O target the process is repeated to drive out any remaining dissolved gas. The water is subsequently allowed to sublimate into the cell and the flux is controlled by fine needle valve. The pressure inside the gas cell is measured by an absolute capacitive manometer (MKS-Baratron). Determination of the gas pressure for water vapour is more difficult than standard molecular gases. Working with H2O requires longer time for the capacitance diaphragm reach the equilibrium (order of few minutes) and significant drift of the zero reading can occur. We overcame this problem by doing a set of shorter measurement
443
runs and checking the zero reading of the gauge each run. Typical pressures used during the measurements in the target cell are between 0.5 to 1 mtorr. Without the target, the pressure is better than 1 0 - 6 torr. Total single electron capture is obtained by the grow-rate method, and is used to obtain the efficiency of the coincidence measurements. This procedure is fully described in Santos et al.24'25. The cross sections for positive target production, namely, H + , 0 + , OH + and I^O"1", are obtained by standard time-of-flight coincidence technique. The use of a strong transverse electric field (960 V/cm) assures the maximum collecting efficiency for all target products. A schematic diagram of the experimental apparatus is shown in Fig.l. The time of flight spectra are recorded simultaneously with the projectile image in an event-by-event mode. The data reduction is made off-line and the coincidence channels (1), (2), and (3), are evaluated.
3. Results. 3.1. Transfer
Ionisation.
Our results are summarised in Figs. 2, 3 and 4 for 0 2 + production through transfer ionisation (1), double ionisation (2) and electron loss (3). In Fig. 2 we present on the left side the transfer ionisation by C 3 + on neon 26 (open triangle) and water (closed triangle) leading to the formation of Ne 2 + and 0 2 + (plus neutrals) - channel (1), respectively. On the right side we show the ternary plot discussed in Ref. 23 for capture data (single capture + transfer ionisation). The collision energy is plotted for each measured point. From the comparison of both targets we can note that the cross sections for the atomic case are roughly twice the molecular one. This is expected since for water molecules, contrary to atoms, double electron removal leading to doubly ionised oxygen is not the only resulting outcome of the transfer-ionisation channel. Other dissociative channels related to the production of two charged species, i.e. H + plus H + , 0 + or OH + , have a significant contribution as well. Following the theoretical analysis of Kirchner et al. 26 , for this energy range post collisional mechanisms, such as Auger decay, can be neglected. In fact, post collisional decay is only expect to play an important role in the multiple ionisation of atoms 2 8 , 2 9 and molecular dissociation 30>23, for projectile velocities much higher than the range studied in this work. Therefore the production of 0 2 + by transfer-ionisation is mostly due to a direct process, in both cases.
444
Energy (MeV)
P, (H,0*)
Figure 2. On left, our results for transfer ionisation for Ne (open triangles) and channel (1) (closed triangles). On right the ternary plot of capture d a t a (single capture plus transfer ionisation - close triangles). The dipole •region is represented by the electron and photon impact dissociation d a t a of Rao et al. (crossed circles) and Tan et al. (side open triangles), respectively.
3.2. Double
Ionisation.
In Fig.3, we compare the double direct ionisation of water and neon by C 3 + impact for energies ranging from 1 to 3.5 MeV. For direct double ionisation (2), the cross sections are also lower than the Ne 2 + production. Here again we shall invoke the competition of the other dissociative channels leading to the production of two ionised species. The comparison on the energy trend between the atomic and molecular cases, for the double ionisation shows a quite different behaviour for energies above 2 MeV. For energies above 2 MeV, there is a pronounced decrease on the 0 2 + production, not seen in the Ne 2 + case. For this particular molecular dissociation channel the maximum is reached at energies around 2.5 MeV while, according to the calculations of Kirchner et al. 26 , the cross sections for direct double ionisation of neon reach its maximum at approximately 5 MeV. Post-collisional decay can be discarded to explain such change on the energy trend for the molecular case; in fact, any contribution from Auger decay would instead lead to an enhancement of the 0 2 + production, via mostly post collisional 0 + * de-excitation. The different behaviour of the 0 2 + production in the water case might be due to the decrease of the branching ratio leading to this particular dissociation channel compared to others, when the double removal occurs through ionisation.
445
Energy (keV/u)
P (H,0+)
Figure 3. On left our results of double ionisation cross sections for Ne (open squares) and channel (2) (closed squares). On right, same as Fig. 1 with the direct ionisation data represented by closed squares.
3.3. Electron
Loss.
The electron loss channel of C 3 + with double target ionisation Ne 2 + and 0 2 + (plus neutrals) is shown in Fig. 4. At the energy range studied in this work, the electron-electron process is below the threshold, given by v2/2 > Ip + Jt, so that the electron loss shall be dominated by the screening interaction. The comparison between water and neon shows clear differences as compared with the previous cases for both the energy trend and the absolute values. For example, for 3.5 MeV the molecular cross section is larger than the atomic one, an inversion which was not observed for the transfer ionisation or ionisation cases. A possible reason for this behaviour might be a multi-centre effect. In the projectile frame, the ionisation is due to either a single centre with charge ten surrounded by an electron cloud, in the Ne case, or by a threecentre body, with two protons and one nucleus with charge eight, also surrounded by an electron cloud, in the water case. Apparently, for some energies, the three body configuration, even presenting a smaller maximum electric potential, can be a more effective ionising agent of the C 3 + ions. Theoretical calculations are needed to clarify this point. A similar behaviour was seen, for example, in the collisional analysis of hydrogen clusters H+ n = 3 to 31 (odd) and atoms at 60 keV/u. For those clusters the electron loss is strongly dependent on the cluster size. The
446
Energy (MeV)
p
(H
Q+)
Figure 4. On left our cross sections of single electron loss with double target ionisation for Ne (open circles) and channel (3) from the water dissociation (closed circles). On right, same as Fig. 1 with the electron loss data represented by closed circles.
electron capture, on the other hand, was found to be independent of it
31
.
4. Discussion and Conclusions. The 0 2 + production is of particular importance to water radiolysis, because its high reactivity with the medium after the first ionisation stage caused by the impinging ion. The 0 2 + is expected to neutralise as 0 ( 1 D ) or 0 ( 3 P ) , where the former will react rapidly with the water molecules while the later can react with OH forming HO2 32 . In order to analyse the efficiency in the production of such cation, we computed the ratio between 0 2 + total production and the total positive ion production (ionisation + capture + electron loss for carbon or double capture for oxygen). This is shown for C 3 + (open squares), 0 5 + (full squares) (our unpublished data) and protons (stars) 16 ' 17 in Fig. 5. It is interesting to note that in the Bragg peak range (50 to 500 keV/u) the ratio remains constant for heavy ions and decrease for protons. The enhancement in the production efficiency between heavy ions and protons is significant. It increases from one to two orders of magnitude along the Bragg peak. The higher efficiency in the production of 0 2 + by heavy ions compared to protons supports the idea of Ferradini et al. 3 3 where the observed increase in the O2 production by particles with high Linear Energy Transfer (LET) is due to the increase of atomic oxygen production in primary collisions. Therefore, heavy ion therapy would release more 0 9 + ions and substantial amounts of energetic
447
10"'-
•
/ total
/•—N
I
D
"
D
D a
N
io2-
Ratio
g
~*~~*lg---**
* &UJK
irr3-
20
100
500
Energy (keV/u) Figure 5. Ratio between 0 2 + + 2H and the total positive ion production, for: C 3 + - (open squares) and our unpublished data of O s + - (closed squares). The velocity equivalent results of protons are represented by stars.
electrons compared to protons. This excess of energetic electrons together with the formation of high amounts of reactive water radicals would explain the different bio-responses observed with C-ion and proton tumour therapies and differences in the production of oxidizing species in water radiolysis. Finally, this paper presents experimental data on the double ionisation, transfer ionisation and electron loss cross sections from the interaction of C 3 + projectile with the water molecule in the gas phase. A particular channel involving the production of a single double ionised specie ( 0 2 + + neutral) was discussed in comparison to Ne, the atomic case with the same number of electrons. We have shown that for the 0 2 + + 2H production by transfer ionisation channel, a similar energy dependence with the neon case can be assigned, and in accord to the analysis of Kirchner et al. 2 6 , Auger decay can be disregarded. Although the double direct ionisation and electron loss channels showed a quite different energy dependence when the molecular cross sections were compared to the atomic one, the presence of any Auger type
448 processes could not be assigned for the 0 2 + production channels. Acknowledgments This work was supported by the Brazilian Agencies C N P q , F A P E R J , C A P E S and M C T ( P R O N E X ) . References 1. 2. 3. 4.
T. E. Cravens, Science 296, 1042 (2002). N. Yamamoto et al., Lung Cancer 42, 87 (2003). L. H. Toburen, M. Y. Nakai and R. L. Langley, Phys. Rev. 171, 114 (1968). K. H. Tan, C. E. Brion, Ph. E. Van der Leeuw, and M. J. Van der Wiel, Chem. Phys. 29, 299(1978). 5. M. V. V. Rao, I. Iga, and S. K. Srivastava, J. Geophys. Res. 100, 26421 (1995). 6. H. C. Straub, B. G. Lindsay, K. A. Smith and R. F. Stebbings, J. Chem. Phys. 108, 109-116 (1998). 7. M. N. Piancastelli, A. Hempelmann, F. Heiser, O. Gesser, A. Rudel and U. Becker, Phys. Rev. A 59, 300 (1999). 8. M. N. Piancastelli, R. Sankari, S. Sorensen, A. De Fanis, H. Yoshida, M. Kitajima, H. Tanaka and K. Ueda, Phys. Rev. A 71, 010703 (2005). 9. W. C. Stolte, M. M. Sant'Anna, G. Ohrwall, I. Dominguez-Lopez, M. N. Piancastelli, and D. W. Lindle, Phys. Rev. A 68, 022701 (2003). 10. M. E. Rudd, T. V. Goffe, R. D. DuBois and L. H. Toburen, Phys. Rev. A 31, 492 (1985). 11. M. E. Rudd, Akio Itoh and T. V. Goffe, Phys. Rev. A 32, 2499 (1985). 12. M. A. Bolorizadeh and M. E. Rudd, Phys. Rev. A 33, 882 (1986). 13. K. W. Hollman, G. W. Kerby III, M. E. Rudd, J. H. Miller and S. T. Manson, Phys. Rev. A 38, 3299 (1988). 14. M. A. Bolorizadeh and M. E. Rudd, Phys. Rev. A 33, 888 (1986). 15. M. A. Bolorizadeh and M. E. Rudd, Phys. Rev. A 33, 893 (1986). 16. U. Werner, K. Beckord, J. Becker, and H.O. Lutz, Phys. Rev. Lett. 74, 1962 (1995). 17. F. Gobet, B. Farizon, M. Farizon, M. J. Gaillard, M. Carre, M. Lezius, P. Scheier, and T. D. Mark, Phys. Rev. Lett. 86, 3751 (2001). 18. F. Gobet, S. Eden, B. Coupier, J. Tabet, B. Farizon, M. Farizon, M. J. Gaillard, M. Carre, S. Ouaskit, P. Scheier, and T. D. Mark, Phys. Rev. A. 70, 062716 (2004). 19. B. Seredyuk, R. W. McCullough, H. Tawara, H. B. Gilbody, D. Bodewits, R. Hoekstra, A. G. G. M. Tielens, P. Sobocinski, D. Pesic, R. Hellhammer, B. Sulik, N. Stolterfoht, O Abu-Haija and E. Y. Kamber, Phys. Rev. A. 71, 022705 (2005). 20. J. B. Greenwood, J. D. Williams, S. J. Smith and A. Chutjian, Astrophys. J. 533, L175 (2000). 21. Z. D. Pesic, J.-Y. Chesnel, R. Hellhammer, B. Sulik, and N. Stolterfoht, J. Phys. B. At. Mol. Opt. Phys. 37, 1405 (2004).
449 22. G. H. Olivera, C. Caraby, P. Jardin, A. Cassimi, L. Adoui, and B. Gervais, Phys. Med. Biol. 4 3 , 2347 (1998). 23. H. Luna and E. C. Montenegro, Phys. Rev. Letters 94, 043201 (2005). 24. A.C.F. Santos, W.S. Melo, M.M. SantAnna, G.M. Sigaud and E.C. Montenegro, Phys. Rev. A 63, 062717-1 (2001). 25. A.C.F. Santos, W.S. Melo, M.M. SantAnna, G.M. Sigaud and E.C. Montenegro, Rev. Sci. Instrum. 73, 2396 (2002). 26. T. Kirchner, A.C.F. Santos, H. Luna, M.M. SantAnna, W.S. Melo, G.M. Sigaud and E.C. Montenegro, Phys. Rev. A 72, 012707-1 (2005). 27. W.S. Melo, M.M. SantAnna, A.C.F. Santos, G.M. Sigaud and E.C. Montenegro, Phys. Rev. A 60, 1124 (1999). 28. T. Spranger And T. Kirchner, J. Phys. B: At. Mol. Opt. Phys. 37, 4159 (2004). 29. E. G. Cavalcanti, G. M. Sigaud, E. C. Montenegro, M. M. Sant'Anna and H. Schmidt-Bocking, J. Phys. B: At. Mol. Opt. Phys. 35, 3937 (2002). 30. H. Luna, E. G. Cavalcanti, J. Nickles, G. M. Sigaud, E. C. Montenegro , J. Phys. B: At. Mol. Opt. Phys. 36, 4717 (2004). 31. S. Louc, B. Farizom, M. Farizon, M. J. Gaillard, N. Goncalves, H. Luna, G. Jalbert, N. V. de Castro Faria, M. C. Bacchus-Montabonel, J. P. Buchet, and M. Carre, Phys. Rev. A 58, 3802 (1998). 32. J. Meesungnoen, A. Filali-Mouhim, N. S. Ayudhya, S. Mankhetkorn, and J. P Jay-Gerin, Chem. Phys. Lett. 377, 419 (2003). 33. C. Ferradini and J. P. Jay-Gerin, Rad. Phys. Chem. 5 1 , 263 (1998).
VECTOR CORRELATION OF FRAGMENT IONS PRODUCED BY COLLISION OF AR11+ WITH DIMETHYLDISULFIDE T. MATSUOKA, N. MACHIDA, H. SHIROMARU AND Y. ACHIBA Department of Chemistry, Tokyo Metropolitan University Hachioji, Tokyo 192-0397, Japan Dissociation scheme of highly ionized dimethyldisulfide was studied, focusing attention onto the vector correlation of C and S atomic fragment ions, which would be a function of the molecular structure. The dihedral angle of the C-S-S-C frame was reasonably reproduced, and two enantiomers, or rotational isomers, were distinguished by the vector correlation.
1. Introduction In our previous papers [1-3], we reported that information on the structure of organic molecules would be obtained by vector correlation of the fragment ions produced from highly charged parent ions, namely, Coulomb explosion imaging (CEI [4]) would be applicable to neutral species. For example, a "dynamic" chirality induced by the zero-point vibrations was observed for methan-d4 [1]. Near Coulombic dissociation of highly ionized benzene [2] and substituted benzenes [3] also allows diagnosis of molecular frame, implying that the CEI technique would be also applicable to polyatomic molecules up to the size of benzene if these are highly ionized and proper molecular parameters were selected. In the present work, the molecular torsion and resultant chirality of dimethyldisulfide (CH3-S-S-CH3, hereafter DMDS) was analyzed by the CEI. The conformation of DMDS is characterized by C-S-S-C bond dihedral angle, known to be the most stable at near 90 degree [5]. In gas- or liquid phase, the enantiomers of DMDS, namely P- and M-DMDS, easily exchange with each other by internal rotation around S-S axis, however, the fragmentation scheme of highly charged DMDS is expected to be chirality-sensitive. 2. Experimental The experimental setup has been described in previous publications, and briefly outlined here. Projectile Ar11+ ions were extracted by 15kV from an electron
450
451 cyclotron resonance ion source [6], and after passing through a 0.5 mnup aperture, these ions were collided with the target molecules. The fragment ions produced by the collisions were extracted and accelerated in an electric field, typically 438 V cm"1 and 300 V cm"1, respectively. The free flight length was 14.45 cm. The position-sensitive time-of-flight (PSTOF) measurements were triggered by the detection of the Auger electron(s), and the x-y position of each detected fragment ion was measured by using a two-dimensional positionsensitive detector, which consisted of a 120 mm
1.0
o.o
2.0
3.0
TOF(ns) Fig. 1. TOF spectrum of fragment ions produced by the collision of Ar"+ with DMDS. The inset is the spectrum in the expanded scale.
latter is most likely originated from the 3 r charge states higher than 10. 1 ' Dissociation of highly ionized large s* molecules naturally provides many fragment ions, and the finite detection 1. efficiency seriously reduces the number of § 1.5 c* multiple coincidence events in which all the ions are detected. In stead, four-fold . " cu coincidence events including all C and S c3* ions were analyzed in the present study, 0.5 assuming the effect of H + in the velocity 0.5 1.5 2 of heavier ions is small. The coincidence TOF(us) map for the relevant events is shown in fig. Fig.2. TOF coincidence map for the C 2. and S ions. Using the initial velocity vectors -
•
•
!
452 calculated from PSTOF data, the vector correlation of the velocities of these ions was examined. Figures 3a and 3b show the schematic drawings of DMDS of different chirality, in which hydrogen atoms are omitted, and subscripts 1 and 2 are used to distinguish lower and upper atom, respectively. Rough images of velocity vectors of fragments C2 and S2 are also shown. Several parameters related to the C-S-S-C molecular frame are defined as follows: P\
= v
x v
c\
;
s\
(3b) M-DMDS
perpendicular to the
plane involving VC1 a n d v x l . 1C2
p2 — vC2 x v S 2 ; perpendicular to the
X
I
X
U.SS = PI P\ \PI P\\
;
•3 the
The vector qcx = (uss • v c l )uss is the
and qC2
Pi
=
(3c) Vectors relevant to the dihedral angle and chirality.
of VC1 onto the Uss axis, is that for v C 2 . The vectors
Vi = vcl - qcx and v 2 = v C 2 - qC2 are projection of the velocity vectors of Q and C2, respectively, onto the axis perpendicular to the S-S axis. The vectors with subscript "2" for the P-DMDS are schematically shown in fig. 3c, together with j3j . Then, the information on the dihedral angle 9 can be derived by 0
;
unit
vector closely parallel to the S-S axis, directed from Si to S2.
projection
C2
M,
plane involving v C 2 and vS2.
c o s
- i ^ )
and the chirality
can be judged by the parameter (p = COS
v2(B)
(3d) Schematic view of the angles 6 and 9 for the P-DMDS. The vector V2 for the M-DMDS is indicated by the dashed
Fig. 3 Schematic view of the relevant vectors. (5, «V2) Ii—j—, as shown in fig. 3d.
453
Figures 4a and 4b show the histograms of 9 and q>, respectively. It should be noted the vectors related to the angle 9 or
(4b)
40
83
•
30 • • •
•
•
0
U 20
% •
•
n/2
7t
• •• • • •• •
10 0
0 (rad)
nil
Fig. 4. Histograms of the angle 9 (4a) and angle 8 (4b).
This work is partially supported by Grant-in-Aid for Scientific Research, 14204062 and 16032211. References 1. 2. 3. 4. 5. 6. 7. 8.
T. Kitamura et al., J. Chem. Phys., 115, 1, 5, (2001). G. Veshapidze et al., J. Phys., B 37, 2969, (2004). M. Nomura et al., Int. J. Mass Spectrom., 235, 43, (2004). Z. Vager et al., Science, 244, 426 (1989). M. Meyer, J. Mol. Struct. 273, 99, (1992). H. Tanuma et al., J. Chinese Chem. Soc. 48, 389, (2001). T. Mizogawa et al., Nucl. Instrum. Methods Phys. Res. A 366, 129, (1995). T. Matsuoka et al., to be published.
SLOW MULTIPLY CHARGED ION-MOLECULE COLLISION DYNAMICS STUDIED THROUGH A MULTI-COINCIDENCE TECHNIQUE
T. KANEYASU UVSOR Facility, Institute for Molecular Science Myodaiji, Okazaki 444-8585, Japan E-mail: [email protected] T. AZUMA AND K. O K U N O Department of Physics, Tokyo Metropolitan University Minami-Ohsawa, Hachioji, Tokyo 192-0397, Japan We have studied collision dynamics and reaction processes of Kr 8 ++N2 system below 200 eV/u by means of a multi-coincidence technique. Reaction channels in the single-, double- and triple-charge changing collisions have been fully resolved and their related electronic states have been revealed using the measured Q-value spectra and kinetic energy release distributions. In the low energy collisions, "anisotropic fragmentation" was found for asymmetrically charged fragmentation channels. This anisotropy is enhanced by decreasing the collision energy and increasing the charge asymmetry. The "anisotropic fragmentation" should be caused from rotation of the molecular axis induced by polarization effect and post collision interaction.
1. Introduction Slow collisions of Multiply Charged Ion (MCI) with molecular targets are dominated by charge transfer processes often followed with fragmentation of molecular target and emission of electron(s). The collision dynamics are much more complicated, comparing with those of atomic targets, because the molecular target has additionally vibrational and rotational freedom. Generally, the Pranck-Condon principle is valid for molecular transitions in the keV energy region, and the potential energy difference between the intermediate molecular ion and the final fragments is released as kinetic energies of fragments. Previous investigations of the MCI-molecule collisions frequently have been done by the measurement of kinetic energy release (KER) distributions in the fragmentation 1 - 6 . However, in their
454
455
experiments, it is impossible to obtain the reaction energy (Q-value) of the related process which is essentially important for analysis of reaction mechanism and collision dynamics. So far energy gain spectra of projectiles in MCI-molecule collisions have rarely been measured in coincidence with fragments to investigate their reaction pathways 7 . Recently, we have developed a multi-coincidence technique by means of simultaneous measurements of angle-resolved energy gains of the charge-changed projectile and time-of-flight (TOF) spectra of fragments in every collision event, which enables us to determine various collision parameters such as Q-value, scattering angle, recoil momentum and KER. We have studied charge changing collisions of Kr 8 ++N 2 below 200 eV/u 8 - n . The detailed analysis using the multi-coincidence experiment has been performed on the single-charge (SC), the double-charge (DC) and the triple-charge (TC) changing collision of Kr 8 + +N 2 at 19 and 48 eV/u 1 0 ' n . In this report, the characteristics of the slow MCI-molecule collision dynamics will be discussed.
2. Experiment The experimental setup and the coincidence technique utilized in the present work have already been shown in the previous papers 10>11. Briefly, the MCI beam extracted from the Mini-EBIS collides with an effusive molecular flow of the target gas in the collision region, where is field free to keep the initial scattering angles unchanged. Two TOF analyzers facing each other are set on each side of the beam axis in the horizontal plane, and the analyzer axis is perpendicular to the beam direction. Fragment ions leaving the collision region are injected into each TOF analyzer, in which an ion beam guide system is used as a flight tube. The acceptance solid angle of each analyzer corresponds to 1/12 of the full solid angle and the length of the flight tube is 25 cm. The use of the ion beam guide system improves detection efficiency for target ions dramatically and makes possible the KER analysis with slowdown of flight velocity. Angle-resolved energy gain spectra of the charge-changed projectile are measured by the parallel plate energy analyzer with a two-dimensional position-sensitive-detector (PSD). In the multi-coincidence experiment, two TOF spectra of a pair of the fragment ions are triggered by the detection of the charge-changed projectile. We obtain four-dimensional data set of (X,Y,TA,TB) for every collision event, where (X, Y) represents the position of the projectile on the PSD and (TA,TB) denotes the flight time set of the fragment ion pair.
456
3. Results and Discussion The details on the reaction channels of the SC, DC, TC and quadruplecharge (QC) changing collisions in the Kr 8+ +N2 system have been reported in the previous papers 8 _ u . The SC collision is dominated by the pure single electron capture of the projectile producing molecular Nf ions, and every dominant process in the DC, TC and QC collisions is multielectron capture processes followed by emission of electron(s). We have found three low-energy collision phenomena, "peak-shifting" of the molecular ions, "peak-splitting" and "anisotropic fragmentation" of the fragment ion pairs, in the TOF spectra of the target ions. By careful analysis of kinematics of all the products, these phenomena have been confirmed to be originated from the collisions! momentum transfer between the ion and the molecule. 3.1. Analysis of reaction pathways in the SC
collision
8+
The SC collisions of the Kr + N2 system have been resolved into following reactions by the TOF measurement in coincidence with Kr 7 + product ion. Kr 8+ + N2 -> Kr 7+ ->• Kr 7+ -+ Kr 7+ -> Kr 7+
+ + + +
Nj N?.+ + e~ N+ + N+ + e~ N + + N 2 + + 2e-
(1) (2) (3) (4)
In order to assign electronic states of related ions in the reaction, the Q-value is required. The Q-value spectra and scattering angle distributions for the reactions (l)-(4) are extracted from the image of the Kr 7+ ions on the PSD as demonstrated in Fig. 1. The KER distributions in the fragmentation and the transverse recoil momentum are derived from the two-dimensional coincidence map of fragments by considering the kinematics of the colliding particles n . By using the KER distributions, Q-value and the potential energy curves of the molecular ions N j + {q = 1 — 3) 12 , we have identified reaction pathways in the SC collisions of the Kr 8+ +N2 below 200 eV/u. The dominant process in the SC collision is identified as follows; Kr 8+ + N2 -> Kr 7+ (n/)(n > 5) + N j . Molecular states are assigned as Nj(X 2 E+, A 2 II 9 ,B 2 E+). The reactions (2)-(4) are multi-electron capture processes followed by the autoionization
457
N + + tvr
N + + NH
»tN+ + N2
N + + N2
x5 O-value / eV
\ x5 Scattering angle 0
/ degree
Figure 1. Q-value spectra (left panel) and scattering angle in the center-of-mass system distributions (right panel) for each reaction in the SC collisions of Kr 8 ++N2 at 48 eV/u. Total amount of the K r 7 + ions is presented as a chain curve.
of the excited Kr ions. In the reaction (2), doubly charged molecular ion N^ + (X 1 S+) is produced; Kr 8+ + N2 -»• Kr6+(5to'Z')(n' > 6) + N^ + -»Kr7++N^+ + e-. For the reaction (3), dissociative N^"1" states contribute. As seen in Fig. 2, the KER distribution of N + + N + has roughly two components: a peak at 6.5 eV and a shoulder at 9 eV. We assign the reaction pathway with the lower KER component at 6.5 eV as follows; Kr 8+ + N2 -> Kr 6 + (5ln'l')(ri > 6) + N|+ ->Kr7+-r-N++N++e-, where low-lying states of N^"1" (a 3 II u , A 1 ^ , d1^, D3IIff) contribute to the process and final states of the fragments are N+( 3 P)+N+( 3 P). For the KER component at 9 eV, molecular states are not resolved due to the existence of various potential energy curves. However, we assigned that a part of the
458 N+ + N+
N + + N 2+
KER/eV
KER/eV
Figure 2. KER distributions of N + + N+ channel (left panel) and N+ + N 2 + channel (right panel) in the SC collisions of Kr*+ + N2 below 200 eV/u.
potential energy curves of N?,4" between 46 and 60 eV corresponds to the reaction; Kr 8+ + N2 -> Kr6+(4Zn'/')(n' > 5) + N^ + ->-Kr7+ + N + + N + + e - . Triple electron capture takes place and a triply excited Kr 5+ ion autoionizes into Kr 7+ in the reaction (4). The potential energy region of N3,4" molecular ions are estimated to be 81 eV to 85 eV and final states are assigned to be N + ( 3 P)+N 2 + ( 2 P). Thus, the following reaction pathway is identified; Kr 8 + + N2 - • Krs+(4l7l'n"l")(n" -•Kr
7+
+
+N +N
2+
> 8) + N?,+ + 2e _ .
As identified in the SC collisions, the reaction pathways in Kr 8+ +N2 collisions can be assigned assuming the Franck-Condon transition even at the lowest collision energy of 9.5 eV/u. 3.2. Anisotropic
fragmentation
When the collision energy decreases, anisotropic fragmentation emerges in asymmetrically charged fragmentation channels. In Fig. 3, the fragment ion pair is observed on the coincidence map as the fast and slow ions owing to the transverse momentum transfer from the MCI to the target. In the
459
4.5 TOFA/ s
Figure 3. Anisotropic fragmentation observed in coincidence map of fragment ion pair in the TC collision of the K r ^ + N a at 48 eV/u. Fragmentation channels are (a) N 2 + + N 2 + , (b) N 3 + + N 2 + and (c) N 3 + + N + .
(a)
(b)
Figure 4. Schematic drawing of rotational effect of the molecular axis induced by post collision interaction between fragment ions and outgoing MCI in the subchannel of slow N« 1 + + fast N « a + (91 > 92). (a) Dissociation into N « 1 + + N * 2 + . (b) Molecular axis rotates by the post collision interaction.
current experiment, the fragmentation channel of N ? 1 + +N* 2 + is divided into two subchannels; Kr«+ + fast N«1+ + slow N" 2 * Kr*+ + slow N* , + + fast N""1".
(5) (6)
Figure 3 shows the coincidence maps of fragmentation channels in the TC collisions at 48 eV/u. The split island peaks on the coincidence map are
460
attributed to each subchannel. In the asymmetric fragmentation channel, the fast ion prefers to have higher charge state. The anisotropy is enhanced when the charge asymmetry of the ion pair increases with decreasing the collision energy. In MCI collision-induced fragmentation, an attractive polarization force is induced in incoming of the MCI to the neutral molecular target and a repulsive Coulomb force interacts among the colliding particles after the charge transfer reaction. Note that both of the interaction forces in incoming and outgoing of the MCI, should create a torque which rotates the molecular axis. When the slow ion (near to the MCI) has a higher charge, the molecular axis can rotate more significantly in comparison to the opposite case. We calculated the trajectories of the MCI and the fragments by numerical simulation for the fragmentation channel of N 2 + + N + in the DC collision of Kr 8+ +N2. It is obvious that the molecular axis rotates more effectively in the subchannel of slow N 2 + + fast N + , and the slow N 2 + moves away from the acceptance angle with decreasing the collision energy as schematically illustrated in Fig. 4. This rotational effect driven by the post collision interaction explains the experimental observation well and the effect should be significant in the lower collision energy and the larger charge asymmetry. Such a post collision interaction is predicted for hydrogen molecules by the CTMC model as an anisotropy of fragment emission angles 13. In addition, the polarization attractive potential between the incoming MCI and the target also rotates the molecular axis and contribute to the anisotropic fragmentation. According to the theoretical calculation using the three-center over-barrier model 14, it is indicated that polarized molecules may cause anisotropic fragmentations in slow MCI-molecule collisions. The incoming MCI induces the polarization effect in the target molecule, which may act as a polarized molecule. We conclude that the anisotropic fragmentation observed results from the rotational effect of the molecular axis due to the incoming and outgoing MCI, and the polarized molecule also enhances the anisotropy.
4. Conclusion The slow MCI-molecule collision dynamics has been investigated by means of the multi-coincidence technique. We have resolved reaction channels in the SC, DC, TC and QC collisions of Kr 8 ++N 2 below 200 eV/u. The slow Kr 8+ +N2 collision is characterized by the transverse recoil momentum, multi-electron capture followed by the autoionization process, and appearance of "anisotropic fragmentation". Using the Q-value spectra and KER
461 distributions, reaction pathways in the SC collision are clearly resolved. The "anisotropic fragmentation" was found in the asymmetric fragmentation channels. The anisotropy, which is strongly dependent on the collision energy and the charge asymmetry, is caused by the rotational effect of the target molecule due to the post collision interaction of the outgoing MCI. Furthermore, the polarization effect of the target molecule induced by the incoming MCI may contribute to the rotation of the molecular axis. References 1. A. Remscheid, B. A. Huber, M. Pykavyj, V. Staemmler and K. Wiesemann, J. Phys. B: At. Mol. Opt. Phys. 29, 515 (1996). 2. H. O. Folkerts, R. Hoekstra and R. Morgenstern, Phys. Rev. Lett. 77, 3339 (1996). 3. M. Tarisien, L. Adoui, F. Fremont, D. Lelievre, L. Guillaume, J-Y. Chesnel, H. Zhang, A. Dubois, D. Mathur, Sanjay Kumar, M. Krishnamurthy and A. Cassimi, J. Phys. B: At. Mol. Opt. Phys. 33 L l l (2000). 4. F. Fremont, C. Bedouet, M. Tarisien, L. Adoui, A. Cassimi, A. Dubois, J-Y. Chesnel and X. Husson, J. Phys. B: At. Mol. Opt. Phys. 33, L249 (2000). 5. I. Ali, R. D. DuBois, C. L. Cocke, S. Hagmann, C. R. Feeler and R. E. Olson, Phys. Rev. A 64, 022712 (2001). 6. P. Sobocinski, J. Rangama, G. Laurent, L. Adoui, A. Cassimi, J-Y. Chesnel, A. Dubois, D. Hennecart, X. Husson and F. Fremont, J. Phys. B: At. Mol. Opt. Phys., 35, 1353 (2002). 7. K. Motohashi and S. Tsurubuchi, J. Phys. B: At. Mol. Opt. Phys. 36, 1811 (2003). 8. M. Ehrich, U. Werner, H. O. Lutz, T. Kaneyasu, K. Ishii, K. Okuno and U. Saalmann, Phys. Rev. A 65, 030702R (2001). 9. T. Kaneyasu, K. Matsuda, M. Ehrich, M. Yoshino and K. Okuno, Phys. Scr. T92, 341 (2001). 10. T. Kaneyasu, T. Azuma and K. Okuno, Nucl. Instrum. Methods B 235, 352 (2005). 11. T. Kaneyasu, T. Azuma and K. Okuno, J. Phys. B: At. Mol. Opt. Phys. 38, 1341 (2005). 12. K. Ohtsuki, in private communication. 13. R. E. Olson and C. R. Feeler, J. Phys. B: At. Mol. Opt. Phys. 34 1163 (2001). 14. T. Ohyama-Yamaguchi and A. Ichimura Nucl. Instrum. Methods B 235, 382 (2005).
RECENT DEVELOPMENTS IN PROTON-TRANSFERREACTION MASS SPECTROMETRY ARMIN WISTHALER Institute of Ion Physics, Leopold-Franzens-University, Technikerstrasse 25, Ionimed Analytik GmbH, Technikerstrasse 21a, Innsbruck, 6020, Austria ARMIN HANSEL Institute of Ion Physics, Leopold-Franzens-University, Innsbruck, 6020, Austria
Technikerstrasse 25,
ALFONS JORDAN Ionicon Analytik GmbH, Technikerstrasse 21a, Innsbruck, 6020, Austria TILMANN D. MARK Institute of Ion Physics, Leopold-Franzens-University, Innsbruck, 6020, Austria
Technikerstrasse 25,
This progress report will cover both the basics and recent advances in Proton-TransferReaction Mass Spectrometry (PTR-MS), which is a successful example of the analytical application of reactive ion-molecule collisions. PTR-MS is a chemical ionization technique for volatile organic compounds (VOCs) based on proton transfer reactions with H30* primary ions. It allows for fast and highly sensitive measurements of organic trace gases in air. Recent technical improvements resulted in a 5 to 10-fold increase in sensitivity with current detection limits ranging from 10 to 100 pptV (3a, 1 sec signal integration). The PTR-MS response time is now on the order of 150 ms. Furthermore, the PTR-MS technique has been extended to the measurement of the inorganic trace gases nitrous acid (HNO2) and nitric acid (HNO3).
1. Basics of PTR-MS Proton-Transfer-Reaction Mass Spectrometry (PTR-MS) is a highly sensitive, real-time analytical technique for detecting volatile organic compounds (VOCs) in air, which was developed in the mid-1990's in the laboratories of the Institute of Ion Physics at the University of Innsbruck [1]. PTR-MS combines the concept of chemical ionization introduced by Field and Munson [2] with the
462
463
flow drift tube technique invented by Ferguson and his colleagues [3]. The PTR-MS technique has been extensively described in the literature [4, 5, 6, and references therein], thus only a brief outline is given here. As an aid to understand the principle of operation a schematic drawing of the PTR-MS is shown in Figure 1.
Figure 1. Schematicrepresentationof the PTR-MS apparatus
A hollow cathode (HC) discharge and a source drift region (SD) act as an ion source producing H 3 0 + ions from pure water vapor. The H 3 0 + ions are injected into a flow drift tube, which is continuously flushed with sample air at a pressure of approximately 2 mbar. The primary ions undergo non-reactive collisions with any of the common components in air (N2, 0 2 , Ar, CO2, ...). Most VOCs have higher proton affinities (PA) than H 2 0 (7.16 eV [7]) and in these cases a collision with the H 3 0 + ion will result in the proton transfer reaction below: H 3 0 + + VOC -» VOCH+ + H20 +
+
(1)
Primary H 3 0 ions and product VOCH ions are mass selected in a quadrupole mass spectrometer and counted by a secondary electron multiplier/pulse counting system. Most VOCs are not fragmented upon protonation and are detected at a mass-to-charge ratio equal to their molecular weight +1 amu. If fragmentation occurs the major fragmentation reactions of VOCH* ions often involve elimination of stable neutral molecules, e.g. proton transfer from H 3 0 + to alcohols or aldehydes involves the elimination of H20 [8, 9]. The electric
464
field along the drift tube maintains a sufficiently high ion collision energy to prevent significant formation of cluster ions of the type H30+(H20)„ and VOCH+(H20)n (n=l,2,3,..). The PTR-MS instrument can also be operated at reduced collision energy where dissociative ligand-switching / proton transfer reactions are the ionizing events: H30+«H20 + VOC -> VOCH+ + H 2 0 + H 2 0
(2)
The various implications of this alternative mode of operation are described elsewhere [6]. Exothermic proton transfer reactions (reaction (1)) proceed at, or close to, the collisional rate, and reaction rate constants k range from 1.5 x 10~9 to 3.0 x 10"9 cm3 s'1. Specific reaction rate constants are obtained both theoretically [10] and experimentally, e.g. using the Innsbruck selected ion flow drift tube (SIFDT) [11], The density of product ions [VOCH+] at the end of the reaction section can be derived from simple pseudo first-order kinetics: [VOCH+] = [H3O+]0 (1 - e"k ^ ^ *) * [H3O+]0 [VOC] k t
(3)
where t is the average reaction time the ions spend in the drift tube (~ 100 us). The ion detection system measures ion currents i ^ O * ) and itVOCH4), which are proportional to the respective densities of primary and product ions. Mass discrimination effects have been studied in detail elsewhere [12] and are not discussed here. According to equation (3) the absolute number concentrations [VOC] can be determined by combining the reaction rate constant k, the reaction time t and the ratio iO/OCrO/i^O 4 ): i(VOCH+) [VOC] =
i(#30+) k t
(4)
PTR-MS is thus able to provide absolute VOC measurements without calibration. However, detailed calibration procedures have been developed to improve the accuracy of the measurements [13]. 2. Improvements of performance characteristics 2.1. Sensitivity and Detection Limit PTR-MS sensitivity is defined as the product ion count rate (in counts per second, cps) divided by the analyte volume mixing ratio (in parts per billion, ppb, 1 ppb = 10'9 v/v). A major limiting factor for the product ion count rate is the ion throughput at the extraction orifice separating the flow drift tube and the
465
detection system (see Figure 1). High vacuum requirements in the detection system (~ 10"5 mbar) constrain the maximum extraction orifice diameter. A significantly higher ion throughput was recently achieved by the addition of a differentially pumped region extending from the exit plate of the drift tube to the high-vacuum chamber orifice. Sensitivity improvements of a factor of 5 to 10 were achieved. Typical detection limits are now in the 10 to 100 pptv range (3a, 1 sec signal integration). 2.2. Response time The response time is defined as the time interval between the instant when a stimulus is subjected to specified abrupt change and the moment when the indication reaches a value conventionally fixed at 90% of the final change in indication. Recently, the PTR-MS response time has been significantly reduced by the use of a low-volume capillary inlet and a low-volume flow drift tube [12]. Also, the communication speed between the quadrupole MS and the data acquisition / storage system has been significantly increased [14]. To measure the response time an abrupt change in toluene levels was produced by toluene addition via a high-speed (response time < 10 ms) small-volume Teflon solenoid valve. As seen in Figure 2, the measured PTR-MS response time is ~ 150 ms. With this, the PTR-MS instrument is among the fastest VOC sensors currently available. 110%
t~0,15s •
100%
!"'"
,i
1/
80%
S-
.—-
IT
80% 70%
/
60% 50% 40% 30% 20% 10% 0% -10% •0.15
J
! i i
I I 1
I -0.10
-0.05
0.00
0.05
'i
i 0.10
time [3]
Figure 2. Response time for a concentration step-change at t = 0
0.15
0.20
0.25
0.30
466
3. Detection of inorganic species PTR-MS detects analytes whose PA exceeds PA (H2O) = 7.16 eV. This criterion is met by the large majority of VOCs with the exception of small aliphatic hydrocarbons. Most of the inorganic trace gases in air have a lower proton affinity than water [7]. Among the few exceptions, nitrous acid (HN02; PA = 8.15 eV [15] and nitric acid (HN03, PA = 7.79 eV [7]) merit particular interest. Both compounds are important atmospheric species affecting the tropospheric HOx/NOx budget, and there is an increasing demand for on-line measurements of these species. We have thus investigated the applicability of the PTR-MS method for real-time measurements of gas-phase acid HN02 and HNO3. The ion chemical processes relevant for H 2 0 based chemical ionization of HN02 are as follows [16]: H30+ + HN02 -> NO+»H20 + H 2 0
(5)
Spanel and Smith [17] have found that at 300 K this reaction proceeds at collisional rate kj, i.e. k = 2.7 x 10"9 cm3 s"1. NO+»H20 has been identified as the energetically most stable protomer of HN02 [18]. We have investigated the reactions H30+«H20 + HN02 -> NO+»(H20)2 + H 2 0 +
H30 «(H20)2 + HN02 -»
+
NO »(H20)3 + H 2 0
(6) (7)
+
in a SIFDT study. H30 »(H20)n=o-2 were simultaneously injected into the flow drift tube and from the relative decay rates of all 3 reactant ions it was found that reaction (6) proceeds with k = 0.9 k^ while reaction (7) proceeds only with k = 0.6 kc. The decreasing reaction efficiency is in agreement with previous findings where it was observed that the reverse reactions NO+«(H20)n + H20 -» H30+.(H20)„., + HN02
(8)
start to play a role at n=3 and become dominant for n=4 [19, and references therein]. It can thus be concluded that only H 3 0 + and H30+»H20 can be used as efficient chemical ionization reagent ions for HN02. H 3 0 + and H30+»H20 are the predominant primary ions in the PTR-MS drift tube if the mean relative collision energy (KEcm) between ions and buffer gas is maintained at sufficiently high levels, typically in the 0.075 to 0.2 eV range. However, at these collision energies the NO+»H20 ions undergo collision-induced dissociation to form NO+ ions (Figure 3).
467 1.00 0.80
FT-KR Cacace amtRicci [1996]
S 0.60
PTR-MS operating conditions
SIFT Spansl and Smith [2000]
0.40
0.20
NO+-H20
Primary ion:
Primary ion:
H30+-H20 0.00 0.000
0.025
0.050
0.075
0.100
HjO+
0.125
0.150
0.175
KEcm (ion - buffer) [eV]
Figure 3. Relative abundance of NO+«H20 ions as a function of their mean relative collision energy with the buffer gas
Cacace and Ricci [16] observed no NO+ at collision-free conditions meaning that the H30+-HN02 reaction exoergicity is not sufficient to induce fragmentation. At thermal conditions, Smith and Spanel [17] observed a 33 % NO+ relative abundance which increases with the mean relative collision energy as shown by our SIFDT data. Consequently, at typical PTR-MS operating conditions only the NO+ product ion is observed from the H30+-HN02 reaction. The ion chemical processes for HN03 detection [20] are similar to those observed for HN02: H30+ + HN03 -> N02+»H2O + H 2 0
(9)
However, in this case the reverse reaction N02+«(H20)n + H20 -> H30+«(H20)n.! + HN0 3 10
(10)
1
was found to proceed at a significant rate (k > 1 x 10" cmV ) already at n=2. Consequently, only H30+ is an efficient chemical ionization reagent ion for HN03. Again, N02+»H20 ions undergo collision-induced dissociation in the PTR-MS drift tube to form N0 2 + ions. The observed collision-induced dissociation processes complicate the unambiguous identification of HN0 2 and HN03. A complex matrix such as
468
photochemically processed air contains organic nitrites (R-ONO, R being an alkyl group) and organic nitrates (R-ON02), which produce the same product ion signals as HN02 and HN03: H 3 0 + + R-ONO -> H30
+
NO+ + R-OH + H 2 0
+ R-ON02 -> N0 2
+
+ R-OH + H20
(11) (12)
However, we have shown that the contribution of HN0 2 and HN03 to the observed NO+ and N0 2 + signals can be quantified by the use of a selective HN02 and HN03 scrubber (Na2C03-impregnated Nylon wool) which is periodically inserted into the sample gas flow. The scrubber was found to be > 99 % efficient for HN02. Organic nitrites are not (< 1 %) removed from the sample gas stream by the scrubber. A similar performance is expected for HN0 3 and organic nitrates, respectively. References 1. A. Hansel, A. Jordan, R. Holzinger, P. Prazeller, W. Vogel and W. Lindinger, Int. J. Mass Spectrom. Ion Proc. 149/150, 609 (1995). 2. F. H. Field and M. S. B. Munson, J. Am. Chem. Soc. 87, 3289 (1965). 3. M. McFarland, D. L. Albritton, F. C. Fehsenfeld, E. E. Ferguson and A. L. Schmeltekopf, J. Chem. Phys. 59, 6620 (1973). 4. W. Lindinger, A. Hansel and A. Jordan, Chem. Soc. Rev. 27, 347 (1998). 5. W. Lindinger, A. Hansel and A. Jordan, Int. J. Mass Spectrom. Ion Proc. 173, 191 (1998). 6. N. C. Hewitt, S. Hayward, A. Tani, J. Environ. Monit. 5,1 (2003). 7. E. P. Hunter and S.G. Lias, J. Phys. Chem. Ref. Data 27, 413 (1998). 8. D. Smith and P. Spanel, Int. Rev. Phys. Chem. 15, 231 (1996). 9. D. Smith and P. Spanel, Rapid Comm. Mass Spectrom. 10, 1183 (1996). 10. T. Su and W. J. Chesnavich, J. Chem. Phys. 76, 5183 (1982). 11. W. Lindinger, in Gaseous Ion Chemistry and Mass Spectrometry, ed. by J. Futrell, pp. 141-153, John Wiley and Sons, New York (1986). 12. M. Steinbacher, J. Dommen, C. Ammann, C. Spirig, A. Neftel, A. S. H. Prevot, Int. J. Mass Spectrom. 239, 117 (2004). 13. J. De Gouw, C. Warneke, T. Karl, G. Eerdekens, C. Van der Veen, R. Fall, Int. J. Mass Spectrom. 223-224, 365 (2003). 14. G. Hanel, W. Sailer and A. Jordan, in Contributions to the 2nd International Conference on Proton Transfer Reaction Mass Spectrometry and Its Applications, ed. by A. Hansel and T. Mark, pp. 168-169, Institut fur Ionenphysik, Innsbruck (2005). 15. G. De Petris, A. Di Marzio and F. Grandinetti, J. Phys. Chem. 95, 9782 (1991).
469 16. 17. 18. 19. 20.
F. Cacace, A. Ricci, Chem. Phys. Lett. 253, 184 (1996). P. Spanel and D. Smith, Rapid Commun.Mass Spectrom. 14, 646 (2000). J. S. Francisco, J. Chem. Phys. 115,2117 (2001). E. Hammam, E. P. F. Lee, J. M . Dyke, J. Phys. Chem. 105, 5528 (2001). F. C. Fehsenfeld, C. J. Howard, A. L. Schmeltekopf, J. Chem. Phys. 63, 2835 (1975).
I N T E R F E R E N C E S I N ELECTRON EMISSION F R O M H 2 I N D U C E D B Y FAST IONS
N. STOLTERFOHT Hahn-Meitner-Institut, Glienickerstr. 100, D-14109 Berlin, Germany E-mail: [email protected] Studies of interferences in electron spectra produced by emission from the identical atomic centers of the H2 molecule are reviewed. Experimental results for fast inicident ions are compared with theoretical models revealing interferences in first and second order. First-order phenomena are treated within the Bethe-Born approximation. To interpret the basic features of second-order interferences, methods known from wave optics are used. Frequency doubling is predicted for second-order interferences in accordance with the experimental observation
1. Introduction During the last few years considerable attention has been devoted to phenomena associated with coherent electron emission from the indistinguishable H centers of molecular hydrogen. Single ionization of H2 resembles Young's two-slit experiment where the atomic H centers simultaneously emit radial waves, leading to interferences in the electron emission. Early work of coUisionally induced interferences from H2 has been focused on the processes of photoionization 1 ' 2 and electron capture 3 - 5 . Recently, experimental evidence for interference effects in electron emission from H2 were observed in collisions with fast Kr ions.6 It was shown that fast collisions involving primarily dipole transitions support the visibility of interference effects. The experimental results motivated theoretical studies 7 - 1 1 which revealed various properties of the interference effects in electron spectra from H2. First of all, care has to be taken with spurious structures due to binary-encounter processes. 7 ' 12 ' 13 Calculations based on the semiclassical approximation showed that the frequency of the oscillation varies with the electron emission angle. 8 This prediction has essentially been confirmed by additional measurements using fast Kr ions 14 and proton impact 15 . The studies of first-order effects associated with Young-type interferences were
470
471 followed by the observation of second-order interferences, where electron scattering between the two centers occurs. 16 ' 17 Related effects have been observed in investigations 18- 2 0 using also synchrotron radiation. An overview of the scattering phenomena are given in the textbook of Messiah. 21 In the present review, interference effects of first and second order in electron emission from H2 are discussed for fast heavy ion impact. Experimentally observed inteference structures are interpreted using the Born approximation and methods known from wave optics. 2. Theoretical Considerations 2.1. Born approximation
in first order
For fast projectiles the cross section for electron emission from an H 2 molecule, involving interference effects in first order, can be described within the Born approximation 22 ' 23
*"•
4
dq de dCl
^ Ai l W e ^ k o > | 2
v%q pi
(1)
where vp and Zp are the velocity and charge of the projectile, respectively. The energy e and the solid angle fi refer to the ionized electron of outgoing momentum k and q is the momentum transfer vector. The wave functions 0o arid <£>k describe, respectively, the initial and final state of the active electron. The Born operator e*q r is obtained from the Fourier transform of the projectile-electron interaction Vv = Zvj |R — r|. With an initial H2 state 0 = [
d02H
dq de dCl
dq dedCl
sin (|k - qj d) |k - q| d
(2)
where the label 2H refers to two separated H atoms. An average over the orientation of the H2 was performed. It can be seen that the averaging procedure preserves an oscillatory term associated with interference effects. It should be emphasized that the characteristic properties of the interference effects follow from the high velocity of the projectile. The interferences result primarily from dipole transitions, which are enhanced when fast projectiles are used. 6 Also, in fast binary collisions, relatively slow electrons are predominantly emitted near 90°. Thus, in regions at forward and backward
472
angles, dipole transitions can be studied without the influence of disturbing binary collisions. 2.2. Second-order
phenomena
in wave
optics
For an interpretation of interferences in first and second order, methods known from wave optics will be used. The important aspect of the analysis is that the Born operator e i q r in Eq. (1) is treated as a particle wave interacting with the centers of the H2 molecule. The case of electron emission in first order is depicted in the left-hand diagram of Fig. 1. The particle wave e t q r with momentum q is incident on both centers a and b, where the electron wave e' k r of momentum k is emitted. In the case of ion impact, the incident wave e i q r represents virtual photons similar to those considered in the early work by Williams. 25 Analyzing phase differences as in the left diagram of Fig.l, it has been shown 16 that the oscillatory structure in the emitted electron spetra is equal to that in Eq. (2).
1. Order
Projectiie
I . + 2. Order
Projectile
Figure 1. Wave diagrams to visualize phase differences relevant for interferences in first and second order.
The analysis within the framework of wave optics reveals that Eq. (2) is also valid for the description of interference effects occurring in different scattering and ionization mechanisms. Indeed, analogous expressions have been derived for elastic electron scattering, 21 ionization by photons, 1 electrons, 10 and heavy ions. 7 In first order, these theories yield the same oscillatory term equal to that in brackets of Eq. (2) representing interference effects. (This term has also been obtained for the stopping power of
473
H2 moving in condensed matter. 26 ) Hence, the first-order interference is governed by phase differences similar to those considered in wave optics. This provided confidence that methods of wave optics can also be applied to treat second-order effects. Interference in second order, involving ionization of one center with rescattering at the second center, is shown in the right-hand diagram of Fig. 1. The intensity in second order, restricted to the incident branch a, is given by /£ = \Aa + Ba\ where Ba is the amplitude for backscattering at center b. In this case the interference is governed by the phase Sab = 6a + S'b — 6a is obtained from phases created close to the centers a and b. After integration over the molecular orientation one obtains 27 7 » _ u | 2 , 9 N R I sin(2fcd + M - s i n ( < S a t l ) ^2 — \Aa\ +t\Aat$a\ —
[6)
Apart from a phase shift, this expression predicts a doubling of the oscillation frequency in comparison with Eq. (2). The frequency doubling is primarily produced by the additional phase 5d = kd acquired in second order as the electron wave propagates along the internuclear axis from one center to the other. It should be mentioned that Eq. (3) has been extended including the primary emission from center b. Then, the second-order interference with doubled frequency occurs as a structure superimposed on the first-order structure. 16 ' 27 3. Comparison with experiment 3.1. Interferences
of first order
Ionization cross sections may vary with energy by several orders of magnitude, 22 ' 23 whereas the variation due to interference effects is limited to a factor of ~ 2 (see Eq. (2)). To remove this strong energy variation, the cross sections for H2 were normalized (divided) by the corresponding quantities for two independent H atoms. 6 ' 14 In Fig. 2 the experimental data for different observation angles are compared with two sets of theoretical results. The plot clearly shows oscillatory structures, in particular, for the observation angles 30° and 150°. For high impact energies it is recalled that forward and backward angles are dominated by dipole transitions, which are primarily responsible for the interference effects. The results labeled Born approximation are obtained by a q integration of the cross section from Eq. (2) using analytical Born cross sections for atomic hydrogen. 23 These calculations are plotted as solid lines in Fig. 2.
474
Furthermore, the dash-dotted lines were evaluated by means of the semiempirical expression for the normalized cross section 14 ( da H2
= F 1+ -
\dCl cte,
\(kcd) kcd
G
(4)
where F and G (with F + G = 1) are cross section fractions. This expression is similar to that of Eq. (2) with the important difference that the frequency parameter c is introduced allowing for a variation of the oscillation frequency with the electron observation angle 6. The frequency parameter c was predicted 8 to be equal to cos 9. Since c may differ from the predicted value cos#, the quantity c was treated as an adjustable parameter. 14
0
1
2
3
4
0
1
2
3
4
J
Electron Velocity (a. u.) Figure 2. Ratios of experimental to theoretical CDW-EIS cross sections 2 8 for electron emission in 68 MeV/u K r 3 3 + + H2 collisions plotted as a function of the ejected electron velocity. From (a) to (d) the electron observation angles are 30°, 60°, 90°, and 150° as indicated. The solid lines represent Born calculations and the dashed-dotted lines are obtained from fits using the analytic function of Eq. (4).
It is seen that the results from the Born approximation are in good agreement with experiment at 30° and 60°. Similar good agreements were
475
obtained between the present experiment and calculations using different theoretical approaches. 7 - 9 However, significant discrepancies between the Born results and experiment occur for 90° and 150°. In particular, for 150°, the oscillation frequency is observed to be enhanced in comparison with the Born calculations. This may indicate higher-order effects9 that lead beyond the Born approximation in the description of ionizing the separated H atoms. Also, it is likely that second-order interferences increase in importance at backward angles. It has been shown previously 23 that electron emission at backward angles involves significant backscattering which, in turn, is required to produce second-order interferences. The interplay of a relatively strong second-order structure with that of first order may result in an enhancement of the oscillation frequency. Finally, it is noted that in Fig 2 below « « l a . u. the experimental results strongly decrease with decreasing velocity in contrast to the calculations. This decrease may indicate that a two-center wave function is necessary for the final state. It should be noted that for slow electrons the corresponding wavelength becomes much larger than the distance between the two atomic H centers. In this case, one would expect that interferences diminish (i. e., the ratio of cross sections approaches unity). Indeed the experimental data show this tendency.
3.2. Interferences
of second
order
As discussed in conjunction with Fig. 1, second-order effects of electron backscattering result in frequency doubling of the interference structures. Indeed, second-order oscillations with an enhanced frequency were observed in the experiments 16 as shown in Fig. 3. In the upper diagrams, the measured cross section ratios for 30°, 60°, and 90° are again shown. The cross section ratios provide evidence for higher frequency oscillations superimposed on the main oscillatory structure for each of the angles displayed. After division of the cross section ratios by the fit curves these secondary oscillations are clearly revealed as seen in the lower part of Fig. 3. In addition to a higher frequency, the secondary oscillations appear to have nearly equal frequencies. An attempt was made 16 to reproduce the secondary oscillations by using the fit function from Eq. (4). In accordance with Eq. (3) the phase Sab was added by replacing kcd by kcd + Sab. The resulting fit curves are given as solid lines in the lower diagrams of Fig. 3. The fit parameters were set to the same values for all angles, yielding c = 2.5 and Sab = vr. This confirms
476
» l ' l ' l '
I ' I ' t ' I ' I '
I
(a) 30°
(b) 60°
« .2 V)
i i i i i> i i i
0
I i L I i-t.i.l. 1 2 3 4 5 0
' I ' I ' l ' l ' I
N
_J»
• i * i • i < i .
„,i.,i I, i t 1
2
3
I. 4
i 5
0
1
2
i i t i i 3 4 5
i
i
Electron Velocity (a. u.) Figure 3. Ratios of experimental to theoretical CDW-EIS cross sections for electron emission by 68 - MeV/u K r 3 3 + impact on H2 for different electron observation angles. In the upper diagrams the ratios are shown together with fits to an analytic function (see text). The ratios are divided by the corresponding fit functions and plotted in the lower diagrams together with a second-order fit.
that the oscillation frequency is at least doubled. Also, the doubling of the oscillation frequency and phase shift appear to be independent of the observation angle in accordance with the theoretical prediction. Recently, Hossain et aZ.17'29 reported on electron spectra observed in MeV H + + H2 collisions, which exhibit oscillatory structures with a frequency more than an order of magnitude higher than that of the first-order oscillations. As a possible explanation it was suggested to consider interferences between direct electron emission and autoionization involving doubly excited initial states 2lel' where one electron is in a continuum state giving rise to free-free transitions 29 . However, further work is needed to confirm the high-frequency oscillations. Acknowledgement I thank the team participating in several experiments at the French accelerator facility GANIL. In particular, I am much indebted to John Tanis, Bela Sulik, and Jean Yves Chesnel for a long-standing motivating collaboration.
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References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.
28. 29.
H. D. Cohen and U. Fano, Phys. Rev. 150, 30 (1966). M. Walter and J. S. Briggs, J. Phys. B 32, 2487 (1999). T. F. Tuan and E. Gerjuoy, Phys. Rev. 117, 756 (1960). S. Cheng et al., Phys. Rev. A 47, 3923 (1993). S. E. Corchs, H. F. Busnengo, and R. D. Rivarola, Nucl. Instrum. Methods in Phys. Res. B 149, 247 (1999). N. Stolterfoht et al., Phys. Rev. Lett. 87, 023201 (2001). M. E. Galassi, R. D. Rivarola, P. D. Fainstein, and N. Stolterfoht, Phys. Rev. A 66, 052705 (2002) L. Nagy, L. Kocbach, K. Pora, and J. Hansen, J. Phys. B 35, L453 (2002). L. Sarkadi, J. Phys. B 36, 2153 (2003). C. R. Stia et al., J. Phys. B 36, L257 (2003). M. E. Galassi et al, Phys. Rev. A 70, 32721 (2004) D. Misra et al., Phys. Rev. Lett. 92, 153201 (2004). J. Tanis, S. Hossain, B. Sulik, and N. Stolterfoht, Phys. Rev. Lett, in print (2005) N. Stolterfoht et al., Phys. Rev. A 67, 030702 (2003). S. Hossain et al., Nucl. Instrum. Methods in Phys. Res. B 205, 484 (2003). N. Stolterfoht et al., Phys. Rev. A (2004) 69, 012701. S. Hossain, N. Stolterfoht, and J.A. Tanis, Nucl. Instrum. Methods in Phys. Res. B 233, 201 (2005). F. Heiser et al., Phys. Rev. Lett. 79, 2435 (1997). A. Landers et al., Phys. Rev. Lett. 87, 13002 (2001) C. Dimopoulou et al, Phys. Rev. Lett. 93, 123203 (2004). A. Messiah, Vol. II, North Holland, Amsterdam, 1970. M. E. Rudd, Y. K. Kim, D. H. Madison, and T. J. Gay, Rev. Mod. Phys. 64, 441 (1992). N. Stolterfoht, R. D. Dubois, and R. D. Rivarola, Electron emission in heavy ion-atom collisions, Springer Series on Atoms and Plasmas, Heidelberg, 1997. H. A. Bethe, Ann. Phys. (Leipzig) 5, 325 (1930). E. J. Williams, Phys. Rev. 45, 325 (1934). N. R. Arista, Nucl. Instrum. Methods in Phys. Res. B 164-165, 108 (2000). N. Stolterfoht and B. Sulik, in Energy Deposition, Advances in Quantum Chemistry, Vol 46, Eds. J. Sabin and R. Cabrera-Trujillo (Elsevier Science, Academic Press, 2004) pp. 307. P. D. Fainstein, V. H. Ponce, and R. D. Rivarola, J. Phys. B 24, 3091 (1991). S. Hossain, A.L. Landers, N. Stolterfoht, and J.A. Tanis, Phys. Rev. A 72 , 010701(R) (2005)
ATOMIC REALIZATION OF T H E Y O U N G SINGLE ELECTRON INTERFERENCE PROCESS IN INDIVIDUAL A U T O I O N I Z A T I O N COLLISIONS
R. 0 . BARRACHINA* Centro Atomico Bariloche and Institute) Balseiro; 8400 S. C. de Bariloche, Rfo Negro, Argentina. E-mail: [email protected] M. ZITNIK J. Stefan Institute, Jamova 39, P. 0. Box 3000, SI 1000 Ljubljana, Slovenia. E-mail: [email protected]
Young's double-slit demonstration, applied to the interference of single electrons, is considered to be one of the most beautiful experiments in Physics. This "gedanken" experiment proposed by R. Feynman in 1963, was achieved quite recently. Of course, the diffraction of electrons by atomic arrays had already been studied many decades before, but the novelty in these experiments was that one electron at a time collides with a single two-slit arrangement. Here we propose a novel atomic realization of a Young interference experiment, where a single electron source and a two-center scatterer are prepared in each collision event.
1. Historical Introduction Even though the concept of interference was already implicit in Newton's 1688 explanation of the anomaly of the tides in the Gulf of Tongkin, it was Thomas Young in his Bakerian Lectures of 1801 who generalized this idea and applied it to a variety of situations. His celebrated double-slit experiment, first described in his Course of Lectures on Natural Philosophy and the Mechanical Arts of 18071, has been regarded as a prime demonstration * Also a member of the Consejo Nacional de Investigaciones Cienti'ficas y Tecnicas (CONICET), Argentina. tComision Nacional de Energia Atomica (CNEA) and Universidad Nacional de Cuyo, Argentina.
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479 of the wave-nature of light and, in its single electron interference version, was recently voted as the most beautiful experiment in Physics 2 . Young's double-slit demonstration applied to the interference of single particles was proposed by Richard Feynman in his famous lectures of 19633 as a "gedanken" experiment. But he warned that nobody should try to set this experiment up. He added that "the trouble is that the apparatus would have to be made on an impossibly small scale to show the effects we are interested in". Contrary to this assertion, we demonstrate the viability of such an atomic size apparatus. Probably Feynman was not aware that a double-slit experiment with electrons had already been carried out in 1961 by Claus Jonsson 4 ; and this was certainly not the first experiment where electron interference was observed. The first experiment to demonstrate electron interference by molecules had been performed by R. Wierl in 1931 5 , shortly after the Nobelprized electron diffraction experiment by Davisson and Germer 6 . The very short wavelength of electrons were afterwards exploited to study molecular structures and for surface crystallography. Particle interference has also been demonstrated with neutrons, atoms and molecules. However, none of these experiments was designed to demonstrate that an interference pattern would build up even if there is just one electron in the apparatus at any one time, i.e. that "each electron interferes only with itself. This was achieved only in the 1970s with a very weak electron source and an electron biprism by Merli et al. 7 and again by Tonomura et al. in the late eighties 8 .
2. A n atomic scale setup One of the major difficulties in the design of single-electron double-slit experiments is to prevent any chance of finding two or more electrons in the apparatus at the same time. Merli et al. and Tonomura et al. achieved this goal by carrying the experiment with extremely low electron intensities. Our proposal is to fulfill this same exigency in a simple and natural way by destroying the apparatus after each single-electron interference event. This idea is not so wild as it might sound, since we are not referring to a macroscopic experimental setup but to atomic-size "apparatuses" inside it. Instead of sending a beam of electrons against some sort of two-slit arrangements, a single electron source and a two-center scatterer are prepared in individual atomic collisions. These different events only amount to repeating an elementary process many times with similar initial conditions. Thus, what is actually measured is the ensemble probability of the
480
diffraction of just one single electron by one single two-center scatterer 9 . As the electron source of this atomic-level laboratory arrangement we propose to employ the spontaneous electron emission with a sharply defined energy and a characteristic angular distribution from an autoionizing atom. A diatomic molecule, taking part in the collision event that leads to the formation of the autoinizing atom, might serve as the atomic-size two-slits arrangement. Note that in this setup the source and the two-center scatterer are well defined and separated. This pinpoints to an essential difference with the interference effects observed by Stolterfoht et al. 10 in the ionization of H2 molecules by energetic ion impact. In this latter case the electron is not coming from a distinct source but from the two-center scatterer itself so that it is much more related to a x-ray-photoelectron or Auger-electron diffraction (XPD/AED) effect than to the famous Young's demonstration. One of the main achievements in the Merli and Tonomura experiments was that the formation of fringes could be observed over time as the electrons were gradually accumulating. In our case, this same result might be achieved by means of standard electron-spectrometry techniques, where the electrons arrive randomly to the detector, so that it would take some time for the interference pattern to build-up. As an example of the aforementioned atomic realization of the Young single-electron interference process we consider the (2s 2 ) 1 5 autoionization of He** induced by a He 2 + + H2 double electron capture collision. It is assumed that the molecule dissociates after the collision. We show in figure 1 a Continuum Distorted Wave (CDW) calculation of this process 9 . We see that, together with a glory enhancement of the autoionization line, the normalized electron distribution shows a noticeable interference structure. This structure is partially washed out when it is averaged on the molecule orientation.
3. Conclusions Up to our best knowledge, the experiment described in this communication has not yet been performed. It will be certainly hindered by a number of difficulties. But, they would not be too much different than those encountered by Swenson et al. 11 in their beautiful observation of the Glory effect in a He + + He collision. As a reward, Feynman's famous double-slit Gedanken experiment might be observed and registered in real time and under the required single-electron conditions.
481
1.52
1.53
1.54
1.55
1.56
1.57
1.58
Electron Velocity (atomic units) Figure 1. Normalized electron intensity as a function of the emission angle and velocity for the (2s2) 1S autoionization of He** induced by a 100 keV He 2 + +H2 double electron capture collision. The results are shown in the coordinate frame of the He atom. The dissociation of the H2 occurs in a direction perpendicular to the projectile*s trajectory.
Acknowledgments This work has been supported by the Argentinean Agenda Nacional de Promocion Cientffica y Tecnologica (Grant 03-12567) and the SlovenianArgentinean S&T Cooperation Programme (Grant ES/PA/00 - EIII/003). References 1. T. Young, A Course of Lectures on Natural Philosophy and the Mechanical Arts (J Johnson, London, 1807). 2. R. P. Crease, Physics World, September, 19 (2002). 3. R. P. Feynman, R. B. Leighton and M. Sands, The Feynrnan Lecture on Physics vol 3 (Addison-Wesley, 1963). 4. C. Jonsson, Zeitschrift fur Physik 161, 454 (1961). 5. R. Wierl, Ann. Physik 8, 521 (1931). 6. C. J. Davisson and L. H. Germer, Phys. Rev. B 30, 705 (1927). 7. P. G. Merli, G. P. Missiroli and G. Pozzi, Am. J. Phys 44, 306 (1976). 8. A. Tonomura et al., Am. J. Phys. 57, 117 (1989). 9. R. O. Barrachina and M. Zitnik, J. Phys. B 37, 3847 (2004). 10. N. Stolterfoht et al, Phys. Rev. Lett 87, 023201 (2001) 11. J. K. Swenson et al, Phys. Rev. Lett. 63, 35 (1989).
MULTIPLE IONIZATION PROCESSES RELATED TO I R R A D I A T I O N OF BIOLOGICAL TISSUE
M. E. GALASSI*AND R. D. RIVAROLA Instituto de Fisica de Rosario (CONICET-UNR),
Rosario,
Argentina
M. P. GAIGEOT LMSMC, Universit6 d'Evry-Val-d'Essone,
France
B. GERVAIS AND M. BEUVE CIRIL - GANIL, Caen, France R. VUILLEUMIER LPTL,
Universite Pierre et Marie Curie, Paris VI, France P. D. FAINSTEIN
Centro Atomico Bariloche , Bariloche,
Argentina
C. R. STIA AND M. F. POLITIS IMPMC, Universit Pierre et Marie Curie, Paris VI, France
Multiple ionization of water molecules, for impact of high LET ions, is included in a Monte Carlo simulation of liquid water radiolysis. According with suggestions of other authors, it is shown that the rearrangement of highly ionized water molecules is consistent with the production of excited atomic oxygen. A Car Parinello molecular dynamics analysis shows that, after the Coulomb explosion of a double ionized water molecule in liquid water, the produced fragments of H+ and O do not recombine but migrate. The presence of this excess of oxygen is responsible for the creation of a large amount of HCh/O^" radicals. The corresponding Monte Carlo yields reproduce existing experimental data.
The ionization of water molecules during the irradiation of biological tissue with fast heavy ions produces the formation of free radicals (water 'Corresponding e-mail: [email protected]
482
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radiolysis), provoking biological damage. The water radiolysis is characterized by the radiolytical yields G (number of species created per unit of deposited energy). The formation of HO2 observed experimentally 1-2 for high linear energy transfer (LET) projectiles has been a long standing problem. Recent experiments 3 based on direct optical measurements of HOg/O^ produced in pure desaerated water reported a yield GHO2 — 5 • 1 0 - 9 mol/J for high energetic Ar18+ and S 1 6 + ions. This yield is lower than it could be expected from extrapolation of previous measurements 1 for a similar LET. Several authors suggested that multiple ionization could be responsible for this effect 4-5 . The main idea is that multiple ionization generates O atoms that reacts rapidly with OH radicals present in the ion track to form finally HO2 following the reactions: H202+ -> 2H+ + O^H 2H30+ + O O + OH -> H02 The first step (femtosecond timescale) of the dissociation pattern of H202+ is not directly known since the best measurement gives the yield of formation of subsequent radicals in the microsecond timescale. In order to investigate the formation of atomic oxygen after double ionization of a single molecule in liquid water, we have performed molecular dynamics calculations within the framework of the ab-initio Car-Parrinello molecular dynamics simulation 6 . The basic idea of the Car Parrinello approach is to exploit the different time scale of fast electronic and slow nuclear motion by transforming that into classical mechanical adiabatic energy scale separation in the framework of dynamical systems theory. In practice a fictitious electron mass is introduced in the lagragian of the dynamics (nuclei +electronic Kohn Sham orbitals) in order to calculate the electronic structure of the molecule "on the fly", i.e. during the nuclei dynamics. The interatomic forces are calculated using Density Functional Theory formalism. The computations are performed using Martins-Troullier pseudopotentials 7 and the BLYP functional8 for a periodic box consisting of 32 water molecules in liquid phase. It has been proved that this kind of system represents well the properties of liquid water 6 . Our simulations show that if the two more external electrons are ionized (most probable double ionization channel), the water molecule dissociates leading to the formation of two hydrated protons and one oxygen atom, independently of the initial vibrational state of the molecule. After a few tens femtoseconds of dynamics the fragments do not recombinate but migrate. An analysis in terms of Wannier orbitals 9 for a predissociated molecule placed in liquid water enables the observation
484
of the evolution of the different orbitals of this molecule and neighbouring molecules. When the 1B1 orbital of the predissociated molecule is empty, ten femtoseconds later, the oxygen orbitals of this molecule are well separated of the ones of other molecules and two hydrated protons are formed. A more detailed analysis will be presented in a forthcoming paper. A Monte Carlo code has been used 10 to quantify the role of multiple ionization in the production of HOi in the water radiolysis. This simulation consider three different stages covering three different time domains: Physical, Physico-Chemical and Chemical stages. The Physical stage describes all the interactions of the projectile with the water molecules and the subsequent electronic cascade during the first femtoseconds. The inputs of the simulation are the cross sectionsCT^for all the interaction processes of the projectile and of the electrons with the medium. For the ions studied here, we have considered excitation and single and multiple ionization processes. The ionization cross sections were obtained in the framework of the Independent Electron Model 11 (IEM). For multiple ionization calculations the IEM requires the computation of single particle probabilities as a function of the impact parameter. In our simulation these probabilities were obtained employing the CDW-EIS theory. The single particle probabilities for the molecular orbitals were approximated by linear combinations of atomic probabilities 12 , where the orbital energies used in the calculations were taken to be the corresponding to water in its liquid phase 13 . We must note that our calculations show that the contribution of multiple ionization represents approximately 12 % of the total ionization cross sections for the Ar and S ions here considered. The Physico-Chemical stage (which ends at 10""12 s) deals with the fast dissociation processes that results from molecular excitation and ionization. During this stage an important amount of atomic oxygen is generated by dissociation of multiple ionized water molecules. Finally, the Chemical stage accounts for the evolution of the radicals and molecular species during their diffusion through liquid 10 and runs until 1 0 - 6 s. The role of atomic oxygen is crucial during this stage as it is the main precursor of HO2 by reaction with the OH radicals produced. In figure 1 the experimental yield G # 0 2 / 0 - corresponding to Arl8+ (LET=280 keV//im) and 5 1 6 + ions (LET=250 keV//im) 3 is compared with the Monte Carlo simulation obtained including multiple ionization. As we can observe, the simulation compares quite well with the measurements. On the contrary, the yield GHOi/0- obtained without multiple ionization (not plotted) is negligible in comparison with experiments. Our study sup-
485
0.10
Radiolytical Yield for HOj/0 2 ' • Experimental data [3] Simulation (single + multiple ioniz.)
1 0.05
n nn 100
1000 LET (keV/um)
Figure 1. Comparison of the theoretical yield G„0 ,Q- with experimental data. ports the hypothesis that multiple ionization is responsible for an increasing production of HO2 at high LET. Although we have shown the formation of atomic oxygen by Car Parrrinello molecular dynamics in the case of empty most external orbital of water in condensed phase, the mechanism of production of the precursors should be studied by more powerfull theoretical tools. The dissociation channels of a doubly ionized water molecule in condensed phase is under study with a Time Dependent Density Functional theory code 14 . References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
J. A. Laverne and R. Schuler, J. Phys. Chem. 91, 7376 (1992). W. G. Burns and H. E. Sims, J. Chem. Soc. Faraday Trans. 77, 2803 (1981). G. Baldacchino et al. NIM B 146, 528 (1998). C. Ferradine and J.-P. Jay-Gerin, Rad. Phys. Chem. 51, 263 (1998). J. Meesungnoen et al., Chem. Phys. Lett. 377, 419 (2003). R. Car and M. Parrinello, Phys. Rev. Lett. 55 2471 (1985). N. Troullier and J. L. Martins, Phys. Rev. B 43, 1993 (1991). A. Becke, Phys. Rev. A 38, 3098 (1988). C. Lee et al., Phys. Rev. B 37, 785 (1988). P. Hunt, M. Sprik and R. Vuilleumier, Chem. Phys. Lett. 68 376 (2003). B. Gervais et al. Chem. Phys. Lett 410 330 (2005). M. M. Sant'Anna et al., Phys. Rev. A 58 2148 (1998). M. E. Galassi et al., Phys. Rev. A 62, 022701 (2000). G. H. Olivera et al. Radiat. Res 144, 241 (1995). I. Tavernelli et al. Molecular physics 103 No 6-8 963 (2005)
ATOM-DIATOM COLLISIONS AT COLD AND ULTRA-COLD T E M P E R A T U R E S
F. D. COLAVECCHIA Centra Atomico Bariloche and Consejo National de Investigaciones Cientificas y Tecnicas, 8400 S. C. de Bariloche, Rio Negro, Argentina E-mail: [email protected] G. A. P A R K E R Department
of Physics and Astronomy, University Norman, OK 73019, USA
of
Oklahoma,
R. T PACK Theoretical Division
(T-12, MS B268), Los Alamos National Los Alamos, NM 87545, USA
Laboratory,
Recent progress in the development of a theoretical method to describe atomdiatom collisions at cold and ultra-cold temperatures is reported. Calculations are performed with hyperspherical coordinates and making use of the SVD-ER.N (Smooth Variable Discretization-Enhanced Renormalized Numerov) algorithm of Colavecchia et al.1. The advantages and disadvantages of the method are analyzed and further ways of improving the calculation are discussed.
1. Introduction The advances of experimental methods for cooling and trapping atoms at cold and ultracold" temperatures in the last two decades lead to the first realization of a Bose-Einstein Condensation (BEC) of an atomic gas in 19952,3. At the beginning, the study of collisions in these systems was motivated by the need to understand the cooling process, but nowadays, many areas of investigation related to the atomic collision physics have flourished by themselves, including the study of atom-atom collisions4, Rya
In this paper 'cold' temperatures are in the range of 1 mK-1 /*K, 'ultracold' temperatures are lower than 1 fiK and 'high' energies refer to temperatures around 1 K.
486
487 dberg atoms5, molecule formation6, exotic atoms production7 and charged particles scattering8 at ultralow energies. The interest of atom-diatom collisions at these temperatures has many motivations. For example, the density of atoms n in a BEC experiment is limited by the three-body recombination rate K3 as | - - * » - .
(i)
Values of the recombination rate are very difficult to obtain experimentally, and can be as small as 10 _ 2 6 -10 - 2 8 cm 6 /s for spin-aligned alkali atoms (see for example9. Several authors have obtained recombination rates using different approximations10'11, and studied the scaling of this rate with the atom-atom scattering length12. Also, production of diatomic molecules in BEC involves high-lying weakly bound ro-vibrational states that can span several hundred atomic units. This paper describes a method to compute collisional properties of atomdiatom collisions in the cold and ultracold regime. The statement of the problem is presented in section 2, while in section 3 the details of the numerical calculations and some typical results are discussed. Finally, future work is summarized in section 4. 2. Statement of the problem The aim of this work is to perform accurate quantum mechanical calculations of all the cold and ultracold collisions
A + BC(u,j)
A + BC(u, j) A + BC(v',j') AB{v',j') + C A+B +C
Elastic scattering Inelastic scattering Reactive scattering Collision Induced Dissociation (CID)
and the CID inverse process, three-body recombination A + B + C->A + BC(v,j). In general, this is a few particle calculation, but since the energy is extremely low, the Born-Oppenheimer separation is assumed and the system is reduced to a three body problem13. Moreover, total angular momentum J is zero in the case of bosonic species. Then, the atoms are considered to interact through the potential energy surface (PES) generated by the electrons: V = VAB(rAB) + VBc{rBc) + VCA(TCA) + VZB{rAB,rBC,rcA),
(2)
488 where Vy(ry) (i,j = A,B,C;i ^ j) are the atom-atom potentials and VZB accounts for three-body effects in the PES. The description of such a system involves a double continuum, and there are basically two general methods that have been used to perform these three-body calculations. In the first one, the Schringer equation can be transformed into the Fadeev equations, and this double continuum casts into a set of integro-differential equations14. The second method is chosen in this work and involves use of hyperspherical coordinates, that transform the double continuum into a single one in the hyperradius p. This hyperradius measures the size of the triangle spanned by the particles15. The other five coordinates Cl = {9,9,a,@, 7} are angles that determine the shape of the triangle {9,8} and its orientation in space throught the Euler angles {a,/?, 7}. The time independent Schrodinger equation [H — E]^ = 0 in hyperspherical coordinates can be written as: {^
+ ^[E-hint(n;p)]}iP(p,{l)
= 0,
(3)
where hint is the internal hamiltonian that includes the internal kinetic energy and the PES V (eq. 2). Let $ ? (A;p) be an eigenfunction of the internal hamiltonian such that hint{tl; p)*,(fi; P) = Uq(P)$q(h; p).
(4)
Then, the solution of the Schrodinger equation can be expanded as
p
for the coefficients GPi of the wave function expansion. This is the standard adiabatic method, where Xqp are known as non-adiabatic coupling terms that involve first and second derivatives of the adiabatic basis functions $,(fi; p) with respect to p. These terms are very difficult to compute near true or narrowly avoided crossings because they behave as a Dirac <5function there. Besides, this fact makes the CC equations stiff to integrate. Since usually there are hundreds of these crossings, a one-by-one analysis is precluded. The Diabatic-by-sectors (DBS) was used for many years to surmount these problems16,17. In this approach, the relevant range of the hyperradius p is divided in M sectors, and a different internal basis is used
489 in each sector. Allthough the DBS method can produce well-converged results, it still has many disadvantages: basis is not optimal in the edges of the sectors and has to be completed if the size of the sectors is not small enough and also the eigenvalues of hint(tl;p) have been shown to go asymptotically only as (1/p2) 18. To overcome all these difficulties, but keeping all the advantages of the adiabatic formulation, the Smooth Variable Discretization - Enhanced Renormalized Numerov (SVD-ERN) algorithm has been recently developed1, inspired in the SVD method of Tolstikhin et al. 19. The main idea behind the method is to discretize the equation (3) before expanding the function in a basis. To this end, the 'smooth' variable p is divided in an equally spaced grid {pn} of size h and the wave function at these points is expanded in Taylor's series. Using the Numerov method, (3) can be rewritten as (1 - T n+1 ) ^ n + 1 + (1 - Tn-0 V„-i = (2 + 107;) Vn - 0(h6),
(5)
where % is related to the internal hamiltonian at point pi. Further improvements can be performed to this formulation, based on the Enhanced Renormalized Numerov method of Thorlacius and Cooper20. In the end, a relation for the matrix R„ that represents the ratio of the wave function in two adjacent points is obtained R-n = Qn — O n , n - l R - n - i O „ _ l , n ,
(6)
where O n _i j n is the overlap matrix between points p„_i and pn, and Q n contains information of the eigenvalues Uq((pn) of the internal hamiltonian. This method is much faster and reliable than previous algorithms1. 3. Calculations At small distances, the potential is repulsive, so tp = 0 and R^" = 0, and then Ri = Qi. This is the starting point of the calculation. To obtain relevant information of the collision, the ratio matrix R is propagated up to some large value of p = PM , and there the boundary conditions are applied by matching with asymptotic wave functions, obtaining the reactance matrix K and the scattering matrix as S = [I + iK] [I — iK]~~ . The system chosen to study is 7 Li 3 . This system is small enough for a feasible calculation of the PES and it is one of the common choices to produce Bose-Einstein condensates. The PES was computed recently21 and describes the physical parameters of the system with excelent accuracy. The
490
spin-aligned Li3 is in the 1 4A' state, while the Li2 molecule is a (a 3 £ j ) state. Calculations were performed in adjusted principal axis hyperspherical (APH) coordinates15,22, using 600 basis functions. In all these calculations, the basis is independent of the collision energy and can be computed only once, and reused for different scattering conditions. Computation of the basis is very expensive from a numerical point of view, taking about the 90% of the complete calculation. Probabilities using this basis are converged with a relative error of 5% at p =70 a.u. where asymptotic conditions are applied. Cross sections for elastic and inelastic processes at cold and ultracold temperatures from 7Li2 {v = 1,2; j = 0) are presented here, computed in two grid of energies, one in the cold and ultracold regime from T=0.45 nK to 1 mK and another for the high energy regime, from T=10 mK to 1 K. The elastic cross sections are shown in fig. 1. The first feature that can be seen in this plot is the well-known Wigner behavior for low scattering energies, in this case, lower than 0.1 mK for both states. Oscillatory behavior at high (i.e. near 1 K) energies for total J = 0 is observed in the figure, however, other partial waves are known to contribute at this regime and the sum over them flattens the cross section23. The inelastic cross sections from 7Li2 (1,0) to 7Li2 (0,0) are shown in fig. 2, for the full potential V of eq. (2) and for the pairwise potential VAB + VBC + VCA- It is clear that the correlation introduced by the threebody interaction is very important and can not be neglected, since the cross section is almost one order of magnitude higher for the complete potential, in agreement with previous calculations for the Na3 system24. The Wigner behavior a ~ l/\/E for the inelastic cross sections extends from 1 mK to 100 nK. However, for energies lower than lOOnK, well in the ultracold regime, the cross section exhibit a different trend. This is due to the fact that probabilities are becoming constant in this energy range, and the Wigner law is not verified. This constitutes an indication that the method is not converging accurately enough in this regime. The reason for this behavior is that the value of p where the boundary conditions are applied is too small at these energies and has to be increased. It should be noted also that the elastic cross sections are less sensitive to the aplication of the boundary conditions and follow the Wigner law in all the cold and ultracold energy range.
491 10
ft::^:*"*:::^::*"*:*::*::*:^:::*::^::^:::^::^;;*..*...*,..^..^^
10
" 10
s 10
10
10
10
10
10 10 Collision Energy (K)
10
10
Figure 1. Total elastic cross section for the collision of a 7 Li atom with a 7 Li2 molecule, for (f, j) = (1,0) state (triangles) and (v, j) = (2,0) state (squares). Lines are only to guide the eye.
4. Outlook It has been shown in the precedent sections that the method of calculation can predict most of the features of the cross sections almost over 10 orders of magnitude. However, it has been pointed out that more accuracy is needed to obtain inelastic cross sections in the ultracold regime. It should also be noted that the use of APH coordinates for values of the hyperradius greater than 100 a.u. becomes extremely expensive (a typical calculation of a basis of 600 elements in 150 values of p can take as long as 10 days in a 32 processors cluster). Besides, the collisions studied in this paper have a small translational energy and the initial Li2 target was considered to be in some of the deeply bound ro-vibrational states. This will certainly not be the case in the BEC regime, where the total energy is slightly (a few nK) above the threshold, and the molecular accesible states are very weakly
492
10
10
10
10
10 10 10 Collision Energy (K)
10
10
10
Figure 2. Inelastic cross section for the collision 7 Li + 7 Li2 (1,0) —> 7 Li + 7 Li2 (0,0) for the pairwise (solid line) and the full potential (dashed line).
bound. Therefore, it could necessary to evaluate the boundary conditions at thousands of atomic units for some total energies in the nK range, and a complementary approach has to be considered. Also, care must be taken with the PES: it has to be accurate enough even at these long distances. Up to now, any attempt to perform such calculation with the required accuracy has not been published. Even though at 100 a.u. the wave functions are not asymptotic enough for the ultracold regime, it is possible that all the channels very well defined in the coordinates space since the particles are well out the interaction region. This means that switching the propagation into Delves hyperspherical coordinates, which are different for each of the three possible final arrangements of the particles, could be a feasible solution. In fact, previous calculations with the SVD-ERN method in the Ne2H were performed in Delves coordinates and extended up to 1000 a.u. without any difficulty25 although in this case there was only one arrangement in the final state. Transformation between APH and Delves coordinates is well known15 and can be made from the current basis calculations. Present work is now devoted to extend the current calculations to the ultracold regime for inelastic processes and to compute a high accuracy
493 PES for the lithium system 26 . Acknowledgments This work has been supported by a reentry grant of Fundacion Antorchas, Argentina. References 1. F. D. Colavecchia, F. Mrugala, G. A. Parker and R. T. Pack: The Journal of Chemical Physics 118, 10387 (2003). 2. E. A. Cornell and C. E. Wieman: Reviews of Modern Physics 74, 875 (2002). 3. W. Ketterle: Reviews of Modern Physics 74, 1131 (2002). 4. N. R. Thomas, N. Kjaergaard, P. S. Julienne and A. C. Wilson: Phys. Rev. Lett. 93, 173201 (2004). 5. A. L. de Oliveira, M. W. Mancini, V. S. Bagnato and L. G. Marcassa: Phys. Rev. Lett. 90, 143002 (2003). 6. M. W. Mancini, G. D. Telles, A. R. L. Caires, V. S. Bagnato and L. G. Marcassa: Phys. Rev. Lett. 92, 133203 (2004). 7. M. H. et al.: Phys. Rev. Lett. 94, 063401 (2005). 8. J. P. Ziesel, N. C. Jones, D. Field and L. B. Madsen: Phys. Rev. Lett. 90, 083201 (2003). 9. B. D. Esry, C. H. Greene and J. James P. Burke: Phys. Rev. Lett. 83, 1751 (1999). 10. E. Nielsen and J. H. Macek: Phys. Rev. Lett. 83, 1566 (1999). 11. H. Suno, B. D. Esry and C. H. Greene: Phys. Rev. Lett. 90, 053202 (2003). 12. J. P. D'Incao and B. D. Esry: Phys. Rev. Lett. 94, 213201 (2005). 13. M. Born and R. Oppenheimer: Ann. Phys. (Leipzig) 84, 457 (1927). 14. J. C. Y. Chen: Case Stud. At. Phys. 3, 305 (1973). 15. R. T. Pack and G. A. Parker: J. Chem. Phys. 87, 3888 (1987). 16. F. T. Smith: J. Chem. Phys. 31, 1352 (1959). 17. D. E. Manolopoulos: J. Chem. Phys 85, 6425 (1986). 18. K. Hino, A. Igarashi and J. M. Macek: Phys. Rev. A 56, 1038 (1997). 19. O. I. Tolstikhin, S. Watanabe and M. Matsuzawa: J. Phys. B: At. Mol. Opt. Phys. 29, L389 (1996). 20. A. E. Thorlacius and E. D. Cooper: J. Comp. Phys. 72, 70 (1987). 21. F. D. Colavecchia, J. J. P. Burke, W. J. Stevens, M. R. Salazar, G. A. Parker and R. T. Pack: The Journal of Chemical Physics 118, 5484 (2003). 22. B. K. Kendrick: J. Chem. Phys. 112, 5679 (2000). 23. M. T. Cvitas, P. Soldan, J. M. Hutson, P. Honvault and J.-M. Launay: Phys. Rev. Lett. 94, 033201 (2005). 24. P. Soldan, M. T. Cvitas, J. M. Hutson, P. Honvault and J.-M. Launay: Phys. Rev. Lett. 89, 153201 (2002). 25. F. D. Colavecchia: Private communication (2003). 26. G. A. Parker: Private communication (2004).
INTERACTIONS OF IONS WITH HYDROGEN ATOMS ALFONZ LUCA, GHEORGHE BORODI, DIETER GERLICH Institutfiir Physik, Technische UniversitSt Chemnitz, Chemnitz, 09107, Germany This progress report presents recent advances in developing a versatile technique for investigating collisions of ions with open shell neutral intermediates. Combination of a 22pole ion trap with abeam of H atoms allows accurate determination of rate coefficients at temperatures between 10 K and 300 K. New experimental results on hydrogen abstraction in collisions of CrT, CH/ and CH5* ions with H atoms are reported at temperatures between 10 K and 100 K.. In the case of CH* and CH/, large rate coefficients of 1.3 x 10* cmV and 6.0 x 10"'° cmV have been observed at 50 K. CH* reacts with D atoms with a total rate coefficient of 2.4 x 10' em's"1 the branching ratio being 50 % for hydrogen abstraction and 50 % for atom exchange. For collisions of CHs* with H atoms rate coefficients of 9 x 10"'2, 1.3 x 10"", and 2.3 x 10'" cmV1 have been determined at trap and nozzle temperatures of 10, 50, and 100 K, respectively. This indicates that this reaction is almost thermoneutral in contrast to thermodynamical data reported in the literature.
1. Introduction Hydrogen, in the atomic or molecular form, is the most abundant species in interstellar clouds and therefore its interaction with other molecules, molecular ions and particle surfaces has to be carefully taken in account in order to understand chemical evolutions and explain observed abundances. The lack of specific information on its reaction dynamics lets plenty of related questions unanswered. For example it is still not yet known how the hydrogen molecule itself or more complex molecules like methanol are formed in space. Do processes in the gas phase or on particle surfaces play the dominant role? In many cases valuable information can be derived from observed abundances of molecules and structures of deuterated species. Laboratory experiments performed at conditions relevant for interstellar space can provide valuable information and help to solve these questions. There are plenty of experimental results on reactions with molecular hydrogen. Unfortunately, radicals such as hydrogen atoms are not as simple to handle and, therefore, only few experiments with H or D atoms have been performed in the gas phase. A general review of ion-atom reactions has been published else-
494
495 where.1 Except early ICR studies2 most experiments are based on the flow tube technique. Using the selected ion flow drift tube approach (SIFDT) reactions can be studied at superthermal energies.3 At temperatures down to 120 K ion hydrogen atom reactions have been investigated by a variable temperature modification of the selected ion flow tube.4 However, no general low temperature reaction studies of ions with H atoms have been reported below 100 K. In this progress report a general methodology is presented which combines a wide field free trapping technique for confining and thermalizing mass selected ions and an atomic hydrogen beam as target. It allows the investigation of reactions of H atoms with ions at temperatures lower than 10 K and can be extended to other radical atoms and condensable neutrals.5,6 Results are reported for three benchmark ion-atom reaction systems. 2. Experimental Fig. 1 shows the novel experimental setup, the Atomic Beam 22-Pole Trap Apparatus (AB-22PT) that has been developed to study H-atom reactions with molecular ions. It is a combination of an effusive source of H / D atoms with a standard trapping apparatus consisting of an ion preparation unit, the central 22PT and a mass selective ion detection system. A thorough description of the used rf devices can be found in Refs. 7 and 8. Discharge tube Hexapole Magnet
'-far-™ I'^^Z, Accommodator 12-300 K
I
—
M a s s Fnter
|
22PT
& Detection
I
S
10- 300 K
CH* Figure 1. Schematic diagram of the Atomic Beam 22-Pole Trap Apparatus (AB-22PT) combined with a low temperature H atom source.
Primary ions are prepared in a standard storage ion source. C0 2 + ions are generated directly by electron bombardment from carbon dioxide, both CH+ and CH4+ from methane, while CH5+ is produced via the subsequent reaction C H / + CHU —> CHs+ + CH3. The ions are extracted from the storage ion source, mass filtered in an rf quadrupole, deflected by 90° in an electrostatic quadrapole bender, and injected into the 22PT. There they are stored for time between ms
496 and some seconds. The translational and internal energy distributions of injected ions accommodate to the cold 22PT environment, Ti0„ = 10 + 300 K, via radiation and via collisions with buffer gas. In order to accelerate the thermalization process, Helium is introduced in a pulsed mode during injection of the ions. For -10 ms, densities of some 1015 cm'3 are achieved. In addition, Helium is let into the 22PT continuously. Typically the He densities, being between 1012 and 1013cm"3, are several orders of magnitudes higher than the density of particles from the beam source. After a certain reaction time, the ions are extracted from the 22PT, mass analyzed, and detected using single ion counting technique. For dissociation of molecular hydrogen resp. deuterium a standard rf driven plasma source9 is used. The generated hydrogen atoms pass through a temperature variable accommodator with 1.2 mm inner diameter and 22 mm length resulting in a translational temperature TH. The effusive beam is skimmed and differentially pumped twice. Two hexapole magnets are used for guiding the H / D atoms (weak field seeking). The number density of H and H2 and deuterated analogues in the interaction region has been determined using a calibrated universal detector based on ionization via electron bombardment at the 22PT position. Comparison of the densities measured with and without hexapole magnets reveals that the magnetic guiding field increases the density by more than a factor 10 at beam temperatures between TH= 35 K and 90 K. The maximal enhancement, a factor of 25, is reached at 60 K. Real in situ determination of atomic and molecular densities is achieved via the reaction of C0 2 + with H / D and H2 / D2. At 300 K the rate coefficients for these reactions are known from previous studies.10 At low temperatures they have been measured carefully with the present AB-22PT. Density determination has been performed before and after each set of measurements with primary hydrocarbon ions. Therefore long time drifts of the discharge source can be excluded or corrected for. At TH~ Tio„ = 100 K, effective H and H2 densities of 109 cm"3 have been obtained typically. At temperatures around 22 K the H - H recombination rate on the accommodator surface is high and atom densities are rather low, ~ 107 cm"3. At the lowest temperature, TH= 12 K, hydrogen condensates on the surface and the atom density increases to 2 x 108 cm"3. If the 22PT is at lowest temperature of 10 K the H2 background, 5 x 107cm"3, is rather low due to condensation. Using the described configuration of the AB-22PT, rate coefficients lower than 10"13 em's"1 can be determined. In order to further reduce the background of molecules, beam catchers based on effective cryo-pumping can be introduced.
497
3. Results and Discussion
3.1. Crt+H,Clt
+D
From a fundamental point of view, the C+ + H2 collision system is one of the model systems for experimental and theoretical studies of the kinetics, dynamics, and energy requirements of endothermic ion-molecular reactions. Consequently, it has been the subject of numerous experimental and theoretical studies, see e.g. Ref. 11 and references therein. The reverse reaction CH+ + H -> C+ + H2 + (0.398 ± 0.003) eV +
(1)
represents an important destruction mechanism of CH , the formation of which is poorly understood in diffuse interstellar molecular clouds. Simple models underestimate the observed abundances and, therefore, it is assumed that shock waves, turbulences or UV radiation must play a role. Until 1984 it was accepted that, at 100 K, the exothermic reaction (1) is slow, k = 2 x 10"12cmV' and even slower at lower temperatures whereas phase space theory predicts that the rate coefficient can approach the Langevin limit of 2 x 10"9cmY' at low temperatures.12 This was confirmed by experimental results obtained with the SIFDT apparatus.3,13 The observed large rate coefficients and a negative temperature dependence indicates that the potential energy surface has no barrier or only a small one. With the AB-22PT technique the rate coefficient for reaction (1) has been determined at 50 K and 100 K. For TH= Tlo„ - 50 K a rate coefficient of 1.3 x 10"9cmV has been obtained. At an accommodator temperature of 100 K and a trap temperature of 80 K, a value of 8.7 x 10"10cmV1 has been measured. Note that in this case the internal temperature of the CH+ ion was somewhat smaller than the collisional temperature. The experimental and theoretical results are summarized in Fig. 2. The non-thermal results of the SIFDT technique have been converted using the approximation KEcm = 3/2 kT, the validity of which has been shown for atomic ions in drift fields. However, the contribution of rotational energy of CH+ can differ from translational energy and this may lead to differences in the "temperature" dependences. Our low temperature data which are close to Langevin limit show that there is no barrier that would significantly hinder the reaction. The theoretical values of phase space theory describe well the behavior of the reaction.12 Recent RIOSA-NIP calculations14 which account for all reactive channels including hydrogen atom exchange, show the correct temperature trend; however, they underestimate the measured
498
value by almost a factor 10. This indicates that more work needs to be done in order to understand low temperature processes from first principles. 1
Phase-Space Theory
1
CH* + H - * C +
+ +
10s
+
H2
AB-22PT
SIFDT E o
•
RIOSA-NIP Theory
KT . . i
10
100
1000
T/K Figure 2. Experimental and theoretical rate coefficients for the indicated hydrogen abstraction reaction.
The H - H exchange in CH+ + H collisions is thermoneutral and it can be expected, e.g. from phase space theory, that the rate coefficient is much smaller than C+ production which is exothermic.12 Using the isotopically labeled system CH+ + D both channels, hydrogen abstraction and atom exchange CH+ + D -> C+ + HD + 0.434 eV -> CD+ + H + 0.046 eV
(la) (lb)
can be distinguished. Also this system has been investigated in the trap at TD = Th„ = 80 K. Surprisingly the same rate coefficient (1.2 ± 0.2) x 10"9cm3s"', has been obtained for both channels indicating the importance of the atom exchange channel. It is obvious that more detailed theoretical studies are needed in order to understand the dynamics of this basic reaction system. 3.2. CH/ + H An interesting reaction system which proceeds via the intermediate collision complex CH5+ is CH4+ + H -> CH3+ + H2.
(2)
499 With the ICR technique,2 no hydrogen abstraction reaction has been observed with H and D atoms although this process is exothermic by 2.7 eV and formation of CH5+ collision complex is as well exothermic by 4.6 eV. Note that the detection limit of the ICR experiment was 10"" em's'1. Our investigations show that reaction (2) is highly reactive at low temperatures. The values 6.0 x 10"10cm3s"' and 5.1 x 10"10cm3s'' have been obtained at TH = Tion = 50 K and at T„ = 100 K and T,on = 80 K, respectively. Based on the Langevin limit, 2 x 10"9cmY', this means that every forth collision leads to reaction. Assuming that the rate coefficient obtained at 300 K by the ICR technique is correct, the reaction shows a very strong negative temperature dependence. This may be explained by the formation of a long lived CHs+ complex in combination with a bottle neck hindering the transition towards the product channel. In order to make final conclusions on energetics and dynamics, additional measurements over the full accessible temperature range are planned.
;
C H / + H -> C H / + H,/ 5 • '
10
4 •
"
2. '.
. i
.
.
100 T/K
.
.
.
.
.
.
1000
Figure 3. Temperature dependent rate coefficients for forward (squares) and backward (circles) direction of reaction (3).
3.3. CH5+ + H An interesting reaction system including two fluxional ions is CH4+ + H2 <-> CH5+ + H.
(3) 13
It has been investigated in both directions by the SIFDT technique in the regime from thermal (300 K) to 0.12 eV center of mass kinetic energy, KEcm. An exoergicity, AH0 = 5 kJ/mol, and an entropy change, AS0297~ 31 Jmor'K"1 has
500
been derived for the forward direction. From these results it has been concluded that reaction (3) is exoergic but endoentropic. Therefore the rate coefficient in backward direction, kb, should decrease steeply from 10"10cmV at 20 meV (150 K) to 10"12cm3s"' at 8 meV (60 K) as indicated by the dotted line in Fig. 3. The rate coefficient in forward direction, k/, has been recently measured from 300 K down to 15 K using a 22PT,15 see full squares in Fig. 3. In the present work, reaction (3) has been investigated in backward direction at 10, 50, and 100 K. The temperature of the accommodator has been set at the 22PT value except for the lowest temperature where only 12 K have been achieved. The rate coefficient, kb, increases slightly from 9 x 10"12cmV at 10 K to 2.3 x 10"" em's"1 at 100 K, see solid circles in Fig. 3. Approaching 300 K, kb should increase significantly according SIFDT results. Our result at 7#= 100 K and Tlo„ = 300 K, see open circles in Fig. 3, shows that kb does not reach SIFDT value and therefore the internal temperature (Tl0„) of CH5+ does not influence reactivity significantly. The small variation of kb with internal temperature of CH5+ ions can be taken as an argument that a direct process is involved and the H atom impact determines predominantly the reactivity. It should be noted that this statement is based on both our and SIFDT results the difference between which may be also caused by experimental uncertainties. Our result at TH = Tio„ = 100 K agrees with prediction done in Ref. 13 within the error of measurement whereas kb does not drop significantly at lower temperatures as predicted. This indicates that the reaction is almost thermoneutral. 4. Conclusion The presented results demonstrate that the combination of an rf ion trap with a neutral beam is a versatile tool for revealing information on reactions between ions and radical atoms at low temperatures. Using H or D atoms, the fundamental collision systems C+ + H2 or HD, CH3+ + H2 and CH4+ + H2 have been studied in detail in the reverse direction. A comparison of the experimental findings with theoretical results or expectations indicate that our understanding of these systems is still quite limited. Some of the observations can be explained with statistical models; however it is obvious that one has to account for nuclear spin restrictions which are known to be important in H and D atoms containing systems at low temperatures. For the simple tri-atomic CH2+ and CHD+ collision system the measurements indicate that a statistical theory is not satisfactory. In order to account correctly for direct collisions, quantum mechanical calculations beyond the so far used approximations13 are needed. Reactions which proceed via the CH5+ intermediate may be described by statistical methods since already
501 the ground state of protonated methane is very fluxional and all H atoms are equivalent. This, however, does not explain the observed increase of reactivity by more than a factor 50 going from room temperature to 50 K. Predictions for the reactions occurring on the CH6+ potential energy surface are handicapped by the fact, that already the asymptotic energies are uncertain. Besides that it is desirable to calculate correctly the actual phase spaces of the two competing channels CH5+ + H and CH/ + H2 at the temperatures of the present work. In contrast to the conclusions made in Ref. 12, it is expected that at low temperatures the formation of CHs+ should be "exoentropic". Acknowledgments The development of this instrument involved contributions of several people. Especially we would like to mention the fruitful cooperation with Mark Smith. Financial support of the Deutsche Forschungsgemeinschaft (DFG) via the Forschergruppe FOR 388 "Laboratory Astrophysics" is gratefully acknowledged. References 1. M. Sablier, C. Rolando, Mass Spec. Rev. 12, 285 (1993). 2. Z. Karpas, V. Anicich, W. T. Jr. Huntress, J. Chem. Phys. 70, 2877 (1979). 3. W. Federer, H. Villinger, F. Howorka, W. Lindinger, P. Tosi, D. Bassi, E. Ferguson, Phys. Rev. Lett. 52, 2084 (1984). 4. N. G. Adams, D. Smith, Ap. J. 294, L63 (1985). 5. A. Luca, D. Voulot, D. Gerlich, WDS'02 Proceedings of Contributed Papers, Part II, Safrankova (ed), Matfyzpress, 294 (2002). 6. S. Schlemmer, A. Luca, D. Gerlich, Int. J. Mass Spectrom. 223-224, 291 (2003). 7. D. Gerlich, Adv. Chem. Phys. 82, 1 (1992). 8. D. Gerlich, Physica Scripta T59, 256 (1995). 9. J. Slevin, W. Stirling, Rev. Sci. Instrum. 52, 1780 (1981). 10. G. B. Scott, D. A. Fairley, C. G. Freeman, M. J. McEwan, J. Chem. Phys. 106,3982(1997). 11. M. P. Hied, R. A. Morris, A. A. Viggiano, J. Chem. Phys. 106, 10145 (1997). 12. W. J. Chesnavich, V. E. Akin, D. A. Webb, Ap. J. 287, 676 (1984). 13. W. Federer, H. Villinger, P., Tosi, D. Bassi, E. Ferguson, W. Lindinger; G. H. F. Diercksen et. al. (eds), Molecular Astrophysics, D. Reidel Publishing Company, 649 (1985). 14. T. Stoecklin, P. Halvick, Phys. Chem. Chem. Phys. 7, 2446 (2005). 15. O. Asvany, I. Savic, S. Schlemmer, D. Gerlich, Chem. Phys. 298, 97 (2004).
ANALYSIS OF ALL STRUCTURES IN THE ELASTIC AND CHARGE TRANSFER CROSS SECTIONS FOR PROTONHYDROGEN COLLISIONS IN THE RANGE OF 10~10 - 1 0 2 EV PREDRAG S. KRSTlC, DAVID R. SCHULTZ, Physics Division, Oak Ridge National Laboratory, P.O. Box 2008 Oak Ridge, TN 37831, USA JOSEPH H. MACEK, SERGEI YU. OVCHINNIKOV Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 379961501, USA
Elastic scattering and spin exchange cross sections in H*+H collisions are computed using accurate adiabatic potential curves for the center-of-mass energy range 10"'° eV < E < 102 eV. Both cross sections show considerable structure which necessitates computation on a fine energy grid to resolve them. Many of these features can be correlated with the poles of the scattering matrix in complex energy plane. Finding stationary phases in the partial wave cross sections, we also explain the glory oscillations of the elastic cross section that extends below 100 eV down to the lowest energies. A complex angular momentum analysis using computed Regge trajectories shows that each peak of the oscillatory structure in the energy range 0.01-1 eV is predominantly associated with one or two trajectories.
1.
Introduction
The elastic scattering and spin exchange cross sections for proton impact on atomic hydrogen are important for applications such as the study of fusion and astrophysical plasmas. Calculations have been published over the years which usually employ the most accurate techniques available at the time [1,2]. In the low energy range (< 10 eV), below the first excitation threshold, the cross sections show considerable structure which makes a detailed physical analysis of the underlying comparison of different calculations problematical unless the energy grid is extremely fine and the results computed with great accuracy. Previous calculations have tended toward this direction, but still greater
502
503
accuracy and finer grid are needed, which we report here over for center-ofmass collision energies E < 100 eV. The details of this calculation, obtained at six digits of numerical accuracy, are given elsewhere [3-5]. It is a particular goal to interpret the source of the structures seen in the computed cross sections for this system, given that some structure is predicted for all ion-atom collisions in this energy range. The phase shifts
10'6
10'5
10"4
10°
10"2 E(eV)
10"'
10°
101
102
Figure 1. Elastic and charge-transfer integral cross sections for H++H collisions system
2. Glory Oscillations Long ago Bernstein [6] pointed out that sums over partial elastic cross sections involving sin Si and constituting the integral cross section may oscillate for some types of the potential if Si has a maxima or minima where dSi/dL vanishes. These are called zero-angle glory oscillations in the integral elastic cross section. The elastic integral cross sections contain sums of terms of that form. The contributions to the sum for regions where dS, I dL = 0 are estimated using the method of stationary phase [3]. This reproduces the oscillations (above 1 eV) and modulate the cross section at lower energies. Agreement is achieved in the phase, frequency and amplitude, removing any doubt regarding the source of the oscillations. The charge transfer cross sections contain terms of the form sin2(££-
504
3.
Resonances and S-Matrix Poles
It is known that structures in cross sections are often related to analytic properties of the underlying scattering matrix elements in the complex energy plane. In the case of narrow, isolated resonances, it is also possible to use the Fano line shape theory [7] or the standard Breit-Wigner resonance theory [8] to characterize the structure. Hodges and Breig [2] identified some of the narrow features that showed a Lorentzian lineshape with shape resonances corresponding to waves trapped in a combination of an attractive potential and an angular momentum barrier. We relate these structures to the values of complex energies where the S-matrix has poles. These poles correspond to resonances associated with potential barriers formed by the attractive polarization and exchange potentials and the repulsive centrifugal potentials. We use the comparison equation technique to calculate the poles of the S-matrix and tabulate them. All narrow, sharply peaked structures in Figure 1 were identified with these poles. We find three types of resonances, below-barrier resonances, top-of-barrier resonances, and above-barrier resonances. All narrow resonances fit well to the Fano line shape formula [7]. 4.
Regge Oscillations
To explain the oscillating features in the H++H spin-exchange cross section sections at energies in the range 0.01-1 eV we introduce a new representation of integral cross sections, due to Mulholland [9]. He showed that the partial wave sum in a cross section may be written 00
/W 7Q l+exp(-i2nA.) MX
-Re y_fr(Am)*m_ (1) l+exp(i2tcAm) m where, in our case /(Z,+1/2)=2TT/£?sin (
505
over a few pole terms and the exact sum over about 300-1000 partial waves is excellent.
Figure 2. Oscillations of the spin-exchange cross sections for H++H collision compared with those obtained from a few terms summed over Regge trajectories.
Acknowledgments We acknowledge support from the US Department of Energy, Offices of Basic Energy and Fusion Energy Sciences, through Oak Ridge National Laboratory, managed by UT-Battelle, LLC under contract DE-AC05-00OR22725. References 1. G. Hunter and M. Kuriyan, Proc. Roy. Soc. 353, 575 (1977). 2. R. R. Hodges and E. L. Breig, J. Geophys. Res. 35, 7697 (1991). 3. P. S. Krstic, J. H. Macek, S.Yu. Ovchinnikov, D. R. Schultz, Phys. Rev. A 70, 042711(2004). 4. J. H. Macek, P. S. Krstid, S.Yu. Ovchinnikov, Phys. Rev. Lett. 93, 183203 (2004) 5. A. E. Glassgold, P. S. Krstid, D. R. Schultz, Astrophys. J. 621, 808 (2005). 6. R. B. Bernstein, Adv. Chem. Phys. 10, 75 (1966). 7. U. Fano, Phys. Rev. 124, 1866 (1961). 8. N. F. Mott and H. S. W. Massey.The theory of Atomic Collisions, Third Edition, p.359, (Clarendon Press, Oxford, 1965) 9. H. P. Mulholland, Proc. Cambridge Phil. Soc. (London) 24, 280 (1928). 10. T. Regge, Nuovo Cimento 14, 951 (1959).
AB-INITO ION-ATOM COLLISION CALCULATIONS FOR MANY-ELECTRON SYSTEMS
J. ANTON, B. F R I C K E University
of Kassel, Institute
of Physics, D-34109 Kassel,
Germany
In order to describe an ion-atom collision in a fully quantum-mechanical way we solve full relativistically the time-dependent Dirac equation. In this coupledchannel formulation which includes not only internuclear distance-dependent optimized atomic basis functions, but also continuum functions we describe electron transfer, excitation and ionization in a unified way in many-electron ion-atom collisions. We present theoretical results for the system H e + + on He and compare it with experimental results measured in p-space.
1. Introduction The description of excitation, transfer and ionization in heavy-ion collision has for long been a subject in theoretical research. A number of reviews have been published over the years L2.3.4.5.6. During the last decades a large number of perturbative methods starting from first Born approximation 7 till more refined approximations like CDW-EIS 8 and others (see 3 ' 4,9 and references therein) have been developed. These are only appropriate for low Z, few electrons and the high velocity regime. Non-perturbative methods are the force impulse (FIM) 1°.11.12,i3,i4j ^.ne hidden crossings 15,1S and the closed coupling method 17,i8,i9,20,2i,22,23) Qf w h ^ t n e last is the most frequently used. A few years ago we have published a paper where the method which we are going to present here was used in a preliminary form 24 . 2. Theoretical Method In order to calculate the physics of ion-atom collision processes we have to solve the time-dependent Dirac equation ih—V{n,...,rN,t)
= Hei'i>(r1,...,rN,t).
506
(1)
507
Hei is the electronic Hamilton operator which includes the kinetic energies of the electrons as well as the electron-nuclei and electron-electron 1/r interactions. In a first step we expand ^ in a time-dependent Slater Determinant ipi(n,t) *(*=!,...,?*,«) =
s/N\
... Vi(rjv,t) (2)
ipN{n,t)
...ipN{rN,t)
where \P is the time-dependent total wave function of the whole system. If we introduce this ansatz in the time-dependent Dirac-Fock equations (1) we get an equation for the single-particle orbitals ipi(f,t) d
ihjt
i>i(?,t) = (t + VN(R(t)) + Vc(t) + VEx(t)) Mr,t)
i=
l,...,N.
hTDDF(t)
(3)
In a second step we make an ansatz for these quasi-molecular timedependent wave functions M
(4)
The £j are in general just parameters. However, it is convenient to use the eigenvalues of the operator h9MO defined in equation (9). This ansatz in eqn. (4) for the wave functions leads to the matrix equation i h S_ 4 = K. a,
(5)
where the matrix elements have the form
Sjj = ( 0 j | ^ ) e - * J ( " - « > * '
Hlj =
(cf>l\ih^t+ej-hTDDF'
(6)
^y
-Tif(.£i-£t)dt'
508
In a third step we expand the ipi(r,t) in "static" molecular wave functions
hi?, R)^J2 dU&) ^(*fc £)••**)• exp { \ ™-vp • n + £
dJv(R) ${({?, R), R) • exp 1 1 mVT • r\
= x:<(^)^|^').
(7)
K',v
This is an expansion in fl-dependent atomic orbitals
K,K' n,v
as well as the Fock matrix hS
h^°=j:Y(d«y-d%(tf\s+sK,(hMO
+
^v^\^)
(9)
becomes diagonal in this basis
509
Having this we go back to the second step: The coupled channel equations for d(j which have to be solved in the second step read in this basis
M
,
/ a \
au = Yl-aJi(^
(57)
+V(R)(r-VR)vK,(R) •i J
(10)
.e-*/(ei-£')*'
where the J^ coupling matrix elements have the form
N
K,K' M,"
K,K'
/x,"
SKSK'
dRh ,
S%SKK,K' li,v
VKX
Vv
»
dn
<j>j ) + M2 + M 5 .
(11)
ZK>
Finally we can go back to the first step. After solving for the {ay} from the equation (11), where i = 1,... ,7V is the number of electrons in the system and j = 1,..., K is the number of levels which have been taken into account, one is able to reconstruct the many particle wave function \P using the Method of Inclusive Probabilities. Thus one has a full quantummechanical description. This formulation with the explicit inclusion of the electronic translation factors is very complicated in the actual application, but it includes many achievements.
510 He
- He (50 keV)
He Is
He~ls
o;ooi
0,01
0,1
1
Internuclear distance (a.u.)
Figure 1.
Correlation diagram for the system H e + + —» He for 50 keV impact energy
• The basis used adapts automatically to the problem. • It allows to describe slow collisions {vorbit 3> vnuci). In this case we can set SK> = 1- The operator tfiMO is equivalent to the operator hMO and the basis functions cf>j (f, R) are equivalent to the molecular orbitals (MO). • It also allows for a description of fast collisions (vorbit <S Vnuci)The SK' are fast oscillating functions; therefore all matrix elements which include these functions go to zero. The overlap matrix §_ and the Fock matrix hQMO
are already diagonal in the atomic basis. • At not too small impact energies it describes the atomic basis which is centered on the center of mass of the collision system. They describe the saddle point electrons. For an actual calculation one needs a successive solution of the atomic DFS equation as well as the quasi- molecular equations with a simultaneous calculation of the matrix elements at all internuclear distances for all impact parameters and impact energies. After checking the phase for all quasimolecular orbitals we need to solve the modified coupled-channel equations. As a last step one gets the many-particle interpretation using the set of time-dependent single particle amplitudes {ay}.
511 3. Results The only example which we were able to perform in parts up to now within this complicated calculation was the two-electron collision system He + + —• He. As incoming energy we used 50 keV. The following processes can occur in this case: He+++He->: He + He++ He+(ls) + He+ He+(n = 2) + He+ He+(n = higher) + He+ He+ + He++ + e He++ + He++ + 2e Very preliminary experimental results from the groups in Frankfurt 25 and Lanzhou 26 are available. In the following we give a few examples of our results. In Fig. 2 we present the results of the single ionization probability as well as the transfer and excitation into the n = 2 states as function of impact parameter. Due to the Method of Inclusive Probabilities there is no distinction where the second electron has gone to because one sums over all processes where this one electron appears in the continuum. This single ionization probability as function of impact parameter has two distinct maxima. It may very well be that this structure allows to interpret the experiments in terms of TS1 and TS2 processes, but this has to be examined in more detail. The most important new development is the fact that we are now able to Fourier-transform the wave functions from the normal space into p-space. This is necessary for a comparison with experimental values because the experimentalists measure the probabilities in this velocity space. Thus we are able to get channel-dependent distributions of the ejected electrons in the momentum space. Fig. 3 presents one of the many possible examples of a channel function for the system He + + —• He for 50 keV. In the near future we have to weigh these channel functions with the amplitudes from our calculations in order to come to a comparison with experimental results. 4. Summary Using this ab-initio method of the solution of the time-dependent Dirac equation for an ion-atom collision we are able to calculate the highly
512
2+
He 1
1
'
'
-He(50keV) 1
1
1 — —
0,25
1
'
1
Single ionization Capruxe in L-shetl of He
_ -
0,2
£>
ha -8 0,15
_ -
Pro
.P
0,1
\ - \ \\
/ /
*• "*\ \
-
V
0,05
\
n
,
1
1
\
2
. _1_
--u_ 3 4 rrrTi^T»-j 5 Impact parameter (a.u.)
t_
Figure 2. The probabilities for single ionization as well as capture into the /-shell of He as function of impact parameter for the system He++ —» He at 50 keV.
A
2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2
r
r
-
0.5
/ + v+;
Stiira
°-r
W&*ZU+2
Pz (au)
WI/J
-0.5
Px(au)
Figure 3. One example of a channel function in p-space for an electron at 2.7 eV in the target system.
513 differential behavior of the processes excitation, transfer and ionization in a unified way. If correlation is defined as the processes which go beyond Hartree-Fock we can state that within this method the behavior of this many-particle system in an ion-atom collision can be described without correlation. Of course correlation in terms of Pauli correlation and the electron-electron interaction is included, but this to our mind is a trivial statement. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.
A. Riera, A. Salin, J. Phys. B 9, 2877 (1976) W. Lichten, J. Phys. Chem. 84, 2102 (1980) J. S. Briggs, J. H. Macek, Adv. At. Mol. Opt. Phys. 28, 1 (1991) B. H. Bransden, M. R. C. McDowell, Charge Exchange and the Theory of Ion-Atom Collisions, Clarendon Press, Oxford (1992) L. F. Errea, C. Harel, H. Jouin, L. Mendez, B. Pons, A. Riera, J. Phys. B 27, 3603 (1994) J. Eichler, W. E. Meyerhof, Relativistic Atomic Collisions, Academic Press, San Diego, Boston, New York, London, Sydney, Tokyo, Toronto (1995) D. R. Bates, G. W. Griffing, Proc. Phys. Soc. 66, 961 (1953) D. S. F. Crothers, J. F. McCann, J. Phys. B 16, 3229 (1983) S. Slim, L. Heck, B. H. Bransden, D. R. Flower, J. Phys. B 24, 1683 (1991) J. F. Reading, A. L. Ford, Phys. Rev. Lett. 58, 543 (1987) J. F. Reading, A. L. Ford, J. Phys. B 20, 3747 (1987) J. F. Reading, T. Bronk, A. L. Ford, J. Phys. B 29, 6075 (1996) A. L. Ford, L. A. Wehrman, K. A. Hall, J. F. Reading, J. Phys. B 30, 2889 (1997) T. Bronk. J. F. Reading, A. L. Ford, J. Phys. B 31, 2477 (1998) M. Pieksma, S. Yu. Ovchinnikov, J. Phys. B 24, 2699 (1991) S. Yu. Ovchinnikov, J. H. Macek, Phys. Rev. Lett. 75, 2474 (1995) D. G. M. Anderson, M. J. Antal, M. B. McElroy, J. Phys. B 4, 118 (1974) W. Fritsch, C. D. Lin, J. Phys. B 27, 1255 (1981) T. G. Winter, C. D. Lin, Phys. Rev. A 29, 3071 (1984) W.-D. Sepp, D. Kolb, W. Sengler, H. Hartung, B. Fricke, Phys. Rev. A 33, 3679 (1986) N. Toshima, J. Eichler, Phys. Rev. A 27, 2305 (1988) P. Kiirpick, W.-D. Sepp, B. Fricke, Phys. Rev. A 51, 3693 (1995) L. F. Errea, C. Hares, C. Illescas, H. Jouin, L. Mendez, B. Pons, A. Riera, J. Phys. B 31, 3199 (1998) J. Anton, K. Schulze, D. Geschke, W.-D. Sepp, B. Fricke, Phys. Lett. A 268, 85 (2000) L. Schmidt, Dissertation, University of Frankfurt (2000) X. Ma, private communication
FULLY DIFFERENTIAL STUDIES ON SINGLE IONIZATION OF HELIUM BY SLOW PROTON IMPACT* A. HASAN Department of Physics, United Arab Emirates University, P.O. Box 17551, Al-Ain, Abu Dhabi, United Arab Emirates N.V. MAYDANYUK, M. FOSTER, B. TOOKE, E. NANNI, D.H. MADISON, AND M. SCHULZ Physics Department and Laboratory for Atomic, Molecular, and Optical Research, University of Missouri-Rolla, Rolla, MO, 65409, USA A. VOITKIVAND B. NAJJARI, Max-Planck-lnstitut fur Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany In this progress report, we present fully differential cross-sections (FDCS) for single ionization in 75 keV p + He collisions using cold-target recoil-ion momentum spectroscopy to measure the recoil momentum and ion energy loss spectroscopy to measure the projectile momentum. At this relatively small projectile velocity, the measured FDCS reveal no recoil peak and a backward shift of the binary peak suggesting a dominant role for the projectile-residual target ion interaction. Such signatures are not observable in single ionization by fast projectiles or electron impact. This interaction appears to be more important than the post-collision interaction, which so far was assumed to be the most important factor in higher-order effects in single ionization.
1. Introduction For two reasons, ionization processes in atomic collisions are particularly suitable to study the fundamentally important few-body problem [1, 2] (and references therein). First, the final state involves, in contrast to pure excitation and capture processes or ionization by photon impact, at least three unbound particles. Second, experimental techniques are now available to efficiently perform kinematically complete experiments to obtain fully differential cross sections both for electron and ion impact [2]. A kinematically complete experiment on single ionization requires that the momentum vectors of all three collision products (the scattered projectile, the *This work is supported by the National Science Foundation under grant No. PHY-0353532 and No. PHY-0070872.
514
515 ejected electron, and the recoil ion) are determined. This, in turn, means that two momentum vectors must be measured directly; the third one is readily obtained by momentum conservation. So far, FDCS were obtained either by measuring the ejected electron and projectile momenta (electron impact)[3] or the ejected electron and recoil-ion momenta directly [2]. In our approach, the fully momentum-analyzed projectiles and recoil ions are measured in coincidence. The main advantage of this method is that, from a direct measurement of the projectile momentum, a better resolution in the momentum transfer q (defined as the difference between initial and final projectile momentum) can be obtained. Thereby, smaller transverse momentum transfers become accessible, a region which turned out to be particularly interesting. In the work reported here, we investigated the role of the projectile-residual target-ion (FT) interaction on the FDCS for single ionization in 75 keV p + He collisions using a new experimental method. Earlier this interaction was found to be surprisingly important even for very fast ion impact [2]. For the relatively slow projectiles investigated here, we found new effects due to the PT interaction which are impossible to observe for fast projectiles and which are very difficult to distinguish from other effects for slow electron projectiles. 2. Experimental Set up The experiment was performed at the University of Missouri-Rolla Ion Energy Loss Spectrometer (IELS) [4, 5]. In brief, a proton beam was produced by a hot cathode ion source with a very narrow energy spread (<1 eV) and extracted at an energy of 5 keV. The proton beam was then accelerated to an energy of 75 keV, steered and collimated by passing through a very narrow set of slits of 0.1 x 0.1 mm in size. Next, the ions were guided to the interaction region where the ion beam intersected a very cold (< IK) neutral He beam from a supersonic gas jet. Two spectrometers were used to detect the collision products and determine the change in their physical properties such as charge and momentum. First, coldtarget recoil ion momentum spectroscopy (COLTRTMS) [4, 6] was used to detect the recoil ions and determine their momentum vectors. Meanwhile, the projectiles which did not change charge state were selected with a switching magnet, decelerated to 5 keV and energy-analyzed by an electrostatic parallel plate analyzer [3-5]. The analyzer voltage was set for a projectile energy loss of e = 30 eV corresponding to an ejected electron energy of Ee = e - I = 5.5 eV (where I is the ionization potential). The resolution (defined as full width at half maximum (FWHM)) in E was 3.0 eV. Furthermore, the analyzer has an entrance and exit slits with a length in the jc-direction of about 2 cm and a width in the ydirection of about 75 nm. After passing the slits, the projectiles were detected by a position-sensitive channel plate detector with a position resolution of 100 ^m
516 FWHM. The longitudinal component (z-direction) of q is given by qz = e / vp (in a.u.), where vp is the projectile speed. Due to the narrow width of the analyzer slits, the ^-component of q is kept fixed at 0 and the ^-component is obtained from the position information. The achieved resolutions are 0.06 a.u. FWHM in ty and qz and 0.10 a.u. FWHM in q,. The experiment was done in double-coincidence mode. A fast timing single derived from the projectile detector was used to start a time-to-amplitude converter (TAC) which was stopped by another fast timing signal from the recoil detector. If there is a coincidence, the data acquisition system was triggered and six analog position signals from the recoil and projectile detectors, and another analog signal from the TAC were read by an analog-to-digital converter (ADC). The time-of-flight (TOF) of the recoil ion from the collision region to the detector and its two-dimensional position in the plane perpendicular to the extraction field were decoded from these signals. The position and TOF of the recoil ion were used to calculate its momentum. The scattered electron momentum was deduced from energy and momentum conservation. Thus, the momenta of all the particles involved in the interaction were determined making the measurement kinematically complete. 3. Results In Figure la, a three-dimensional image of the FDCS = d5a/(dfiedQpdEc) (where ne and £lp are the solid angle for the electron and the projectile, respectively) is shown for an ejected electron energy E,, = 5.5 and a projectile scattering angle of less than 0.15 mrad as a function of the polar and azimuthal electron ejection angle. The scattering plane, which is spanned by the initial and final projectile momentum vectors, is not defined since both vectors are in the same direction. At this projectile scattering angle, Figure 1 shows that the FDCS is completely dominated by a single peak in the forward direction. Similar maxima are routinely observed in the FDCS both for electron and ion impact [2-5] and can be explained in terms of a binary interaction between the projectile and the ejected electron. It is therefore commonly referred to as the binary peak. In a first-order treatment it points in the direction of q, which in this case coincides with the initial beam direction. The most dramatic feature in the FDCS is the complete absence of a peak in the direction of -q (backward direction). Here, the first Born approximation (FBA) predicts the so-called recoil peak, which results from a two-step process: the electron first is knocked off by the projectile and then rescatters in the backward direction by the residual target ion. To investigate the complete absence of the recoil peak in the data, in Figure lb, we present a cut through the three-dimensional data along the xz-plane and compare to three different
517
calculations: the FBA (dashed curve in Figure lb), the continuum distorted wave-eikonal initial state (CDW-EIS, dotted curve), and the three distorted wave (3DW). In contrast to the FBA calculations, the CDW-EIS and 3DW models do include higher-order effects in the projectile-electron interaction. More specifically, the post-collision interaction (PCI) between the outgoing projectile Mid the ejected electron after the actual ionization process is accounted for. In addition, the 3DW includes the PT interaction, which is not freated by CDWEIS and the FBA. The three calculations are reduced by a factor (indicated in Figure lb) in order to qualitatively compare these theoretical cross sections with the experimental data.
Figure 1. (a) Three-dimensional image of the electrons ejected in 75 keV p + He. The initial and final direction of the beam is marked by an airow. (b) Triply differential cross-sections for electron emission plane that contains the momentum transfer vector q in the same collision system. Solid circles, experimental results; dashed curve, FBA calculation; dotted curve CDW-EIS calculation, solid curve, 3DW calculation. All calculations are reduced by a factor, see text for explanation.
Clearly, as stated above, the FBA shows a distinct recoil peak. In the CDWEIS, in contrast, it is strongly reduced. This can be understood as follows: the attractive PCI "drags" the electrons in the forward direction, which coincides with the direction of q. Therefore, an electron initially ejected in the backward direction, where the recoil peak is expected, is bent by the PCI in the forward
518 direction and occurs in the region of the binary peak. Finally, in the 3DW model the recoil peak is completely wiped out. Since the only difference between CDW-EIS and 3DW is that the latter accounts for the ¥F interaction, this shows that the recoil peak is eliminated by a combination of the PCI and the FT interactions. Although the 3DW gives nice qualitative agreement with the data, there is a large discrepancy in magnitude, which will be discussed below. In Figure 2, another three-dimensional image of the FDCS is shown for an ejected electron energy Ef = 5.5 ± 1.5 eV and a fixed momentum transfer q = 0.67 a.u. in magnitude. The direction of q is indicated by an arrow in Figure 2 It no longer coincides with the beam direction and as a result, the scattering plane is now defined, unlike in the case of Figure 1 The pronounced peak structure, which points approximately in the direction of q, is the binary peak. However, again we do not observe any noticeable contributions in the direction of -q, where one would expect to see the recoil peak.
Figure 2. Three-dimensional fully differential angular distribution of electrons with an energy of 5.5 eV ejected in 75 keV p + He collisions. The momentum transfer is 0.67 a.u. The arrows labeled p„ and q indicate the directions of the initial projectile momentum and the momentum transfer, respectively.
A closer inspection of Figure 2 reveals that the binary peak is not pointing exactly in the direction of qs but rather it is somewhat shifted in the backward direction (i.e. away from the beam direction). This is more clearly seen in a cut through Figure 2 for the scattering plane, which is shown in the left part of Figure 3 along with the corresponding cuts for momentum transfers of 0.77 a.u. (center) and 0.97 a.u. (right). Electrons ejected into the scattering plane are selected within a bin of Aq>e = ± 10°. The backward shift of the binary peak relative to q systematically decreases with increasing q from about 20° at q =
519 0.67 a.u. to no significant shift at q = 0.97 a.u. Furthermore, at small q a second structure is visible with a maximum at an angle approximately equal to -©q, where ©q is the direction of q. Both effects, the backwards shift of the binary peak for ion impact and a structure at - 0 q , have never been observed in any previous experiment.
q = 0.67
q = 0.77
q = 0.97
Figure 3. Fully differential cross sections for electrons with an energy of 5.5 eV ejected into the scattering plane in 75 keV p + He collisions plotted at different momentum transfer q. The scattering angle 9, is defined in the text. The solid and dashed arrows indicate the angles 0 q and -©,, respectively, where 0 q is the direction of q. The solid curves show our 3DW calculations, which are multiplied by a factor of 0.2 (0.67 a.u.), 0.25 (0.77 a.u.) and 0.6 (0.97 a.u.), to compare the shape to the experimental data (see text for explanation). The features observed in the data can plausibly be explained by the same higher-order ionization mechanism involving the PT interaction that was held responsible for the surprising discrepancies between experiment and theory for 100 MeV/amu C 6+ + He [2]. Since the backward shift of the binary peak increases with decreasing q, which in turn favors large impact parameters, we consider cases where the projectile passes the target atom at a large distance (let's say on the left side of the target atom) and the electron stays between both nuclei. First, the projectile interacts with the electron and, since this interaction is attractive, gets scattered to the right. The corresponding momentum transfer qe, which exclusively goes to the electron, points to the left and in the forward direction. In the second step, the projectile elastically scatters from the residual target ion. Since that interaction is repulsive, this time the projectile is deflected to the left relative to the direction after the projectile-electron interaction. The corresponding momentum transfer qr, which goes exclusively to the recoil ion, points to the right (for elastic scattering, the longitudinal momentum transfer is negligible). The total momentum transfer is q = qe + qr. The transverse component of q is in the same direction, but smaller than the one of q e because qe and q r point in opposite directions and qe > qr since the projectile passes closer to the electron than the nucleus. At the same time, the longitudinal component of q is equal to the one of qe so that the direction of qe is shifted
520
backwards relative to q. The direction of the final electron momentum pe is basically given by qe convoluted with the initial momentum distribution on the target. The centroid of this convolution is for symmetry reasons still the same as the direction of qe. The backward shift suggests that the PT interaction is more important than the PCI, which so far was assumed to be the most important factor in higher-order effects for slow ion impact. One possible explanation for the contribution near -0 q is also based on the PT interaction. However, in this case we consider collisions where the target nucleus stays between the electron and the projectile. Then q predominately results from the PT interaction so that there is only little correlation between 0e and q. However, one would expect the electron to be ejected into the semi-plane containing -q because qe points in the opposite direction to qr, which dominates q. Furthermore, the PCI drags the electron in the forward direction so that for this particular mechanism one would expect contributions at relatively small negative angles, as observed in the experiment. The solid curves in Figure 3 show our 3DW calculations. The agreement with the data is not good. There is a discrepancy in magnitude which ranges from 1.6 for large q to 5 for small q. Furthermore, neither the structure around -0 q nor the backward shift of the binary peak is reproduced. On the contrary, at large q the calculation is even shifted slightly in the forward direction relative to q. Preliminary new theoretical results suggests that the discrepancies in magnitude (also those seen in Figure 1) can be attributed to treating the few-body system p + He as a three-body system consisting of the p, the active electron and the residual He+ ion. These discrepancies are strongly reduced if proper twoelectron wavefunctions are used both in the initial and final state [7]. The disagreement in shape may be due to the final state wavefunction being exact only if at least one particle is far away from the other two. As a result, the accuracy of the description of processes happening at small distances is not known. For example, at small distances the PT interaction may be correlated with PCI, while the 3DW wavefunction treats these interactions as being mutually independent. One question that needs to be answered is why a backward shift of the binary peak was never observed in earlier studies for fast heavy-ion impact. This can easily be understood by recalling that the longitudinal momentum transfer component is given by qz = e / vp (see above), which is close to 0 for large vp. Therefore, the direction of both q and qe is usually close to 90° regardless of the momentum transfer occurring in the elastic scattering between the projectile and the residual target ion. For electron impact, on the other hand, PCI readily leads to a backward shift, which cannot be distinguished from effects due to the PT interaction.
521 4. Conclusion We measured FDCS of single ionization for 75 keV p + He collision system. We have observed signatures of the post-collision interaction and the projectileresidual target-ion interaction which are, because of the different kinematic boundary conditions, not observable for fast projectiles or electrons. Among the signatures of these interactions are: the complete absence of the recoil peak at 0° projectile scattering angle, the backward shift of the binary peak at fixed momentum transfer q, and the peak structure at -®q electron scattering angle. Not all of these features are reproduced by theoretical calculations. Indications are accumulating that the description of the projectile-residual target-ion interaction is one of the largest remaining problems in the theoretical treatment of the atomic few-body problem. References 1. T. N. Rescigno, M. Baertschy, W.A. Isaacs, C. W. and McCurdy, Science 286, 2474 (1999) 2. M. Schulz, R. Moshammer, D. Fischer, H. Kollmus, D. H. Madison, S. Jones, and J. Ullrich, Nature 422, 48 (2003) 3. H. Ehrhardt, M. Schulz, T. Tekaat, and K. Willmann, Phys. Rev. Lett. 22, 89 (1969) 4. A. Hasan, N. V. Maydanyuk, B. J. Fendler, A. Voitkiv, and M. Schulz, J. Phys. B: At. Mol. Opt. Phys. 37, 1923 (2004) 5. A. D. Gaus, W. Htwe, J. A. Brand, T. J. Gay, and M. Schulz, Rev. Sci. Instrum. 65, 3739 (1994). 6. N. V. Maydanyuk, A. Hasan, M. Foster, B. Tooke, E. Nanni, D. H. Madison, and M. Schulz, Phys. Rev. Lett. 94, 243201 (2005) 7. M. Foster, D. H. Madison, J. L. Peacher and M. Schulz, book of abstract this conference
DIPOLE POLARIZATION EFFECTS ON HIGHLY-CHARGEDION-ATOM ELECTRON CAPTURE C. C. HAVENER, S. L. HOUGH, AND R. REJOUB Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6372, USA D. W. SAVIN AND M. SCHNELL Columbia Astrophysics Laboratory, Columbia University, New York, New York 10027-6601, USA Dipole polarization effects are one of the dominant features in electron capture (EC) at low collision energies. The Oak Ridge National Laboratory ion-atom merged-beams apparatus has been used to explore low energy ion-atom EC for fundamental systems in the energy range of meVAi to keV/u. While the EC cross section often increases toward lower energies due to trajectory effects caused by the ion-induced dipole potential, several systems have been found where the cross section "oscillates" towards lower energies due to the quantal nature of the collisions. The merged-beams apparatus has recently been upgraded to take advantage of the high energy ion beams from the new Multicharged Ion Research Facility High Voltage Platform.
1. Polarization Effects in Low Energy Electron Capture The electron capture (EC) process, Xq+ +A->X("-1)+
+A+
(1)
by multicharged ions (X*+) from neutral atoms (A) at low collision energies (meV/u - keV/u) is characterized by large cross sections, on the order of 10"14 10"16 cm2 and is therefore important in many plasmas where ions and neutrals exist. Low energy EC is important for interpreting spectroscopic diagnostics and modeling of core, edge, and diverter regions of magnetically confined fusion plasmas. In astrophysics, electron capture by multicharged ions from H is important in planetary nebulae and H II regions. While scaling laws have been successful [1] in describing electron capture at higher energies; at low energies (< 1 keV/u), models must correctly handle both the quasi-molecular and fully quantum nature of the collision dynamics. Molecular Orbital Close Coupling (MOCC) calculations are deemed most appropriate but are difficult to perform and often have not been extended to eV/u energies and below.
522
523
A dominant feature in EC at eV/u energies is the effect that the ion-induced dipole has on the collision dynamics. During the collision process, as the ion and the neutral approach, a dipole is induced in the neutral atom, causing an attractive force between them. The resultant interaction potential is given by V(r) = -a
^ /
4
(2)
where a is the polarizability of the neutral, q is the charge of the ion , and r is the inter-nuclear separation. For eV/u collision energies and below, the attraction is strong enough to significantly modify the trajectories of the reactants and thereby affect the total capture cross section. Collisions with D rather than H experience the same attractive force but due to the larger mass have different trajectory effects and hence isotope effects can be present in the EC cross sections [2,3,4]. Indeed, the simple classical orbiting model (Gioumousis and Stevenson [5]), which uses a straightforward geometrical interpretation of orbits that decay into a reaction sphere influenced by the interaction potential of Eq. 2, predicts a strong 1/v increase in the cross section at these low energies. This has been experimentally observed [6] for numerous ion-He and ion-molecule reactions where the cross sections typically converge to the Langevin cross section. A theoretical survey [3] of EC for multicharged ions on H an D was performed using Landau-Zener cross section estimates and predicts that isotope effects and hence trajectory effects increase for higher incident charge and can occur at energies as high as a keV/u, especially for heavy highly charged ions. The Oak Ridge National Laboratory (ORNL) ion-atom merged-beams apparatus [7] provides benchmark fundamental measurements with H and D to explore trajectory effects. 2. Experimental Method Low energy electron capture is performed at the Multicharged Ion Research Facility (MIRF) at ORNL using the ion-atom merged-beams apparatus which has previously been described in detail [7]. The newly upgraded version of the apparatus is shown in Figure 1. In this technique, intense relatively fast (keV) ion and atomic beams are merged producing center-of-mass collision energies from meV/u to keV/u. A neutral ground state hydrogen (or deuterium) beam is obtained by photodetachment of an H" beam as it crosses the optical cavity of a
524
Figure 1. Schematic of the current ORNL ion-atom merged-beams apparatus. The inset compares +45 deg. (H') and -45 deg. (V) beam profiles at two positions along the merge path for the neutral (dashed) and the ion beam (solid) beams from the old CAPRICE ECR (a) and the new high velocity beams (b) from the HV platform.
1.06 /Jm cw Nd:YAG laser where kilowatts of continuous power circulate. The H" is extracted from a duoplasmatron ion source. The ion and neutral beams interact along a field free region, after which H+ product ions are magnetically separated from the primary beams. The neutral beam is monitored by measuring secondary electron emission from a stainless steel plate, and the intensity of the ion beam is measured by a Faraday cup. The product signal of H+ ions is detected with a channel electron multiplier operated in pulse counting mode. The beam-beam signal rate (Hz) is extracted from (kHz) background with a two-beam modulation technique. The technique has been highly successful in providing benchmark EC total cross sections [8] for a variety of multiply charged ions in collisions with H and D.
525 The independently absolute charge transfer cross section is determined at each velocity from directly measurable parameters from the following formula, Syqe2v,v2 a =
——5-?—
(3)
I1I2vrL
526
velocity ion beam will make possible measurements with both H and D at energies below an eV/u. Previously, the higher velocity ion beams needed to match typical H beam velocities were not available from the CAPRICE ECR. Measurements at low center-of-mass collision energies had to be performed with D, especially for heavier lower charge ions. 3. Low Energy Electron Capture Measurements
0.01
0.1
1
10
100
1000
Energy (eV/u)
Figure 2. ORNL ion-atom merged-beams measurements for various q=4+ ions on H (D). For Si44 and C* the measurements are compared to MOCC and HSCC calculations. See text for details.
ORNL merged-beam measurements for Si4+ [4], Ne4+ [9], N4"" [10] and C4+ [11] + H (or D) are shown in Figure 2 along with two MOCC calculations which extend to low energies for Si4+ [4]. Calculations for C4* [12] from a more recently developed Hyperspherical Close Coupling (HSCC) method is also shown. All measurements below 10 eV/u were performed with D. As can be seen in the figure, all the q=4+ cross sections are similar around 1000 eV/u and scale with the empirical scaling law proposed by Phaneuf [1]. As the EC cross section decreases to lower energies the measurements show a marked difference for the different ions with different electron cores, over a factor of ten at 10
527
eV/u between C + and Si +. The measurements for Si and Ne + have been extended low enough to observe the enhancement in the cross section due to trajectory effects caused by the ion-induced dipole potential. The Si4+ measurements show excellent agreement with the MOCC calculations for D; the MOCC calculations for H exhibit a large isotope effect indicative of trajectory effects. For C4+ the HSCC calculation also shows the 1/v increase. In fact all the other calculations (not shown) for the various q=4+ ions, benchmarked to the merged-beams measurements and extended to lower energies, exhibit a 1/v increase. The temporary decrease in the cross section or "oscillation" is due to the quantal nature of the electron capture process. Of course, all ion-atom EC do not exhibit a Langevin increase at low energies. Systems whose capture channels are endoergic (e.g., Ne2+ + H [13]) or degenerate (e.g., He2+ + H [14]) decrease toward a lower energy threshold. According to Equation 2, however, one would expect that for exoergic collisions with ions of higher q, the trajectory effects would be greater and would move to higher energies [2,3]. ORNL merged-beams measurements for Cl7+ + D [15], the highest incident charge to date, show a surprisingly decreasing cross section. This sharp decrease can be understood when compared to MOCC calculations for N7+ + H (and D) where the large energy diabatic avoided crossings between initial and final potential curves leads to sharp decreases in the cross section. However, as indicated by the MOCC calculation for N7+, the sharp decrease is eventually followed by a Langevin type increase for energies < 1 eV/u. A collision system which is not predicted to follow this trend is N2+ + H and is shown in Figure 3. MOCC calculations by Bienstock et al. [16], Herrero et al. [17] and Barragan et al. [18] all show a cross section decreasing at lower energies. ORNL merged-beam measurements by Pieksma et al. [19] did not extend to low enough energies to establish the low energy dependence and have received new attention. This system is different from the q=4+ ions presented above because capture occurs to a state which involves excitation of the ion core. New measurements for this system are presented here with D using the old CAPRICE ECR and with H using the new HV platform. The measurements with D clearly show an increasing cross section toward lower energies in sharp contrast to the calculations. The measurements with H, which are now being performed with ion beams from the HV platform, are yet to be extended to low enough energies to test whether an isotope effect is present. Landau-Zener
528
calculations (see Figure 3) have been performed which take into account the ion-induced dipole effects. These calculations show a Langevin type increase below 10 eV/u with a strong observable isotope effect below 0.1 eV/u.
50
\ \ \
• • o • — —
Present w/D Present w/H Pieksma (97) Wilke(85) • Bienstock (86) Barragan(04) Herrero (95) — Landau-Zener w/D — Landau-Zener w/H
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# *\ *
E o
10
/ft"
20
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•
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O 30
03
w
' •••.."¥
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0.01
0.1
5
a
**JKt« : <sisa»*' 1
10
100
Energy (eV/u) Figure 3. Present merged-beams measurements for N2+ with H and D are compared with our previous merged-beams measurements of Pieksma et al. [7] and with measurements of Wilke et al. [17]. Comparison is also made with a Landau-Zener and several MOCC calculations. See text.
4. Future Directions The HV platform provides quality high velocity ion beams which allow much higher resolution measurements with both H and D below an eV/u. It should be possible to explore low energy EC for structure, e.g., due to Regge oscillations [21] or shape resonances [22]. The ion beams are now of sufficient intensity that state-selective EC may now be possible using photon spectroscopy. A Cs negative-ion sputter source can be exchanged with the duoplasmatron and used to provide a variety of multlielectron neutral beams, e.g., Li, B, Na, Al, P, K, Cr, Fe and molecular beams like 0 2 and CH2. The HV platform will soon be configured with a cold molecular ion source which will allow measurements with molecular ions.
529 Acknowledgments This work is supported by the Division of Chemical Sciences, Office of Basic Energy Sciences and the Division of Applied Plasma Physics, Office of Fusion Energy Sciences, U.S. DoE, Contract No. DE-AC05-00OR22725 with UTBattelle, LLC, and by the NASA SARA program under Work Order No. 10,060. DWS is supported in part by NASA SARA Grant NAG5-5420 and MS was supported in part by NSF Galactic Astronomy Program Award 0307203. SLH was appointed to the Higher Education Research Experiences at ORNL, administered by the Oak Ridge Institute for Science and Education. References 1. R. A. Phaneuf, Phys. Rev. A 28, 1310 (1983). 2. C. C. Havener, F. W. Meyer, and R. A. Phaneuf, in Proceedings of the International Conference on the Physics of Electronic and Atomic Collisions, Brisbane (IOP, Bristol, 1992), p. 381. 3. P. C. Standi and B. Zygelman, Phys. Rev. Lett. 75, 1495 (1995). 4. M. Pieksma, M. Gargaud, R. McCarroll, and C. C. Havener, Phys. Rev. A 54, R13 (1996). 5. G. Gioumousis and D. P. Stevenson, J. Chem. Phys. 29, 294 (1958). 6. K Okuno et al., AIP Conference Proceedings 360 (AIP, New York, 1995), p. 867. 7. C. C. Havener, in Accelerator-Based Atomic Physics Techniques and Applications, edited by S. M. Shafroth and J. C. Austin (AIP, New York, 1997), p. 117. 8. C. C. Havener, in The Physics of Multiply and Highly Charged Ions, Vol. 2, (Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003), p. 193. 9. C. C. Havener et al., Phys. Rev. A 71, 034702 (2005). 10. L. Folkerts et al., Phys. Rev. A 51, 3685 (1995). 11. F. W. Bliek et al., Phys. Rev. A 56, 426 (1997). 12. C-N Liu, A-T Le, and C. D. Lin, Phys Rev A 68, 062702 (2003). 13. T. Mroczkowski et al., Phys. Rev. A 68, 032721 (2003). 14. C. C. Havener et al, Phys. Rev. A 71, 042707 (2005). 15. J. S. Thompson et al, Phys. Rev. A 63, 012717 (2000). 16. S. Bienstock, A. Dalgarno, and T. G. Heil, Phys. Rev. A 33, 2078 (1986). 17. B. Herrero, I. L. Cooper, A. S. Dickenson, and D. R. Flower, Phys Rev A 28,711(1995). 18. P. Barragan, L. F. Errea, L. Mendez, A. Macias, I. Rabadan, and A. Riera, Phys. Rev. A 70,022707 (2004).
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19. M. Pieksma, M. E. Bannister, W. Wu, and C. C. Havener, Phys. Rev. A 55,3526(1997). 20. F. G. Wilke et al., J. Phys. B 18,479 (1985). 21. J. H. Macek et al., Phys. Rev. Lett. 93, 183293 (2004). 22. M. Rittby et al., J. Phys. B 17, L677 (1984).
PROTON-, ANTIPROTON-, AND PHOTON-HE COLLISIONS IN THE CONTEXT OF ULTRA FAST PROCESSES
TORU MORISHITA, SHINICHI WATANABE, MICHIO MATSUZAWA Department of Applied Physics and Chemistry, The University of Electro-Communications, 1-5-1 Chofu-ga-oka, Chofu-shi, Tokyo 182-8585, JAPAN C. D. LIN Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA
The time-dependent Hyperspherical method is used to study the strongly correlated two-electron dynamics of He under proton, antiproton, and photon impact. Our results for double ionization by fast proton and antiproton impact agree well with the experimental data. The charge sign dependence of single and double ionization cross sections is discussed. By using an attosecond light pulse we also illustrate the feasibility of probing molecule-like motion of the two electrons in the doubly excited states of He in the time domain.
1. I n t r o d u c t i o n The investigation of electron correlation of an atomic system under photon or charged particle impact is one of the most challenging problems in atomic physics. In particular, ultrafast processes where the interaction time is short compared to the electronic motion inside an atom are of fundamental interest as a novel tool for probing electron correlation of the target atom. From the theoretical point of view, a nonperturbative treatment of the correlated electrons is required for describing ultrafast processes of multi-electron systems. For this end, we have been developing a theoretical method based on hyperspherical coordinates. The method treats electron correlation very efficiently by exploiting the L 2 integrable hyperspherical wave functions 1 ' 2 . In this article, we apply the method to two ultra-fast ionization processes:(l) double ionization of He by a few MeV protons and antiprotons; (2) single ionization of doubly excited states of He by attosec-
531
532
ond light pulses. In Section 2 we describe briefly the time-dependent Hyperspherical method for two-electron systems in an external field. Our numerical results for double ionization by proton and antiproton impact are presented in Section 3, and by attosecond light pulses are discussed in Section 4, respectively. Atomic units are used throughout unless otherwise stated. 2. Time-dependent Hyperspherical method The time-dependent hyperspherical method has been presented previously1, thus only the essential points will be given here. We solve the timedependent Schrodinger equation
ift*(t) = [Ho + V(t)]*(t),
(1)
where Ho is the time-independent Hamiltonian for the target He, and V(t) is the time-dependent interaction potential between the target and the projectile ions or photons. For collisions with ions, we use the semiclassical impact-parameter approximation with straight line trajectories. For photon impact, dipole approximation in the length gauge was used. The time-dependent two-electron wavefunctions are expanded by L 2 hyperspherical wavefunctions, {
*(*) = X > < m
(2)
o
where R = yV 2 + r\ is the hyperradius for the two electrons with the nucleus at the center. Inserting this into the time-dependent Schrodinger equation, Eq. (1), gives the standard form of the Close-Coupling equations for the expansion coefficient Cj. We obtained the L 2 hyperspherical wavefunctions by using the discrete variable representation and the slow/smooth variable discretization (SVD) 3 methods, and the matrix elements of the interaction potential are evaluated efficiently. We solved the time-dependent Close-Coupling equations by the 4-th order Runge-Kutta method and the 2nd order split operator method. After the collision, we extracted the transition amplitude by projecting the box-normalized function onto the energy normalized Hyperspherical wavefunctions. Thus, the transition amplitude is given by AE
= ( V i _ ) I *(t - oo)} ,
(3)
533
where ip^T' represents a physical scattering state at a given value of the target energy E, namely, at one of the asymptotic S-matrix states. We generated very accurate energy normalized wavefunctions ip^' with the correct scattering boundary condition by the hyperspherical method used in Ref.4, and implemented the projection in Eq. (3) numerically. Although the final physical state wavefunctions ip at an arbitrary energy E do not vanish at R = i?box, the time-dependent wavefunction <]>(£) declines as 1/R. We set the box size Rmax to some suitable value, which is large enough to accommodate the collision dynamics properly. Thus, the projection in Eq. (3) for the transition amplitude can be rigorously evaluated. In this way, we analyze the system's time evolution within the box and impose the proper asymptotic boundary condition to evaluate cross sections.
3. Double Ionization Cross Sections for proton- and antiproton collisions with He For fast proton and antiproton impact on He in the collision energy of a few MeV/u (or velocity of a few a.u.), the projectile can be regarded as to give an impulsive force, where the interaction time is much shorter than the time scale of the electron motion in the initial ground state of He. In such cases, the interaction of the target with the impinging ion is normally treated by a perturbative theory such as the Born approximation. In the Born approximation, the cross sections are scaled as the square of the charge of the projectile and the cross sections are identical for proton and antiproton impacts. However, experimental results by Andersen et al.5 in 1986 showed strong charge sign dependence of the projectile in double ionization cross sections, whereas the single ionization cross sections are almost identical for both proton and antiproton impacts. The ratio of the antiproton-impact double ionization cross section to the proton-impact cross section turns out to be about 2 at the incident energy of 4.5 MeV. Since the report of experimental finding, various theoretical approaches, including higher order theories, have been used to obtain the strong charge sign dependence in the double ionization cross sections generated by a few MeV proton and antiproton impacts 6>7'8'9. The difference has been attributed mainly to electron correlation in the initial and final states of the target, as well as to electronic states during the time propagation. We performed a time-dependent hyperspherical calculation including 1 e S , 1P°, lDe, 1F°, and 1Ge target He states. These are considered to be the most important states in the collision process. Fig. 1 shows the result-
534
• A
" *•• o— ••— • v
c .2 o
antiproton proton proton antiproton proton antiproton proton proton antiproton
(Andersen et al) (Andersen et al) (Shah et ai) (with interpolation) (with interpolation) (without interpolation) (without interpolation) (Ford & Reading) (Ford & Reading)
w CO
o
o
t€»
2
3
4
I m p a c t energy (MeV)
Figure 1. Double ionization cross sections for proton and antiproton collisions with He as a function of incident energy. The present calculated results with and without extrapolation from L > 4 components are plotted and connected with lines. Experimental data are from Andersen et al.5 and Shah 10 . Other theoretical results are from Ford and Reading7.
ing double ionization cross sections of He for proton and antiproton impacts together with other theoretical calculations and experimental results. Our theoretical results are in fair agreement with the experimental data and the theoretical result by Ford and Reading 7 . It can be seen that the absolute values of the double ionization cross sections are slightly smaller than the experimental values at lower collision energies, particularly for proton impact. The discrepancy is mainly due to the lack of higher angular momentum components in the basis set of the calculation. We estimate these contributions by extrapolation based on a rational function. This brings the result closer to the experimental data. Let us discuss the origin of the charge sign dependence of the ionization cross sections. We plot the energy resolved single and double ionizations
535
in Fig. 2 for impact energy at 5 MeV. It can be seen that single ionization cross section for proton impact is larger than that for antiproton impact, and the difference is of the same order of magnitude as for the double ionization cross sections. When the total ejected electron energy distribution, i.e., the sum of single and double ionization cross sections, is calculated at each total electron energy, the charge sign dependence almost disappears. This cancellation of the charge sign dependence can be attributed to the interference amongst degenerate final continuum states in the framework of the Sudden approximation. 1
0
2
Total electron energy (a.u.)
0.51
0.52
0.S3
Total electron energy (a.u)
Figure 2. Left: Total electron energy distributions of single (cr+) and double (
4. Probing molecule-like modes of doubly excited states of He Very recently, high-order harmonic generation by short intense laser pulses has been used to generate ultra-short XUV light pulses with duration of several hundred attoseconds (or a few a.u.) 11 ' 12 ' 13 . These pulse durations are comparable to the time scale of the electronic motion in the ground and lower excited states of an atom or a molecule, and thus opens up the route to the time domain study of electron dynamics in matter. Indeed, several time domain measurements such as Auger electron spectroscopy 12 and molecular clock experiments 14 ' 15 have been done. Here, we consider the strongly correlated motion of two electrons in doubly excited states of He. Theoretical and experimental investigations of multiply excited states
536
e12 He2+ b
8
A V
2
3 4 5 Delay time (fsec)
Figure 3. Top: Definition of the angle between the two electrons with nucleus at the center. Middle: Delay time dependence of single ionization probability from a coherent state of 2s 2 S e and 2p 2 S e of He by an attosecond pulse. Bottom: Calculated time dependence of the average of angle #12 of the above coherent state.
of atoms in the past few decades have revealed that the conventional independent electron model is inadequate16'17'18. For such multiply excited states, the motion of the electrons is highly correlated and they are better described as analogous to the rotation and vibration of a polyatomic
537
molecule. Thus doubly excited states of a two-electron atom can be described qualitatively in terms of the ro-vibrational motion of a linear XY2 molecule where X stands for the nucleus and Y for the electron. In this section, we study the feasibility of probing the molecule-like motion of doubly excited states of atoms in real time by using an attosecond light pulse. Fig. 3 shows the calculated ionization probability from a coherent state, i.e., the sum of two doubly excited states, 2s 2 1 S e and 2p2 1Se, by a 240 attosecond probe pulse, as a function of delay time measured from the time the coherent state is created. In this calculation, the initial doubly excited states are prepared as bound states, excluding the ionization channels of He + +e. The ionization probability oscillates with a period of 960 attoseconds, which corresponds to the inverse of the energy separation between the two states. In the picture of molecule-like modes 16 , the doubly excited 2s 2 1Se and 2p2 1Se states may be considered as the ground and the first excited bending vibrational modes of the two electrons with the nucleus at the center, respectively. In Fig. 3, we also plot the time evolution of the average of the angle between the two electrons with respect to the nucleus, (^12)- Clearly, (612) oscillates at the same frequency whereby ionization probability has maxima when the two electrons are on the opposite sides of the nucleus. We note that the decline of the oscillation in the ionization probabilities is due to the autoionization of the 2s2 1 S e state whose lifetime is about 6 femtoseconds. In this manner, the vibrational motion in 612 as well as the information on the Auger decay in real time can be extracted from the time-resolved single ionization spectra.
5. Conclusions We have presented our recent progress made in the application of the timedependent Hyperspherical method to ultrafast processes of proton, antiproton, and photon impacts with He. It is one of the best methods of evaluating double ionization cross sections of He by fast proton and antiproton impacts. We also have shown the feasibility of probing molecule-like motion of the two electrons in doubly excited states, by using an attosecond light pulse. The latter serves to show how to probe and to control and manipulate the collective motion of the multi-electron systems- a real challenging problem for the years to come.
538
Acknowledgments We would like to thank our former and present students for computational assistance during an early stage of the work. TM also thanks Dr. X. M. Tong for useful discussion on numerical techniques. This work was supported in part by a Grant-in-Aid for Scientific Research(C) from the Ministry of Education, Culture, Sports, Science and Technology, Japan, and in part by the 21st Century COE program on "Coherent Optical Science" at the University of Electro-Communications. TM wish to acknowledge financial support from the Matsuo foundation. References 1. T. Morishita, K. Hino, T. Edamura, D. Kato, S. Watanabe, and M. Matsuzawa, J. Phys. B 34, L475 (2001). 2. T. Morishita, T. Sasajima, S. Watanabe, and M. Matsuzawa, Nucl. Inst. Method B 214, 144 (2004). 3. O. I. Tolstikhin et ai, J. Phys. B 29, 389 (1996). 4. D. Kato and S. Watanabe, Phys. Rev. A 56, 3687 (1997). 5. L. H. Andersen, et aZ.,Phys. Rev. Lett. 57, 2147 (1986). 6. J. F. Reading and L. Ford, Phys. Rev. Lett. 58, 543 (1987). 7. L. Ford and J. F. Reading, J. Phys. B 27, 1994 (1994). 8. C. Diaz, A. Salin, and F. Martin, J. Phys. B 33, L403 (2000). 9. C. Diaz, F. Martin, and A. Salin, J. Phys. B 35, 2555 (2002). 10. M. B. Shah et ai, J. Phys. B. 18, 899 (1985). 11. M. Hentschel et ai, Nature (London) 414, 509 (2001). 12. M. Drescher et ai, Nature (London) 419, 803 (2002). 13. T. Sekikawa, et al. Nature (London) 432, 605 (2004). 14. H. Niikura et ai, Nature (London) 427, 817 (2002). 15. A. S. Alnaser et ai, Phys. Rev. Lett. 93, 183202 (2004). 16. CD. Lin, Adv. Atom. Mol. Phys. 22, 77 (1986), and references therein. 17. T. Morishita and C. D. Lin, Phys. Rev. A 67, 022511 (2003). 18. T. Morishita and C. D. Lin, Phys. Rev. A 71, 012504 (2005).
IMPACT PARAMETER DEPENDENT CHARGE EXCHANGE STUDIES WITH CHANNELED HEAVY IONS D. DAUVERGNE, M. CHEVALLIER, J.-C. POIZAT, C. RAY, E. TESTA Institut de Physique Nucleaire de Lyon, CNRS- IN2P3 and Universite Claude Bernard Lyon I, F-69622 Villeurbanne, France A. BRAUNING-DEMIAN, F. BOSCH, S. HAGMANN, C. KOZUHAROV, D. LIESEN, P. MOKLER, TH. STOHLKER, M. TARISIEN 1 , P. VERMA Gesellschaft fur Schwerionen Forschung (GSI), D-64291 Darmstadt, Germany
C. COHEN, A. L'HOIR, J.-P. ROZET, D. VERNHET Institut des Nano-Sciences de Paris, CNRS-UMR75-88, Universites Paris Viet Paris VII, 75251 Paris cedex 05, France H. BRAUNING Institut fur Atom- und Molekiilphysik, Justus Liebig Universitat, D-35392 Giessen, Germany M. TOULEMONDE Centre Interdisciplinaire de Recherche Ions-Lasers, UMR 11 CEA-CNRS, 14040 Caen cedex, France
We use decelerated (below 20 MeV/u) H-like heavy ions extracted from the GS1-ESR storage ring to study electron capture processes such as Radiative Electron Capture (REC) and Mechanical Electron Capture (MEC) in channeling conditions. With die help of simulations, we show that MEC occurs at relatively large impact parameters into highly excited states. REC studies provide information about the electron gas polarization.
1
Present address: CENBG, CNRS-IN2P3 and Universite Bordeaux l, Le Haut Vigneau, 33175 Gradignan cedex, France.
539
540
1. Introduction Bare heavy ions can be decelerated down to a few MeV/u at the Experimental Storage Ring facility (GSI, Germany). Such ions are very far from their charge equilibrium in matter, since their velocity is much smaller than the velocity of their inner-shell bound electrons. The extraction of such beams allows one to study their collision with solid targets. Their interaction with matter should provide a very strong perturbation, along with a very high cross section for electron capture. We present here some results concerning the impact parameter dependence of the electron capture processes competing inside a crystalline target under alignment conditions. Indeed, channeling of charged particles in a crystal leads to a redistribution of the ion flux inside the target. Channeled ions have a restricted accessible transverse space, which is determined by their transverse energy [1], In the continuum potential approximation, the collisions of particles along atomic strings or planes are described as deflections by a continuum potential, which is averaged along the crystallographic direction. With the help of simulations, detailed information can be extracted on the impact parameter dependence of interaction processes such as charge exchange and energy loss, provided that the transverse energy of channeled ions can be determined. This is what has been done in this work, which presents part of the results obtained recently with decelerated heavy ions at 20 MeV/u and below.
2. Experiment A detailed description of the production of decelerated H-like heavy ions has been given in ref. [2]. Briefly, some 107 highly-charged ions, accelerated up to a few hundreds of MeV/u by the heavy-ion synchrotron SIS-18, are fast extracted. They are further totally stripped in a thick stripper foil placed between the SIS and the storage ring ESR, and then injected at once inside the ESR. After cooling and deceleration, they are extracted continuously from the ring by means of radiative recombination inside the electron cooler, which changes the magnetic rigidity relative to stored bare ions. Due to different orbits, the H-like ions can be deflected into the extraction channel by a septum magnet. The electron current in the cooler is tuned in order to adjust the extracted ion beam intensity. Thus, within a full cycle of about 6 minutes, a continuous beam is extracted during 4 minutes, exponentially decreasing with time from a few 104 ions/s
541 down to 5.103ions/s typically. The beam is transported towards the experimental cave and focused with the most possible parallel optics on the crystal target. Behind the target, transmitted ions are analyzed in charge and momentum by a magnetic spectrometer. As targets, we have used silicon crystals of various thicknesses and orientations. Before setting a crystal under vacuum, its surfaces were cleaned by means of a fluorhydric acid solution. In all experiments, X-rays are detected at 90° from the beam direction. The target is biased, in such a way that emitted electrons from the surfaces are collected by grounded silicon detectors located in front of the two surfaces of the thin crystal. At the focal point of the spectrometer, a position sensitive detector (microchannel plate counter with delay-line readout) allows to detect the selected ions and to perform an event by event acquisition containing coincidences between X-rays, electron multiplicities and transmitted ions of identified magnetic rigidity. 3. Results and simulations We will concentrate mainly on the experiment performed with 20 MeV/u U91+ ions channeled in an 11.7 micrometer thick crystal. Some of the results have been presented in ref. [3]. Here we add more refined analysis obtained by means of simulations, which need to be described first. 3.1. Principles of the simulations These simulations are aimed to estimate the mean number of electron captures by aligned projectiles as a function of their transverse energy, assuming statistical flux equilibrium for channeled ions. The simple idea behind the statistical flux equilibrium is that channeled ions of given transverse energy explore uniformly all their accessible transverse space. Thus the transverse energy of a channeled ion defines its impact parameter distribution along the path inside the crystal. The charge state at emergence is then calculated by injecting in Monte Carlo simulations an impact parameter dependent capture probability. Such simulations have the advantage to avoid full trajectory calculations, which spares computation time (trajectory calculations are made once for each transverse energy in order to implement the impact parameter distributions). The drawback is that multiple charge exchange effects, arising when an ion approaches close to a string or a plane, cannot be taken into account. This is why we have limited these simulations to ions with a relatively low transverse energy, i.e. for which each single charge exchange event can be considered independently. For high transverse energy ions, suffering close collisions along atomic strings, full Monte Carlo calculations are needed to
542
follow the evolution of the electronic configuration. Such a work, devoted to the study of a "super-density effect" associated to the very high rate of atomic collisions near strings, has been described separately [4]. The transverse energy distribution of the incoming beam depends on the crystal orientation and on the beam angular distribution. The latter is a parameter in the simulations, which has to be adjusted according to our observations. We take into account the dechanneling effects that tend to increase the transverse energy of channeled ions inside this relatively thick crystal. The number of electron captures is estimated as following: REC probabilities are proportional to the sampled local electron density, and depend on the occupation of inner shells (REC cross sections decrease as the mean quantum number n of the final state increases). MEC probabilities are adjusted as a function of impact parameter to get the best possible agreement with the various measurements. A small probability of MEC into the thin amorphous surface layers is also considered, which does not depend on the ion transverse energy. 3.2. Results Figure 1 shows the charge state distributions obtained for random, (110) planar and <110> axial orientations, after crossing a 11.7 um thick crystal. In such a thick crystal, the charge equilibrium is reached only for a random target orientation. In channeling conditions, the charge state distributions are much broader and extend from frozen 91+ ions to very low charge states.
-•••.
10' a
lio°
—•— random A <no>axis • (110) plane
° D D °^S\ A
V
as
Simulations
UL
10" 69 71 73 75 77 79 81 83 85 87 89 91
Charge (QJ Figure 1. Charge state distributions obtained for 20 MeV/u incident U"+ ions on a 11.7 |im thick Si crystal for various orientations. The thick solid lines are simulations (see text).
543 These distributions reflect the transverse energy distributions of channeled ions, frozen ions being the best channeled ones. The results of the simulations are superimposed. They agree fairly well, both in the shape and in the absolute amplitude of the distributions (although ions with a high transverse energy are not considered in the simulations, we evaluated this fraction of ions that reach charge states below 82+). Tilting the crystal by an angle 8\)/ relative to the incident beam increases the transverse energy E± of each incident particle by the amount 5Ej. = E(S\|/)2, where E is the total ion kinetic energy. Thus the charge state distribution strongly depends on the crystal orientation. This is shown in figure 2, where we present the evolution of charge fractions 91 and 87 as a function of the tilt angle relative to the <110> axis. The frozen ion fraction disappears almost completely at a tilt angle which is less than half the channeling critical angle. The fraction of the lower charge state 87, increases for increasing small angles and rapidly decreases at angles only slightly larger than for frozen ions. This shows that many electron capture events occur for ions with relatively small transverse energy, since an incidence angle of 0.04° corresponds to a minimum distance of approach to atomic strings of about 0.4 A for ions entering the crystal at the center of the channel. Again the simulations are able to reproduce the data.
20
k
Experiment Simulations
^ —»
Q...=91 ~w
H\
10
\
I 0
'X
o
4
H "X c^=87
2 0
0.04 0.08 Tilt angle (degrees)
Figure 2. Evolution, with the angle relative to the <110> axis, of charge state fractions 91 and 87 for 20 MeV/u incident U ,l+ on a 11.7 um thick Si crystal. The dashed lines are simulations.
544
Information on the nature of electron capture is deduced from the X-ray observation. This is illustrated in figure 3, where two X-ray spectra are shown: one for axial crystal orientation (in coincidence with 90+ transmitted ions), and the other one for a random orientation. Both spectra show mainly transitions into n=l and n=2 levels of the uranium projectiles. They correspond either to inner-shell transitions (K and L-lines) or to REC into K- and L-shells. As MEC occurs into excited states, the filling of the K and L-shells following MEC causes the emission of K and L lines. In the random spectrum, a large fraction of the L-lines is also due to the creation of L vacancies once the charge equilibrium is reached in this thick target, or at least once the L-shell is filled. Note that Kand L-REC lines are almost absent from the random orientation spectrum. The reason is that those inner shells are very rapidly filled inside the target by MEC, which prevents REC from occurring. On the contrary, ions emerging as 90+ under axial alignment are well channeled ions, for which MEC is strongly reduced inside the crystal.
L-lines
K-REC
L-REC
A-
—i
40
1
60
1
•
I
80
100
H«U"120
140
Laboratory energy (keV) Figure 3. X-ray spectra recorded at 90° for 20 MeV/u incident U" + on a 11.7 urn thick Si crystal. Upper spectrum: axial orientation, in coincidence with U** transmitted ions. Lower spectrum: random incidence. The spectra are normalized to the same number of transmitted ions.
For those ions, REC is the dominant capture process, and the corresponding peaks are easily observed. Here, even K<« lines are mainly due to the decay of electrons captured by REC into low j-values of the L-shell (note that the ratio Ka]/Ka2 is inverted on the two spectra in fig. 3). Thus, REC and MEC capture rates can be evaluated for any transverse energy of channeled ions, that are
545
selected either by their charge state at emergence, or by their electron multiplicities from the crystal surface. This is shown in figure 4, where average MEC and REC rates are represented as a function of the minimum distance of approach to the atomic strings along the path inside the crystal (axial orientation). This curve is obtained as a direct output of the simulations. One can see the very fast increase of MEC events when ions are able to approach the strings at distances smaller than 0.4 A to atomic strings. REC contributes significantly at large distances. However, no increase of the REC yield is found close to the target atoms, although the mean electron density sampled by ions with increasing transverse energy increases. This is again due to the rapid filling of inner shells by MEC and electron cascades close to the entrance of the crystal (ions with parallel incidence with the crystal axis penetrate the crystal at the minimum distance of approach to strings, and so the MEC rate is maximum there). 10- \
2 Q >, Q) -t—•
5-
Q.
o
Q j—,—(—,—,—,—(—i
0.3
0.5
r r
|—i—i—,—|—i—i—,—|—,
0.7
0.9
1.1
minimum distance of approach (A) Figure 4. Estimates, deduced from simulations, of the total capture yields for 20 MeV/u incident U"* inside the 11.7 um thick Si crystal, as a function of the minimum distance of approach to the <110> atomic strings for channeled ions. Solid line: MEC yield, dashed line: REC.
4. Discussions 4.1. Mechanical Electron Capture The knowledge of the complete impact parameter distribution for channeled ion trajectories inside the crystal is needed to extract the atomic impact parameter
546
probabilities of MEC. In particular, one has to take into account the thermal vibrations of the target atoms, and dechanneling effects. This makes the dependence with atomic impact parameter of MEC significantly narrower than shown in Fig.4. Our experiments are mainly relevant in the impact parameter region 0.2 - 0.4 A, where a maximum of constraints on the fitting procedure can be extracted from the experimental observations. Actually, we show in Fig.4 an effective capture probability, i.e. the probability to capture an electron and not to lose it by ionization afterwards. At distances of approach smaller than 0.2 A, a much thinner crystal would be needed to limit the number of electron captures so that information can still be extracted from X-rays (no more L-lines consecutive to capture are emitted beyond 9 captured electrons). At distances of approach larger than 0.4 A, the origin of the uncertainties is the determination of the absolute REC probabilities, of the MEC capture yield in the thin surface amorphous layers and the knowledge of the beam angular divergence. The impact parameter dependent MEC probabilities have been deduced from the capture yield presented in Fig.4, and the impact parameter distributions calculated by means of trajectory simulations. They have been compared with CDW-EIS calculations performed by P. Abufager et al. [5]. These calculations were limited up to n=5 due to the very large complexity of such analytical calculations for higher projectile n-shell values. These calculations show that for n<6 MEC occur mostly at impact parameters smaller than 0.25 A, i.e. in a region where our experiments do not provide very accurate information. In fact, MEC capture into these "inner" shells is not the dominant process.. Actually, integrated CDW calculations show that the cross section is maximum for final states equal to 5 and 6, and only slowly decreases for higher n-shells. Additional CTMC calculations of MEC probabilities as a function of impact parameter are now in progress. 4.2. Radiative Electron Capture The analysis of the K- and L-REC peaks (energy values, shape and amplitude) provide detailed information on the ion-electron interaction by such highly charge ions in a dense electronic medium. We have reported in ref. [6] that a shift of about -100 eV of the REC lines is observed compared to the calculated values corresponding to the capture of a free electron isolated in vacuum. This shift is attributed to the dynamic electron gas polarization by the high projectile charge, slowly moving inside the medium. This energy shift is found in agreement with values calculated by the linear response theory [7],
547
Another consequence of the dynamic response of the electron gas is the local increase of the local electron density at the ion site, which may increase the REC yield compared to a non perturbed electron gas. Indeed, we do observe an increase of about 40% [6]. This increase of the local electron density is much smaller than predicted by the linear response theory. Actually, this is not surprising, because the first order perturbation calculations are certainly not valid for such a system. Non perturbative calculations are obviously needed to provide an accurate description of the electron gas polarization by such high charges moving in matter at these velocities.
5. Conclusion We have shown that charge exchange by decelerated highly charged ions can be studied in details as a function of impact parameter using crystal channeling. For 20 MeV/u U9I+ ions, non radiative capture (MEC) into highly excited states is the dominant capture process at small impact parameters. Complete calculations of the impact parameter dependence of MEC are still in progress, the analytical CDW-EIS being limited to relatively low-lying states. REC is the dominant capture mechanism at large distances from the target atoms, and provides interesting information on the dynamic electron gas polarization. In a more general review on these experiments, to be published, we will also discuss particular aspects of energy loss, the very high charge of channeled ions being responsible for very high energy loss rates. Acknowledgments We gratefully thank P. Abufager and R. Rivarola who provided us with calculations of electron capture. This work was supported by the French - German GSI-IN2P3 collaboration agreement 97-35. References 1. 2. 3. 4. 5. 6. 7.
D. S. Gemmell, Rev. Mod. Phys. 46 (1974) 129. H. T. Prinz et al, Hyperfine Interactions Cf22, 1729 (1995). D. Dauvergne et al, Nucl. Instr. And Meth. Phys. Res. B205, 773 (2003). A. L'Hoir et al, to be published in Nucl. Instr. and Meth. Phys. Res. B. P. Abufager and R. Rivarola, private communication E. Testa et al., to be published in Nucl. Instr. and Meth. Phys. Res. B P. M. Echenique, R. H. Ritchie, and W. Brandt, Phys. Rev. B20, 2567 (1979).
CRYSTAL ASSISTED ATOMIC PHYSICS EXPERIMENTS USING HEAVY IONS* K. KOMAKI Institute of Physics, Graduate School of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan Various atomic processes experienced by energetic heavy ions in a crystal target were experimentally investigated. Peculiar incident angle dependence of projectile X-rays was observed. Through resonant coherent excitation (RCE) measurements, Stark effect due to crystal potential and alignment in the excited state were systematically investigated. Resonance conditions for two different transitions were simultaneously fulfilled by tuning beam energy and incident angle.
1. Introduction One of the major characteristics of ion-solid interaction in comparison with ionatom interaction is the correlation between collisions experienced by an ion. Projectile-bound electron(s) excited through impacts of target electrons or nuclei are subject to further collisions (excitation, ionization) or intrinsic processes (radiative or Auger de-excitation). Competition between these processes gives rise to variety of phenomena in ion-solid interaction, i.e., evolution of the electronic state of the projectile inside the solid plays an important role. When a collimated ion beam enters a crystal parallel to a low-indexed axial or planar direction, major part of the ions undergo correlated small angle collisions with target atoms and are "channeled", i.e., are confined in the "channel" surrounded by atomic strings or atomic planes. In the case of planar channeling, the ion trajectory is governed by the planar "continuum potential", which is obtained by averaging the crystal potential along the atomic plane and is a function of the distance from the atomic plane. Probabilities of various atomic processes experienced by a channeled ion depend on the ion position in
This work was in part supported by Grant-in-Aid for Scientific Research (no. 13440126) from Japan Society for the Promotion of Science, Matsuo Foundation, the Sumitomo Foundation, and the Mitsubishi Foundation. This experiment is one of research projects with heavy ions at NIRSHIMAC.
548
549 the channel. Well channeled ions experience less stopping power and much reduced collisional excitation and ionization processes. The continuum potential, which governs the ion motion, exerts an enormous electrostatic field of the order of 10" V/m on the bound electron, resulting in Stark shift and split of the energy levels and Stark mixing of the wave functions. The channeled ion feels the periodic crystal potential as a temporally oscillating potential with various frequencies determined as ion velocity divided by the periods along the trajectory. If one of such frequencies coincides with a transition frequency of the bound electron, it can be resonantly excited (RCE, resonant coherent excitation)[l]. Amplitude of the oscillating field amounts to 1010V/m, which corresponds to photon flux with power density of 1017 W/m2. RCE condition for planar channeling can be fulfilled by either scanning the beam velocity or by rotating the crystal. RCE can be detected through subsequent processes, either ionization[2] or radiative de-excitation[3]. Measurement of RCE provides the electronic energy level information of the ion which reflect its environment, i.e., strong static field as well as strong virtual photon flux and also with collisional relaxations. Solid targets are, in general, so dense and thick that some integrated results on equilibrium state are observed and detailed analyses of the phenomena are limited to the cases of thin foils. By choosing heavy ions with relativistic velocities as projectiles in channeling experiment we can realize "few-collision regime" where analyses of the experimental results are much easier since the number of collisions and various cross sections are reduced and especially electron capture process can be safely neglected. In the present we report on recent results on these atomic processes observed in passage of highly charged heavy ions in crystal target at relativistic velocities. 2. Experimental techniques
Si(l.i)defec?orfV)
Figure 1 shows a schematic of the experimental setup. A heavy ion synchrotron, Heavy Ion Medical Accelerator at Chiba (HIMAC) supplies SJ v x ^ «••» ~~ .jjfCufoil Ar, Fe and Kr ions with a few bound SitLi)detector(H) electron(s) of ~ 400 MeV/u (fl=vlc~ Si(Li) detector 0.7 and y~ 1.4). Relativistic channeling Figure 1. Experimental setup. experiments require a beam with a very small divergence because of its small critical angle, yr9 = ^•KZ^L^'Na-^d^pv •
550 The beam divergence of ~ 0.15 mrad and the beam spot size of a few mm were attained both by the beam transfer magnet system and a 1 -mm<)> Fe collimator of 50 mm thickness. A crystal target was mounted on a high-precision three-axis goniometer. Thickness of the crystal ranged from 1 |J.m to 100 Jim. On purpose we adopted an SSD (Si surface barrier detector) as the target crystal to obtain energy deposition signals. Transmitted ions were charge analyzed by a 0.5-T magnet and detected by a two dimensional (2D) position sensitive Si detector (PSD) placed 5.6 m downstream of the target. Charge state and exit angle signals from the 2D-PSD together with energy deposition signal, if available, due to the identical ion were recorded event by event. Two Si(Li) X-ray detectors were placed at 41° from the beam direction, which roughly corresponds to 90° in projectile-frame. Since probabilities of various processes depend on the ion position in the channel it is important to obtain information of the ion trajectory. This can be achieved by measuring energy deposition of the ion which has one-to-one correspondence to the ion trajectory in the case of planar channeling[4,5]. Alternatively, when an ultra-thin (-1 |j,m) crystal is adopted as the target, ions are bounced by the atomic plane at most once then the trajectory of the individual ion can be traced back from the exit angle. 3. Experimental Results 3.1. Directional effect in projectile X-ray yield Under the channeling condition yields of various collision processes such as excitation, ionization and X-ray emission of target atoms are generally reduced. For projectile ions, excitation and ionization processes are depressed as well. However, the yield of the projectile X-rays is not so straightforward. Figure2 shows the charge state fraction(upper), the target X-ray yield (middle), and the projectile X-ray yield(lower) as a function of incident angle with respect to the (220) plane for H-like Ar17+(left) and He-like Fe24+(center) injected to a 21-um thick Si crystal, and H-like Kr^right) injected to a 28-um thick crystal. For all the ions injected under the channeling condition, the survived fractions increase and the target X-ray yields decrease. On the other hand, the projectile X-ray yields under the channeling condition are enhanced for Ar'7+ ions and depressed for Fe24+ and Kr35* ions. This peculiar behavior of the projectile X-ray yields comes from the fact that projectile X-ray emission is a two step process, i.e., collisional excitation of
551 an electron and its radiative decay, and that the latter process is in competition with further collisional ionization. The evolution of the electronically excited states of heavy ions plays a crucial role. In the case of a thin crystal, smaller
,f*iii-
,*.',
IcKH.y
-0.03
(C)
0
0.03
-0.03
0
0.03
Tilt angle [degree] Figure 2. Channeling profiles of (a) charge state fraction, (b) target X-ray yield, and (c) projectile Xray yield as a function of the incident angle with respect to the (220) plane for 390MeV/u Arl7+ (Left), 423MeV/u Fe2,+(Center), and 430MeV/u Kr"+(Right) ions. X-ray yields are normalized to unity for random incidence.
population of the excited states results in depression of the X-ray yield in the channeling condition. When the crystal is thick enough, on the other hand, the X-ray yield is rather larger for channeled ions, since smaller ionization probabilities lead to more survived bound electrons which may emit deexcitation X-rays. Therefore the X-ray yields in channeling and random conditions are inverted at a certain thickness, which depends on projectile species. For heavy ions, the inversion thickness is larger due to smaller ionization probabilities and higher radiative decay rates than light ions. In our experiments, the crystal is thick enough for the light Ar17+ ions to allow larger X-ray yields under the channeling condition, not being thick enough for the heavy Fe24+ and Kr35* ions. This tendency is confirmed by a simulation taking account of excitation, ionization, intra-shell mixing processes with probabilities depending on the ion position in the channel which gives inversion thickness of 12-(im for Arl7+, 120 um for Fe24+ and 600 (xm for Kr35+ ions in accordance with the experiment.
552 3.2, Exit angle distribution of channeled ions through a ultra-thin crystal Figure 3 shows 2-D display of exit angle and charge state distribution of 390 MeV Ar ions transmitted through a 1 pm thick Si crystal in (220) planar channeling condition. Incident charge state was 17+. It is noted that the ionized ions are those with large exit angle. The ion trajectory simulation shows that ions with large exit angle are those enter the crystal close to the channel wall, i.e., an atomic plane. Fig. 4(Right) shows tilt angle dependence of survived charge fraction. Survived fraction was about 69 % in random direction and 83 % for (220) channeling condition. Maximum ionized fraction of 37 % was observed at tilt angle of 0.012° where ions with "quasi-channeled*9 contribute to ionization. 2D-PSD imaae
*~" C h a r g e S t a t e - »
nit angle A* from (220)[d£fl.J
Figure 3. Calculated ion trajectories(Left), 2-dimensional display (Middle) of observed charge state and exit angle distribution in (220) planar channeling condition and tilt angle dependence of survived fraction of initial charge state(Right) for 390 MeV/u Ar ions transmitted through a 1 \ua thick Si crystal. Incident charge state was 17+.
3 3 . MCE RCE condition for a channeled ion in Si crystal along the (220) plane is given by, ^E = hvkie) = -^~- (V2*cos0+ Mn#), (1) where M is the transition energy, y= l/^/l-v 2 /^ , (3 = vie, v is the beam velocity and 6'm the angle between the beam direction and the [110] axis. Index (k9i) specifies an array of parallel atomic strings constituting the (220) atomic plane. A. Stark effect We have demonstrated that RCE measurement using an SSD as a target provides a powerful tool in high-precision spectroscopy of highly charged
553 heavy ions under a strong (typically 3xlOl! V/m) crystal field[6,7]. While the tilt angle, 0, corresponds to the transition energy through Eq. (1), the energy deposition to the SSD can be converted to the oscillation amplitude of the ion trajectory, which somehow corresponds to the ion position in the channel.at the moment of excitation. Thus obtained 2-dimensional contour display of RCE yield as a fraction of the transition energy and the trajectory amplitude visualizes the energy level structure as function of ion position. Figure 4 shows 2D displays for «=1~»2 and /i=l—»3 transitions in Helium-like Arl6+ ions. He-like Ar //-i-->2
Transition energy (cV)
He-like Ar /;-! >3
' s3p ^ i
'sM
:i)
i
Transition energy (eV)
Figure 4. RCE yields as a function of trajectory amplitude and transition energy for ir*l—»2 and «=1~*3 transitions in He-like Au,6+ions.
It is noted that, while n=l—»3 transition shows clear Stark effect w=l—>2 does not. This can be explained by a simple comparison of intrinsic sublevel splitting, A£y(0), vs. Stark matrix element, Fy = 2 |(i|e!-rjj>|, which is estimated to be 15.0 vs. 8.3 eV for w=l—»2 and 4.1 vs. 14.4 eV for «=!—»3 transitions. B. X-ray emission and its anisotropy As the alternative way of the detection of RCE, de-excitation X-rays from the projectile ion were measured using two Si(Li) detectors located at -90° in Pframe, one in parallel and in perpendicular directions to the channeling plane, aiming at detection of anisotropy in emission angle distribution. In the case of (£,/)=( 1,1) resonance for n = 1—>2 transition of 390 MeV/u Ar17+ ions, RCE was also observed in the X-ray RCE profile at the same energies as charge state profile, i.e., two peaks corresponding to lsi/2-»2pi/2and lsi/2—>2p3^ transitions but with depressed X-ray intensity for 2^m peak[8]. Reduction of j = 1/2 peak
554
for X-ray profile is due to the fact that they = 1/2 peak is contributed by lower two substates of Stark mixed w=2 manifold and are heavily populated with 2s component, resulting in a lower radiative rate. The oscillating crystal field is Tilt angle |degree| polarized in a specific way to the index (k,l) and depending on the ion position S 1.5 in the channel and excited state through the (k,l)-RCE is expected to be aligned. In the cases of (£,/)=( 1,1), X-ray emission in parallel direction to the channeling plane is expected to be stronger but significant difference Transition energy |eV| between yields in the two directions was Figure 5. The RCE profiles for (k; I) not observed. This is because of the "de= (2, -1) resonance of ls 2 -»ls2p alignment mechanism" due to collisional transition in (220) planar channeled Fe24* ions for de-excitation X-rays transition between Stark-mixed measured in the parallel (•) and the eigenstates through 2s-2p dipole perpendicular (o) directions. transition, which results in mixing among 2px, 2py and 2pz components. Then how can we observe anisotropy? There are two key points for above mentioned de-alignment mechanism to work. One is competition between radiative decay of the excited state and collisional mixing. The other is the fact that without Stark mixing direct collisional mixing among px, py and p2 component is dipole-forbidden. From these points, alignment in the excited state is expected to be retained in the cases of He-like ions where Stark effect is weak and of heavy ions where radiative rate is high. Actually clear anisotropy was observed for (&,/)=(2,-l) resonance of ls2->ls2p('P) transition in 423 MeV/u Fe24+ ions as shown in Fig. 5. Significant anisotropy was also observed for He-like Ar case where Stark effect was not observed, again indicating the importance of Stark effect in the collisional mixing mechanism. 2.6
• + I •• • I .
6651)
6660
6670
6680
6690
6700
6710
67,
C. Double resonance For a given beam velocity, v, the frequency, vK{6), felt by an ion (220) planar channeled in Si crystal is given by Eq. (1). Index (&,/) specifies an array of parallel atomic strings constituting the (220) atomic plane. As easily understood, by continuously tuning two parameters, tilt angle, 6, and beam velocity, v, it is possible to make two frequencies with different indexes, (k,l) and (ft",/1), satisfy the resonance conditions for two excitation
555 energies, A£ and AF, at the same time, which we call double resonance. This situation may simulate the two X-ray laser irradiation. We have tried to realize ladder type double resonance involving three levels. At beam energy of 387.90 MeV/u, resonance conditions for (£,/)=( 1,-1) of ls 2 ls2p and (^/)=(1,1) of ls2p-2p2 transitions are simultaneously satisfied at the same incident angle 0= 1.23°, while at the beam energy of 388.54 MeV/u, these two resonance conditions are satisfied at 0 = 1.27° and 1.16°, respectively. Figure 6 shows incident angle dependence of survived Ar16+ fractions measured at the two beam energies. Enhanced ionization was observed under the double Incident angle 0 [degj for SR resonance condition indicating that the 1.2 1.3 doubly excited state 2p2 is produced. Trajectory-wise analyses utilizing energy deposition signals are under way. 4. Outlook As shown in Fig. 3, ~ 70 % of incident charge state fraction survived the passage of l|^m thick Si crystal even in a non-channeling direction. This means that the survived fraction can carry Incident angle u [deg] for DR information on atomic processes Figure 6. Survived fractions of incident experienced by the ion inside the crystal. charge state, Ar'6+, as a function of tilt Actually we recently succeeded in angle around lsz-ls2p single resonance (o) and ls2-ls2p-2p2 ladder-type double observing RCE in non-channeling resonance (•) conditions. condition, where the ion penetrates periodic array of atomic planes. In axial or planar channeling RCE, the ion velocity is restricted in axial or planar direction and we call them 1-D RCE or 2-D RCE. Similarly, non-channeling RCE can be called 3-D RCE. The resonance condition of 3-D RCE is given by, AE = hvki,,m(0, (P)=-^-(^2{kcos
556
References 1. 2. 3. 4. 5. 6. 7. 8.
V.V. Okorokov, Yad. Fiz. 2, 1009(1965) [Sov. J. Nucl. Phys. 2, 719(1966)]. S. Datz et al., Phys. Rev. Lett. 40, 843 (1978). F. Fujimoto et al., Nucl. Instr. and Meth. B22, 354(1988). T. Ito et al., Nucl. Instrum. and Meth. B135, 132(1998). T. Azuma et al., Nucl. Instr. and Meth. B193, 178(2002). K. Komaki et al., Nucl. Instr. & Meth. B146, 19(1998). T. Azuma et al. Phys. Rev. Letters 83, 528( 1999). T. Ito et al., Nucl. Instr. & Meth. B164-165, 68(2000).
COLLISIONS INVOLVING CLUSTERS AND SURFACES
S T R U C T U R E A N D D Y N A M I C S OF V A N D E R WAALS COMPLEXES: FROM TRIATOMIC TO M E D I U M SIZE CLUSTERS
G. DELGADO-BARRIO? D. LC-PEZ-DURAN, A. VALDES, R. PROSMITI, M. P. DE LARA-CASTELLS, T. GONZALEZ-LEZANA, AND P. VILLARREAL Instituto de Matemdticas y Fisica Fundamental Serrano 123, 28006 Madrid, SPAIN
(CSIC),
Weakly bound complexes of a diatomic molecule and one or several rare gas atoms are analyzed from first principles. Focusing the study on Br2-(He)N clusters and increasing the size N, their relevant electronic potential energy surfaces, structure and photodynamics, are presented and discussed.
1. Introduction Complexes composed by a di-halogen molecule and one or several rare gas atoms surrounding it are ideal systems to study the intermolecular forces. In fact, and depending on their sizes, these clusters, produced by jet supersonic expansion at extremely low temperatures, are amenable for performing spectroscopic studies where the diatomic molecule acts as chromosphere. Thus, for the smaller complexes incorporating one or two rare gas atoms, spectroscopy in the visible region involving an electronic B «— X transition 0 ' 0 offers the possibility of a detailed comparison with the theory 0,0 . In this case, an accurate description of the driving forces through the relevant electronic potential energy surfaces (PES), and also of the photo-predissociation dynamics and energy redistribution mechanisms become necessary. In turn, for helium droplets doped with a variety of molecules, rotational and infra-red spectroscopic studies are currently conducted in order to answer new and challenging questions on the role of the "quantum environment" 0,0 ' 0 . A number of additional experiments, based * e-mail: [email protected]
559
560
on helium nanodroplet isolation technique 0 , on small and intermediate-sized doped helium clusters 0 ' 0 have been recently performed. The first issue in this context, from the theoretical side, is how to properly describe the multidimensional potential energy surface or, in other words, at what extent the usual assumption of additive forces holds. Then, some approximate treatment to study the spatial structure, and therefore the corresponding spectroscopy, has to be used in order to deal with the many-body system. This review is devoted to Br2 • • • HeN clusters and is organized as follows. In Sec. 2 we briefly overview, for N = l , the photo-dissociation process Br2(X) •••H.e+hu —>BT2{B,VB, j s ) + H e and discuss the different PES's used, namely empirical and ab initio surfaces. Then, in Sec. 3, we show, through ab initio calculations, how the full B ^ X ) • • -He2 surface can be accurately described by the addition of two triatomic Br2(X)---He potentials plus the He-He interaction, enabling the study of larger clusters. Then we apply this kind of approach and show through Diffusion Monte Carlo (DMC) calculations that, for clusters involving more than twenty He adatoms, the structural differences induced by the use of the two triatomic PES's above mentioned essentially drop out. Finally, we present the effect of the symmetry when the bromine is embedded in an environment of 3 He or 4 He atoms.
2. Photo-predissociation of B r 2 • • • He In this process, complexes of Br2(X) • • • He are formed in a supersonic expansion at very low temperatures, seemingly at very low vibrational and rotational states of both the diatomic and triatomic systems. In the simplest picture, a photon promotes selectively the complex towards an state in which the bromine is in an excited electronic and vibrational state. The excess of vibrational energy stored in the diatom flows to the van der Waals bond giving rise to its breaking up, constituting the so called vibrational predissociation (VP) process. This produces a broadening in the spectral lines which is related to the VP rate. Within the electric dipole approximation, denoting by J the quantum number associated to the total angular momentum, the selection rules (assuming that the diatomic dipole moment is not affected by complexation) are A J — 0, ±1,0 •/* 0. Thus, even at low temperatures, a large amount of rotational states have to be included in the simulations 0 . Two kind of potentials were used to describe the X and B states of this triatomic cluster: (1) The simple addition of Morse atom-atom
561
interactions 0 , and (2) An ab-initio surface at the CCSD(T) level of the theory 0 for the X state combined with a perturbation model based on the diatomics-in-molecule approach to represent the B surface 0 . By fitting the potential parameters within the scenario (1) to reproduce the experimental blue-shifts at low diatomic VB vibrational excitations 0 , the calculations reproduce this magnitude (and also VP rates) even for moderate VB values (< 30)°. However only the potentials of the framework (2) were able to reproduce the oscillations of such magnitudes appearing at higher VB levels. For the (B, VB = 8 <— X, vx — 0) transition there is also a very good agreement as regards the main band of the measured excitation spectrum 0 , corresponding essentially to transitions B <— X keeping a T-shaped geometry of the complex. Moreover, a weak secondary band could be mainly assigned to a transition from the collinear X configuration, almost degenerated in energy with the T-shaped one, to excited bending states in the B state 0 by using this set of more elaborated surfaces, see Fig. .
Main band
2.5
10
Secondary band
3-5
Spectral shift < cm -1 )
+0
80
6,5
M
W
10,0 10.5
11.0 11.6 12.0
Spectral shift (car 1 )
Figure 1. B, VB = 8 *— X, vx = 0 excitation spectra. Solid lines: experiment, dotted lines: simulations. Main (left panel) and secondary (right panel) bands, where the peaks are assigned to different nx — H B vibronic transitions.
For the this system, laser-induced fluorescence spectra have been recently recorded at different temperature regimes 0 . Besides, the X surface has been recalculated and for the B state a further ab initio surface from our group 0 , performing also theoretical simulations of the spectra which
562
confirm the main conclusions of the precedent work 0 . 3. B r 2 ( X ) • • • H e n clusters 3.1. Br2(X)
• • • He2:
Additivity
of the PES
Electronic studies of larger species are more complex and the difficulty in the evaluation of the PES increases with their size. Four-body systems as Br2(X) • • • He2 are now amenable for performing ab initio calculations with a satisfactory degree of accuracy, which then permit the testing of various models of additivity in order to describe the PES of larger B ^ X ) • • • HeN clusters. Recently, ab initio calculations ° at the fourth-order M0ller-Pleset (MP4) and coupled-cluster [CCSD(T)] levels of theory have been performed 0 for the above mentioned tetra-atomic system. The surface is characterized by three minima and the minimum energy pathways through them. The global minimum corresponds to a linear He-Br2-He configuration, while the two other ones to 'police-nightstick' (one He atom in the linear configuration, and the other in the T-shaped one with respect to the bromine) and tetrahedral (with the two He atoms along a plane perpendicular to the bromine bond) structures. Analytical representations based on a sum of pairwise atom-atom interactions and a sum of three-body HeBr2 CCSD(T) potentials ° and He-He interaction ° were checked in comparison with the tetratomic ab initio results. The sum of the three-body interactions form is found to be able to accurately represent the MP4/CCSD(T) data (see Fig.2). For first time an analytical expression in accord with high level ab initio studies is proposed for describing the intermolecular interactions for such two atoms rare gas-dihalogen complexes. Variational bound state calculation is carried out for the above surface and vdW energy levels and eigenfunctions for J = 0 are evaluated for He2Br2- Radial and angular distributions are calculated for the three lower vdW states and three different structural models, which correspond to linear, police-nightstick' and tetrahedral isomers are determined. The binding energies and the average structures for these species are computed to be D o =32.240 cm" 1 with i?? 2 =4.867 A, D 0 =31.437 cm" 1 with i?? 2 =4.491 A, and D o =30.930 c m - 1 with R^ 2 =4.171 A, respectively. The above values are in excellent agreement with recent LIF experimental data available °. This finding in combination with the very good agreement with the MP4/CCSD(T) tetratomic calculations, contribute to evaluate the present surface and justify our predictions.
563
-50
* -60
•
•
•
t
i
i
-70
-80
-90!
i
0
i
30
i
i
60
i
i
i
90
120
i
150
i
i
180
e2 (deg)
Figure 2. MP4 (crosses), CCSD(T) (circles) interaction energies and potential values for the He2-Br2 complex, obtained using the sum of three-body MP4 (diamonds), CCSD(T) (triangles) HeBr2 potentials , at selected points along to the minimum energy path.
We conclude, therefore, that the potential surface based on the sum of the He-Br2(X) 06 initio CCSD(T) potentials plus the He-He interaction, provides reliable results quantitatively comparable with the experimental observations. 3.2. Br2(X)
• • • i f e N - DMC
Analysis
Searching the connection between the smallest complexes containing a few atoms, and which are reasonably well understood, and the mesoscopic and macroscopic world of a continuum liquid or solid medium, is one of the more relevant issues in the field of molecular clusters. Taking advantage of the precedent result about additivity of PES, one can deal with larger clusters as Br2(X) • • • HeN, with N> 2, representing the full PES as an addition of N Br 2 (X) • • He triatomic PES's plus all the He-He interactions. One approach that is largely used to study boson clusters doped with some impurity is the diffusion Monte Carlo method 0,0 ' 0 . It essentially consists in solving the diffusion equation coming from the usual time-dependent Schrodinger equation, once an imaginary time r = it/h is introduced, in terms of the many-body ground state wave-function ^(Xi, r ) . In practice, to improve the efficiency of the method, an importance sampling procedure is commonly applied. Assuming a trial function ^T(Xi) as good approx-
564
imation to the actual one, the product $?$ satisfies a modified diffusion equation, which incorporates a drift force, and is then solved by using a random walk technique. In this way, we have studied the microsolvation of B r 2 p 0 in boson He clusters 0 of sizes up to N=24. In representing the corresponding PES, and provided that the above mentioned additivity holds, one wonders at what extent the initial triatomic He-Br2 is driving the solvation process, or, in other words, if there is a loss of memory of such interaction as the cluster size increases. To this end, we have tested the two kind of interactions already mentioned in Sec. 2, i.e. an empirical pair-wise potential 0 , and an ab initio potential 0 which exhibit a very different anisotropy: the former displays just one minimum at the T-shaped configuration, meanwhile the latter presents a comparable minimum at linear arrangements. The main conclusion is that, as regards binding energies as well as structural properties, the differences produced by the use of one potential or the other gradually disappear as the cluster grows. This is important when one has to decide the simplest way of modeling such interactions to study larger clusters, for which often direct experiments are available 0 ' 0 . In Fig. 3 we show, through angular distributions, how the two different triatomic potentials lead essentially to the same structural features as the cluster size increases. As can be seen, the distribution tends to be isotropic, although one can distinguish three main regions as belts around the 90 degrees (T-shape), 50 degrees, and 0 degrees. This last feature, i.e. the coUinear arrangement, is of course more pronounced when the ab initio triatomic potential is used. Anyway, including the volume element sin(0) to get a physical picture, one realizes that the He atoms tend to form a football balloon around the bromine independently of the triatomic potential used to describe the full PES.
4. B r 2 ( X ) • • • HeN: Role of Boson-Fermion Statistics One of the most outstanding experimental findings in doped helium clusters is the microscopic manifestation of superfluidity by analyzing the rotation of the dopant inside the cluster. For instance, for OCS in He nanodroplets, and depending on the character of the environment (bosonic or fermionic), the IR spectra near the v\ band are completely different0. For droplets constituted by 4 He atoms, the spectra are similar to that of the isolated OCS, showing well defined P and R branches, in such a way that the molecule seems to be almost freely rotating inside this environment. On the contrary,
565
Figure 3. Angular density distributions for the He atoms surrounding the Br2pf) molecule for different cluster sizes and depending on the triatomic He-Br2(X) interaction used.
for 3 He droplets the spectra become broad and unstructured. Moreover, starting with 3 He nanodroplets and adding gradually bosons, one recovers the bosonic spectrum from a number of about 60 4 He adatoms in the mixture. This behavior can be understood within a simpler scenario by studying the rotation of a bromine molecule surrounded by boson and/or fermion helium atoms, although due to the homonuclear character of this dopant one has to consider Raman spectroscopy. To this end, one also needs some many-body treatment able to provide the necessary wave-functions to perform the corresponding spectral simulations. Making an analogy between He atoms and electrons, with the Br atoms playing the role of nuclei, Hartree or Hartree-Fock quantum chemistry-like treatments have been applied within an adiabatic separation of the bromine vibration to bosonic or fermionic clusters, respectively. This allows one to study the diatomic molecule as perturbed by the presence of the surrounding He atoms. According to the Raman selection rules predicted by the model, only O, Q,
566
and S branches can appear in the boson scenario, that is, the same than that for the isolated diatomic molecule. In this case, it has been shown that a Hartree methodology 0 reproduces accurately well energies and structural properties obtained through diffusion Monte Carlo calculations 0 . For fermions P and R additional branches become allowed, and Hartree-Fock calculations show that the spin multiplicity gives rise to several levels almost degenerated in energy. So, this multiplicity is the main responsible of the observed unstructured spectra since there are many lines contributing to the spectral congestion. Moreover, by using a combined Hartree-Fock/Hartree methodology to study mixed fermion/boson clusters, the congestion gradually disappears by adding boson atoms and the corresponding spectra are seen to be very similar to those corresponding to bosons in qualitative agreement with the experimental findings0,0. -3.56
-3.54
-3.52
CKJ&oJ
i
-3.5
-3.48
-3.46
18 fermions 18/18 mixture 18 bosons
60
• 40 4 -
20
2 -
-3.4
-3.38 -3.36 -3.34 Frequency Shift A© (cm )
-3.32
Figure 4. Raman spectra of different clusters showing Q branches.
Fig. 4 displays, at a temperature of 2 K the simulated vibrotational (v — 1 <— 0) Q branch Raman profiles for three complexes of bromine with 18 bosons, 18 fermions, and the mixture of 18 fermions plus 18 bosons. Assignments of the main contributing lines are also shown. They are denoted by Js,ns» where J is the total angular momentum, S is the spin and Qs
567 its projection on the bromine bonding axis. Intensities for fermion complexes are indicated on the left vertical axis, while those for pure bosons are shown on the right vertical axis. The frequency shift Aw corresponds to the difference between the exiting and the incoming photon frequencies. The latter was fixed at 320 c m - 1 which is close to the above mentioned vibrational transition for the isolated B ^ X ) molecule. The lower x axis accounts for the frequency shifts of pure fermion and boson clusters, while those shifts for the mixture of 18 fermions and 18 bosons are on the top x axis. One can realize the gradual change from a broad profile for pure fermions (arising from several transitions), through the more structured profile for the mixture, towards the almost single peak corresponding to pure bosons. Therefore, the spin multiplicity emerges as the responsible for the effect experimentally observed. Acknowledgments This work has been supported by the DGICYT Spanish Grant No. FIS200402461. References 1. D. H. Levy, Adv. Chem. Phys. 47, 323 (1981). 2. A. Rohrbacher, N. Halberstadt, and K. C. Janda, Annu. Rev. Phys. Chem. 51, 405 (2000). 3. J. A. Beswick and J. Jortner, Adv. Chem. Phys. 47, 363 (1981). 4. M. I. Hernandez, T. Gonzalez-Lezana, A. A. Buchachenko, Ft. Prosmiti, M. P. de Lara-Castells, G. Delgado-Barrio, and P. Villarreal, Recent Res. Devel. Chem. Physics 4, 1 (2003). 5. S. Grebenev, J. P. Toennies, and A. F. Vilesov, Science 279, 2083 (1998). 6. K. Nauta and R. E. Miller, Science 287, 293 (2000). 7. J. P. Toennies and A. F. Vilesov, Angew. Chem. Int. Ed. 43, 2622 (2004). 8. C. Callegari, K. K. Lehmann, R. Schmied, and J. Scoles, J. Chem. Phys. 115, 10090 (2001). 9. J. Tang, Y. Xu, A. R. W. McKellar, and W. Jager, Science 297, 2030 (2002). 10. J. Tang and A. R. W. McKellar, J. Chem. Phys. 119, 5467 (2003). 11. T. Gonzalez-Lezana, M. I. Hernandez, G. Delgado-Barrio, A. A. Buchachenko, and P. Villarreal, J. Chem. Phys. 105, 7454 (1996). 12. R. Prosmiti, C. Cunha, P. Villarreal, and G. Delgado-Barrio, J. Chem. Phys. 116, 9249 (2002); A. Valdes, R. Prosmiti, P. Villarreal, and G. Delgado-Barrio, Mol. Phys. 102, 2277 (2004). 13. A. A. Buchachenko,T. Gonzalez-Lezana, M. I. Hernandez, M. P. de LaraCastells, G. Delgado-Barrio, and P. Villarreal, Chem. Phys. Lett. 318, 578 (2000).
568 14. D. J. Jahn, S. G. Clement, and K. C. Janda, J. Chem. Phys. 101, 283 (1994) 15. D. J. Jahn, W. S. Barney, J. Cabalo, S. G. Clement, A. Rohrbacher, T. J. Slotterback, J. Williams, K. C. Janda, and N. Halberstadt, J. Chem. Phys. 104, 3501 (1996). 16. A. A. Buchachenko, R. Prosmiti, C. Cunha, G. Delgado-Barrio, and P. Villarreal, J. Chem. Phys. 117, 6117 (2002). 17. D. S. Boucher, D. B. Strasfeld, R. A. Loomis, J. M. Herbert, S. A. Ray, and A. B. McCoy, J. Chem. Phys., in press. 18. M. P. de Lara-Castells, A. A. Buchachenko, G. Delgado-Barrio, and P. Villarreal, J. Chem. Phys. 120, 2182 (2004). 19. Gaussian 98, Revision A.7, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery, Jr., R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, A. G. Baboul, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, J. L. Andres, C. Gonzalez, M. Head-Gordon, E. S. Replogle, and J. A. Pople, Gaussian, Inc., Pittsburgh PA, (1998). 20. A. Valdes, R. Prosmiti, P. Villarreal, and G. Delgado-Barrio, J. Chem. Phys. 122, 044305 (2005). 21. R. A. Aziz and M. J. Slaman, J. Chem. Phys. 94, 8047 (1991). 22. R.A. Loomis (private communication). 23. D. M. Ceperly and B. Adler, Science 231, 555 (1986). 24. M. Lewerentz, J. Chem. Phys. 104, 1028 (1996). 25. F. Paesani, F. A. Gianturco, and K. B. Whaley, J. Chem. Phys. 115, 10225 (2001). 26. C. Di Paola, F. A. Gianturco, D. L6pez-Duran, M. P. de Lara-Castells, G. Delgado-Barrio, P. Villarreal, and J. Jellinek, Chem. Phys. Chem. 6, 1 (2005). 27. M. P. de Lara-Castells, D. L6pez-Duran, G. Delgado-Barrio, P. Villarreal, C. Di Paola, F. A. Gianturco, and J. Jellinek, Phys. Rev. A 71, 033203 (2005). 28. D. L6pez-Duran, M. P. de Lara-Castells, G. Delgado-Barrio, P. Villarreal, C. Di Paola, F. A. Gianturco, and J. Jellinek, J. Chem. Phys. 121, 2975 (2004). 29. D. Lopez-Duran, M. P. de Lara-Castells, G. Delgado-Barrio, P. Villarreal, C. Di Paola, F. A. Gianturco, and J. Jellinek, Phys. Rev. Lett. 93, 053401 (2004).
Evaporation, Fission and Multifragmentation Processes of Multicharged C60 Ions versus Excitation Energies SMartin', L.Chen', B.Wei2, J.Bernard'
andR.Bridy1
'Laboratoire de Spectromitrie lonique & MoUculaire, University Lyon 1, UMR CNRS 5579, Campus de la Doua - 69622 Villeurbanne Cedex, France 2
Institute of Modern Physics, Chinese Academy of Sciences - Lanzhou 730000, China
We present main results about fragmentation of multicharged Cw ions prepared in collisions between slow ion beams Xeq* (q=25, 30), Ar8*, P* (q=l-3), H* and fullerene CM target. Probabilities of evaporation, asymmetrical fission and multifragmentation processes are given versus the charge state r of Cm" parent ions. For CM'* at high charge state (r>=5), unexpected channels like the emission of doubly charged light fragments and the emission of two odd light fragments are observed and discussed. The Emission of two odd light fragments is explained by the formation of hot C w ions which can no longer be considered as a rigid structure but rather a floppy structure close to the liquid phase. This phase transition leads to the dropping of the fission barrier for the emission of odd light fragments. We describe also a new method to measure the energy deposition on the C w by analyzing the kinetic energy loss of the scattered projectile negative ions in collisions of P* or H+ ions with C«,. This method is an extension of the well-known Double Charge Transfer spectroscopy (D.C.T.). The measured experimental energy distribution of Cw2* parent ions undergoing further decay by the evaporation of C2 fragments is compared with a simple statistical evaporation model.
1. Introduction The relaxation of hot fullerenes provides opportunities to study the dynamical behaviour of complex systems with a large number of degrees of freedom [1]. lonisation, fragmentation and radiative decay processes have been intensively studied during the past few years [2-5], Recently, special attention has been devoted to the study of fragmentation of multicharged fullerene ions produced in collisions
569
570
between slow multicharged ions and Cw. At large impact parameters, the over barrier extraction of electrons is dominant and leaves the C60r+ ion in a stable charge state. At smaller impact parameters, a large variety of degrees of excitation occurs leading to the fragmentation of multicharged C^ following different decay channels. The dominant fragmentation mechanism for C^*ions with low excitation energy is described as a sequential emission of Q units. Larger light fragments like C4+, C6+, Cg+, Cio+ have been observed also for Qo at low charge state and are explained by unzipping mechanisms of the Qo [6, 7]. For higher degree of excitation or (and) for Qo at higher charge states, unexpected channels have been observed as the emission of two odd fragments (C++C3+) [5, 8] or the emission of doubly charged fragment (C22+ or C42+) [5,9]. Dynamics of emission of two odd fragments have been studied and shown that the fragments are ejected successively from the hot Qo. Up to now in our experiments, due to the large potential energy contribution of highly charged projectiles, it has not been possible to estimate the excitation energy of parent Qo ions from the kinetic energy loss measurement of the scattered projectiles. The excitation energy has been estimated only using the theoretical model like Rice, Ramsperger and Kassel (RRK) model. In this progress report, results concerning the measurements of branching ratios of different fragmentation processes will be given for multicharged Qor+ with r ranging from 4 to 9. A method allowing to measure the excitation energy of C^ parent ions will be presented. Finally the average excitation energies for the evaporation, fission and multifragmentation processes will be briefly given and discussed.
2. Experimental method Projectile ion beams were extracted from the ECR source at AIM in Grenoble (Xe25,3(H) or from the ECR Nanogan 3 source, an upgrade of Nanogan, in Lyon (Ar8+, P + and H+). A C^, effusive jet was evaporated from an oven at 480°. Figure 1 shows the experimental set up used in these experiments. Depending on the type of measurement, a pulsed beam (pulse width ~50 ns) or a continuous beam has been used. The charged reaction products (electrons and recoil ions) are extracted by a transverse electric field (typically 50-100 V/mm). In the interaction region the potential is kept at 300 V. The ionised C^," fullerene or heavy and light fragments are analyzed by a standard time of flight mass spectrometer of about 320 mm in length. The particles are post accelerated with a 5 kV Voltage towards a detector using two Multi Channel Plates M.C.P. and a multi anode of 128 pixels. The ejected electrons extracted from the collision region are post accelerated at 25 kV and detected using a semiconductor detector (P.I.P.S. Canberra).
571
Si Detector (PIPS)
Figyre. I. Experimental set up. The number of ejected electrons by event is measured using the silicon detector (PIPS). Stable CM ions and fragments are detected using the two M.C.P. and a home made multianode of 128 pixels. The outgoing projectiles are selected in charge and in kinetic energy by a cylindrical electrostatic analyzer and detected with a standard channeltron electron multiplier.
The electron signal pulse height analysis provides information on the number n of emitted electrons in a single collision event. Outgoing projectiles, with s stabilised electrons, are selected and analysed in kinetic energy by an electrostatic analyser (radius E-200 mm). For analyzing the negative ions, the polarity of the analyser has to be reversed. Resolution of the analyser is typically about 1/300. At the exit of the analyser, the ions are detected by a channeltron with a good efficiency fc95%) except for the negative ions at low kinetic energy. The signal of the outgoing projectile is used as the common stop trigger in the event by event acquisition mode. Multi-coincidence measurements are performed between the outgoing projectile, the charged fragments of target and the number of ejected electrons. By scanning the analyser, each charge state of outgoing projectile is precisely recorded in the same conditions (time, beam intensity, ...). The charge of the parent ion is determined with the electron number conservation rule r=n+s. A multianode detector is employed to analyse precisely all charged fragments which is especially useful in certain fragmentation channels for example the emission of two or more light fragments, as the C2*f"-C2+ emission in successive asymmetrical fission process or the emission of many medium carbon fragments Cm+ (l<=m<=19). in multifragmentation process. The number of pixels activated by each detected ion is also recorded. This number provides information on the charge state of recoil ions and is used to separate the multicharged fullerene ions and the medium light fragment (for example C^4* and C,4+ ions) [5].
572
Measurements under identical conditions were performed during about 20h with a flux of about 300 coincidence events per second especially to measure the fragmentation processes of highly charged state of Cm like the asymmetrical fission ofCM9+. 3. Experimental results and discussion 3.1. Fragmentation processes of multicharged CyJ* (r=4-9) Figure 2 shows an example of two-dimensional spectrum corresponding to events with at least two charged fragments detected in the Xe<25+,-C60 collisions. Here, the outgoing projectile Xe(23+> (s=2) is selected by the analyser. The TOF of the heavy fragment is plotted along the horizontal axis and the TOF of the light fragment along the vertical axis. The main spots are attributed to the asymmetrical fission channels C60r+^C60.mq++Cm+ (r=q+l, q=3-8; m=2,4, 6, 8). •J+l 3V. 3*
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Figure 2. Two-dimensional spectrum of correlated recoil ions. The spots and tails correspond to the detection in coincidence of a light and a heavy fragment from asymmetrical fission of C«,'* ions.
The charge of the heavy fullerene fragment ranges from 3 to 8 corresponding to the state of parent ions CV* from 4 to 9. The slope of the tails due to the delayed fragmentation process depends sensitively on the fission process and especially on the charge difference between the parent ion and the fullerene fragment. That allows to assign the doubly charged fragment emission channel as the C60frt-*C584++C22+ reaction. For a given initial parent charge state, the fragmentation spectra depend strongly on its formation process which is related to the final charge state of the projectile. In Xe^-Qo collisions [5], the dominant reaction channels are characterised by the final charge state Xe(30s)+ with s ranging from 1 to 4. Several formation channels are then possible for a Qo'+ parent ion in the following reactions, Xe^+Qo -> Xe<30s)++ CMr+ + (r-s) e", with l<=s<=min(4,r). For collisions
573
with s=l, only stable C^'* ions are observed with l<=r<=7 while for s=2 to 3, the evaporation (neutral fragment emission), asymmetrical fission and multifragmentation processes compete. For s=4, the multifragmentation process is dominant. From these measurements taking into account of all possible formation channels for a Cw'+, we have deduced the relative probabilities of evaporation, fission and multifragmentation channels and also the relative probability of stable channel as a function of the parent charge state CMr+. Figure 3 shows a sensitive dependency of the measured probabilities on the parent charge state r. The evaporation process is observed for r=3 to 5, whereas the asymmetrical fission is observed for r up to 9 with a maximum close to r=6. For r=3, the fission is observed but with very low relative probability and not shown here. The evaporation and fission processes are thermally activated and the competition between these two processes has been mainly explained by an electron transfer mechanism from the light fragment to the multicharged fullerene [10] during the fragment emission process. The electron transfer efficiency increases with the charge of the fullerene, which explains the transition of the relative probability at about r=4. For Cw at higher charge state, the emission of a charged light fragment is dominant compared to the neutral emission. For QQ with a charge state larger or equal to 5, the successive emission of several charged light fragments is possible. The multifragmentation process starts to be observable at r=4 and becomes the dominant channel from r=7. The relative probability to observe stable Cw ions is quite large from r=l to 6 but decreases strongly from r=7 to 9. It shows that at large impact parameters, many electrons (up to 9) can be transferred from the Qo to the projectile leaving the target in a low excitation energy level (excitation energy lower than 30 eV for C^9*).
1 Probabilities 0.1
0.01 0.001 1
2
3
4 5 6 7 8 9 Initial charge states of C60
10
Figure 3. Relative probabilities of different fragmentation channels versus the charge state of parent ions CMr* (r=2-9) in Xe™* - C«, collision. The lines are included to guide the eyes.
574
As we will see in the following, the branching ratio between the fragmentation and stable channels depends also on the initial charge state of the projectile. Using projectiles at medium charge states as Ar8*, the probability of evaporation is larger for C603+ than in Xe 30 *-^ collisions, the multifragmentation process is dominant for Qo6+ and the stable C^6* is quasi negligible. For projectiles at lower charge state like F+ or H+, the evaporation and multifragmentation processes start from r=2 for CM2+ ions. 3.2. Emission of doubly charged light fragment and successive emission of odd and even monocharged light fragments As shown in Fig.3, for C^4* ions, the probability of emission of light monocharged fragment is higher than that of neutral fragment. It can be roughly explained by comparing the (LP.) Ionisation Potentials of the two fission products. In the fission channel C^,4* -> C583+ + C2+ for example, the IP of the fission products C583+ and C2+ are respectively 13.4 eV and 12.15 eV [11-12]. Due to the very near potentials, an electron, initially on the C2 fragment, can be captured by the multicharged partner Cs£*. In similar way, the emission of a doubly charged light fragment can occur when the IP of the multicharged heavy fragment is comparable to the IP of the doubly charged light (or medium) fragment. For example, for the fission channel, C605+ -> C503+ + C,02+, the IP of the two fragments C^3* and C,02+ are very close, 13.9 eV and 14 eV [13] respectively. It explains why the doubly charged fragments around C82+ have been observed in asymmetrical fission processes [9]. Figure 4 shows the probabilities of emission of mono and doubly charged light fragments in Xe25+-Cw collisions [5]. The emission of doubly charged fragment Cm2+ increases from less than 2% to 25% with the increasing charge r. Similar to the emission of a monocharged fragment, the probability for the transfer of a second electron from the light fragment to the multicharged fullerene is higher when C6or+ parent ions are in a higher charge state. 1 Probabilities
0.5
5
6
7
8 9 Charge state of C a 0
Figure 4. Relative probabilities of the emission of a monocharged (solid line) and a doubly charged light (dash line) fragment versus the charge of Cm'* ions. The lines are included to guide the eyes
575 For CJO parent ions at high charge state, we have also observed the successive emission of several monocharged light fragments. The branching ratios of successive emission of two and three monocharged even fragments are shown on the Fig. 5a and Fig. 5b respectively for CMU parent ions produced in Ar^-Qo collisions [9]. The probability of asymmetrical fission is optimum for Cmu produced by impact of this charge state of argon. We found high branching ratios for the channels of successive emission of C2+-C2+ and C2+-C4+. For the emission of three light fragments, high branching ratios are found for C2+-C2+-C4+ and C2+-C4+-C4+ channels. These experimental branching ratios are in good agreement with the estimation of a fission model in cascade using the measured branching ratios of onestep fission of C^6*, Ceo5* a n d C^ parent ions. The main channels for asymmetrical fission process are the emission of fragments with an even number of carbon atoms. Indeed, the predominance of such even numbered fragment emission channels is related tightly to the stable cage structure of even numbered fullerenes and the instable structure of odd numbered fullerenes. [7]. Branching ratios
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Figure.5. Branching ratios for successive emissions of two (a) and three (b) light fragments in asymmetrical fission processes for Qo6* parent ions. Square: Experimental values, triangle: Theoretical values fromreference[9]. The numbers m,-m2 in (a) and m,-m2-mj in (b) above each point denote the fission process with the ejection of Cml*, C „ / or Cm,*, C^* and C^*.
However, the emission of odd numbered fragments has been observed in many experiments and the explanation concerning the emission mechanism is still an open question. Figure 6 shows the correlation spectra between the two light fragments in
576 fragmentation channels CM7+^C565++Cm++Cn+ induced in Xe25+-C60 collisions. Two main spots are observed and attributed to the emission of (V-CV and Cj'N-C*. The tail of each spot gives information on the dynamic of the fragmentation [9]. The tail of the spot C2+-C2+ is explained by the slow successive emission of two fragments with typical lifetimes estimated to be less than 4 ns and about 250 ns for the first and the second step respectively. The tail of the spot C3+-C+ is explained by the fast sequential emission with a lifetime estimated to be less than a few nanoseconds for the second step. The odd numbered fragment emission channel is opened in two fragment emission processes but it is forbidden in one fragment emission process. This puzzling experimental observation is
TOF( pa)
21-
3i_
TOF( /IS) Figure 6 .Correlated spectrum of the two light fragments in coincidence with the detection of a heavy C565* ion.
interpreted recently as due to the drop down of the fission barrier of CMr+ for the emission of an odd numbered fragment at high initial excitation energies close to the solid-liquid phase transition [14,15]. Under such high temperature conditions, the C^ loses its rigid structure; isomers with many dangling bounds exist and favour the ejection of odd fragments like C+, C3+. 3.3. Measurements of excitation energies of evaporation, fission and multifragmentation processes To measure the excitation energy of the Cgo we have used a method similar to the technique developed to measure the IP of doubly charged molecular ions (dications) [16] called Double Charge Transfer (DCT) spectroscopy[17, 18]. This technique involves the measurement of the translational energy of the negative ions formed by double electron capture of incident monocharged ions as in the reaction :
577
A++M-»A"+M2+* The energy loss AE of the projectile is related to the double ionisation potential of the target I2+ (M) (equal to IF+IP2+) in the following way, AE=I2+(M)+Ex(M)-I+(A)-EA(A)-EM + where I (A) is the IP of A, EA (A) is the electron affinity, Ex (M) is the excitation energy of the target and EM is the recoil energy of the target M. The recoil energy of the target is negligible compared to the other terms especially when the target is significantly heavier than the projectile ion. The excitation energy of the negatively charged outgoing projectile is also neglected taking the assumption that the negative ions are formed by double electron capture directly in the fundamental state. Using proton as projectiles, it has been shown that most excited states of H" are auto ionizing states with very short lifetimes compared to the time of flight of projectiles inside the electrostatic analyser (about 10'6 second) [19]. The I+ (A) and EA (A) terms are in general well known for many ions [20]. For proton, the I+(H)+EA(H) term is equal to 14.35eV. By analysing the energy loss of the projectiles H", it is possible to measure the double ionization potential I2+(M) or (and) the excitation energy Ex (M). The best energy resolution of this method reaches about 120 meV and allows to separate the vibrationnal levels of molecular dictations [16]. The scale of the translational energy loss has been calibrated using the DCT peaks of Ar target, Ar^'Dj) and Ar2* ('S0) at 45.126 eV and 47.514 eV respectively. We have extended this method to Multiple Charge Transfer (MCT) processes with Ox, as target in reaction channels, A^+Ceo-^A'+Cy-^** H+ and P+(q=l-3) have been used as incident projectiles. The energy loss AE of the projectile is related to the excitation energy Ex(C6o) of the recoil target C60(q+1)+* in the following way: AE=I^+,)+(C60)+E)l(C60Hq+(A)-EA(A)-EM The recoil energy EM of a Cw target is negligible. The terms I^'^Ceo) and Iq+ (A) are well known [21]. As in the previous DCT experiments using proton projectiles, it seems fair that no multiexcited state of negative ions populated during the multielectron transfer process should be stable during a time scale longer than the microsecond. Therefore, we take the assumption that to produce stable negative ions, the MCT process occurs directly to the fundamental state. Figure 7 shows the recoil ion spectra when the scattered negative ions F" are selected using F*, F2+ and F3+ projectiles at low velocity (v^.18 a.u.). The yield of negative ion formation found to be close to 10% for F* ions is much larger than the yield obtained using atomic targets estimated to be about 0,1% [17]. The yields in the case of Qo target are rather comparable to those found in ion-surface collisions. Indeed, up to 5% of ions have been found with a negative charge after scattering from a gold surface [22] and up to 90% from a dielectric surface like LiF [23-24]. Therefore, the mechanism of production of negative ions using the CM target should be closer to the case of metallic surface. That is probably due to the similarity between the ionisation potentials of the first electrons of the C^, and the work
578 function of the metal. However it is still astonishing that the yield of formation of negative ions using F3+ projectiles, found to be in the order of 1 %, is so large. Time of Flight spectra of recoil target ions produced by P + impact on Qo in F^+Qo -> F +C60
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Figure 7. Recoil ion spectra in coincidence with the detection of a F scattered ion using P* incident projectiles at a constant velocity of 0.2 a.u.. F>-»F(a); F ^ F f t ) ; F*-»F (c)
In Fig. 7a, the predominant stable C^2* peak shows that in F->F reactions the excitation energy of recoil ions C^2* is very low. Indeed the calculated energy defect of the reaction without excitation of C60 is about -4eV. This reaction is therefore quasi-resonant and it explains the high value for the production of negative ions 7%. Using F2+ ions (Fig. 7 b), stable C603+ ions represent only 20% of the total recoil ions. The other peaks correspond to decay products of hot C603+ ions, Qo-2m3+ i° n s due to C2 evaporation process, Qo4+ ions due to electron evaporation process and fragments Cm+ with medium size due to multifragmentation process. With the assumption that the three captured electrons occupy directly the fundamental states of F", the calculated energy defect of the reaction without excitation of target C603+ is about -32eV. An excitation energy of C^3* around 32 eV is then expected for this reaction under quasi-resonant conditions, which is in good agreement with our observation that 80% of C603+ population carry on further decay process via ionisation or fragmentation. Using F3+ projectiles (Fig. 7c), only medium fragments are observed (C3+-C15+) showing that the C^ ions are produced with higher level of excitation energy. For this reaction, the energy defect without excitation of C^ is estimated to -80 eV. The excitation energy of C^44 is then expected to be around 80 eV close to the threshold of the multifragmentation process. Details of these measurements and discussions about the formation of negative ions will be given in a forthcoming paper.
579 In the Fig. 8a, a typical two dimensional (2D) spectrum of recoil ion TOF versus the electrostatic analyser voltage is presented for F++C60->F+C602+* reaction. Horizontal projection of this 2D spectrum gives the time of flight spectrum of recoil ions (Fig. 8b).
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Fiureg 8. (a): Two-dimensional spectrum for F*"+F reaction; the horizontal axis stands for the TOF of recoil ions and the vertical axis stands for the voltage of the electrostatic analyzer, (b): horizontal projection of the 2D spectrum (a) with a maximum intensity w the small peaks due to the evaporation and multifragmentation processes, (c) and (d): partial vertical projections of (a) associated to the detection of Qo2* (narrow peak) and C,,* (broad peak) respectively.
Partial vertical projections presented in Fig. 8c and Fig. 8d allow to measure the energy loss of projectiles F" related to different decay channels of the target C^2*. The narrow peak associated to stable Ca)2* (Fig. 8c) is measured with a small energy loss corresponding to a low excitation energy of Ex(C6o) ~10eV. On the other hand, the broad peak associated to the detection of a CM+ (Fig. 8d) shows a excitation energy of about 150 eV. The energy loss of scattered projectiles F has been measured for each Cm+ peak. The excitation energy of C602+, the parent ion of these multifragmentation products, has been deduced to be in the range of 80eV to 180 eV for m varying from 15 to 3. These values correspond roughly to the expected values for the multifragmentation process [1] of C w . More precise measurement of excitation energy for evaporation process has been performed for C^2* produced in the reaction H++ Cm-$ H"+ C60z+*. The 2D spectrum of the TOF of recoil ions versus the kinetic energy of the negative projectile ions is shown on Fig. 9a. The TOF spectrum of recoil ions (Fig.9b) is obtained by horizontal projection of Fig. 9a. The series of fullerene ions C60.2m2+ (m=0-3) due to the evaporation process is observed. Partial vertical projections corresponding to Qo2*, C582+, C562+ and C542+ recoil ions (Fig. 9c) are well fitted with gaussian shapes. In this Fig., the intensity scale of the curves are normalised to allow a better comparison in energy loss.
580
Time of flight of recoil ions (ps) Figure 9. (a): Two dimensional spectrum in H*->H" reaction; the horizontal axis stands for the TOF of recoil ions and the vertical axis is calibrated for the kinetic energy of the scattered projectile H". Only the T.O.F. region with doubly charged fullerenes is shown, (b): horizontal projection of the two dimensional spectrum of (a), the number of carbon atoms of the doubly charge fullerenes is given above each peak. (c): Partial vertical projection of each spot associated to the detection of Qo2*, C582\ C562* and Q / * ions showing different energy losses.
A large energy shift of about 40eV is observed between the H" peaks corresponding to stable Cw2+ and the fullerene after the evaporation of one C2, C582+ Smaller shifts are measured between the H" peaks associated to the products of successive evaporation channels, C582+, C562+ and C542+. We can remark on the Fig. 9c that the width of the peak corresponding to stable Qo2* is narrower than the other peaks. From these measurements, taking into account of the instrumental resolution, we have obtained the excitation energy distribution of the C^2* parent ions for each evaporation channel. Figure 10 gives also the comparison between the experimental distributions of excitation energy of Qo2* parent ions and the theoretical distributions obtained with the RRK Model [5] for evaporation channels leading to Css2*, C562+ and C542*.To apply the RRK model, we have used the pre-factor and the dissociation energies of the fullerenes C^^m published recently by the Aarhus group [2]. The shifts between the excitation energy distributions seem to be rather well reproduced but not the absolute values of excitation energies. As observed in other experiments [1-25] the experimental widths are larger than the theoretical widths. This statistical model is probably too simple to take into account precisely the relaxation of the QQ
581
90 i
Intensity 60-
30-
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40
50
60
70
80
90 100
Excitation energy(eV) Figure 10. Comparison between the adjusted experimental Co* parent ion excitation energy distributions (solid-lines) and the theoretical distributions (dash lines) for evaporation channels Qo2* -> C582*+C2,
Conclusion In conclusion, an overview of the main fragmentation processes of highly charged fullerenes and a new method to determine the excitation energies of the parent Cm are presented and discussed. For multicharged C w r+ , charge dependency of different decay channels is illustrated by the measured relative probabilities for stable channel and, evaporation, fission, multifragmentation channels with r ranging from 2 to 9. Detailed information about the relaxation of hot multicharged C^ via the successive emission of a doubly charged fragment or several monocharged even and odd numbered light fragments has been obtained for the CM5+> C^6* and C^ 74 parent ions. The process of the evaporation of Qo2* ions has been studied using the DCT method. By analysing the kinetic energy of scattered negative projectile ions, the excitation energy is measured and it is no longer a free parameter in the RRK model. Better comparison with the statistical model becomes possible. Further investigations using the new method are planned to study the fragmentation processes of highly charged Qo. References 1. 2. 3. 4. 5.
6.
E.E.B.Campbell. and F.Rohmund, Rep.Prog.Phys. 63, 1061(2000). S.Tomita, J.U.Anderson, K.Hansen and P.Hvelplund, Chem.Phys.Lett. 382, 120 (2003). F.Lepine and C.Bordas, Phys.Rev.A 69,053201 (2004). T.Schlatholter, R.Hadjar, R.Hoekstra and R.Morgenstern, P.R.L. 82, 73. (1999). S.Martin L.Chen, R.Bredy, J.Bernard, M.C.Buchet-Poulizac, A.Allouche and J.Desesquelles, PRA 66, 063201 (2002).; S.Martin et al, PRA 62,022707 (2000). R.Vandenbosch, et al., Phys.Rev.Lett. 81, 1821 (1998).
582 7. 8. 9. 10. 11. 12. 13.
14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.
P.W.Fowler, and D.E.Manolopoulos, an atlas of fullerenes (Oxford University Press, Oxford, 1995). L.Chen, S.Martin, R.Bredy, J.Bernard, and J.D6sesquelles, PRA 64, 031201 (2001). L.Chen, S.Martin, R.Bredy, J.Bernard, and J.D6sesquelles, Europhysics Letters 58, 375 (2002); S.Martin accepted in ISSPIC 2004. T.D.Mark and P.Scheier, Nucl.Instrum.Methods, Phys.Res.B 98,469 (1995). G.Herzberg, Spectra of Diatomic Molecules. S.Diaz-Tendero et al, to be published 2005. S.Diaz-Tendero, F.Martin, and M.Alcami, J.Phys.Chem. A 106, 10782 (2002).Spielgmann, private communication. S.Martin, and al., to be published. P.A.Marcos, EPJ D6, 221 (1999). O.Furuhashi et al, Chem. Phys. Letters 337, 97 (2001). J.Appell, Double Electron Transfer and Related Reactions in Collision Spectroscopy, ed. Cooks, Plenum Press (1978). P.G.Fournier, et al. Phys.Rev. A34,1657 (1986). G.W.F.Drake, PRL 24, 126 (1970). T.Andersen, Physics Reports 394, 157 (2004). C.Yannouleos and U.Landman, Chem.Phys.Lett. 217,175 (1994). L.Folkerts and al. PRL 74, 2204 (1995). Auth, C, Borisov, A.G. and Winter, H., PRL 75, 2292 (1995). Borisov, A.G., and Esaulov, V.A., J.Phys. : Condens. matter, 12, R177 (2000). Rentenier, A.et al., J.Phys.B. 37,2429 (2004).
FRAGMENTATION OF COLLISIONALLY EXCITED FULLERENES
M. ALCAMI, S. DIAZ-TENDERO AND F . MARTIN Departamento
de Qumica, C-9, Universidad Autnoma 28049, Madrid, Spain E-mail: [email protected]
de Madrid,
In the present report we show how the combination of different theoretical techniques can help to understand and reproduce the results of collision and fragmentation experiments of fullerenes. Density functional theory can provide values of the energies, structures and vibrational frequencies in good agreement with experimental values. In particular the dependence of the dissociation energies with the fullerene size and the Coulomb stability limit for dissociation have been obtained. These results are the basic ingredients needed in the statistical theories used to describe the fragmentation. The energy deposited in the cluster during the collisional process can also be estimated by theoretical methods allowing a full theoretical description of the collision and fragmentation using first principles
1. Introduction In the last decade considerable attention has been devoted to the study of the stability of fullerenes. Ceo and C70 have been used in collision experiments with ions, electrons and/or short laser pulses1,2. These experiments cover a wide range of energies, from slow collisions with singly charged ions, up to fast collisions with highly charged ones. Different decay modes can compete in the fragmentation process: successive emission of neutral C2, ejection of one or more light charged carbon clusters, or fragmentation into several singly charged carbon clusters with small masses. These three processes are respectively known as sequential evaporation, asymmetric fission and multi-fragmentation. It is now well established that moderately excited fullerenes preferentially decay by emission of a neutral C2, while in those cases where a large energy is deposited in the fullerene, multifragmentation can be observed. Highly charged fullerenes as Cgo", with charges up to g=12, have been also observed when Ceo is exposed to intense laser radiation3. One of the key quantities to achieve a correct description of the frag-
583
584 mentation mass spectra is the dissociation energy of the different fullerenes produced. In the case of neutral and singly charged Ceo the value of this quantity has been a subject of a large debate for many years, and only recently it has been settled down2,4. Also recently, different groups have measured the C2 dissociation energy for a wide range of singly-charged fullerenes (C n for n=40—70) and shows a significant variation as a function of fullerene size 5,6,7 ' 8 . A fundamental question that has been raised9 in recent experiments is how large is the charge a C£+ fullerene can hold without spontaneously dissociating due to Coulomb repulsive forces. For a correct interpretation of these experiments, theory plays an important role as a tool able to reproduce the main experimental findings and to offer an explanation for the observed trends in fullerene stability. In the present report we summarize recent theoretical progress in understanding the experimental findings.
2. Theoretical methods In order to simulate the experiments we can separate the global process into two different steps occurring at different time scales: in the first one, which occurs in the order of femtoseconds, the fullerene is excited by laser pulses or by collisions with ions or electrons, and a certain quantity of energy is deposited in the system. In the second one, this excitation energy is redistributed among the vibrational degrees of freedom, which leads to fragmentation. Therefore fragmentation takes place well after the collision and, in many cases, occurs through a sequential process in which different fragments are emitted at different times. Thus the Time of Flight (TOF) at which the fragments are observed becomes a critical parameter in order to reproduce the experiments. Molecular Dynamics (MD) methods 10 have been used to describe the time evolution of the excited clusters. The atom-atom interactions that govern the nuclear dynamics can be evaluated by means of simple analytical interaction potentials, or by ab initio interaction potentials obtained on the "fly" n . However, previous studies have shown that the dynamical evolution of a complicated many-body system is mainly guided by the accessible phase-space 12. Thus a statistical treatment, which is computationally much cheaper, may explain the outcome of such fragmentation reactions. We have used two different statistical methods to treat the fragmentation process: (i) a sequential evaporation model in which the individual rate constants are obtained within the Weiskoppff theory and (ii)
585
the Microcanonical Metropolis Montecarlo Method (MMMC), which consists in partitioning the mass, charge, total energy, total linear and angular momenta of the system (conserved in the microcanonical approach) among all possible final channels with probabilities governed by considerations of maximum entropy. The details of these two methods have been described elsewhere 13 ' 14 and have been succesfully applied to the description of the fragmentation of small carbon clusters15. It is important to stress that, in the sequential evaporation model the time is explicitly included in the treatment and the fragmentation patterns observed at different TOF values can be predicted. On the contrary, the MMMC method considers the system in internal thermodynamic equilibrium and, therefore, it can only provide information for t = oo. The basic ingredients of these two statistical models are the geometries, the harmonic frequencies and the binding energies of all the fragments. In the MMMC simulations, the rotational constants are also needed. It is important to have all this information for every possible size and charge of the different fragments, in a consistent way. This can be achieved by using density funcional theory (DFT). In particular the hybrid B3LYP functional16 for exchange and correlation has proved to give excellent results in the description of carbon clusters and fullerenes. Fully optimized geometries have been obtained for neutral and charged C n fullerenes for even values of n between 40 and 70 17,18 and for small C n carbon clusters up to size n=12 19 . The harmonic vibrational frequencies have been calculated for selected species. One important aspect to consider in these calculation is the stability of different isomers since in many cases the expected energy ordering based on simplified models is not the correct one. Therefore, for each size and each value of the charge, different isomers have to be taken into account, including non-classical forms, i.e. fullerenes having heptagonal rings or squares in their structures. Also different spin states have to be considered for each species. In order to study the problem of the Coulomb stability, highly charged fullerenes, C£ + , with charges q up to 14, have also been considered for vales of n=70,68,60 and 58. Several important aspects related to structure have been discussed in detail in a series of articles 20 ' 21 ' 22,23 . In the following section we will summarize the most important findings directly related with the fragmentation process.
586
3. Stability of fullerenes 3.1. Dependence with the fullerene
size
Figure 1. Comparison between calculated and experimental C2 dissociation energy as a function of cluster size. Circles: this work. Experimental values: Squares: Barran et al. 5 scaled to Cj|^; triangles up: Laskin et al. 6 ; triangles left: Tomita et al. 7 ; triangles right: Concina et al. 8 .
Figure 1 shows the dissociation energy for C2 emission from singlycharged C+ as a function of cluster size. Experimental values7,8,5'6 are also shown for comparison. The theoretical results follow the same trends as the experimental values. The maximum dissociation energies correspond to magic number fullerenes: C$0, C ^ and C+Q. The great stability of Cg"0 and CT"0 is due to the absence of adjacent pentagons in the cage, which implies low ring strain. In addition, CQ0 is nearly spherical (~I/i symmetry), which provides a surplus of stability. Cj, is the smallest fullerene in which pentagons can be arranged in pairs of adjacent pentagons. Furthermore, in a spherical electronic model of fullerenes, the neutral C50 analogue has a closed electronic shell which results in spherical aromaticity and, therefore, in additional stability 24 ' 21 . These two reasons make C50 and its corresponding cationic partner singular cases in a wide range of sizes: n = 40-58. The lowest dissociation energies correspond to C$2- In this case, the product of dissociation is Cg"0. Therefore it is not surprising that the energy required is smaller than for the other fullerenes. For C62 there are two non classical structures more stable than the classical ones: an isomer containing a square ring 25,26 and the most stable isomer27 which contains an heptagon ring. If the most stable classical isomer of C ^ is considered, instead of the one containing the heptagon, the dissociation energies for Cg"4 and Cg"2 &re, respectively, ~ 1 eV larger and smaller than those shown in Fig. 1. This would deteriorate the agreement with experiment, and points out to the
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non classical structure as the one obtained in the experiments. 3.2. Dependence
with the fullerene
charge
In the case of the multicharged CgJ different dissociation channels can be envisaged. Our previous results28 show that neutral C2 ejection is the channel with lowest dissociation energy for charges lower than 2 (see Fig. 2a). The inset of the figure shows that the C2 dissociation energy exhibits pronounced maxima at q = 0 and 10, which correspond, to the closing of the electronic shells. For charges between q=3 and 6 the lowest energy channel is the asymmetric fission into Cg"8 + C j . For higher initial charges fragmentation into two charged C atoms becomes the most favorable process. This is compatible with the experimental results of Martin et al 29 who have observed that multifragmentation of highly excited Cgo becomes important for q > 6. It can also be seen that for q > 6 fragmentation is already an exothermic process. The fact that higher charges are observed in the experiments is an indication of the existence of fission barriers that prevent fragmentation for q > 6. To evaluate the fission barriers, and therefore, to know the stability upon Coulomb explosion it is necessary to identify the corresponding transition states. This has been done by locating the minima and transitions states corresponding to the last steps of the fission process in the corresponding potential energy surface28,23. The main results are shown in Figure 2b. It can be seen that the fission barrier decreases with q. For q > 14 the barrier
588 disappears and the fullerene dissociates spontaneously.
4. Global treatment of the collision and fragmentation We will consider, as an application, the collision of a particles with Ceo at low impact energies (less than 20 keV) where charge exchange is the dominant process. Previous works for these systems are based on extensions of the classical over-barrier model. The main reason for the absence of more refined theoretical treatments is the large number of active electrons and the existence of many electron processes (such as double charge exchange) that cannot be described in terms of a single electron picture. Also, the large number of nuclear degrees of freedom in Ceo prevents one from obtaining a fully quantum mechanical description of the collision dynamics. Since the collision time is much shorter than the vibrational relaxation we can freeze the cluster geometry during the collision and use a single nuclear degree of freedom: the cluster-projectile distance. The simplest way to implement such an idea is to use the spherical jellium model 30 which can lead to an accurate description of the shell structure for Ceo31 • The ion-cluster electron density is described in terms of single-particle orbitals evaluated with a time-dependent method which makes use of the Kohn-Sham formulation of density functional theory in the local-density approximation with exchange, correlation and a self-interaction correction for the cluster 32 . These orbitals are then used to expand the one-electron time-dependent wave function as in the standard close-coupling method of ion-atom collisions. The collision is treated in the framework of the impact parameter method and expanding the one-electron wave function in a basis of BornOppenheimer (BO) molecular states. The transition probability to a specific final configuration is evaluated by using inclusive probabilities. As shown in Ref.[32], these probabilities can be used to evaluate the energy deposit after the collision. The main limitation of using the jellium shell approach is the impossibility to describe the collision dynamics below the cluster surface. Therefore, the method is only appropriate when electron transfer occurs far outside the Ceo surface. The energy deposit evaluated with this method is given in figure 3a. This energy deposit can be used to model the evaporation of C2 and C j units by using either Weiskopff or MMMC statistical theories. An interesting experimental result is that for an energy deposit of 70 eV (i.e. impact velocity of 0.44 a.u.) no evaporation is observed, although
589
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Figure 3. (a) Energy deposited in the cluster for the single charge exchange process as a function of the velocity, (b) MMMC results, (c) Times required for the appearance of Cj"g using the Weiskpoff method for different values of the energy deposit.
the dissociation energy is only 10 eV. The MMMC method (see figure 3b) predicts that fragmentation is not observed up to an energy deposit of 20.5 eV; this is due to entropic effects. The time-dependent Weiskpoff method (see figure 3c) shows that evaporation requires more than a microsecond, which is a time longer than the TOF of the experiments. This means that, although there is enough energy to produce evaporation, this cannot be seen in the experiments unless a larger TOF is used. More extensive work to consider higher energy deposits is in progress. References 1. E. E. B. Campbell, Fullerene Collision Reactions, 1st ed. (Kluwer Academic Publishers, Dordrecht, 2003). 2. C. Lifshitz, Int. J. Mass Spectr. 198, 1 (2000). 3. V. R. Bhardwaj, P. B. Corkum, and D. M. Rayner, Phys. Rev. Lett. 9 1 , 203004 (2003). 4. S. Matt, O. Echt, P. Scheier, and T. D. Mark, Chem. Phys. Lett. 348, 194 (2001). 5. P. E. Barran, S. Firth, A. J. Stace, H. W . Kroto, K. Hansen, and E. E. B . Campbell, Int. J. Mass Spectrom. 167, 127 (1997). 6. J. Laskin, B. Hadas, T. D. Mark, and C. Lifshitz, Int. J. Mass Spectrom. 177, L9 (1998). 7. S. Tomita, J. U. Andersen, C. Gottrup, P. Hvelplund, and U. V. Pedersen, Phys. Rev. Lett. 87, 073401 (2001).
590 8. B. Concina, K. Gluch, S. Matt-Leubner, O. Echt, P. Scheier, and T. D. Mark, Chem. Phys. Lett. 407, 464 (2005). 9. H. Cederquist, J. Jensen, H. T. Schmidt, H. Zettergren, S. Tomita, B. A. Huber, and B. Manil, Phys. Rev. A 67, 062719 (2003). 10. R. T. Chancey, L. Oddershede, F. E. Harris, and J. R. Sabin, Phys. Rev. A 67, 043203 (200). 11. H. O. Jeschke, M. E. Garcia, and J. A. Alonso, Chem. Phys. Lett. 352, 154 (2002). 12. S. Wearasinghe and F. G. Amar, J. Chem. Phys. 98, 4967 (1993). 13. P. A. Hervieux, B. Zarour, J. Hanssen, M. F. Politis, and F. Martin, J. Phys. B 34, 3331 (2001). 14. S. Diaz-Tendero, P. Hervieux, M. Alcami, and F. Martin, Phys. Rev. A 033202 (2005). 15. G. Martinet, S. Diaz-Tendero, M. Chabot, K. Wohrer, S. D. Negra, F. Mezdari, H. Hamrita, P. Desesquelles, A. L. Padellec, D. Gardes, L. Lavergne, G. Lalu, X. Grave, J. F. Clavelin, P. A. Hervieux, M. Alcami, and F. Martin, Phys. Rev. Lett. 93, 063401 (2004). 16. A. D. Becke, J. Chem. Phys. 98, 5648 (1993). 17. S. Diaz-Tendero, M. Alcami, and F. Martin, J. Chem. Phys. 119, 5545 (2003). 18. G. Sanchez, S. Diaz-Tendero, M. Alcami, and F. Martin, Chem. Phys. Lett. 416, 14 (2005). 19. S. Diaz-Tendero, F. Martin, and M. Alcami, J. Phys. Chem. A 106, 10782 (2002). 20. S. Diaz-Tendero, F. Martin, and M. Alcami, Chem. Phys. Chem. 6, 92 (2005). 21. S. Diaz-Tendero, M. Alcami, and F. Martin, Chem. Phys. Lett. 407, 153 (2005). 22. S. Diaz-Tendero, F. Martin, and M. Alcami, Comp. Mat. Sci. 35, 203 (2006). 23. S. Diaz-Tendero, M. Alcami, and F. Martin, J. Chem. Phys. 123, 184306 (2005). 24. M. Buhl and A. Hirsch, Chem. Rev. 101, 1153 (2001). 25. W. Qian, M. D. Bartberger, S. J. Pastor, K. N. Houk, C. L. Wilkins, and Y. Rubin, J. Am. Chem. Soc. 122, 8333 (2000). 26. W. Qian, S. Chuang, R. P. Amador, T. Jarrosson, M. Sander, S. Pieniazek, S. I. Khan, and Y. Rubin, J. Am. Chem. Soc. 125, 2066 (2003). 27. A. Ayuela, P. W. Fowler, D. Mitchell, R. Schmidt, G. Seifert, and F. Zerbetto, J. Phys. Chem. 100, 15634 (1996). 28. S. Diaz-Tendero, M. Alcami, and F. Martin, Phys. Rev. Lett. 95, 013401 (2005). 29. S. Martin, L. Chen, A. Denis, R. Bredy, J. Bernard, and J. Desesquelles, Phys. Rev. A 62, 022707 (2000). 30. M. Brack, Rev. Mod. Phys. 65, 677 (1993). 31. L. Ruiz, P. Hervieux, J. Hanssen, M. Politis, and F. Martn, Int. J. Quantum Chem. 86, 106 (2002). 32. M. Politis, P. Hervieux, J. Hanssen, M. Madjet, and F. Martn, Phys. Rev. A 58, 367 (1998).
LIFETIMES OF C620 AND C720 DIANIONS IN A STORAGE RING S. TOMITA*, J.U. ANDERSES, B. CONCINA } , P. HVELPLUND, B. LIU, S. BR0NDSTED NIELSEN Department of Physics and Astronomy, University of Aarhus, Aarhus C, DK-8000, Denmark H. CEDERQUIST, J. JENSEN, H.T. SCHMIDT, H. ZETTERGREN Physics Department, Stockholm University, SCFAB, Stockholm, SE-106 91, Sweden O. ECHT Department of Physics, University of New Hampshire Durham, NH 03824, USA J.S. FORSTER Departement de Physique, Universite de Montreal Quebec, H3C 3J7, Canada K. HANSEN Department of Physics, Goteborg University Gothenburg, SE-41296, Sweden B.A. HUBER, B. MANIL, L. MAUNOURY, J. RANGAMA Centre Interdisciplinaire de Recherche Ions Lasers 14070 Caen Cedex 5, France
We have studied the lifetimes of C w and C70 ions in a storage ring. The dianions were produced by electron attachment to the monoanions in a Na vapour cell. In agreement with earlier studies, we find that C7j is stable on a time scale of seconds. However, contrary to the results of earlier experiments, we find that C^ decays on a time scale of milliseconds. The decay is dominated by electron tunnelling through a Coulomb barrier, mainly from thermally populated triplet states about 0.1 eV above the singlet ground state. The electron binding in CM is estimated to be - 0.20 eV, and the lifetime of the ground state is then of the order 20 s.
' Present address: Institute of Applied Physics, University of Tsukuba, Ibaraki 3005-0006, Japan. * E-mail [email protected] ' Present address: Forschungszentrum Karlsruhe, Institut fur Nanotechnologie, D-76021 Karlsruhe, Germany.
591
592 In recent years there has been a great interest in free, doubly charged anions [1,2]. Owing to the electron-electron Coulomb repulsion, atomic dianions are not stable and the binding of two electrons in a molecule depends strongly on its size [3]. The second electron is confined by a Coulomb barrier, and even for negative binding energy the lifetime for tunnelling through this barrier can be very long. The fullerenes are ideal for studying the dependence of the stability of dianions on the size of the molecule, and C{n with 2« > 70 have been produced directly in the gas phase by electrospray [4,5]. These dianions can also be formed by electron attachment to monoanions in a Penning trap [6,7]. The free dianion of Cm is predicted to be at the limit of stability with a small negative affinity for the second electron [8]. This ion has been identified by mass spectrometry in an ion trap after laser desorption of fullerenes from a surface [9,10], and from observation of the survival time of the signal a lifetime of more than 3 min was inferred [9]. However, it has not been possible to create the dianion in a more controlled manner, e.g., by electrospray or by attachment of a free electron to the monoanion. The lowest unoccupied orbitals in C6o are triply degenerate and have t]u symmetry. The coupling of two electrons in t\u orbitals is analogous to the LS coupling of two p electrons in an atom and results in multiplets analogous to the [ 3 S, P, and XD atomic terms. It turns out that the theory of atomic multiplets can be applied to calculate the term splittings and, in accordance with Hund's rules, the energy from Coulomb repulsion between the two electrons is lowest in the triplet states and highest in the singlet S state [11]. The Coulomb energy can be lowered by mixing with orbitals in the neighbouring tig level: the wave functions have opposite parity and hence "hybridised" wave functions may be created by linear combination, which are localised far apart in the molecule. The effect of mixing depends strongly on the energy splitting between the t\u and t\g levels; for the measured optical transition energy -1.3 eV, the triplet level remains lowest but the splitting of the three dianion levels is considerably reduced according to a recent calculation [12]. The electrons are also stabilised by JahnTeller distortions of the molecule and this may change the order of the levels. From electron-spin resonance measurements on C«, ions in solution a singlet ground state with a triplet level about 0.1 eV above has been inferred [13,14]. The interest in the anions of C6o has been spurred by the discovery of superconductivity in C6o based materials at quite high temperatures [15], and there is a need for experiments on isolated C6o anions to provide results which can serve as benchmarks for theory. We have recently measured the near-infrared absorption spectrum for C60 in the gas phase and have proposed an identification of the observed bands [16]. The electronic states of the doubly charged anion are of particular interest in that they reveal the magnitude of the effective gas-phase Coulomb and exchange interactions. We have succeeded in creating beams of C60 with sufficient intensity to allow a study of the lifetime in a storage ring
593
[17]. For comparison, we have also observed C7„ which has been reported to have a lifetime of 80 s in an ion trap at room temperature [5]. As demonstrated in [17], about 30% of a beam of C^ ions may be converted to doubly charged anions by electron capture in collisions with Na atoms in a metal-vapour cell. A simple view of the process is shown in Fig. 1. Compared with attachment of a free electron, the capture of the loosely bound electron in Na is facilitated by the presence of the positive Na ion core which lowers the Coulomb barrier from the negatively charged fullerene. At a distance of about 7A the barrier is so low that the electron can move freely across it. In this way the electron can be captured directly into the ground state or into a very low lying excited state, without much excitation of the molecule. Since the dianion of C6o is close to the limit of stability even in its ground state, this 'cold' capture is decisive for the survival of the ion.
Figure 1. Illustration of over-the-barrier model of electron transfer from Na to C^. At smaller distances the Coulomb barrier between the negative fullerene ions and the Na* core is lowered, and the electron energy levels in the two regions (dashed lines) approach each other [17].
The experiments were carried out at the small storage ring ELISA (Electrostatic Ion Storage Ring, Aarhus) illustrated in Fig. 2 [18]. Singly charged anions of C60 (or C70) were sprayed from a solution of C6o (or C70) and tetrathiafulvalene in toluene and dichloromethane [19]. They were stored for typically 0.1 s in a linear ion trap with a He trapping gas at a temperature between 225 K and 355 K. After ejection from the trap, acceleration to 22 keV, and mass selection with a magnet, ion bunches were passed through a cell containing Na vapour and then injected into ELISA. First, with low Na pressure in the cell, the electrostatic ring parameters were adjusted for optimal storage of singly charged ions. The revolution time was 108.15 us for C^. The pressure in the ring was a few times 10" mbar and for monoanions the storage lifetime was limited by colli-
594
sions with the residual gas to ~10 s. The temperature of the Na cell was then increased and all deflection voltages were reduced by a factor of two to store doubly charged fullerene ions. The main decay channel for the dianions is electron detachment, and the yield of singly charged ions was monitored with a channeltron positioned just after a 10°-deflection plate (Fig. 2). However, here we focus on results obtained with the other detection system. At varying times after beam injection, the stored beam was dumped onto a micro-channel plate (MCP). This is a very sensitive method because all ions are counted, and the decay of a short lived beam can be followed over several orders of magnitude. Channeltron detector j
ton
bunch —•-I
Magnet H
la
MCP detector
Electrospray
Figure 2. Schematic view of the electrostatic storage ring ELISA. Results are shown in Fig. 3. For C70, only a relatively small decrease in the beginning is observed. Our interpretation is that the dianion is stable at room temperature on a time scale of seconds. The small initial reduction of the beam is due to decay of ions that have been excited in collision with residual gas atoms, mainly just after exit from the trap [20]. The depletion is much stronger for the C<5o beams and it depends on the temperature of the trap. The shape of the spectra is straightforward to interpret qualitatively: The decay is dominated by a thermally activated process, presumably electron emission via tunnelling from excited states. The distribution of excitation energy in the ensemble of stored ions is determined by the equilibration with the He gas in the trap, by subsequent excitation in gas collisions just after leaving the trap, and by electron capture into excited states in the Na cell. The distribution has a lower cut off around the energy corresponding to the trap temperature. If the ion is unstable with lifetime r at this temperature, the number of stored ions will decrease exponentially with this lifetime for times / >T. However, the cut off is not sharp, so the distribution
595
Figure 3. Time dependence of the number of ions stored in the ring, measured by dumping the beam onto a microchannel plate with a varying delay after injection. The injected ions were C70 ( • ) and C60, produced by electron transfer to monoanions from a trap with temperatures of 225 K (A) and 300 K (o). The curves for C^ are from simulations with a barrier-penetration model. The full drawn curves include absorption (and emission) of thermal radiation.
has a tail towards lower energies where only the ground state is populated. Hence, if the ground state lifetime is long, there should be a small fraction of quite stable molecules, as is indeed observed. A more complete presentation of the data and a detailed analysis will be published elsewhere [21]. Here we introduce the main ingredient in the analysis, the Coulomb barrier. The second electron in the dianion is confined by this barrier, as illustrated in Fig. 4, and the lifetime of states with positive energy is determined mainly by the probability for tunnelling through the barrier. The effective potential has three components, the electrostatic repulsion from a charge -e at the centre, an attraction due to polarisation of the anion, and a repulsive angular-momentum barrier corresponding to / =1. We treat the anion as a conducting sphere with radius R= 4.5 A, corresponding to a polarisability, a=R3, which is -15% larger than for neutral C^ [22]. The polarisation potential may then be obtained from a standard calculation of image charges,
r
2r2(r2-R2)
r2
596 1,6
Potential barrier for emission o f / = 1 electron from C.
1,4 —
1,2
&
1,0
>
Vibrationally assisted tunnelling
5" 0,8 0,6 3
P0,4
1
S
Tunnelling from thermally jlated excited state
0,2 0,0 0
10
20
30
40
50
60
70
80
90
r(A) Figure 4. Coulomb barrier for l=\ (Eq. 1). Channels for tunneling are indicated by arrows.
where ao=0.53 A is the Bohr radius. An electron with positive energy E can tunnel through the barrier with a rate given in the WKB approximation by (2)
k = vexp(-W),
W=-
\r2J2m(V(r)-E)dr
where the limits of the integral are the classical turning points. A rough estimate of the attempt frequency v can be obtained from the uncertainty principle, v » h/mR2 = 6 l O ' V . However, this value should probably be reduced considerably due to a poor match of an emitted /?-wave to a bound state with strong /=5 character [8], and in the modelling we have used the value v = 3-1013s"' [21]. In solution the ground state of C M is found to be singlet, with a thermally populated triplet level about 0.1 eV above [13,14]. We have carried out near2-
infrared spectroscopy on stored C60 ions and from the great similarity to spectra for ions in solution we conclude that the ground state is singlet also in the gas phase [23]. From the modelling, electron tunnelling via thermal population of the triplet level is found to dominate the decay, and the observed dependence on the trap temperature is in good agreement with a separation of about 0.1 eV from the ground state. At high temperatures there is a strong contribution from vibrationally assisted tunnelling (hot band emission). The curves in Fig. 1 are from this modelling, with lifetimes of ~10 s for the ground state at +0.2 eV relative to the monoanion and a free electron, and ~1 ms for the triplet states with ~0.1 eV higher energy. To describe the decay for the lower trap tempera-
597 ture it is seen to be important to include heating by the blackbody radiation in the ring. Our findings are in good agreement with theoretical estimates and consistent with results obtained for dianions in solution. Also, there is agreement with earlier observations on gas-phase dianions of C70. However, there is a puzzling discrepancy from the early observations of quite stable C60 ions in ion traps [9,10]. Our finding that the decay is dominated by electron tunnelling via thermal population of the triplet level suggests that a possible explanation might be an influence of the strong magnetic field in these traps on the coupling between the singlet and triplet states. Acknowledgements This investigation was supported by a grant from the Danish National Research Foundation to the research centre ACAP (Aarhus Centre for Atomic Physics). The collaboration was initiated by the European network LEIF, contract HPRICT-1999-40012, and has been supported also by the EU Research Training Network, contract HPRN-CT-2000-0002. It is a pleasure to acknowledge Robert N. Compton for discussions. References 1. M.K. Scheller, R.N. Compton, and L.S. Cederbaum, Science 270, 1160 (1995). 2. X.-B. Wang and L.-S. Wang, Nature 400, 245 (1999). 3. L.-S. Wang, C.-F. Ding, X.-B. Wang, and J.B. Nicholas, Phys. Rev. Lett. 81, 2667 (1998). 4. G. Khairallah and J. B. Peel, Chem. Phys. Lett. 296, 545 (1998). 5. O. Hampe, M. Neumaier, M.N. Blom, and M. Kappes, Chem. Phys. Lett. 354, 303 (2002). 6. A. Herlert, R. Jertz, J.A. Otamendi, A.J.G. Martinez, and L. Schweikhard, Int. J. Mass Spectrom. 218, 217 (2002). 7. J. Hartig, M.N. Blom, O. Hampe, and M. Kappes, Int. J. Mass Spectrom. 229, 93 (2003). 8. W.H. Green, Jr., S.M. Gorun, G. Fitzgerald, P.W. Fowler, A. Ceulemans, and B.C. Titeca, J. Phys. Chem. 100, 14892 (1996). 9. P.A. Limbach, L. Schweikhard, K.A. Cowen, M.T. McDermott, A.G. Marshall, and J.V. Coe, J. Am. Chem. Soc. 113, 6795 (1991). 10. R.L. Hettich, R.N. Compton, and R.H. Ritchie, Phys. Rev. Lett. 67, 1242 (1991). 11. M.C.M. O'Brien, Phys. Rev. B 53, 3775 (1996). 12. A.V. Nikolaev and K.H. Michel, J. Chem. Phys. 117,4761 (2002).
598 13. P.R. Trulove, R.T. Carlin, G.R. Eaton, and S.S. Eaton, J. Am. Chem. Soc. 117,6265(1995). 14. C.A. Reed and R.D. Bolskar, Chem. Rev. 100, 1075 (2000). 15. M. Capone, M. Fabrizio, C. Castellani, and E. Tosatti, Science 296, 2364 (2002). 16. S. Tomita, J.U. Andersen, E. Bonderup, P. Hvelplund, B. Liu, S. Brandsted Nielsen, U.V. Pedersen, J. Rangama, K. Hansen, and O. Echt, Phys. Rev. Lett. 94, 053002 (2005). 17. B. Liu, P. Hvelplund, S. Brandsted Nielsen, and S. Tomita, Phys. Rev. Lett. 92, 168301 (2004). 18. S.P. Mailer, Nucl. Instrum. Meth. A 394, 281 (1994). 19. J.U. Andersen, J.S. Forster, P. Hvelplund, T.J.D. Jargensen, S.P. Mailer, S.B. Nielsen, U.V. Pedersen, S. Tomita and H. Wahlgreen, Rev. Sci. Instrum. 73, 1284 (2002). 20. J.U. Andersen, H. Cederquist, J.S. Forster, B.A. Huber, P. Hvelplund, J. Jensen, B. Liu, B. Manil, L. Maunoury, S. Brandsted Nielsen, U.V. Pedersen, H.T. Schmidt, S. Tomita, and H. Zettergren, Eur. Phys. J. D 25, 139 (2003). 21. S. Tomita, J.U. Andersen, H. Cederquist, B. Concina, O. Echt, J.S. Forster, K. Hansen, B.A. Huber, P. Hvelplund, J. Jensen, B. Liu, B. Manil, L. Maunoury, S. Brandsted Nielsen, J. Rangama, H.T. Schmidt, and H. Zettergren, to appear in J. Chem. Phys. 07 Jan. 2006. 22. M.R. Pederson and A.A. Quong, Phys. Rev. B 46, 13584 (1992). 23. J.U. Andersen, E. Bonderup, O. Echt, K. Hansen, P. Hvelplund, B. Liu, S. Brandsted Nielsen, J. Rangama, and S. Tomita, to be published.
CLUSTERS AND CLUSTERS OF CLUSTERS IN COLLISIONS B. MANIL, V. BERNIGAUD, P. BODUCH, A. CASSIMI, 0 . KAMALOU, J. LENOIR, L. MAUNOURY, J. RANGAMA AND B.A. HUBER Centre Interdisciplinaire de Recherche Ions Lasers - CEA-CNRS-ENSICAEN (CIRIL) Bv. Henry Becquerel, BP5133, F-14070 Caen Cedex 05, France J. JENSEN, H.T. SCHMIDT, H. ZETTERGREN, AND H. CEDERQUIST Physics Department, Stockholm University, S-106 91 Stockholm, Sweden S. TOMITA AND P. HVELPLUND Department for Physics and Astronomy Aarhus, University DK-8000 Aarhus C, Denmark
ofAarhus
F. ALVARADO, S. BARI, A. LECOINTRE AND T. SCHLATHOLTER KVI Atomic Physics, Rijksuniversiteit Groningen, Zernikelaan 25, NL-9747AA Groningen, The Nertherlands Pure and mixed clusters of fullerenes (CM and C70) as well as of nucleobases have been produced within a cluster aggregation source and have been multiply ionised in collisions with highly charged ions. Multiply charged clusters and the corresponding appearance sizes have been identified for charge states up to q=5. In the fullerene case, the dominant fragmentation channel leads to the emission of singly charged fullerenes. Furthermore, it is concluded that the fullerene clusters, which in their neutral state are insulators, bound only by weak van der Waals forces, become conducting as soon as being multiply charged. Thus, the excess charges turn out to be delocalised. This phenomenon is explained by a rapid charge transfer to neighboured fullerene molecules well in agreement with predictions of the conducting sphere model. In the case of biomolecular clusters, it is found that the aggregation probability varies strongly for different nucleobases. In some cases the cluster distributions show strong variations due to possible shell effects. In the case of mixed biomolecular clusters a strong enhancement is observed for those clusters containing a so called Watson-Crick pair, for example a dimer of thymine and adenine.
I. Introduction Collisions between ions and clusters, in particular fullerenes like C^ or C70, have been studied since more than 20 years and many specific properties and dynamic processes occurring within these clusters have been studied. Among these, multi-electron processes [1-3], the stability of the complex system with respect to an excess charge [4-11], instabilities and different modes of fragmentation [3,12-16], phase transitions [17] as well as the phenomena of energy sharing and repartitioning between the electronic and vibrational systems [18,19] should be mentioned. More recently, larger systems like clusters of fullerenes [20-22] or clusters of biomolecules [23,24] have attracted an increased interest as they allow to study the structure and the behaviour of systems which are composed of large, structured building blocks including different types of bindings. Thus, questions related to electronic communication between individual structures, to the
599
600
mobility or delocalisation of charges within the whole system, to the preference of certain geometrical arrangements and, in the case of different molecular components, to the molecular recognition during cluster formation are to be addressed. Concerning clusters of fullerenes, the first experiments have been performed by the group of T.P. Martin et al. [20] proving the icosahedral structure for these singly and doubly charged van der Waals-type clusters and the occurrence of magic numbers (13, 55 as well as 19, 23, 27,...). More recently, it was shown by theory [25] that depending on the internal energy also close-packed and decahedral structures become possible. Furthermore, it was shown by the experiment [21 ] that C6o and C70 molecules are rather equivalent, not changing the properties of mixed clusters essentially. The binding energy of a neutral dimer is of the order of 265 meV and the centre-centre distance amounts to about 10 Angstrom. In relation with radiation damage studies, collision processes between slow ions and molecules of biological interest have been studied on a molecular level [2628], however, due to experimental difficulties these experiments have been limited so far to smaller molecules. More recently, charged clusters of amino acids have been produced with the aid of an electrospray ion source [23,24], Collision induced dissociation experiments showed magic numbers and in the case of protonated serine clusters a strong chiral recognition effect has been reported [24]. In the present contribution we will discuss some recent results concerning pure and mixed clusters of fullerenes and clusters of nucleobases. In particular, we will address the aspects of charge stability, of appearance sizes for multiply charged systems and of the occurrence of shell effects. In addition, we will discuss in the case of fullerene clusters the phenomenon of charge mobility, whereas for biological clusters the difference in the aggregation probability will be investigated. II. Experiment Neutral clusters of fullerenes and of nucleobases are produced in a cluster aggregation source [22]. A powder of C6o (C70) or of nucleobases is heated in an oven to a given temperature (fullerenes between 500 and 570 °C; nucleobases between 150 and 230°C). For the production of mixed clusters two ovens can be heated and controlled separately. When leaving the oven, the vapour enters a region of cold He-gas (p~10 mbar, T~77 K) where condensation and cluster formation occurs. The formed clusters leave the source region through a 2 mmaperture and pass several differential pump stages before interacting with a
601 beam of highly charged ions. The neutral cluster distribution contains monomers, dimers and larger clusters. Clusters containing up to 50 molecules have been observed for optimum temperature and He-pressure. Highly charged ions are produced in an ECR ion source. Typically the ion beam is accelerated to a voltage of 10 or 20 kV before it intercepts the cluster beam at the object point of a linear time-of-flight mass spectrometer. The ion beam is pulsed with a repetition rate of several kHz and a pulse width of 1 to 10 us. The ionised clusters and the charged fragments formed during the ion-cluster collisions are extracted perpendicular to the two beams with a voltage of ~7 kV over a distance of 14 cm and their mass/charge ratio is determined with a 1 meter-linear Wiley-McLaren type spectrometer. The extraction voltage is pulsed (pulse length is of the order of 60 us) and synchronised with the ion beam pulse. After passing the field free drift region the ions are post-accelerated towards a conversion plate (-25 kV) in order to increase the detection efficiency. The secondary electrons emitted from the conversion plate are focused on a channelplate detector, the pulses of which are treated in a multi-hit TDC (timeto-digital converter) on an event-by-event basis. Thus, spectra for a given number offragments(stops or multiplicity) can be analysed separately allowing the classification of the type of collisions (distant and close). HI. Clusters of fullerenes A typical mass spectrum obtained in collisions of Xe3(H ions with neutral fullerene clusters is shown in Fig.l. The upper part shows the cluster distribution, the lower one the fragment spectrum with sizes equal or below the fullerene monomer. As a mixture of C6o and C70 (5%) is used, in addition to the dominant (C6o)n+'2+ peaks, contributions from mixed ((C6o)n(C7o)i,2) + ' 2+ clusters are present as well (see Fig.la). A more detailed analysis shows that (meta)stable clusters are formed in charge states up to q=5, the corresponding appearance sizes are found to be surprisingly low taking into account the low binding energy in the van der Waals cluster («app = 5, 10, 21 and ~33 for q=2, 3, 4 and 5). In particular, they are much lower than those reported earlier obtained by using laser ionisation and for other types of van der Waals clusters. Furthermore, when deconvoluting the intensities for a given charge state, shell effects are clearly observed as reported earlier [20]. In particular, the intensities for «=13 and «=19 indicate geometrical shell closures. This property is present not only for pure (C6o)n3+ clusters, but also for the mixed ((C6o)n-iC7o)3+ species. Thus, we may conclude that the size difference is less important during the aggregation process, at least when the number of included C70 molecules is small.
602
time-of-flight (channel)
Figure 1: Fullerene clusters and fragments ionised in collisions with Xe3<* projectiles at a collision energy of 600 keV. Upper part (la): Intact pure and mixed clusters in the size range up to n=10 for q=\ ; lower part (lb): Fragment spectrum, containing single, doubly and triply charged monomers, those which have lost C2 units and small carbon clusters.
In order to analyse the fragmentation pattern of unstable multiply charged clusters of fullerenes we show in Figure 2 the two-particle correlation, i.e. we select events where two charged particles have been detected. The time of flight of the first detected ion is shown on the horizontal axes (selected for C60q+ in different charge states, see notation on the top), the time-of-flight of the second ion is plotted on the vertical axes (see notation on the right-hand side). We find that larger fullerene cluster ions are only correlated with singly charged fullerene monomers (C6o*)- Multiply charged fullerenes are only correlated with other monomers: C«)2+ mainly with C702+ and C6o+, C6o3+ with C703+ and C6o2+ and C6u4+ mainly with C704+ and C6u3+. Therefore, we identify these products as due to the fragmentation of multiply charged dimers, where symmetric charge separation is favoured. The fact that only singly charged monomers are correlated with larger clusters might not be as astonishing as the initial charge was lower or equal to 3 (with the exception of the dimer case). However, when spectra for higher multiplicities are analysed, i.e. clusters in higher charge states are studied, also only singly charged fragments are observed. As an example, Figure 3 shows the fragmentation spectrum for events where 12 singly charged fragments are observed. This fact as well as the small widths of the small sized fragments can only be explained when the 12 charges have been well distributed over the
603 entire cluster of fullerenes. In fact, this behaviour can be explained within the conducting sphere model [29,30]. The corresponding calculation of the critical distances for electron transfer between two fullerenes yields values which are always larger than the equilibrium distance in the cluster of 19 a.u. as soon as it is charged. Hence an isolating neutral fullerene cluster becomes conducting as soon as it is more than doubly charged. < c 6<>>:
n= 7 6 5 4 3 2 4000
staStei 1170
iliJJaJlKm^^iM^'i
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time-of-flight of first ion (channel)
Figure 2: Two-particle correlation between charged fullerene monomers and larger fullerene clusters. The first ion is identified on the top, the second one on the right hand side.
15
45 number of carbon atoms
Figure 3: Fragmentation spectrum containing events where 12 ions have been detected in correlation (12-stop spectrum). An analysis shows that the correlation exists among the light fragments (<30) as well as among the heavier particles. Thus both groups result from collisions with different impact parameters.
604
IV. Clusters of nucleobases In contrast to earlier studies, where protonated clusters are formed in an electrospray solution, we produce neutral clusters of nucleobases by gas aggregation at low temperatures. They are softly multiply ionised in distant collisions with slow multiply charged ions. Figure 4 shows as an example a spectrum of cytosine clusters obtained in collisions with 50 keV 0 5+ projectiles. 5000
1000
1000
2000
3000
4000
time-of-flight (channels)
Figure 4: Time-of-flight spectrum of Cytosine clusters, ionised by 0 5+ ions at 50 keV.
The cluster sizes reach out to n ~ 60, in addition to singly charged species clusters in charge states up to q=4 are identified. The appearance sizes are higher than in the case of fullerenes, they amount to 12, 27 and 54 for charges of 2, 3 and 4, respectively. These values depend on the nucleobase. They are somewhat larger (napp ~ 14 or 15 for q=2) for adenine and guanine where the aggregation probability and stability is rather low. Under similar source conditions only small cluster sizes (n<10) are obtained in the latter cases. Differences are also observed with respect to the smoothness of the cluster distributions. Whereas in some cases a rather smooth intensity distribution is obtained, uracil (see Fig.5) exhibits strong minima and maxima which are probably related to the limitations for possible geometrical cluster structures. These observed variations do not depend on the ionising projectile and, therefore, are thought to arise from the aggregation process. We have also analysed the formation of mixed clusters containing different nucleobases. In the case of adenine and thymine the most prominent mixed cluster contains one adenine-thymine pair, more or less independent of the relative vapour pressure in the cluster source. Similar results are obtained for
605
uracil/adenine, but not for cytosine/adenine. Whether these results can be linked to the formation of Watson-Crick pairs has to be clarified in future experiments. O2* (20keV) + Uracil clusters
5
10
15
20
Figure 5: Distribution of singly charged uracil clusters. The integrated intensity has been corrected for background and contributions of double charged clusters.
Acknowledgments : The authors acknowledge thefinancialsupport received by the European network LEIF (HPRI-CT-1999-40012), the ESF program COST (P9) and the French/Dutch programs Van Gogh (08415QC) and IN2P3/FOM. References: 1. S.Martin, R. Br6dy, J. Bernard, J. Desesquelles, and L. Chen, Phys. Rev. Lett. 89, 183401 (2002) 2. S. Martin, J. Bernard, L. Chen, A. Denis, and J. Desesquelles, Eur. Phys. J. D 4, 1 (1998) 3. S. Tomita, H. Lebius, A. Brenac, F. Chandezon, and B.A. Huber, Phys. Rev. A 65, 053201 (2002) 4. P. Scheier and T.D. Mark, Phys. Rev. Lett. 73, 54 (1994) 5. Jian Jin, K. Khemliche, and M.H. Prior, Phys. Rev. A 53, 615 (1996) 6. A. Brenac, F. Chandezon, H. Lebius, A. Pesnelle, S. Tomita, and B.A. Huber, Physica Scripta, T80, 195 (1999) 7. F. Chandezon, S. Tomita, D. Cormier, P. Grubling, C. Guet, H. Lebius, A. Pesnelle and B.A. Huber, Phys. Rev. Lett. 87, 153402 (2001) 8. V.R. Bardwaj, P.B. Corkum, and D.M. Rayner, Phys. Rev. Lett. 91,203004 (2003) 9. S. Diaz-Tendero, M. Alcami and F. Martin, Phys. Phys. Rev. Lett. 95, 013401 (2005)
606
10. J.Jensen, H. Zettergren, H.T. Schmidt, H. Cederquist, S. Tomita, S.B. Nielsen, J. Rangama, P. Hvelplund, B. Manil, and B.A. Huber, Phys. Rev. A 69, 053203 (2004) 11. H. Cederquist, J. Jensen, H.T. Schmidt, H. Zettergren, S. Tomita, B.A. Huber, and B. Manil , Phys. Rev. A 67,062719 (2003) 12. F. Chandezon, C. Guet, B.A. Huber, D. Jalabert, M. Maurel, E. Monnand, C. Ristori and J.C. Rocco, Phys. Rev. Lett. 74, 3784 (1995) 13. H. Shen et al, Phys. Rev. A 52, 3847 (1995) 14. A. Langereis, J. Jensen, A. Fardi, K. Haghighat, H.T. Schmidt, S.H. Schwartz, H. Zettergren, and H. Cederquist, Phys. Rev. A 63,062725 (2002) 15. L.Chen, B. Wei, J. Bernard, R. Br6dy and S. Martin, Phys. Rev. A 71, 043201 (2005) 16. S. Martin, L. Chen, A. Denis, and J. D&esquelles, Phys. Rev.A 57,4518 (1998) 17. F. Rohmund, E.E.B. Campbell, O. Knospe, G. Seifert, and R. Schmidt, Phys. Rev. Lett. 76, 3289 (1996) 18. J.Opitz, H. Lebius, S. Tomita, B.A. Huber, A. Bordenave-Montesquieu, D. Bordenave-Montesquieu, P. Moretto-Capelle, U. ReinkSster, U. Werner, H.O. Lutz, A. Niehaus, M. Benndorf, K. Haghighat, H. T. Schmidt, and H. Cederquist: Phys. Rev. A 62, 022705 (2000) 19. T. Kunert and R. Schmidt, Phys. Rev. Lett. 86, 5258 (2001) 20. T.P. Martin, U. Naher, H. Schaber, and U. Zimmermann, Phys. Rev. Lett.70, 3079 (1993) 21. K. Hansen, R. Muller, H. Hohmann, and E.E.B. Campbell, Z. Phys. D 40, 361 (1997) 22. B. Manil, L. Maunoury, B.A. Huber, J. Jensen, H.T. Schmidt, H. Zettergren, H. Cederquist, S. Tomita, and P. Hvelplund, Phys. Rev. Lett. 91, 215504(2003) 23. R.G. Cooks, D. Zhang, K.J. Koch, F.C. Gozzo, M.N.Eberlin, Anal. Chem 73, 3646 (2001) 24. B. Concina, P. Hvelplund, B. Liu, A.B. Nielsen, S. Bremdsted Nielsen, J. Rangama, and S. Tomita, JASMS, submitted (2005) 25. J.P.K. Doyle, D.J. Wales, W. Brantz, and F. Calvo, Phys. Rev. B 64, 235409 (2001) 26. J. de Vries, R. Hoekstra, R. Morgenstem, and T. Schlatholter, J. Phys. B 35, 4373 (2002) 27. B. Manil, H. Lebius, B.A. Huber, D. Cormier, and A. Pesnelle, Nucl. Instr. Methods Phys. Res. B 205, 666 (2003) 28. J. de Vries, R. Hoekstra, R. Morgenstem, and T. Schlatholter, Phys. Rev. Lett. 91,053401(2003) 29. H. Zettergren, H.T. Schmidt, H. Cederquist, J. Jensen, S. Tomita, P. Hvelplund, H. Lebius, and B.A. Huber, Phys. Rev. A 66,032710 (2002) 30. H. Zettergren, J. Jensen, H. T. Schmidt, and H. Cederquist, EJPD 29, 63 (2004)
FRAGMENTATION OF SMALL CARBON CLUSTERS
M.Chabot1, F.Mezdari2, G.Martinet1, K.Wohrer-Beroff2, S.Della Negra1, P.Desesquelles1, H.Hamrita1, A.LePadellec3, L.Montagnon3,
Hnstitut de Physique Nucleaire, IN2P3-CNRS, F-91406 Orsay Cedex, France Laboratoire des Collisions Atomiques et Moleculaires (LCAM, UMR Universite Paris Sud et CNRS, N° 8625), F-91405 Orsay Cedex, France 3 IRSAMC, Universite Paul Sabatier 31062 Toulouse Cedex 4, France 2
Introduction: Small carbon clusters are present in various media, flames, plasmas as well as in the interstellar medium. They are building blocks of larger systems such as fullerenes and carbon nanotubes extensively studied for fundamental interest and potential applications. They have been observed, mostly as neutrals or cations, in the fragmentation of these large systems. Their structural properties have been the subject of numerous works [1]. Still, their stability properties with respect to a high degree of internal excitation and/or charge are largely unknown. Indeed, most of the fragmentation studies refer to the case of low excited states created by photofragmentation [2] or collision induced dissociation [3]. In these studies the ionic fragments only are detected so that a partial information is derived. We present in this paper fragmentation patterns of excited Cnq+ clusters created in Cn+-He collisions in high velocity collisions (n<10, q<4). Thanks to recent experimental developments on the fragment detection system [4], all neutral or charged fragments are separately identified, allowing to resolve all fragmentation channels. Highly excited species are created in these experiments either by charge exchange (q=0), electronic excitation (q=l) or ionization (q=2,3,4). Using the results of a statistical fragmentation theory [5], it is possible to extract from the fragmentation patterns the energy deposited in the cluster by the various processes. This will bring new information on electronic processes in these complex atomcluster collision systems.
Experimental set-up: The experiments were done at the Tandem accelerator (Institut de physique Nucleaire, Orsay) with Cn+ ionic carbon clusters (n<10) of 2nMeV kinetic energy 607
608
(constant velocity of 2.6 a.u). The experimental set-up has been described previously [6]. With seven silicium detectors operating in coincidence and suitably placed, all neutral, singly, doubly and triply charged fragments were intercepted. In standard operation of these detectors, charge signals are recorded, which provides the total kinetic energy of the fragments hitting the detector, that means, the total mass of the fragments. Recently, we showed that the analysis of the transient currents delivered by the detectors could be used to determine the number of fragments hitting the detector and the mass of each fragment [4]. This technique is illustrated in figure 1 for the case of neutral fragments emitted in C10+ -He collisions and all impinging on a single detector placed along the beam axis. This technique has been applied to all detectors of charged fragments as well, which allowed to measure all fragmentation channels [7].
i
6
12 Energy (Mev)
Figure 1: Two-dimensional representation of current signals for neutral clusters created in Cio+ +He collisions. The integral of the current signal is given in abcissa and the peak amplitude in ordinate. Fragmentation of neutral clusters: In the figure 2 are presented the measured branching ratios of fragmentation of Cn clusters in a given number of fragments Nf (Nf=l to n, n=5-10). Quite similar fragments distributions are obtained for all n values, in particular a dominance of two-fragments probability, in accordance with previous results on n=3,4 [6]. This indicates quite similar internal energy distributions of excited C„, as discussed below. An odd-even oscillation is observed on dominant channels (see figure 3) that may be explained by odd-even oscillations on the dissociation energies [5]. Inside a given number of fragments, branching ratios for the various channels are inversely proportional to the apparition energy of the channel (see figure 4).
609 BR(%)
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5678910 5 6 7 8 9 10 5 6 7 8 9 10 Cluster size Cluster size Cluster size Figure 3: Evolution of the measured branching ratios with the cluster size for intact, two and three fragments emission. 2 fragments.
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Figure 4 :Measured branching ratios for various channels of C9 within a given number of fragments This behaviour is compatible with statistical fragmentation approaches. The Microcanonical Metropolis Monte Carlo (MMMC) statistical fragmentation theory,
610 based on quantum chemistry calculations, has been used to interpret these data. In the figure 5 are reported an example of calculated branching ratios as a function of the internal energy for C9. As explained in [8], the fit of experimental branching ratios with the calculated branching ratios using relation (1) allowed to determine the energy distributions D(E) of Cn clusters after the collision. These energy distributions were found to be almost independent of n. We assumed a single energy distribution associated to the charge transfer process for n=5,7,9 that was derived from the best fit of all branching ratios RB(Nf) following relation (2). (1) (2)
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Figure 5 (left): Theoretical branching ratios as functions of the cluster excitation energy predicted by the MMMC theory for C9. For all partitions (down), summed in number of fragments (up) Figure 6 (right): Branching ratios for de-excitation of C5> C7, C9. Full circles :experiment; open squares xonvolution of the theoretical branching ratios (MMMC) with the energy distribution shown in figure 7. In (2), D(E) is the sum of the cluster energy before the collision D(E)ENT (which is known, slightly increasing with n [7]) and the energy associated to the charge transfer process D(E)CT- In the figure 6 is reported the comparison between experimental and calculated branching ratios using the best fit of D(E)cr. which is presented in the figure 7. It is seen that the agreement between experimental and
611 calculated branching ratios is quite good. The D(E)CT distribution provides the energy deposited by charge transfer in Cn clusters. The component at higher energy is attributed to charge transfer process accompanied by electronic excitation. Indeed the position of the peak, as well as its relative intensity, both estimated using the IAE (Independent atom and electron model) supports this interpretation [9].
Single process : capture
Energy (ev) Figure 7: Energy distribution of excited Cn which fits the experimental branching ratios Fragmentation of monocharged C„+ clusters: In the figure 8 are presented the measured branching ratios of fragmentation of C„+ clusters in a given number of fragments Nf for n=5-10 and Nf=2 to n (only the dissociative part of electronic excitation is measured in the experiment). Contrary to the case of neutrals, we have a calculation of the energy deposited by electronic excitation which may be tested through the fragmentation pattern. The energy deposited by electronic excitation is calculated using the IAE model and the Classical trajectory Monte Carlo Method (CTMC) for the calculation of the energy deposited in individual carbon atoms [7,10]. In this model, the energy deposit is continuous, lower and higher limits for excitation of 2s and 2p electrons in carbon atoms corresponding to the energy of the first observed transitions and ionization potentials. Since first transitions [11] are above the dissociation energy of C„+ clusters, the whole calculated electronic excitation is dissociative, then comparable to the experiment. In the figure 9 is shown the internal energy of C5+ due to electronic excitation (IAE distribution convoluted with the energy of Cs+ before the collision). The first peak (-14 eV) corresponds to excitation of 2p electrons, the second (-20 eV ) to excitation of 2s electrons and the higher energy tail to double excitation processes. This energy distribution is superimposed to MMMC breakdown curves calculated for C5+ that will be used, following equation (2), to derive theoretical branching ratios RBfl,(Nf).
612 50-
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Figure 8: : Measured distributions of fragmentation into a given number of fragments for monocharged Cn+ clusters A comparison between measured and calculated branching ratios is presented in the figure 10. The agreement is not good, but a slight shift of the IAE distribution towards higher energy (+2eV) allows the dominant channels to be well reproduced. Nevertheless, there is still a lack of probability in the calculated energy distribution in the four fragments region. This result points out the occurrence of higher energy transitions in the cluster, due to more bounded molecular states ( for instance the 2s binding energy is 19 eV in the carbon atom as compared to a 22-28eV band for o electrons in C5 [12]) which are not present in the atomic model. 2Fj,
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613 Fragmentation of multicharged Cnq+ clusters (q>2): In the figure 11 is reported a two-dimensional representation of measured branching ratios of Cnq+ clusters for n=5-10. We see that the distributions are very similar for n=7-10 with a dominance of respectively, two, four/five and seven fragments for q=2s3,4. As dissociation energies are slightly increasing with n (case of doubly ionised clusters [13]), this would indicate a slightly higher internal energy for higher n clusters due, for a part, to ionization in deeper bound inner valence a states. For the case of n=5s6 there is a limitation at 5 and 6 of the number of emitted fragments and it would be necessary to look at the kinetic energy of the fragments to have a complete energetical balance. Calculations of molecular dynamics, taking into account the coulombic energy barriers and currently performed on those systems [14], will help to interpret these data.
Figure lis Two-dimensional representation of measured branching ratios in a given number of fragments (ordinate) as a function of the charge q (abscissa) for Cnq* clusters, e=5 to 10.
614 References: [I] Van Orden A. and Saykally RJ.Chem.Rev. 98 (1998) 2313 [2] Geusic M.E. et al J.Chem.Phys. 84 (1986) 2421 ; Choi H. et al J.Phys.Chem. 104 (2000) 2025 [3] McElvany S.W. at al J.Chem.Phys.86 (1987) 715 ; Lifshitz C. et al Int.J.Mass.Spectr.Ion.Proc. 93 (1989) 149 [4] Chabot M. et al NuclJnstr.Meth.B 197 (2002) 155 [5] Diaz-Tendero S. et al Phys.Rev.A 71 (2005) 033202 [6] Wohrer K. et al J.Phys. B. At.Mol.Opt.Phys. 33 (2000) 4469 [7] Mezdari F. Thesis Universite Pierre et Marie Curie (2005), unpublished [8] Martinet G. et al Phys.Rev.Lett. 93 (2004) 063401 [9] M.Chabot et al (to be published) [10] F.Mezdari et al ArXiV physics/0410008 (2004) [II] C.E.Moore Atomic Energy Levels National Bureau of Standards (1971) [12] Ohno M. et al J.Chem.Phys. 106 (1997) 3258 [13] Diaz-Tendero S.et al J.Phys.Chem. A 106 (2002) 10782 [14] L.Montagnon, F.Spiegelman, to be published
Acknowledgments: The authors thank S.Diaz-Tendero, M.Alcami, P.A.Hervieux and F.Martin for the theoretical support and helpful discussions.
COLLECTIVE EXCITATIONS IN COLLISIONS OF P H O T O N S AND ELECTRONS W I T H METAL CLUSTERS AND FULLERENES
A. V. SOLOV'YOV * Frankfurt Institute for Advanced Studies, Max-von-Laue Str. 1, D-60438 Frankfurt am Main, Germany E-mail: [email protected]
This paper gives a brief survey of physical phenomena manifesting themselves in electronic and photonic collisions with metal clusters and fullerenes. The work is mainly addressed to theoretical aspects of electronic and photonic collisions with clusters, however some experimental results are also discussed. It is demonstrated the essential role of the multipole surface and volume plasmon excitations in the formation of cross sections of the mentioned collision processes. The mechanisms of the formation of electron excitation widths and the relaxation of electronic excitations in metal clusters and fullerenes are also briefly discussed.
1. Introduction Aggregation of atoms and small molecules into clusters, nanoparticles, microdroplets with complex molecular structure is a process in which a diversity of complex nano- and mesoscopic objects and systems can be created. There are many examples of such systems, e.g. fullerenes, carbon nanotubes, endohedral objects, quantum dots, quantum wires, nano-fractals, nanoparticles embedded into thin films or attached to biomolecules and many more.1,2'3 Some of these objects have been discovered only recently, other became a subject of intensive investigations because of their potential important applications, e.g. in miniaturizing of electronic devices, advancing new bio-medical technologies, development of quantum computers. For some of the systems, e.g. for deposited clusters, nano-fractals, quantum dots etc, their contact with surface plays an important role in the formation *On leave from A.F. Ioffe Physical-Technical Institute, Russian Academy of Sciences, St. Petersburg 194021, Russia
615
616 of their structure and properties. Investigation of clustering, self-assembly, stability, dynamic, thermal, optical and conductive properties of different mesoscopic, nano- and complex molecular structures is one of the focuses of atomic cluster science.2 Another topical issue is the behaviour of these systems in external electric, magnetic and laser fields, as well as the structure transformations and radiative processes induced by collisions, fission and fusion processes.3 Properties of clusters can be studied by means of photon, electron and ion scattering. These methods are the traditional tools for probing properties and internal structure of various physical objects.3 In this paper we focus on electronic and photonic collisions involving metal clusters and fullerenes, being in a gas phase. Let us mention some of the important developments in this field made during the recent years. Manifestation of electron diffraction both in elastic and inelastic collisions was investigated in Refs. 4, 5, 6, 7. The role of surface and volume plasmon excitations in the formation of electron energy loss spectra (differential and total, above and below ionization potential) as well as the total inelastic scattering cross sections was elucidated in Refs. 4, 5, 6, 7, 8. The importance of polarization effects in the electron attachment and photon emission processes was demonstrated in Refs. 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19. Mechanisms of formation of electron excitation widths and the relaxation of electronic excitations in metal clusters and fullerenes have been described in Refs. 20, 21, 22. Many more references one can find in the mentioned publications. Plasmon excitations in the process of photoionization of the fullerene Ceo have been well investigated both experimentally and theoretically.23'24'25'26'27'28'29'30'31'32-33 Usually, they manifest themselves as giant plasmon resonances in the excitation spectrum of Ceo- Recently, the photoionization cross section of singly charged fullerene ion CQ0 has been experimentally measured34 and calculated theoretically.34'35 The role of dynamical screening in the photoionization or photoabsorption process of an atom, which is either confined within a fullerene shell or is adsorbed onto its surface has been elucidated in Ref. 36. This effect is of a general nature. Thus, it will also appear for impurity atoms or molecules embedded into or attached onto a metallic cluster. A dynamical screening factor was determined in Ref. 36, and was shown to lead to an enhancement of the amplitude of the electromagnetic wave within a specific range of frequencies. This range is determined by the characteristics of the fullerene plasmon. Plasmon excitations play the very prominent role in the formation of
617 photon absoption spectra of metal clusters, e.g. Na and Mg clusters, see Ref. 37 and references therein. In the multiphoton absorption regime higher multipope plasmons can also be excited.38 Plasmon exciations can be also seen in the polarizational bremsstrahlung spectra emitted in collisions of electrons and other charged particles with metal clusters and fullerenes, for a review see Ref. 39. 2. Inelastic scattering of fast electrons on metal clusters and fullerenes Metallic clusters are characterized by the property that their valence electrons are fully delocalized. To some extent this feature is also valid for fullerenes, where the derealization of electrons takes place on the surface in the vicinity of the fullerene's cage. When considering electron collisions involving metal clusters and fullerenes, often, namely the valence delocalized electrons play the most important role in the formation of the cross sections of various collision processes. Therefore, an adequate description of such processes is possible to achieve on the basis of the jellium model (see e.g. Ref. 3 for a review). We now consider the inelastic scattering of fast electrons on metal clusters and fullerenes. This process is of interest because many-electron collective excitations of various multipolarity provide significant contribution to the cross section as demonstrated in Refs. 4'5>6>7. In photoionization experiments with clusters only dipole collective excitations can be probed. Electron collective modes with higher angular momenta can be excited in metal clusters and fullerenes by electron impact if the scattering angle of the electron is large enough.4'5'6'7 The plasmon excitations manifest themselves as resonances in the electron energy loss spectra. Dipole plasmon resonances of the same physical nature as in the case of the photo-absorption, dominate the electron energy loss spectrum if the scattering angle of the electron, and thus its transferred momentum, is sufficiently small. With increasing scattering angle plasmon excitations with higher angular momenta become more probable. The actual number of multipoles coming into play depends on the cluster size. The triply differential cross section of fast electron inelastic scattering on a cluster in the atomic system of units, h=\e\ = me = 1, reads as 4
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.(£•.,-*-,).
(1)
Here, dfi is the solid angle of the scattered electron of energy e', q is the momentum transfer defined as the difference between the initial, p, and final, p', momenta of the electron, q = |p — p'|. The summation over / implies the summation over the discrete spectrum and the integration over the continuous spectrum of the final states of the cluster. We calculate the many electron wave functions \Pj, $>f and the excitation energies ey and e* using the Hartree-Fock jellium model. The matrix elements contain sum over the atomic electrons (with a being the summation index and ra the corresponding radius vectors). Each term in the sum is a multiplication of the spherical Bessel function of order I, ji, and the spherical harmonic Yjm. As soon as collective electron excitations in a cluster play a significant role, then in order to obtain the correct result when calculating the matrix elements in (1), one should properly take into account many-electron correlations. This problem can be solved within the frame of the random phase approximation with exchange (RPAE) 5 ' 8 ' 14 . 3. Plasmon resonance approximation Besides complex numerical calculations of the cross section (1) one can derive the so-called plasmon resonance approximation giving the distinct physical picture of the process.4 Indeed, let us consider the behaviour of the inelastic cross sections in the vicinity of a giant collective resonance when surface plasmon excitations give the main contribution. In this case the interaction of the projectile with electrons in the surface layer play the most significant role in the inelastic scattering process. The width a of this layer is determined by the width of the region near the surface of the cluster where oscillations of electron density mainly occur. This width is of the same order of magnitude as the size of a single atom. Oscillations of electron density take place mainly near the surface, because the electron density inside the cluster is well compensated by the oppositely charged density of the ionic background. Mathematically this means that theory has a small parameter, namely a/R
619 The condition ra ss R allows us to simplify the matrix elements in (1) and express them via the multipole matrix elements QlV> as 2l +
<*/ ^Mqr^Yimin*)
*
*
)
•
4TT
ljl{qR)nim Bf
W
'"
(2)
where
^ = V^T^Z>i*Wn.)
*i>.
Substituting these equations to (1) and using the relationship /
\Qft\2 5{Ae + £i - e,)d/ =
-Imat(Ae),
(3)
Ae = p 2 /2 - p' 2 /2 where a; is the multipole dynamic polarizability of the cluster, we finally obtain the expression for the cross section via the imaginary parts of the multipole dynamic polarizabilities
4p'
de'dQ, ~ npq* 5
> + l) a3?(QR) ^/ma,(Ae)
(4)
Integrating the cross section (4) over d£l, we derive the expression for the total spectrum of the electron energy loss /+ 1) 2LCS, (Ae)/ma .. , r ... ^da 7 8LV ^ ( i2- 55 TT2 ( i (Ae). de'
p 2 *-f
R21'2
(5)
Here, A e = e — e'. W e have also introduced functions S'i(Ae) as follows
St(Ae) =
%jf{x). JqminR
(6)
X
The limits qmin and qmax are equal to qmin = p(l - ^/l - Ae/e), qmax = p(l + i / l — Ae/e). In the region the most interesting for our consideration, one derives Ae ~ wp and e ~ u>2R2. Therefore, Ae/e
620
of frequencies where collective electron modes in a cluster can be excited. In the plasmon resonance approximation40 the polarizability ai(u) can be written as
a,H = fi2,+1
2
i
. r,
(7)
where w; is the resonance frequency of the plasmon excitation with the angular momentum I, which for metal clusters according to the Mie theory is equal to w; = J (2f+ifR^ a n d wi = y ™ + M f° r fullerenes.4 Here, Ne is the number of delocalized electrons in the cluster. The parameter T; in (7) is the width of the plasmon resonance with the angular momentum I. These formulae demonstrate that due to the resonance behaviour of the polarizability, the differential inelastic scattering cross section should also exhibit resonances, if the transferred energy lies in the range characteristic for plasmon excitations. The plasmon resonance approximation provides a simple criterion for the estimation of the relative importance of various plasmon modes. Indeed, according to the plasmon resonance approximation the minima and the maxima of the contribution of the plasmon mode with the angular momentum I are determined by the minima and the maxima of the diffraction factor jf(qR) as it follows from (4). This factor shows that diffraction phenomena arise also in electron inelastic scattering on clusters. The main maximum of the partial contribution with the angular momentum I arises when qR ~ I. This condition reflects a simple fact that the probability of the excitation of the collective plasmon mode is maximum, when the characteristic collision distance is about the wave length of plasmon. This results in the significant dependence of the profile of the spectrum on the angle of the scattered electron. In figs. 1 and 2 we exemplify the behaviour of the cross sections for the electron-fullerene C60 collision (fig. 1) and the electron-iVa4o collision (fig. 2). Figs, la, b show quite reasonable agreement of theoretical results with the experimental data. At low momentum transfer (9 = 1.5°) the dipole excitation dominates in the energy loss spectrum (fig. 1 a), while for 9 = 10° the quadrupole contribution (fig. 1 b) provides the main contribution. As a result the position of the maximum of the energy loss spectrum shifts from the dipole plasmon frequency ui\ at 9 = 1.5° to the quadrupole plasmon frequency w2 at 9 = 10°. At 9 — 5°, the position of the maximum is close to the octupole plasmon resonance frequency UJ% (fig. 1 c). We note, that the plasmon resonance approximation is justified for description of the collective electronic excitations only, while single electron transitions are
621
0,0 ^ - ~ '
10
0,0001 10
I
,-..-!
20
.
. IS
' '•
30
.
1 20
• • T ... •
40
,
. 25
60
,
1 30
4E, eV
Figure 1. The differential cross section da/de'dQ, (1) as a function of transferred energy AE calculated for electron-fullerene Ceo collision.6 The impact electron energy is e = IkeV. The scattering angle is 6 = 1.5° (a), 6 = 10° (b) and 0 = 5° (c). Results of the plasmon resonance approximation are shown by solid lines. Dots in figures (a) and (b) represent the experimental data from Ref. 41. Dashed lines show the leading multipole (dipole (a), quadrupole (b) and octupole (c)) plasmon contribution to the spectrum. For 6 = 5°, the contributions from the qudrupole and the dipole plasmon modes are shown by dotted and dashed-dotted lines, respectively.
out of the scope of the approximation, as the additional structures seen in fig. la indicate. Comparison of the results derived from the RPAE calculations with those obtained in the plasmon resonance approximation (fig. 2) shows that, in spite of the simplicity, the plasmon resonance treatment is in quite good agreement with the consistent many-body quantum calculation. The main discrepancy between the two approaches arises from the single particle transitions omitted in the plasmon resonance approximation, but taken
622
Ac eV
Figure 2. The differential cross section (1), dc/de'dfl, as a function of transferred energy Ae calculated for electron-JVa4o collision.8 The impact electron energy is e = 50eV. The electron scattering angle is 6 = 1° (a), 0 = 6° (b) and 0 = 8° (c). Solid lines represent results of the RPAE calculation with the Hartree-Fock jellium model basis wave functions. Thick solid line is the total energy loss spectrum. Thin solid lines marked with the angular momentum number represent various multipole contributions to the energy loss spectrum. By dashed line we plot the electron energy loss spectrum calculated in the plasmon resonance approximation.
into account in the RPAE calculation. These transitions bring some structure to the final energy loss spectra manifesting themselves over the smooth resonance behaviour which is reproduced by the plasmon resonance approximation. At larger scattering angles plasmons with larger angular momenta can be excited. However, as we know, excitations with large enough angular momenta occur due to single particle transitions rather than due to collective excitations. Therefore, the agreement between the plasmon resonance approximation and the RPAE is better at small angles.
623 4. Concluding remarks The have discussed a number of problems arising in collisions of electrons and photons with metal clusters and fullerenes The choice of these particular problems was greatly influenced by the experimental efforts undertaken in the field. However, there are many more interesting problems in the field3 which we were not be able to consider in a short report. Without doubts all these problems deserve careful theoretical and experimental consideration. Acknowledgements This work is partially supported by the European Commission within the Network of Excellence project EXCELL, by INTAS and by the Russian Foundation for Basic Research. The author is grateful to Dr. O. Obolensky for technical help in preparation of the manuscript. References 1. C. Guet, P. Hobza, F. Spiegelman and F. David (eds.), NATO Advanced Study Institute, Session LXXIII, Summer School "Atomic Clusters and Nanoparticles", Les Houches, France, July 2-28, 2000, EDP Sciences and Springer Verlag, Berlin, Heidelberg, New York, London, Milan, Paris, Tokyo (2001). 2. J.P. Connerade, A.V. Solov'yov and W. Greiner, Europhysicsnews 33 , 200 (2002). 3. J.P. Connerade and A.V. Solov'yov (eds.), Latest Advances in Atomic Clusters Collision: Fission, Fusion, Electron, Ion and Photon Impact, Imperial College Press, World Scientific, London (2004). 4. L.G. Gerchikov, J.P. Connerade, A.V. Solov'yov and W. Greiner, J.Phys.B.At.MoLOpt.Phys. 30, 4133 (1997). 5. L.G. Gerchikov, A.N. Ipatov and A.V. Solov'yov, J.Phys.B:At.Mol.Opt.Phys. 30, 5939 (1997). 6. L.G. Gerchikov, A.N. Ipatov, A.V. Solov'yov and W. Greiner, J.Phys.B.At.MoLOpt.Phys. 31, 3065 (1998). 7. L.G. Gerchikov, P.V. Efimov, V.M. Mikoushkin and A.V. Solov'yov, Phys.Rev.Lett. 81, 2707 (1998). 8. L.G. Gerchikov, A.N. Ipatov, R.G. Polozkov and A.V. Solov'yov, Phys.Rev. A 62, 043201 (2000). 9. J.P. Connerade, A.V. Solov'yov, J.Phys.B.-At.Mol.Opt.Phys. 29, 365 (1996). 10. J.P. Connerade, A.V. Solov'yov, J.Phys.BiAt.Mol.Opt.Phys. 29, 3529 (1996). 11. L.G. Gerchikov and A.V. Solov'yov, Z.Phys.D.-Atoms, Molecules, Clusters 42, 279 (1997). 12. A.V. Korol and A.V. Solov'yov, Topical Review, J.Phys.B:At.Mol.Opt.Phys. 30, 1105 (1997). 13. J.P. Connerade, L.G. Gerchikov, A.N. Ipatov and A.V. Solov'yov, J.Phys.B.At.MoLOpt.Phys. 31, L27 (1998).
624 14. L.G. Gerchikov, A.N. Ipatov and A.V. Solov'yov, J.Phys.B:At.Mol.Opt.Phys. 31, 2331 (1998). 15. J.P. Connerade, L.G. Gerchikov, A.N. Ipatov and A.V. Solov'yov, J.Phys.B:At.Mol.Opt.Phys. 32, 877 (1999). 16. V. Kresin, A. Scheidemann and W.D. Knight, "Electron Collisions with Molecules, Clusters and Surfaces", H. Eberhardt and L.A. Morgan (ed.) (New York: Plenum) 183 (1994). 17. V. Kasperovich, G. Tikhonov, K. Wong, P. Brockhaus and V.V. Kresin, Phys. Rev. A 60, 3071 (1999). 18. V.V. Kresin and C. Guet, Philosophical Magazine 79, 1401 (1999). 19. S. Sentiirk, J.P. Connerade, D.D. Burgess and N.J. Mason, J.Phys.B: At.Mol.Opt.Phys. 33, 2763 (2000). 20. L.G. Gerchikov, A.V. Solov'yov and W. Greiner, Int. Journal of Modern Physics E8, 289 (1999). 21. L.G. Gerchikov, A.N. Ipatov, A.V. Solov'yov and W. Greiner, J.Phys.B: At.Mol.Opt.Phys. 33, 4905 (2000). 22. A.G. Lyalin, S.K. Semenov, N.A. Cherepkov, A.V. Solov'yov and W. Greiner, J.Phys.B:At.Mol.Opt.Phys. 33, 3653 (2000). 23. G.F. Bertsch, A. Bulgac, D. Tomanek et al, Phys. Rev. Lett. 67, 2690 (1991). 24. N. Ju, A. Bulgac and J.W. Keller, Phys. Rev. B 48, 9071 (1993). 25. K. Yabana and G.F. Bertsch, Physica Scripta 48, 633 (1993). 26. G. Wendin and B. Wastberg, Phys. Rev. B 48, 14764 (1993). 27. M.J. Puska and R.M. Nieminen, Phys. Rev. A 47, 1181 (1993). 28. F. Alasia, R.A. Broglia, H.E. Roman et al, J.Phys. B: At.Mol.Opt.Phys. 27, L643 (1994). 29. J.H. Weaver, J.L. Martins, T. Komeda et al, Phys.Rev.Lett. 66, 1741 (1991). 30. I.V. Hertel, H. Steger, J. de Vries et al, Phys. Rev. Lett. 68, 784 (1992). 31. T. Liebsch, O. Plotzke, F. Heiser et al, Phys. Rev. A 52, 457 (1995). 32. V.K. Ivanov, KG.Yu. Kashenock, R.G. Polozkov and A.V. Solov'yov, J. Phys. B: At. Mol. Opt. Phys., 34 L669 (2001). 33. V.K. Ivanov, G.Yu. Kashenock, R.G. Polozkov and A.V. Solov'yov, J. of Exp. And Theor. Phys., 96 658 (2003). 34. S.W.J. Scully, E.D. Emmons et al, Phys. Rev. Lett, 94 065503 (2005) 35. Ivanov V K, Polozkov R G and Solovyov A V , J. Phys. B: At. Mol. Opt. Phys., in press (2005) 36. J.P. Connerade, A.V. Solov'yov, J.Phys.B: At.Mol.Opt.Phys. 38, 807 (2005). 37. I.A. Solov'yov, A.V. Solov'yov, W. Greiner, J.Phys.B:At.Mol.Opt.Phys. 37, L137 (2004). 38. J.P. Connerade, A.V. Solov'yov, Phys.Rev. A 66, 013207 (2002). 39. A.G. Lyalin and A.V. Solov'yov, Radiation Physics and Chemistry (2005). 40. U. Kreibig and M. Vollmer, Optical properites of metal clusters, Berlin:Springer (1995). 41. J.W. Keller and M.A. Coplan, Chem. Phys. Lett. 193, 89 (1992).
D Y N A M I C S OF H 2 C H E M I S O R P T I O N O N M E T A L SURFACES
H.F. BUSNENGO1*, C. DIAZ2, P. RIVIERE 3 , M.A. DI CESARE 1 , F. MARTIN3, W. DONG 4 AND A. SALIN5 1 Instituto de Fisica Rosario and Universidad National de Rosario Av. Pellegrini 250, 2000 Rosario Argentine E-mail: [email protected] Leiden Institute of Chemistry, Leiden, The Netherlands. 3
Departamento de Quimica C-9, Universidad Autdnoma de Madrid, Spain. 4
Ecole Normale Supirieure de Lyon, France.
Laboratoire de Physico-Chimie Moliculaire, Universit6 Bordeaux I, France We present a theoretical study of H2 dissociative chemisorption on metal surfaces based on classical trajectory calculations for the dynamics, and Density Functional Theory to describe the molecule-surface interaction potential. We summarize the mechanisms that come into play and their relation with surface structure and reactivity. We discuss how these mechanisms can be related with measurements under various experimental conditions, for dissociative adsorption as well as for unreactive molecular scattering from the surface.
1. Introduction Dissociative adsorption of H2 is an important step in many chemical reactions on surfaces and a reference to understand adsorption of more complex (heavier diatomic and polyatomic) molecules. Despite the simplicity of H 2 , the mechanism of chemisorption on transition metal surfaces (e.g. Pd, Ni, Pt, W) at low energies has been a matter of debate over the last ten years, in particular, concerning the existence of an indirect mechanism involving a so called precursor s t a t e 1 - 8 . Molecular beam experiments allow to determine, for instance, the dependence of the sticking probability on the kinetic energy of impinging molecules, E;, the initial ro-vibrational molecular state H2(2>,J), the angle of incidence, 6i, surface temperature, T s , etc.
625
626
Recently, the possibility of elucidating reaction mechanisms by looking also at the angular distribution of scattered (unreactive) molecules was also investigated5,9. However, extracting information on reaction mechanisms from experimental data is not a trivial task and dynamical simulations are necessary. In this paper we summarize a series of results of classical trajectory calculations for H2 interacting with surfaces characterized by different reactivities. These results shed light on the connection between some typical behaviours found in molecular beam experiments and various possible reaction mechanisms.
2. Theory H2-surface dynamics is usually described within the Born-Oppenheimer approximation which assumes that the system remains throughout in its ground electronic state 10 . A further approximation consists in neglecting the effect of surface atom motion: rigid surface (RS) model. Within the RS model, the description of the reaction dynamics for a diatomic molecule consists in solving the equations of motion on a single six-dimensional (6D) potential energy surface (PES) 10 . The 6D-PES depends on the coordinates of the molecular center of charge, R(X,Y, Z), the internuclear distance, r, and the molecular orientation denned by the polar and azimuthal angles The most widely used methods to compute molecule-surface PES's are based on the Density Functional Theory (DFT). Due to the high computational cost of these calculations, dynamical studies, in general, employ a continuous representation of the PES obtained by interpolation of DFT results for various positions and orientations of the molecule in front of the surface. One of the most successful interpolation method developed so far for diatomic molecules interacting with metal surfaces is the Corrugation Reducing Procedure (CRP) 11 . This is the method employed to build the PESs used throughout this paper 7 ' 12 ' 13 ' 14 . Once the PES is known, the dynamics can be described using quantum and/or classical mechanics. In this paper we adopt the latter approach, usually called classical molecular dynamics (CMD). The suitability of CMD calculations to describe adsorption and scattering at low energies is today well established for the systems considered in this paper 7 ' 15 ' 16 . Still, one shortcoming of CMD in relation with the evolution of vibrational zero point energy (ZPE) must be taken into account depending on the process under scrutiny. A description of the two methods used in our work, i.e., quasi classical (QC) and classical with
627
ZPE (CZPE), and the conditions under which one should choose each of them is beyond the scope of this paper and can be found elsewhere6. The classical trajectory results presented in this paper were obtained using the CZPE method for H 2 /Pd 12 and the QC one for H 2 /NiAl 17 . The main shortcoming of the RS model is that energy exchange with surface phonons is not accounted for. To study some of the effects due to coupling with phonons (energy exchange with the surface, temperature effects, etc.) we use the so-called Surface Oscillator (SO) model18. This model represents surface motion in terms of a single 3D harmonic oscillator of mass ms (the mass of surface atoms) with coordinates Rs(XB,Ye,Zs) and associated frequencies u)XlV,x = y/kXtytZ/ms (see Fig. 1). The H2phonon coupling is described by a space rigid shift Re of the 6D-PES, VSD(R,r,0,
adsorption
Dissociative adsorption is qualified as activated if all possible pathways in configuration space connecting the reactants (i.e. the molecule and the surface far from each other) with the products (i.e. dissociated fragments bound to the surface) exhibit an activation energy barrier [e.g. H2/NiAl(110)]. On the other hand, dissociation is nonactivated if there exist pathways without an energy barrier (e.g. H 2 /Pd). In the case of nonactivated adsorption the sticking probability is high even for low Ej values whereas for activated adsorption, it becomes significant only for E<
Figure 1. Coordinates defining the position of H2 in front of a surface and schematic representation of the dynamical models: (a) RS, (b) SO (see the text).
628
Figure 2. (a) H2 dissociative adsorption probability as a function of E<. Theory: full lines. Experiments: full squares, Pd(llO) 1 ; full circles, NiAl(llO) 21 ; open squeres, P d ( l l l ) 6 ; open circles, P t ( l l l ) 2 0 . (b) Direct and dynamic trapping contribution to adsorption of H 2 on Pd(llO) (full lines) and P d ( l l l ) (dashed lines).
greater than a threshold value (associated with the minimum energy barrier). CMD results and experimental data of the dissociative adsorption probability of H2 on Pd(lll) 6 ' 5 , Pd(llO) 12 ' 1 and NiAl(llO)17'21 are presented in Fig. 2a. On Pd surfaces dissociative adsorption is nonactivated whereas it is activated on NiAl(llO) (minimum activation barrier of ~ 300 meV). For the sake of completeness we also include results for Pt(lll) 1 5 ' 2 0 , a system characerized by an intermediate reactivity (i.e. lower than Pd and higher than NiAl). In all cases, CMD results well reproduce the experimental trends. This strongly supports the use of the present theoretical approach to investigate reaction mechanisms and their connection with experiment. The main difference between Pd surfaces on the one hand, and NiAl(llO) on the other, is that, in the latter case the probability increases monotonously with Ej. The analysis of the CMD calculations shows that this is associated with a single mechanism responsible for adsorption in the whole energy range. It is a direct mechanism through which the molecules approach the surface and directly dissociate or are scattered back to the vacuum after a single rebound on the surface17. For Hj/Pd, at low energies an indirect adsorption channel also exists6'12: dynamic trapping (Fig. 2b) . At low energies, many molecules remain trapped during a long time, explore a large area of the surface and undergo many rebounds before dissociation or reflection. This is due to energy exchange from perpendicular motion to rotation and parallel motion which prevents the molecules from escaping
629
1/
W
Bj (degree)
7\l
V
U.J
1
E±(eV)
Figure 3. (a) Pdia S (0i)/ p di«(0»=O) for H 2 /Pd(110) (Ej=30, 400 meV) and for H 2 /NiAl(110) (E<=800 meV). (b) P , K „ ( E J . ) for H 2 /NiAl(110) for different E<'s.
the surface attraction and favors adsorption. When Ej increases, trapping decreases which produces the initial decrease of the sticking probability as a function of E* observed in experiments. An important difference between direct activated and trapping mediated nonactivated dissociation appears in the dependence of the dissociative adsorption probability, Pdj„s, on the angle of incidence with respect to the surface normal, 6{, (see Fig. 3a). For H2/NiAl(110) [and other systems of similar reactivity, e.g. H 2 /Cu] Y<nss sharply decreases when 0; increases (for Ej fixed). In fact, Fig. 3b shows that Pdiss scales roughly with the normal energy, E±. This is because perpendicular energy is required to climb a repulsive PES in the entrance channel to approach the surface22'17. For H 2 /Pd, even for high values of E; for which the direct mechanism dominates, Pdiss decreases much more slowly when 9i increases. Furthermore, Pdiss does not go to zero when 8i -> 90 deg. because direct dissociation is still greater than zero even for Ex -> 0 (Fig. 2b). On the other hand, for H 2 /Pd at low energies, dynamic trapping dominates and Pdiss barely depends on the angle of incidence due to the memory loss of trapped molecules after several rebounds22. Thus, at low energies ~PnS8 roughly satisfies total energy scaling (Fig. 3a). Another difference between direct activated and dynamic trapping mediated adsorption is found in T,-effects (Fig. 4). For H 2 /Pd, it is found that at low energies (for which dynamic trapping dominates) Pdiss decreases when T s increases because low energy molecules take energy from the sur-
630
100
200
300
400
100
E (meV)
200
300
400
E. (meV)
Figure 4. TVeffects on P d i ^ E j ) (a) and the direct and dynamic trapping mechanisms (b) for H 2 /Pd(110) (T s =10, 400 and 900 K).
face (that plays the role of a heat bath) which quenches trapping 8 ' 23 . For H 2 /Pd [and H2/NiAl(110)], direct dissociation barely depends on T„. 3.2. Angular distribution
of scattered
molecules
A relatively small difference in reactivity like the one found between H 2 /Pd(lll) and H2/Pd(110) can still entail different behaviours of scattered molecules. In Fig. 5a, we show the ratio of scattered molecules that have been temporarily trapped and the total number of unreactive scattered molecules as a function of Ej [for normal incidence and H2(i> = 0, J = 0)]. For Pd(110), at low energies a large fraction of scattered molecules have been trapped, whereas on Pd(lll) scattering is essentially direct. This does not mean that trapping does not take place on P d ( l l l ) (see Fig. 2b). Both
-60
-30
0
6r(deg.)
30
60
-60
-30
0
30
60
ef(deg.)
Figure 5. (a) Fraction of reflected molecules after trapping as a function of Ej (at normal incidence) for H 2 / P d ( l l l ) and H 2 /Pd(110). Angular distribution of scattered low energy Hi molecules (6\=45 deg. and T„ ~ 500KT): (b) theory for H 2 / P d ( l l l ) and H 2 /Pd(110) (Ei=50meV); (c) experiments for H 2 / P d ( l l l ) and H 2 / P d ( l l l ) + V (E<=20meV) 5 .
631 surfaces attract H2 molecules in the entrance channel (i.e. above ~ 2 A) and the variation of the PES with molecular orientation and position on the unit cell produces energy exchange between degrees of freedom that results in molecules becoming trapped. However, the larger number of energetically accessible dissociation pathways makes that on P d ( l l l ) , almost all trapped molecules dissociate whereas on Pd(llO), trapped molecules still have a non negligible probability to be scattered back to vacuum. This entails a very different angular distribution of molecules scattered from Pd(lll) and Pd(llO) at low energies (Fig. 5b). For H 2 /Pd(110) a cosinelike distribution is observed as a consequence of the memory loss of a large fraction of scattered molecules whereas for H2/Pd(lll), the essentially direct scattering provokes a pronounced peak of reflected molecules in the specular direction (6f = $i)22'24. These different behaviours have been experimentally observed in H2 scattering from P d ( l l l ) and P d ( l l l ) + V alloy surface (Fig. 5c)5. Sticking experiments and DFT calculations suggest that Pd(lll)+V presents a smaller fraction of energetically accessible dissociation pathways than Pd(lll) at low energies, but preserves the attraction in the entrance channel and the nonactivated character of dissociation5. This validates the comparison of our results for Pd(lll) and Pd(llO) with experiment for Pd(lll) and Pd(lll)+V. It is important to emphasize that a cosine-like distribution of scattered molecules is an indication of an indirect scattering mechanism but the absence of such a behaviour is not enough to rule out the role of dynamic trapping in dissociative adsorption. Our results for H 2 /Pd(lll) (Fig. 2b, 5a and 5b) clearly show that this can be due to the fact that all trapped molecules dissociate and accordingly, cannot be observed in a scattering experiment that, then, explores unreactive molecules.
4. Conclusions In this work we have described the different mechanisms responsible for the dissociative adsorption of H2 on metal surfaces with different reactivities. Direct dissociation and dynamic trapping were considered and the possible consequences on molecular beam experiments was discussed. Our theoretical results are in general, in good agreement with available experimental data, and strongly support the existence of an indirect adsorption mechanism for H2 on Pd and other similar transition metal surfaces at low impact energies: dynamic trapping.
632 Acknowledgments This work has been partially supported by the Scientific Cooperation Program ECOS-SUD, Project N° A03E04 between Argentina and France and by the Direcci6n General de Investigaci6n (Spain), Project N° BFM200300194 and CTQ2004-00039/BQU. References 1. Ch. Resch, H.F. Berger, K.D. Rendulic and E. Bertel, Surf. Sci. 316, L1105 (1994). 2. A. Gross, S. Wilke and M. Scheffler, Phys. Rev. Lett. 75, 2718 (1995). 3. M. Beutl, M. Riedler and K.D. Rendulic, Chem. Phys. Lett. 247, 249 (1995). 4. G.R. Darling, M. Kay and S. Holloway, Surf. Sei. 400, 314 (1998). 5. M. Beutl, J. Lesnik, K.D. Rendulic, R. Hirschl, A. Eichler, G. Kresse and J. Hafner, Chem. Phys. Lett. 342, 473 (2001). 6. H.F. Busnengo, C. Crespos, W. Dong, J. C. Rayez and A. Salin, J. Chem. Phys. 116, 9005 (2002). 7. H.F. Busnengo, E. Pijper, M.F. Somers, G.J. Kroes, A. Salin, R.A. Olsen, D. Lemoine and W. Dong, Chem. Phys. Lett. 356, 515 (2002). 8. H.F. Busnengo, W. Dong and A. Salin, Phys. Rev. Lett. 93, 236103 (2004). 9. M.F. Bertino and D. Farias, J. Phys.: Condens. Matter 14, 6037 (2002). 10. G.J. Kroes, Prog. Surf. Sci. 60, 1 (1999). 11. H.F. Busnengo, A. Salin and W. Dong, J. Chem. Phys. 112, 7641 (2000). 12. M. A. DiCesare, H.F. Busnengo, W. Dong and A. Salin, J. Chem. Phys. 118, 11226 (2003). 13. R. Olsen, H.F. Busnengo, A. Salin, M.F. Somers, G.J. Kroes, E.J. Baerends, J. Chem. Phys. 116, 3841 (2002). 14. P. Riviere, H.F. Busnengo and F. Martin, J. Chem. Phys. 121, 751 (2004). 15. E. Pijper, M.F. Somers, G.J. Kroes, R.A. Olsen, E.J. Baerends, H.F. Busnengo, A. Salin and D. Lemoine, Chem. Phys. Lett. 347, 277 (2001). 16. C.Diaz, M.F. Somers, G.J. Kroes, H.F. Busnengo, A. Salin and F. Martin, Phys. Rev. B 72, 035401 (2005). 17. P. Riviere, H.F. Busnengo and F. Martin, J. Chem. Phys. 123, 074705 (2005). 18. M. Hand and J. Harris, J. Chem. Phys. 92, 7610 (1990). 19. H.F. Busnengo, W. Dong, P. Sautet and A. Salin, Phys. Rev. Lett. 87, 127601 (2001). 20. A.C. Luntz, J.K. Brown and M.D. Williams, J. Chem. Phys. 93, 5240 (1990). 21. M. Beutl, K.D. Rendulic and G.R. Castro, J. Chem. Soc. Faraday Trans. 91, 3639 (1995). 22. C. Diaz, F. Martin, H.F. Busnengo and A. Salin, J. Chem. Phys. 120, 321 (2004). 23. H.F. Busnengo, M.A. DiCesare, W. Dong and A. Salin, Phys. Rev. B 72, 125411 (2005). 24. C. Diaz, H.F. Busnengo, F. Martin and A. Salin, J. Chem. Phys. 118, 2886 (2003).
INTERACTION OF SLOW MULTIPLY CHARGED IONS WITH INSULATOR SURFACES W. MEISSL, J. STOCKL, M. FURSATZ, HP. WINTER AND F. AUMAYR* Institutflir Allgemeine Physik, TV Wien Wiedner Haupstr. 8-10/E134, A-1040 Vienna, Austria J.R. CRESPO L6PEZ-URRUTIA, J. SIMONET, W. CHEN, H. TAWARA AND J. ULLRICH Max-Planck-InstitutfiirKernphysik, P.O. Box 10 39 80 D-69029 Heidelberg, Germany We have investigated electron emission for impact of slow multiply charged ions on an atomically clean and flat insulating LiF(OOl) surface. For grazing scattering of Arq* projectiles from LiF time-of-flight spectra and the number of emitted electrons have been determined in coincidence. By relating projectile energy loss to kinetic electron emission we were able to determine contributions from potential electron emission even in the presence of a considerable number of kinetically excited electrons. Furthermore, in noncoincident measurements with Xe ions in charge states up to 52+ we compare potential electron emission from a conducting Au(lll) and an insulating LiF(OOl) single-crystal target at different impact velocities and ion impact angles. Preliminary results suggest that for normal incident very highly charged ions electron emission from LiF is obstructed by the finite hole mobility.
1. Introduction Impact of slow ions (impact velocity < 1 a.u. = 25 keV/amu) on solid surfaces is of genuine interest in plasma- and surface physics, and related applications. Nature and intensity of the resulting inelastic processes depend both on the kinetic and the potential (= internal) ion energy carried toward the surface [1-6]. For slow multiply charged ions (MCI) this potential energy can become comparable to or even considerably exceed the ions kinetic energy, resulting in additional electron emission or sputtering (potential electron emission PE [4, 5, 7, 8], potential sputtering [9-11]), phenomena which are usually dominated by kinetic effects (kinetic electron emission KE [1-4], kinetic sputtering [12, 13]). The relative importance of ion induced PE and KE from solid surfaces is not easy to determine. Measurements performed under grazing angles of incidence corresponding author; e-mail: [email protected]
633
634
are of particular interest here, since the projectiles interaction with the surface proceeds along a well-defined trajectory (surface channeling [6]). More detailed information can be obtained if electron emission is observed in coincidence with the angular distribution of scattered projectiles. Recently, such measurements for multiply charged Ar ion impact on Au(lll) have permitted a clear distinction of the contributions from PE and KE [14]. For slow, very highly charged ion impact PE usually becomes dominant and a separation procedure from KE is no longer needed.
Figure 1; Experimental setup for measuring the number statistics of ejected electrons from grazing incidence of slow MCI on a flat target surface in coincidence with scattered projectiles [15,16].
In this work we describe experimental investigations of electron emission due to multiply and highly charged ion (HCI) - impact on insulator targets, where electronic properties (dielectric response, band gap, limited charge carrier mobility) may strongly affect the interaction scenario and add complexity to its theoretical description [17, 18]. For these investigations we have chosen a LiF(OOl) crystal as a prototype wide-band gap insulator. 2. Separation of potential and kinetic emission for grazing Ar4* impact A first attempt to separate PE and KE in coincidence measurements of electron emission statistics (ES) and angular distributions of scattered projectiles
635 as described in [14] was unsuccessful [19]. This was mainly due to the fact that KE from LiF starts at much smaller impact energy (lower KE threshold than for Au), increases faster with projectile velocity and shows an "inverse" dependence on incident charge state q of the Ar^ projectile ions [20,21]. cuts &i co-nsfan! energy tes =
i
m
i \
E»i8k*v y«3.«*
m
Figure 2: (a) Coincidence spectra of ES vs. projectile energy loss for 18 keV Ar3+ impact on a LiF(001) surface (angle of incidence 3.8°). (b) Cuts through these coincidence spectra at constant energy losses provide related mean numbers of emitted electrons, and cuts for given numbers of emitted electrons show related mean energy losses. The two curves can be extrapolated to zero energy loss and zero number of emitted electrons, respectively (for further details cf. text).
Therefore, we made use of the close relationship between kinetic electron emission and inelastic energy losses for the projectile ions to separate KE and PE contributions. Adding a time-of-flight (TOF) unit to our experimental setup (fig. 1) permitted to measure the projectile energy loss during grazing scattering from the surface in coincidence with the number of emitted electrons for individual trajectories. Fig. 2 shows, as general trend for such studies, a direct correlation of the mean number of emitted electrons with projectile energy loss. For farther analysis mean values for certain cuts through such coincidence spectra have been evaluated. Cuts at fixed energy loss give the respective mean numbers of emitted electrons. Extrapolation of the resulting curve to the hypothetical case of projectiles with no energy loss at all (not directly observable in our experiment) leads to an electron emission yield which is not associated with any kinetic
636
energy loss of the projectile [16]. Since these electrons are not emitted at the expense of the projectile's kinetic energy, they result from deposition of projectile potential energy Ep0t, i.e. give rise to the "pure" potential electron emission yield YPE (AE = 0).
0
100
200
300
400
500
600
potential energy (eV)
Figure 3: "Pure" potential electron emission contribution (c.f. text) vs. available potential energy (full symbols) as compared to model predictions (solid line).
Plotting such extrapolated YPE (AE = 0) values for different Arq+ projectiles as a function of the related potential energy supports this interpretation. In fig. 3 we find a linear relationship between the "pure" PE yield and the potential energy brought towards the surface by the different MCI, with no dependence on the kinetic energy, which was varied between 18 and 54 keV [16]. Moreover, our data points are situated right at the border of the region allowed by potential energy conservation (shaded triangular area in fig. 3). PE results from Auger processes, which require a minimum potential energy of at least twice the binding energy W+ of the highest occupied state of the solid (corresponding to the work function in the case of metal targets). The maximum possible number of electrons emitted via PE is therefore given by nmax = Epot / (2 W+). This maximum possible number of PE electrons is indeed obtained from our experimental data, taking into account a binding energy of about 12 eV [22] for the highest occupied states in the F"(2p) valance band of LiF (solid line in fig. 3). Experimental data for y?E reflect the highest yields possibly produced via PE. It is remarkable that these PE yields are considerably higher than those measured for normal incident ion impact on polycrystalline LiF [20, 23], which is a clear hint that electron capture from an insulator surface critically depends on the ion trajectory.
637
3. Electron emission for highly charged Xeq+impact on Au(lll) and LiF(OOl) surfaces Highly charged ions (HCI) carry a large amount of potential energy (e.g about 120 keV for He-like Xe52+) and are a promising tool for future nanostructuring efforts [11, 24], Their interaction with metal surfaces, which leads to the formation of so-called "hollow atoms", has been studied extensively over the past 15 years [5, 25, 26] and is now well understood. Due to the dielectric response of insulator surfaces (less image charge acceleration, slow hole mobility) results for the interaction of HCI with insulator surfaces are difficult to predict from available theoretical models. We have therefore constructed an experimental setup similar to the one shown in fig. 1, which allows to compare electron emission from a conducting Au(lll) and an insulating LiF(OOl) single-crystal target (mounted on the same target holder). As projectile ions we used HCI from the Heidelberg-EBIT, where Xe projectile charge states up to 52+ can be reached. Measurements of the electron emission statistics [27] have been performed under UHV conditions and atomically clean target surfaces have been prepared by sputter cleaning and heating, respectively [5]. Electrons emitted from the target are extracted by a weak electric field and accelerated onto a surface barrier detector for recording the number statistics of emitted electrons. For this purpose the primary ion flux has to be kept typically to below 104 ions/sec. The electron emission yields (derived from the mean value of the electron emission statistics spectra [28, 29]) are studied at different impact velocities (typ. 5xl05 - lxlO6 m/s corresponding to a few keV/amu) and ion impact angles (0° - 60° with respect to the target surface normal). Total electron yields measured for normal impact of Xeq+ ions onto the Au(lll) surface are consistent with earlier results obtained at the Lawrence Livermore-EBIT for the same projectiles and normal impact on a polycrystalline Au surface [30, 31]. When comparing total electron emission from the Au(lll) and the LiF(OOl) target under otherwise identical conditions we note the following preliminary trends. * For a fixed impact velocity electron emission yields strongly increase with Xe projectile charge state (see example shown in fig. 4), reaching values as high as 100 electrons per single ion impact. * For normal ion impact electron yields from LiF are always smaller than for impact of the same ion on Au; this deviation increases with increasing projectile charge state (seefig.4). * For both targets electron yields increase with ion impact angle (see e.g. fig. 5). The difference between Au and LiF results, however, decreases with
638
increasing impact angle leading to similar yield values at large impact angles (typ. > 60° with respect to the surface normal). 80 c o
70
X e q + - A u ( 1 1 1 ) , LiF(001)
60
ion impact angle: 0"
Au(111)
50
|
LiF(001)
40 30
1
20 (full symbols)
10
v = 7 x 105 ms"1 (open symbols)
0 15
20
25
30
35
40
45
50
55
charge state q Figure 4: Total electron emission yields versus projectile charge state q measured for normal impact of highly charged Xe ions on single crystal Au(lll) and LiF(OOl) target surfaces. Full and open symbols correspond to ion impact velocities of 6 and 7 x 10s ms"1 respectively. 120 §
100 I-
Xe^-LiFfOOl)
v = 6x10 m/s 0 0
10
20
30
40
50
60
70
ion impact angle [deg] Figure 5: Total electron emission yields versus ion impact angle (with respect to the surface normal) for Xe44* ion impact on single crystal Au(l 11) and LiF(OOl) target surfaces (impact velocity 6 x 105 ms'1).
639
Although still preliminary, our results suggest that for high projectile charge states and normal ion impact the number of captured and subsequently emitted electrons is limited by the reduced hole mobility in LiF. Unlike in metals, holes created by electron capture in (insulating) LiF may not be rapidly refilled. Thus hole formation reduces the capture rate for electrons unless the holes diffuse through the crystal. The mobility of the holes in the crystal and the subsequent capture of more tightly bound electrons by the same projectile will have a decisive influence on the number of emitted electrons. For larger impact angles a more continuous supply of electrons for subsequent electron capture is possible, since more extended surface areas are sampled by the projectile trajectory. Electron emission can then reach similar values as in the case of conducting surfaces. We currently plan to extend our measurements (a) to higher projectile charge states (e.g. U80+) (b) to lower ion impact velocities (using deceleration optics) (c) by a more systematic variation of impact angle and impact velocity and to compare our results with those of recent model calculations for HCI impact on LiF [18, 32]. The outcome will depend critcally on the details of the projectile- and hole dynamics in the target and therefore give important information on the latter. Acknowledgments This work has been supported by Austrian Fonds zur Forderung der wissenschaftlichen Forschung (FWF) and was carried out within Association EURATOM-OEAW. References [1] D. Hasselkamp, in Particle Induced Electron Emission II, edited by G. Hohler (Springer, Heidelberg, 1992), Vol. 123, p. 1 [2] J. Schou, Scanning Microsc. 2, 607 (1988). [3] M. Rosier and W. Brauer, in Particle Induced Electron Emission I, edited by G. Hohler (Springer, Berlin, 1991), Vol. 122. [4] R. Baragiola, in Chap. IV in Low energy Ion-Surface Interactions, edited by J. W. Rabalais (Wiley, 1993). [5] A. Arnau, et al., Surf. Sci. Reports 229, 1 (1997). [6] H. Winter, Physics Reports 367, 387 (2002). [7] H. D. Hagstrum, Phys.Rev. 96, 325 (1954). [8] H. D. Hagstrum, Phys.Rev. 96, 336 (1954).
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.9] T. Neidhart, F. Pichler, F. Aumayr, HP. Winter, M. Schmid, and P. Varga, Phys.Rev.Lett. 74, 5280 (1995). ;10] M. Sporn, G. Libiseller, T. Neidhart, M. Schmid, F. Aumayr, HP. Winter, P. Varga, M. Grether, and N. Stolterfoht, Phys.Rev.Lett. 79,945 (1997). ;i 1] F. Aumayr and HP. Winter, Phil. Trans. Roy. Soc. (London) 362,77 (2004). ;i2] P. Sigmund, (Mat.Fys.Medd., Copenhagen, 1993), Vol. 43, p. 2. [13] H. Gnaser, Low-Energy Ion Irradiation of Solid Surfaces (Springer Berlin, 1999). [14] C. Lemell, J. Stockl, J. Burgdorfer, G. Betz, HP. Winter, and F. Aumayr, Phys.Rev.Lett. 81,1965 (1998). [15] J. Stockl, PhD Thesis, TU Wien, (2003). [16] J. Stockl, T. Suta, F. Ditroi, HP. Winter, and F. Aumayr, Phys. Rev. Lett. 93, 263201 (2004). [17] L. Hagg, C. O. Reinhold, and J. Burgdorfer, Phys.Rev.A 55,2097 (1997). [18] L. Wirtz, C. O. Reinhold, C. Lemell, and J. Burgdorfer, Phys.Rev.A 67, 12903 (2003). [19] J. Stockl, C. Lemell, HP. Winter, and F. Aumayr, Phys. Scr. T92, 135 (2001). [20] M. Vana, F. Aumayr, P. Varga, and HP. Winter, Nucl. Instrum. Meth. Phys. Res. B 100, 284 (1995). [21] M. Vana, H. Kurz, HP. Winter, and F. Aumayr, Nucl. Instrum. Meth. Phys. Res. B 100, 402 (1995). [22] D. Ochs, M. Brause, P. Stracke, S. Krischok, F. Wiegershaud, W. MausFriedrichs, V. Kempter, V. E. Puchin, and A. L. Shluger, Surf.Sci. 383, 162 (1997). [23] M. Vana, F. Aumayr, P. Varga, and HP. Winter, Europhys. Lett. 29, 55 (1995). [24] F. Aumayr and HP. Winter, e-J. Surf. Sci. Nanotech. 1, 171 (2003). [25] HP. Winter and F. Aumayr, Euro. Phys. News 33, 215 (2002). [26] HP. Winter and F. Aumayr, J. Phys. B: At. Mol. Opt. Phys. 32, R39 (1999). [27] F. Aumayr, G. Lakits, and HP. Winter, Appl.Surf.Sci. 47, 139 (1991). [28] H. Kurz, K. Toglhofer, HP. Winter, F. Aumayr, and R. Mann, Phys.Rev.Lett. 69, 1140 (1992). [29] H. Kurz, F. Aumayr, C. Lemell, K. Toglhofer, and HP. Winter, Phys.Rev.A 48, 2182 (1993). [30] F. Aumayr, H. Kurz, D. Schneider, M. A. Briere, J. W. McDonald, C. E. Cunningham, and HP. Winter, Phys.Rev.Lett. 71, 1943 (1993). [31] H. Kurz, F. Aumayr, D. Schneider, M. A. Briere, J. W. McDonald, and HP. Winter, Phys.Rev.A 49,4693 (1994). [32] L. Wirtz, J. Burgdorfer, M. Dallos, T. Muller, and H. Lischka, Phys.Rev.A 68,032902 (2003).
ELECTRON EMISSION DURING GRAZING IMPACT OF ATOMS ON METAL SURFACES
HELMUT WINTER* Institutfiir Physik, Humboldt Universitat, Newtonstr. 15 Berlin, D-12489, Germany Electron emission from metal surfaces induced by grazing impact of fast atoms is studied via the coincident detection of energy loss of scattered projectiles with the number of electrons emitted during a scattering event. We will show that this method combined with the feature of well defined trajectories located in front of the surface allows one to reveal details on the electronic excitation and emission mechanisms. It turns out that binary collisions between atomic projectiles and conduction electrons play the dominant role for electron emission from metal surfaces. For scattering of keV He atoms from an Al(lll) surface we derive information on the momenta of Fermi electrons in the selvedge of the surface and on the effective electronic surface potential. Energy loss spectra can be described in term of collisions of low energy electrons with free atoms.
1. Introduction The emission of electrons induced by impact of atomic projectiles on solid surfaces plays an important role in a variety of applications and processes, as e.g., particle detection, surface analysis, modern display technology, or plasma wall interactions. Therefore a fundamental understanding of the underlying mechanisms is very important and motivated a substantial number of studies on this problem. Aside from considerable progress in the last decades, a detailed microscopic understanding is far from being complete. As a prominent example we mention here the threshold behaviour of ion induced electron emission, which implies considerable challenges from the experimental as well as from the theoretical point of view. For metal surfaces, the mechanism of electron emission is described in terms of an energy transfer in elastic binary encounters between fast atomic projectiles and conductions electrons. Since such electrons have to overcome the surface barrier in order to reach vaccuum, the minimum of energy transfer to Fermi electrons amounts to the target work function. This feature is the basis of a simple classical estimate on the threshold velocity for f
Work supported by grant Wil336 from Deutsche Forschungsgemeinschaft (DFG)
641
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electron emission, derived from conservation of energy and momentum [1]. From the experimental point of view, a main problem consists in the reliable measurement of very small electron yields present in the near threshold region. 2. Experiment and results With the setup displayed in Figure 1 we have studied electron emission during grazing impact of fast neutral atoms and identify the relevant interaction mechanisms [2]. In an UHV chamber at a base pressure of some 10"" mbar pulsed beams of noble gas atoms with energies ranging from some 100 eV to some 10 keV are scattered under a grazing angle of incidence Oin (from about 1° to 6°) from a clean and flat surface of a crystal. Scattered projectiles are recorded by means of a channelplate which serves as start detector of our timeof-flight (TOF) system for recording the overall projectile energy loss. Electrons emitted from the target are recorded by a surface barrier detector (SBD) at a potential of about 25 keV where the pulse heights are proportional to the number of electrons emitted during single collision events [3]. This coincident combination of the two detection channels allows one to relate the overall electronic excitations to the emission of a specific number of electrons. We used neutral atomic projectiles, since ions give rise to contributions from potential emission (PE) of electrons and their trajectories are affected by external fields.
Figure 1. Sketch of experimental setup for coincident TOF-electron number studies.
643 In Figure 2 we present a spectrum of projectile energy loss (TOF-signal) vs. electron number for scattering of 12 keV He° atoms from Al(lll) under a grazing angle of incidence of #§„ = 1.7°. We reveal a maximum for one emitted electron per complete scattering event and a substantial energy loss of about 350 eV. Since, for grazing incidence, scattering from the surface proceeds in the regime of surface channeling, the elastic energy transfer to lattice atoms amounts to only some eV here so that the observed dissipation of projectile energy results completely from electronic interactions, i.e. the excitation of the electron gas.
ft 300 -1 <5 200 i 0
1 2 3 4 electron number
5
Figure 2. 2D-specteum of energy loss vs. electron number for scattering of 12 keV He° atoms from Al(l 11) under a grazing angle of incidence #,„ = 1.7°,
In Figure 3 we plot energy loss spectra for an increasing number of emitted electrons showing an additional energy loss of about 10 eV for the emission of one electron. Since the normalized mean number of emitted electrons (electron yield) amounts of 1.5 electrons, electron emission has a small contribution to the overall energy loss only and most energy is absorbed in internal excitations of conduction electrons within the metal. Since in our method SBD pulse heights are recorded only if an event is registered by the channelplate detector, we can obtain accurate information on events related to the emission of no electron (noise level of SBD). This is the basis for precise measurements of low total electron yields y from measured probabilities»Wn for a specific number n of emitted electrons via
r = Z n W,/Iw, •
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Figure 3. Energy loss spectra for specific number of emitted electrons (upper panel) and pulse height spectrum (lower panel) of surface barrier detector (electron number spectrum) for scattering of 12 keV He" atoms from Al(l 11) under a grazing angle of incidence <„= 1.7°.
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645
For low y W0 will dominate the electron number spectrum. In contrast to a free running SBD, this information and y as small as about 10"5 can reliably be obtained. As an example we show in Figure 4 total electron yields as function of projectile velocity for scattering of He° atoms from Al(l 11). The solid curves in the graph and in the insert represent best fits to a threshold behaviour with a quadratic velocity dependence which result from phase space arguments in the framework of a classical model of energy transfer in binary collisions of projectile atoms with conduction electrons as outlined in the next section.
3. Model of energy transfer in collisions of atoms with conduction electrons The momentum and resulting energy transfer in elastic binary collisions of fast atoms with conduction electrons can be visualized by the scheme of a shifted Fermi sphere in momentum space [4]. This concept results from the feature that the component of momentum for the (light) electron parallel to the direction of the incident (heavy) atom is inverted and enhanced by q = 2 m vp with vp being the projectile velocity. Since the distribution of occupied states for a free electron metal can be represented by the Fermi sphere in momentum space, the result of binary collisions on the final momentum distribution can be visualized by a Fermi sphere shifted by momentum q (see Figure 5). As an example, we show the effect for a Fermi momentum vector kF where the final electron momentum (red arrow in figure) is obtained by inversion with respect to the direction of the incident projectile and adding of q . Excitations of the electron gas can take place only, if the final electron momentum lies outside the Fermi sphere (cross section in kxkz-plane is drawn in dark blue); emission of electrons to vacuum is possible, if the final kinetic energy is larger than the surface potential, i.e. (kF+q)2/2 > EF+W with EF being the Fermi energy (10.6 eV for Al) and W the work function (4.3 eV for Al(lll)). From the latter condition follows for the emission of electrons a threshold of minimum energy transfer qth = 2 m vth with threshold velocity
v l h =^[(l + W/E F r-l]
(2)
which amounts for Al(lll) to vth = 0.088 a.u. This is somewhat smaller than observed in the experiment (cf. Figure 4) which can be explained by the surface potential, since trajectories for grazing scattering do not penetrate the
646
bulk of the crystal and projectiles are specularly reflected in front of the topmost surface layer. As a consequence, electrons in the surface selvedge must have a component kz in the surface potential at distance z» since EF+W. Then the parallel component of electrons with Fermi momentum is reduced to k = (kF2 - kz2)1/2 and v^, is enhanced accordingly.
fo-*OJV2 ** £,+W
Figure 5. Visualization of momentum transfer in collision of atoms with conduction electrons by concept of shifted Fermi sphere in momentum space.
We have studied this feature for scattering of He atoms from Al(l 11) in the near threshold kinetic domain by changing the energy for the motion of projectiles normal to the surface Ez = Ep sin2€»in (corresponds to distance of closest approach to surface plane) via tuning of the incidence angle #„,. The phase volume for elecfrons excited to vacuum energies (cf. Figure 5) scales near threshold with (v - v^)2 so that we expect a threshold law quadratic in projectile velocity. In Figure 6 we have plotted the square root of electron yields as function of projectile velocity. The data shows a linear dependence and clearly different va, for different scattering conditions. Since the threshold velocity probes the maximum of the momentum component k , we can derive - in a classical picture - for trajectories with a given distance of closest approach (obtained from scattering potential at surface for fast atoms) kz and the effective electronic surface potential Vsurf(z) in fair agreement with the description of this barrier from density functional theory and LEED fine structure analysis [5],
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velocity (a.u.) Figure 6. (Electron yields)"2 as function of velocity for He atoms scattered from Al(l 11).
The energy loss spectra reveal defined shifts related to the emission of additional electrons (cf. Figure 3). The origin of this shift stems from the condition that the emission of an electron is related to a clearly higher energy transfer compared to excitations of the electron gas. For an estimate of this feature we consider collisions of electrons with free Ar atoms and derive from phase shifts the differential cross sections as function of scattering angle as shown in Figure 7. The energy transfer from projectiles with vproj = 0.11 a.u. shows a pronounced dependence on angle, and only close to backscattering this transfer exceeds the energy for emission to vacuum, i.e. the kinetic energy (dashed curve in Figure 7) has to be larger than EF+W = 14.9 eV.
60
90
120
150
scattering angle (°)
Figure 7. Diff. cross section (black solid curve) and energy transfer (red solid curve) for collisions of 15 eV electron with Ar atom. Dashed curve: electron energy after impact.
648
In computer simulations we assume an effective trajectory length which is equivalent to 70 individual collisions (nint). For each collision the probability for scattering under a specific scattering angle and for a corresponding elastic energy transfer is calculated from the data shown in Figure 7. The energy loss for Fermi electrons in individual events are summed up and plotted as total energy loss in Figure 8 (open circles). Electron emission is taken into account for sufficient energy transfer; electron transport in bulk and through interface is estimated by the assumption that about one out of 60 electrons (Ptrans) reaches vacuum. The full circles show a spectrum coincident with the emission of one electron. The dashed curve represents the energy loss without emission of an electron plus maximum energy transfer. The simulation shows that the shift of the two spectra is close to the energy for emission of a single electron. — 1 — 1 — • — 1 — • — 1 — I
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Acknowledgments The fruitful collaboration with S. Lederer (Berlin) and Profs. HP. Winter, F. Aumayr, J. Burgdorfer, Dr. C. Lemell (Vienna) is gratefully acknowledged. References 1. R. A. Baragiola, in "Low Energy Ion-Surface Interactions", ed. J. W. Rabalais, Wiley, New York 1994. 2. A. Mertens et al., Nucl. Instr Meth. B182, 23 (2001). 3. F. Aumayr, G. Lakits, and HP. Winter, Appl. Surf. Sci. 63, 177 (1991). 4. H. Winter and HP.Winter, Europhys. Lett. 62, 739 (2003). 5. R. O. Jones and P. J. Jennings, Surf. Sci. Rep.9,165 (1988).
INNER-SHELL COLLECTIVE EFFECTS FOR PROTONS BACKSCATTERED FROM THE AL(llO) SURFACE
P. L. GRANDE, A. HENTZ Institute de Fisica da Universidade Federal do Rio Grande do Sul, Avenida Bento Gongalves 9500, 91501 - 970, Porto Alegre, RS, Brazil G. SCHIWIETZ Hahn-Meitner-Institut, Abteilung SF4 Glienicker Str. 100, 14109 Berlin, Germany
The surface peak, a high-energy structure that appears in backscattering experiments for crystalline materials, has been studied in detail for a clean Al (110) surface. The corresponding energy-loss distributions are asymmetric due to the single and double ionization of the Al inner-shell electrons (L-shell). Effects beyond the independent-electron model (inner- shell collective effects) have been observed by using Monte-Carlo simulations for the ion ballistic and coupled-channel calculations for the inelastic energy-loss.
1. Introduction An investigation of the full energy-loss distribution allows for a better understanding of inner-shell collective effects in ion-atom interactions and is a prerequisite for monolayer resolution in ion-beam techniques used for depth profiling such as Nuclear Reaction Analysis (NRA) and Medium Energy Ion Scattering (MEIS) 1. Measurements in solids under shadowing and blocking conditions involving collisions with very small impact parameters are used in this work to study energy-loss processes involving inner-shell electrons. These conditions are realized in high-precision (resolution and statistics) measurements of the so-called surface peak, a high-energy structure that appears in backscattering experiments for crystalline materials. In this paper, we review the threoretical methods used to simulate the surface peak. Special emphasis will be drawn to role of the dynamic polarization of inner-shells as well as the influence of multi inner-shell ionization on the energy transfer. Further details may be found in refs.2,3.
649
650 2. Theoretical Procedure In order to describe the energetic shape of the surface peak, we have performed Monte-Carlo calculations where the inelastic energy losses are sampled in each collision using the program SILISH (Simulation of Line SHape)3 in connection with coupled-channel calculations4,5. Semiclassical coupled-channel calculations are the best tool to describe inner-shell ionization and excitation of atoms 4 ' 5 as a function of the impact parameter. For a given impact parameter b the amplitudes a*-,/ are calculated for any transition from an initial occupied state i to unoccupied bound or continuum states / and thus the probability corresponding to atomic excitation or ionization is determined. The independentelectron model (IEM) 7 is adopted for one active electron in the target atom moving in the electrostatic field due to both nuclei and the other electrons, which are included in a frozen-core Hartree-Fock-Slater framework 6 . Since each excited or continuum state corresponds to a well defined energy transfer T = ej — £*, the electronic energy-loss probability is given by dPi/dT{b) = J2f \ai->f(b)\2$(T - (e/ - £j)), where the sum above means an integral over e/, in the case of continuum states. In the framework of the IEM, the probability for a certain total electronic energy-loss AE transferred during an individual ion-atom collision can be written as
^g|( b )=(n/dT i g(6))x*(AS-5»
(1)
where the index i runs over all electrons for each subshell. The main fea/ture of the energy-loss distributions calculated above, for impact parameters close to zero, as the one at the backscattering collision, is the significant contribution of the inner-shells at large energy transfers. The contribution of the valence electrons for the width of the surface peak is of minor importance since the corresponding energy loss is much smaller than the experimental resolution. Using the coupled-channel calculations we can go beyond the independent electron model by introducing a dynamical screening of the projectile that can be determined selfconsistently from the time-dependent electronic density delivered by the coupled-channel calculations. In this way, the influence of the collective screening of the passive electrons on the active one has been estimated. Besides the dynamical screening we have also taken into account the effect of the modification of the target potential after a fast ionization process. According to the IEM the probability, in the case of double ionization, to remove the second electron is equal to the one for
651 the first electron. Here we have adopted instead a sequencial two-step process for double ionization. Instead of using Eq.(l) to describe, for instance, double ionization events, we use the energy loss probability in an ionized Al (Al + ) with a hole in the L-shell. This corresponds to the so-called two-step ionization model 8 yielding results similar to the average-electron model 9 . 3. Discussions and Conclusions The experimental energy distribution for 98 keV incident protons backscattered from a clean Al(llO) surface is shown in Fig. 1 (open symbols) in comparison with simulations. The dashed curve corresponds the SILISH simulations using the inelastic energy loss according to the IEM as described by Eq. (1) for the calculations of excitation/ionization of Al as a function of impact parameter. The agreement between the experimental data and the SILISH simulation is good (and even better for other geometries 3 ) but important deviations can be observed for larger energy losses. The effects concerning the Al (110) structure and the ion collision including all higher-order effects have been very accurately included 3 . In addition, from the simulations we have noticed besides the dominance of the L-shell electrons on the energy-loss shape of the surface peak a significant contribution of double inner-shell ionization of Al (the triple inner-shell ionization contribution is negligible). The solid curves in Fig. 1 corresponds to the SILISH calculations including collective effects such as dynamical screening and suppressed double ionization due to increased L-shell binding. As can be observed, the inclusion of collective effects for the inner-shell electrons is responsible for the deviations and reproduces rather well the experimental data. In fact, as shown in ref3, this particular geometry enhances the effects beyond IEM. This is the first evidence for an influence of the dynamic response of inner-shell electrons on the ion energy loss. In summary, we have observed the influence of inner-shell collective effects such as dynamical screening and target-potential rearrangement in the energy loss of backscattered protons for a special geometry where the number of near central collisions is maximized.
Acknowledgments This work was partially supported by the Brazilian agencies CNPq and CAPES, and by the program of Brazilian-German cooperation PROBRAL 166/04.
652 10 1 F
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s
r
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Experimental SILISH SILISH + + Dynamic Screening + Multiple Ionization .
..
i
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98.0
Shifted Proton Energy (keV) Figure 1. Experimental data (the open symbols) from ref[2,3] for 98 keV H+ backscattered in Al(110). The dashed line corresponds to coupled-channel calculations without collective effects. Effects beyond IEM are considered in solid line (including dynamical screening and two-step ionization). References 1. J.R. Bird and J.S. Williams, Ion Beam for Material Analysis, Academic Press, Australia (1989). J.F. Van der Veen. Surf. Sci. Rep. 5, 199 (1985). 2. P.L. Grande, A. Hentz, G. Schiwietz, W.H. Schulte, B.W. Busch, D, Starodub and T. Gustafsson, Phys. Rev B 69, 104112 (2004). 3. P.L. Grande, A. Hentz, G. Schiwietz, B.W. Busch, D, Starodub and T. Gustafsson, Phys. Rev A 72, 012902 (2005). 4. J.F. Reading, T. Bronk, A.L. Ford, L.A. Wehrman and K.A. Hall, J. Phys. B: At. Mol. Opt. Phys. 30, L189 (1997). 5. G. Schiwietz, Phys. Rev A42, 296 (1990); P.L.Grande and G. Schiwietz, Phys. Rev A47.1119 (1993). 6. F. Herman and S. Skillmann, in Atomic Structure Calculations, (PrenticeHall, Inc. Englewood Cliffs, New Jersey,1963). 7. M.R. Flannery and K.J.MacCann, Phys. Rev A8, 2915 (1973). 8. R. Hippler, J. Bossier and H.O. Lutz, J.Phys. B 17, 2453 (1984). 9. M. Schultz, R. Moshammer, W. Schmitt, H. Kollmus, R. Mann, S. Hagmann, R.E. Olson and J. Ulrich, J. Phys.B:At.Mol.Opt.Phys. 32 L557 (1999).
GUIDING OF HIGHLY CHARGED IONS BY SiOz NANOCAPILLARIES M . B. SAHANA*, P. SKOG, GY. VIKOR, R.T. RAJENDRA KUMAR, AND R. SCHUCH Atomic Physics, Fysikum, Albanova, S-106 91 Stockholm, Sweden
We report transmission of 7 keV Ne 7+ ions through highly ordered arrays of parallel SiOj nano-capillaries with diameters of about 100 nm and with an aspect ratio close to 300. The capillary membranes were fabricated by photo-assisted electrochemical etching of n-type silicon. The nano-capillaries guide the Ne7+ ions at capillary tilt angles of up to 4?, by a self-organizing capillary wall charge-up process, so that the large majority of the transmitted ions still exist in their initial charge state, i.e. Ne 7+ .
1. Introduction The transmission of Highly Charged Ions (HCI) through nano-capillaries has attracted considerable attention during recent years1,2. It has been shown that HCI transmitted through metallic capillaries have angular distributions given by the capillary aspect ratio and that ions, when they come within the critical distance from the capillary walls, can capture several electrons resulting in hollow atom formation''3. Recently, it was reported that 3 keV Ne^-ions, transmitted through insulating polyethylene terephthalate (PET, or Mylar)2 capillaries, have much broader angular distributions than the capillary aspect ratio, in contrast to the case with metallic capillaries, and that the majority of the transmitted ions have passed through the capillaries without changing their initial charge state, even though the capillaries were tilted up to 25?. The capillary guiding was attributed to a self-organizing charge-up effect that inhibits HCI from coming in close contact with the capillary walls, thus preserving the incident charge states. Because the capillaries in PET were randomly distributed, due to the fabrication method of etching ion tracks, and the fact that the angular spread of the capillaries might be as large as 2° we were encouraged to fabricate, and perform experiments on, highly ordered, parallel capillaries in Si0 2 . In this paper we report 7 keV Ne^-ion transport properties through ordered SiO : nanocapillaries. 2. Introduction Ordered Si nano-capillaries were fabricated on pre-patterned n-type silicon using the photo-assisted electrochemical etching technique4. For the HCI guiding, it is essential that the walls of the capillaries be dielectric. This is achieved by thermally oxidizing Si nano-capillary arrays to grow 100 nm thick silicon dioxide layers on the capillary walls. The diameter of the capillary after oxidation is around 100 nm, and the length is estimated to be between 25 - 30? m.
653
654
To prevent the charging-up of the surface of the capillary membrane by the Incident HCI, a gold layer with a thickness of 30 nm was grown by ©-beam evaporation. The inter-capillary distance of 1.4 ?m yields a geomertcal transparency of about 0.4%s which has been verified with Scanning Electron Microscopy (SEM) analysis. SEM micrographs of one of the fabricated capillary wafers are given in Fig. 1» depicting the uniform and highly ordered nature of the capillary arrays. The experiments on ion transmission through nano-capillaries were carried out with Ne7+ ions from a 14GHz Electron Cyclotron Resonance Ion Source (ECRIS) located at the Manne Siegbahn Laboratory Stockholm. An
Figure 1. SEM images of a cut through a membrane of Si nano-capillaries (left), and endview of Si0 2 capillaries (right).
accelerating voltage of 1 kV is used to give the ions extracted from the ECWS their desired kinetic energy and the ion transport to the experimental chamber is performed using an electrostatic lens system. The experimental chamber was evacuated down to 10"9 ton. A spectrometer of acceptance angle 0.36? and two channeltrons were used for analyzing the ions transmitted through the capillaries. The detailed description of the experimental chamber is given elsewhere5. Hie angle between the capillary axis and the incident beam direction is referred to as the tilt angle in the following discussion. The observation angle is measured with respect to the incident beam direction. 3. Results and discussion Bending of 7 keV Ne7+ ion beams by angles up to 4? is observed^ with the centre of the transmitted beam profiles being parallel to the capillary axes. Furthermore* the FWHM of the angular distribution of the transmitted beam is only 0.8?, much smaller than the values of 50 reported for PET capillary experiments The presence of different charge states in the transmitted beam are analyzed for various tilt angles by keeping the spectrometer at an angle equal to the centre position of the transmitted beam* which was derivedfromthe angular
655
Ne" 10000
0° tilt angle
N." 0.7%
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6
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4
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Figure 2. Transmitted Ne ion charge state fractions for different tilt angles.
distribution. The charge state distributions of the transmitted beam for capillary tilt angles 0° and 1° are given in Figures 2a and 2b respectively. For both tilt angles < 4 % of the ions of lower charge states
-4-
656 Classical over-the-Barrier model (CBM) . The reason for this deviation from the CBM can not be understood, presently. It calls for further detailed measurements and theoretical calculations. It is expected, according to the capillary dimensions, that all the incident ions will interact with the capillary walls when the tilt angle is > 0.2°. After a charge-up time in the order of seconds, the incident HCI beam deposited positive charge patches on the surface of the capillary wall. The ions entering the capillary, at a later instant are deflected by the Coulomb field of this self-organized charge patch close to the entrance of the capillary2. Irrespective of the capillary tilt angle, only a small percentage of charge changed ions are present in the transmitted beam. This suggests that the HCI ions are completely guided, once they enter the SiO 2 nano-capillaries. Because of the very small conductivity of the nano-capillary walls the charge patches seem to remain for times in the order of hours. 4. Conclusions The study of transmission of HCI through Si0 2 nano-capillaries revealed some interesting phenomena. The insulating capillaries charge up and form self arranged ion guiding, bending ~keV ion beams by a few degrees without essentially changing the charge states or kinetic energies of the transmitted ions. The angular distribution of the guided beam is very narrow, close to the value given by the capillary geometrical aspect ratio, quite different from results with PET. One could use this guiding effect of insulator capillaries to develop HCI focusing elements. The effect can also be used to investigate and characterize the electric properties of nano-capillary walls due to the HCI sensitivity on electric properties. References 1. 2. 3. 4. 5. 6.
S. Ninomiya, Y. Yamazaki, F. Koike, H. Masuda, T. Azuma, K. Komaki, K. Kuroki, and M. Sekiguchi, Phys. Rev. Lett, 78 4557, (1997). N. Stolterfoht, J.-H. Bremer, V. Hoffmann, R. Hellhammer, D. Fink, A. Petrov, and B. Sulik Phys. Rev. Lett.SS, 133201,(2002). K. Tokesi, L. Wirtz, C. Lemell, J. Burgdorfer, Phys. Rev. A 64, 042902 (2001). R. T. Rajendra Kumar, X. Badel, Gy. Vikor, J. Linnros and R. Schuch, Nanotechnology 16,1697, (2005). Gy. Vikor, R.T. Rajendra kumar, Z.D. Pesic, N. Stolterfoht and R. Schuch, Nuclear Instruments and Methods in Physics Research B 233, 218 (2005). J. Burgdorfer, P. Lerner, and F. W. Meyer, Phys. Rev. A 44,5674 (1991).
LOW-ENERGY ELECTRON IMPACT ON HYDROGENATED POLYCRYSTALLINE DIAMOND AND CONDENSED MOLECULES A. LAFOSSE, D. CACERES, M. BERTIN, D. TEILLET-BILLY, AND R. AZRIA Laboratoire des Collisions Atomiques et Moleculaires, CNRS-Universite (UMR 8625, FR LUMAT), Bat. 351, Universite Paris Sud, Orsay Cedex, F-91405, France
Paris-Sud
A. HOFFMAN Chemistry Department, Technion — Israel Institute of Technology Haifa 32000, Israel Interaction of low-energy electrons, first with hydrogenated polycrystalline diamond surfaces, second with films of acetonitrile molecules condensed on such substrates in order to induce their functionalization, has been studied using High Resolution Electron Energy Loss Spectroscopy (HREELS). The elastic and inelastic scattering of low-energy electrons on hydrogenated diamond have been studied by measuring energy loss spectra, elastic reflectivity, and excitation functions of CH stretching modes. The elastic reflectivity is related to the global reflectivity of the substrate-adsorbate complex and governed by its density-of-states above the vacuum level. The reflectivity of the local environment, in which the probed hydride species sp"-CH], are embedded, influences the vibrational excitation functions. The functionalization of the hydrogenated diamond, performed by irradiating with 2 eV electrons a condensed film of CH3CN, is initiated by dissociative electron attachment and consists almost exclusively in the covalent attachment of H2CCN fragments on diamond through Cu™,—C or Cu™—N bonds.
1. Introduction Organic modification of semiconductors or functionalization is a fast growing field due to the need to create devices, taking advantage of the properties of organic and inorganic materials capable of molecular recognition and chemical or biological sensing. Different methods, some of them being photo-assisted, in wet or dry environment have been developed. Silicon substrates have been widely used for these studies [1] and only recently diamond substrates have been considered.[2] In the present case, the chosen functionalization method consists in condensing a film of molecules containing a given organic function onto an inert substrate (here hydrogenated polycrystalline diamond), and then in
657
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irradiating it using low-energy electrons (1-25 eV). The aim is not only to produce reactions on a well controlled and initially inert surface but also to understand the mechanisms underlying the processes. Thus, interactions of electrons with the inert substrate need to be characterized and understood, prior to undertake its functionalization by electron impact on condensed films. Accordingly, the elastic and inelastic scattering of low-energy electrons has been studied using High Resolution Electron Energy Loss Spectroscopy (HREELS) for hydrogenated CVD polycrystalline diamond films, which contain various types of hydride groups, dominantly sp3-(—CRX, x=l-3) and sp2(=CHX, x= 1, 2) hybridized ones. Energy loss spectra, elastic reflectivity, and excitation functions of C—H stretching modes have been measured. We will show that the elastic reflectivity is related to the Density-Of-States (DOS) above the vacuum level of the substrate-adsorbate complex, which governs the electron backscattering probability. We will focus on the energy region of the diamond second absolute band gap and demonstrate that the reflectivity of the local environment, in which the vibrationally excited hydride species are embedded, influences the vibrational excitation functions. Preliminary results on the hydrogenated diamond/acetonitrile (CH3CN) system are also shown to illustrate the feasibility of an electron induced functionalization of this passivated substrate. The irradiation by 2 eV energy electrons of the deposited CH3CN film induces exclusively covalent attachment of H2CCN fragments on diamond through Cdian,—C and Cdiam—N linkages. This reaction is initiated by a Dissociative Electron Attachment (DEA) process on CH3CN, leading to [H2CCN]" + H' fragments. This DEA reaction is followed by depassivation of the hydrogenated diamond surface via recombinative abstraction of H atoms leading to H2 desorption. Simultaneously the H2CCN fragments bond to the created dangling bond of diamond and the electron is ejected in vacuum or leaks into the substrate. 2. Experimental part The polycrystalline diamond films were deposited on p-doped silicon substrates by Micro-Wave Chemical Vapor Deposition (MW-CVD) and consists of crystallites having a size of 2-3 |im and separated from each others by grain boundaries. After growth the samples were further exposed to a MW hydrogen plasma, which results in fully hydrogenated crystallite surfaces. Bare diamond surfaces were prepared in-situ by several annealing cycles to 1400 K and could be in-situ hydrogenated by exposure to activated hydrogen.[3,4] The sample is adapted on the cold end of a helium-cooled cryostat, so that its
659 temperature can be set down to 20 K and up to 1400 K, when using resistive heating. CH3CN films were condensed equally on both ex-situ and in-situ hydrogenated diamond samples by dosing 99.995 % purity CH3CN at 35 K with a typical coverage of 1-2 monolayers (ML). The molecular films were further irradiated by low energy electrons, which are produced by a tungsten filament (approximate energy resolution 350 meV). The electron incident energy was changed by adjusting the bias voltage between the filament and the sample, and the typically used electron dose was 1016 electrons/mm2. The HREEL spectrometer (Omicron, model IB500) is housed in a UHV chamber (base pressure in the 10~" Torr range) and consists of a double monochromator and a single analyzer. It has been specially designed to record energy loss spectra, as well as quasi-elastic (elastic reflectivity) and inelastic (vibrational) excitation functions in the energy range 2-30 eV.[4] The elastic reflectivity curve is recorded by following the elastic peak absolute intensity variation as a function of the incident electron energy. Inelastic excitation functions are recorded by following the variation of the number of detected electrons having lost the considered amount of energy upon surface scattering (peak count rate given in cts/s). The presented spectra were obtained in the specular geometry with an incident direction of 55 degrees with respect to the surface normal and an overall resolution of -5-7 meV, measured as the full width at half maximum of the elastic peak. 3. Results Energy loss spectra recorded for the ex-situ hydrogenated polycrystalline diamond films at different incident electron energies Eo are shown in Figure 1(a). Briefly, since the band attributions are quite well-understood [5], the broad feature located around 360 meV results from the overlapping of the losses attributed to the stretching modes of the various hydrid groups spmCHx. The broad structure observed in the region 125-190 meV is attributed to the CTL. bending modes mixed with lattice modes (phonons).[6] The first overtone of this intense band is observed around 300 meV, while higher harmonic orders and combinations of stretching and bending modes contribute to the vibrational spectrum at 450, 520, 600, 720, and 750 meV, as shown in Fig. 1(b). The observation of such a collection of combination and overtone losses for the lower incident electron energies is a clear signature of the involvement of resonant mechanism(s).[7] Note that for the higher incident electron energy of 13 eV, most of the overtone and combination bands vanish.
660
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i
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'
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150 300 450 450 600 750 Energy loss (meV)
• i i i • )
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Figure 1. Energy loss spectra recorded at Eo = 3, 6, 8, 13 eV for the ex-situ hydrogenated diamond films are presented in the panels (a) and (b). Intensities are given in number of counts per second. The spectra are shifted by 50 cts/s from each other in panel (a). The measured intensities have been multiplied by 5 and the spectra have been arbitrarily shifted vertically in panel (b). Specular excitation functions recorded for the losses 350 ( ), 362 (•), and 380 meV (A) attributed to v(CHJ.
The elastic reflectivity curves recorded for ex-situ and in-situ hydrogenated polycrystalline diamond are dominated by a strong enhancement around 13 eV incident electron energy.[4] This feature can be understood if we consider that once hydrogenated, the diamond films maintain the bulk electronic band structure up to the surface, as demonstrated by near-edge X-ray absorption fine structure spectroscopy.[8] In particular the electronic structure exhibits a second absolute band gap, which splits into two parts the conduction band, [9] generating the strong enhancement observed in the elastic reflectivity curves. Indeed electrons cannot propagate into the sample since no electronic state is available in this energy region; this leads to an enhancement of the electron backscattering probability. The electron elastic reflectivity probed using HREEL spectroscopy is therefore related to the DOS of the system above the vacuum level. This is the global reflectivity of the surface, which is probed in this way, since the whole area reached by the incident electron beam is contributing to the detected signal. In the present diamond films, the area occupied by the crystallite facets is much bigger than the area represented by the grain boundaries. The fully hydrogen saturated facets consist dominantly of .s^-CH* hydride species embedded in a diamond-like environment. The probed global
661 reflectivity can therefore be assimilated to the facet surface reflectivity, which possesses the characteristics of the diamond reflectivity. We have studied the influence of this particular feature of the diamond DOS, the second absolute band gap, on the inelastic backscattering of electrons leading to the excitation of stretching modes of the spm-CH^ hydride groups. The related elastic reflectivity enhancement observed around 13 eV should generate a peak at about the same electron energy in any recorded inelastic excitation function, as a consequence of the electron enhanced backscattering probability, provided that the probed CH* groups are all jp3-hybridized, i.e. embedded in a diamond-like environment. The excitation functions recorded for the losses at 350, 362, and 380 meV in the case of ex-situ hydrogenated polycrystalline diamond are compared in Figure 1(c). For the three curves, we associate the trend observed below 10 eV to features related to resonant mechanism contributions,[3,10] superimposed on a decreasing background attributed to dipolar scattering. Above 10 eV the excitation function recorded at 380 meV behaves differently than the two other functions, for which an enhancement is observed around 13 eV incident electron energy. This enhancement is related to the reflectivity enhancement induced by the diamond second absolute band gap, since at this energy, (i) no resonance is known for gas phase hydrocarbons, and (ii) the collection of observed overtone and combination bands is strongly reduced (Fig. 1(b)). Whereas the global reflectivity of the sample is probed by recording elastic excitation function (as discussed above), by recording inelastic excitation functions, we probe the reflectivity of the excited species environment, i.e. the local reflectivity. Therefore the losses at 350 and 362 meV must be ascribed to diamond-like CHX groups, while the loss at 380 meV must be ascribed to species located at grain boundaries (which are not diamond-like). These attributions are in agreement with spectroscopic data of the literature, according to which the losses associated to the stretching modes of sp1- (—CHX) and sp2- (=CHx)-hybridized CHX groups are expected in the regions -345-372 and -372-384 meV, respectively.fi 1,12] In conclusion, measuring inelastic excitation functions allow us to determine the nature of the nanoscale environment, in which the probed vibrationnaly excited species are embedded. The electron scattering experiments presented above are part of the studies, which have been undertaken in order to understand the interaction of lowenergy electrons with the hydrogenated diamond substrate. In the following we will present a study on the functionalization of these passivated surfaces, as induced by electron bombardment at 2 eV of condensed CH3CN films.
662
Figure 2 gathers HREEL spectra, recorded at 5 eV incident electron energy, successively for in-situ hydrogenated diamond (a), for a 2 ML film of CH3CN condensed on hydrogenated diamond before (b) and after (c) electron irradiation at 2 eV energy. The last spectrum was recorded for the substrate after evaporation of the condensed/physisorbed species by heating the irradiated film to about 400 K (d). The HREEL spectrum (a) recorded for the in-situ hydrogenated diamond differs slightly from the one of ex-situ hydrogenated diamond (shown in Fig. 1), in particular a supplementary loss observed for the former at 180 meV is generally attributed to CH bending vibration.[5] The compositions in various hydrid spm-CRx species of both substrates are comparable (same energy loss bands) but not strictly equivalent. The HREEL spectrum of condensed CH3CN (b) is in general agreement with those obtained in previous studies,[13,14] and only the striking features are described in this paper. This spectrum is mainly characterized by peaks associated to 5(C—CN) bending modes around 48 meV, C—C stretching mode at 117 meV, methyl rocking and bending vibrations respectively at 129 and 180 meV, C=N stretching mode at 280 meV and finally CH stretching vibrations at 370 meV. This spectrum is only slightly modified upon irradiation by 2 eV electrons (c), essentially we observe a change in the relative intensities of the loss peaks. After evaporation to 400 K of the irradiated film, only chemisorbed species remain on the diamond surface. The associated HREEL spectrum (d) presents major differences with both hydrogenated diamond and condensed CH3CN film spectra. The peaks at 50, 117 and 129 meV attributed to CH3CN molecular vibrations are no more observed, whereas the C=N stretching vibration at 280 meV is still present, and new peaks show up at 32 and 200 meV, this last peak being associated with v(C=N) and/or v(C=C) vibrations. Thus species containing C=N and/or C=C and species containing O N bonds are chemisorbed on the diamond substrate. By comparison with the spectrum of the hydrogenated diamond (a) we see that the 180 meV loss is more pronounced, that the CH stretching band is shifted to higher energies, and finally that the 450 meV overtone of the C—C stretching vibration is no more observed which means that the vibrational signatures of hydrogenated diamond are no more observed in spectrum (d). These transformations must be initiated and associated with electron dissociation processes in CH3CN condensed layer on hydrogenated diamond since (i) hydrogenated diamond surfaces are known to be chemically very stable, and we have checked that condensation of few ML of CH3CN on this surface only followed by desorption at 400 K leaves the HREEL spectrum of the substrate unchanged, and since (ii) the interaction of 2 eV
663
electrons on the hydrogenated Diamond leads only to vibrational excitation, H" desorption being observed only above 4.5 eV.[3]
200
300
Energy Loss (meV) Figure 2. Energy loss spectra recorded at Eo = 5 eV for in-situ hydrogenated diamond (a), for a 2 ML film of CH3CN condensed on hydrogenated diamond before (b) and after (c) electron irradiation at 2 eV, and for the functionalized diamond surface after evaporation of the condensed species by heating to 400 K (d). For all spectra, the elastic peak intensity was normalized to 200.
DEA is the only known electron dissociation mechanism in CH3CN at energies below 4 eV. This process has been studied in the gas phase [15], and it has been shown that CN" ions are produced around 2 eV impact energy, CHCN and CH2CN" around 3.2 eV. Since in the condensed phase, resonances are observed at energies about 0.8 eV lower than in the gas phase due to the polarization energy, and considering that the cross section for CH2CNT formation is about 4xl0"23 m2, i.e. two orders of magnitude higher than for CHCN" and CN" formation, we will consequently discuss the spectrum (d) exclusively in terms of interaction of CH2CN" and H' fragments with the hydrogenated diamond substrate. If we take into account (i) the fact that two mesomeric forms can be written for CH2CN" ions, so that the probability of presence of the negative charge in these ions is probably distributed around the N atom as well as around the C atom and (ii), that the 32, 180 and 200 meV losses can be associated respectively with C&sm—(CH2CN) stretching, CH2 scissor and v(C=C) and/or v(C=N) vibrational modes i.e., consistent with vibrational signatures of chemisorbed CH2CN fragments through Cdiam—C and
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Qiam—N covalent linkage on diamond, the overall mechanism for the functionalization reaction of diamond can then be described as follow: 1. DEAprocess: e'{2eV) + CHiCN -> {CH^CN')' -> [CH2CN]' + H', 2. Depassivation of the hydrogenated diamond surface via recombinative abstraction of H atoms by H' radicals,[16] 3. Simultaneous bonding of H2CCN fragments through C or N linkage to the dangling bond of diamond and the electron ejection in vacuum or leakage into the substrate. 4. Conclusion Interaction of low-energy electrons, first with hydrogenated polycrystalline diamond surfaces, second with films of CH3CN molecules condensed on such substrates in order to induce their functionalization, has been studied using HREEL spectroscopy. Concerning the low-energy electron interaction with the passivated diamond substrate, we have in particular shown that (i) the elastic reflectivity is related to the diamond DOS, and (ii) that inelastic excitation functions bring insight into the nanoscale environment of the probed species. Electron irradiation at 2 eV of a film of condensed CH3CN molecules induces the substrate functionalization. The understanding of the electron interaction with the hydrogenated substrate and with condensed CH3CN film allowed us to establish the mechanisms of the covalent bonding of CH2CN fragment to the substrate through Cdiam—C and Cdiam—N linkages. Acknowledgments C. Jaggle and Pr. P. Swiderek from the Universitat Bremen are gratefully acknowledged for their contribution to the work on condensed CH3CN. The group of Orsay acknowledge the support provided by the EPIC EU Network, "Electron and Positron Induced Chemistry", Framework, 2002-05. References 1. e.g. S.F. Bent, Surf. Sci. 500 (2002) 879; W. Di, P. Rowntree and L. Sanche, Phys. Rev. B 52 (1995) 16618. 2. e.g. A. Haiti et al., Nature Materials 3 (2004) 736; W. Yang et al., Nature materials 1 (2002) 253. 3. A. Hoffman et al., Phys. Rev. B 63 (2001) 045401. 4. A. Lafosse et al., Phys. Rev. B 68 (2003) 235421. 5. e.g. J. Kinsky et al., Diamond Relat. Mater. 11 (2002) 365; B.D. Thorns and J.E. Butler, Phys. Rev. B 50 (1994) 17450.
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6. B. Sandfort, A. Mazur, and J. Pollmann, Phys. Rev. B 51 (1995) 7150. 7. R.E. Palmer and P.J. Rous, Rev. Mod. Phys. 64 (1992) 383; J.W. Gadzuk, J. Chem. Phys. 79 (1983) 3982. 8. A. Hoffman et al, Phys. Rev. B 59 (1999) 3203. 9. e.g. J.F. Morar et al., Phys. Rev. Lett. 54 (1985) 1960; M.-Z. Huang and W.Y. Ching, Phys. Rev. B 47 (1993) 9449. 10. e.g. H. Tanaka et al., J. Phys. B 16 (1983) 2861; M. Allan, J. Am. Chem. Soc. 115 (1993) 6418; I.C. Walker, A. Stamatovic, and S.F. Wong, J. Chem. Phys. 69 (1978) 5532 11. J. Kuppers, Surf. Sci. Rep. 22 (1995) 249 12. H. Ibach and D.L. Mills, in Electron energy loss spectroscopy and surface vibrations, Academic Press (1982) 13. B.A. Sexton and N.R. Avery, Surf. Sci. 129 (1983) 21. 14. F. Tao et al.„ J. Phys. Chem. B 106 (2002) 3890. 15. M. Heni and E. Illenberger, Int. J. Mass Spectrom. Ion Proc. 73 (1986) 127; W. Sailer et al., Chem. Phys. Lett. 381 (2003) 216. 16. T. Bakos, M.S. Valipa, and D. Maroudas, J. Chem. Phys. 122 (2005) 054703.
LOW ENERGY SPIN-POLARIZED ELECTRON-PAIR (e,2e)-INREFLECTION FROM VARIOUS SURFACES
J.F. WILLIAMS, S.N. SAMARIN, A.D. SERGEANT, A.A. SUVOROVA Centre for Atomic, Molecular and Surface Physics, School of Physics, University of Western Australia, Perth, WA 6009, Australia O.M. ARTAMONOV Research Institute of Physics, St. Petersburg University, St.Petersburg, Russia The mechanisms of dipole and binary scattering are discussed for electron emission from surfaces. The nature of single and double electron emission are compared. Recent observations using spin-polarized (e,2e) spectroscopy are presented and the technique is applied to study ferromagnetic layers deposited on nonmagnetic substrate. Experimental results confirm, that the Fe film changes the easy magnetization axis when the film thickness reaches the critical value of about 50 ML (monolayers). Spin-dependent total energy distribution and spindependent parallel-to-the-surface momentum distribution reflect scattering dynamics and spindependent distributions of electronic states in energy-momentum space.
1. Introduction. Current scientific and social applications of materials focus on the nanoscale where their use covers the breadth of human imagination. We are interested in metals, semiconductors and insulators and their interfaces. Classification of these materials has traditionally been done using single particle impact of photons, electrons and ions with observation of single scattered or ejected electron spectroscopies [1]. The extension of these observations, their modeling and applications have given rise to much knowledge and many industries. The energy distribution of electrons scattered from a surface was shown by single electron spectroscopy to consist of an elastic maximum and the inelastic scattering showed 'secondary ' electron and energy losses. The mechanism for emission of 'secondary' electrons arises from multiple scattering and deexcitation of collective excitations with emission of an electron. The energy loss spectra arise from single electron excitations, interband transitions and collective excitations of plasmons and excitons. The physical origin of these spectra can be modeled as a superposition of dipole and binary scattering. Dipole scattering arises from the Coulomb interaction of the incoming electron with the electric field fluctuations outside the surface from oscillating surface atoms. Binary scattering usually describes the scattering of an incident electron with atoms within the first few surface monolayers in short range interactions and produces electron-hole pairs. Frequently observations of electron scattering 666
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from surfaces add to the body of knowledge of the consequences of these interactions. However it is two-electron (or synonymously electron pair or e,2e) spectroscopy, in reflection from the surface [2,3] that has enabled further significant progress. Kirschner et al [1995] showed how the observation of two electrons revealed the electronic surface structure, particularly the electron-pair correlations, and subsequently the spin-dependent magnetic surface properties in a series of novel measurements [4,5,6,7]. Now in Perth, in a series of papers we have extended the use of the electron-pair technique, confirmed some earlier results and revealed new features of various surfaces. Those results include: (i) comparisons and contrasts of single versus double electron spectroscopy [8];
(ii) left / right scattering asymmetries arising from spin-orbit effects [9]; (iii) spin-orbit coupling in the inelastic scattering channel of low energy electrons from W(100) and W(110) as well as spin-related features of their electronic band structure [10]; (iv) experimental [6,7,8] and theoretical [11-13] works demonstrated how this technique revealed electron scattering dynamics, surface electronic structure and electronic correlations; (v) how the exchange interaction and the spin-orbit interaction could be observed and analyzed. Exchange is observable in a ferromagnetic surface (where the population of spin-up and spin-down states is unequal) with appropriate orientation of the magnetization direction and the polarization vector of the electron beam because it is proportional to the scalar product of the average spin of the target and the polarization vector of the incident beam. The spin-orbit interaction is dominant for non-magnetic heavy (large Z) targets, such as tungsten. The calculated spin asymmetry of the (e,2e) cross-section on W(100) was found to be due mainly to the spin-orbit coupling in the valence electron states [13]. This progress report gives some insight into aspects of these phenomena and how they can be observed. Recent work on magnetic surfaces is indicated. 2, Experimental approach. The starting point is to establish an ultra clean 10" Torr vacuum system with low partial pressure of contaminant atoms for the surface under study. Then appropriate methods of cleaning the surface and then establishing the morphology of the surface. The laboratory now has, or has access to, Low Energy Electron Diffraction, Auger electron spectroscopy, ion sputtering gun,
668 electron microscopy, surface ellipsometry, spin-polarized electron sources and Mott detectors. The incident electron beam originated from a strained GaAs photo-emission source and is characterized by 75% spin-polarization, electron beam energy 15 eV to 50 eVs 1 ns beam pulse width for time-of-flight spectroscopy* repetition rate of 2.5 x 106 and an average current of about 10"12 amps. To avoid the influence of the incident electron current drift and the sample surface modification (contamination) on the spin-asymmetry during the measurements we altered the polarization of the beam every 5 seconds and the (e,2e) spectra were measured for spin-up and spin-down polarization of the incident beam. We used a combination of time-of-flight energy analysis and coincidence technique to collect .data in two files for spin-up and spin-down incident electrons. Then these two spectra were compared in terms of difference and asymmetry. The substrate (W crystal) was cleaned prior to film deposition using the usual procedure [14]. The iron film was deposited at about 1 ML per minute using a commercial evaporator (Omicron) calibrated using a quartz microbalance. The crystallinity of the film was controlled using low-energy electron diffraction. To reverse the magnetization of a Fe film we used a magnetizing coil inside the vacuum chamber. A typical LEED pattern from a clean W(110) single crystal and 3 ML Fe film are shown in Fig. 1.
Figure 1. LEED patterns from a clean single crystal of W(l 10) and 3ML Fe on W(l 10).
3. The basic observations. The energy and momentum conservations, indicated in Figure 2$ indicate the basic observations. In a single collision event the energy of primary electron E0 and two outgoing electrons Eh E2 define the binding energy of the valence
669
electron: Eb = Ei + E2 - E0. The number of correlated electron pairs as a function of the total (sum) energy Etot = Ei + E2 then represents the total energy distribution. In the case of a crystal surface, the component parallel-to-thesurface of the electron momentum is a good quantum number for four relevant electronic states of the scattering event. Therefore: K^ + Kb|| = K^ + K2||, where Ko, Kb, Ki, K2 are the momenta of the incident, bound, first detected and second detected electrons, respectively. Hence, we can present our measured spinpolarized (e,2e) spectra as projections on the total energy of a pair or, if we select a certain band of the total energy, we can plot the number of pairs as a function of Kby. Position sensitive detection
,
^
momentum - resolved spectroscopy
Measurement: {x1,y1,t1,X3,y2,t2) = electron pair ^ ^ > k k
(
k2
l||+k2||=
kflM — 0 because of the normal incidence
±b —On - momentum in11 ~ 1*211 — ^||
" of the valence electron ( E , + E 2 ) - E 0 - E b - binding energy of the valence electron
Figure 2. Basic experimental approach.
4. Electron -pair energy sharing. Now we can establish the basic spin observables of a clean single crystal W(l 10) substrate by presenting the binding energy spectra and the distributions of correlated electron-pairs as a function of the parallel-to-the-surface momentum of the valence electron, as indicated in Figure 3. These distributions were constructed using mentioned above momentum conservation law: Koy + Kb]| = Kin + K2y (for the component in the scattering plane that is: Kox + Kbx = K|X + K2x). The binding energy of the valence electron was selected to be within 2 eV energy band just below the Fermi level.
670
K
„(A>
-2.0
-1.5 -1.0 -0.5
0.0
0.5
K^i
Fig. 3. Spin-dependent K, - distributions of correlated electron pairs excited by 25.5 eV primary electrons from W(l 10) at three different positions of the sample.
When the incidence angle changes from zero to +12° or to -12° the distributions change, both in shape and in spin-dependence. For normal incidence the spinintegrated distribution is symmetric with respect to the zero point where K)x = K.2x and Kbx = 0. For off-normal incidence (panels a and c) the distributions are not symmetric relative to the zero point. This is the consequence of the changes in the scattering dynamics and diffraction conditions for correlated electron pairs. We note here that the off-normal incidence allows to extend the range of the valence electron momentum that can be probed by this technique from ±1.5 A"1 to ±2.4 A'. Regarding the spin-dependence, one can see that the KbX - distributions for offnormal incidences exhibit large differences between spin-up and spin-down spectra. The difference spectra possess broad maxima located at Kbx = - 0.44 A"1 for positions (a) and at K|,x = + 0.44 A"1 for position (c). The asymmetry A = (I+ - I")/(I+ + I") reaches -10% and 10%, respectively. The I+ and I" spectra and difference spectrum D = (I+ -1") show an interesting symmetry property. Let us denote by Ia and Ic spectra recorded at geometry (a) and geometry (c), respectively. Reflection at the (y,z)-plane reverses the spin of the primary electron and transforms the geometry (a) into geometry (c) with interchange of the outgoing electrons. It implies that Ia+(Kbx) = Ic"(-Kbx) and, by consequence, Da(Kbx) = - Dc(-Kbx). Comparing the spectra in panels (a) and (c) one can see that difference spectra exhibit such symmetry.
671 For the normal incidence (position b) the spin-difference spectrum shows "leftright" symmetry of spin-orbit coupling. From the energy sharing distributions, measured at two azimuthal positions of the W(110) crystal, we deduce that the sign and magnitude of the spin-orbit coupling depends on the azimuthal orientation of the crystal. This anisotropy indicates the anisotropy of the orbital moments of the valence electrons in W(110). 5. Magnetic surface Then, using a magnetic target we check that it is in a single domain state, and at the same time check the polarization of the incident beam, by using spinpolarized electron energy loss spectroscopy measurements. The asymmetry of Stoner excitations observed on thick (>50 ML) layer of iron at energy loss of about 2 eV (asymmetry as measured was up to 16-20 %) confirmed, that the incident beam is polarized and the film is in a single domain state. The polarization of the incident beam was about 70 %, the angle of incidence 0° (normal incidence) and the detection angles were ± 50°. Low-energy (e,2e) spectroscopy, in reflection mode with spin-polarized incident electrons, has been used to study spin-dependent scattering dynamics and surface magnetism of a single crystal of iron [5]. It is known [15] that a ferromagnetic layer of iron deposited on W(110) exhibits an in-plane magnetic anisotropy with easy magnetization direction perpendicular to [100] direction of the substrate for the layer thickness below 45-50 monolayers. When the thickness reaches a critical value of about 50 ML the easy magnetization axis rotates by 90° and become parallel to the [100] direction of the substrate. So we chose thin ferromagnetic layers on nonmagnetic substrates to search for new details of magnetic anisotropy. Since the spin-effect in polarized electron scattering from ferromagnetic surface is observable when the dot-product of the incident beam polarization and the magnetization direction of the film is not zero, one would expect to observe the change in the spin-dependent electron scattering when the magnetization direction of the film rotates by 90°.
At Fe film thicknesses below 45 ML the spectra for spin-up and spin-down incident electrons are identical. When the film thickness reaches 50 ML, the total energy distributions for spin-up and spin-down incident electrons becomes different (Fig. 4). The difference spectrum has a maximum (negative) just below the Fermi edge and it changes the sign at about 2 eV below the Fermi level.
672
When the magnetization of the film was reversed the difference spectrum reverses its sign that shows clearly that the difference between two spectra is caused by the magnetization of the film and the origin of the observed spin effect is the exchange interaction. Using parallel-to-the-surface momentum conservation we can plot the number of correlated electron pairs as a function of the parallel to the surface momentum of the bound electron involved in the electron-electron collision (Fig. 4). Fe IHm on W(110), 50 ML, Ep = 25 fiV
binding energy relative to EF (eV)
Kj (A"1)
Figure 4. Spin-resolved binding energy spectrum (left) and Kt,u distributions of Fe film.
One can see that within 2 eV total energy band, just below the Fermi level, the difference spectrum as a function of the valence electron momentum K^ is concentrated mostly in the centre of the Brillouin zone. When the magnetization of the film is reversed the difference spectrum change the sign. The detailed analysis of the (e,2e) reaction on a ferromagnetic surface shows [11] that at the symmetrical kinematics the asymmetry of the binding energy spectrum reflect the spin-asymmetry of the spin-resolved spectral density function of the ferromagnet. References 1. M. A. Van Hove "Overview of surface structures" Ch 11, 313-337 in Solid State Photo-emission and related Methods, Eds. W. Schattke and M. A. Van Hove, Wiley Germany (2003). 2. J. Kirschner, O.M. Artamonov, A.N. Terekhov, Phys. Rev. Lett. 69 1711(!992). 3. J. Kirschner, O.M. Artamonov, S.N. Samarin, Phys. Rev. Lett. 75 2424(1995). 4. S.N. Samarin, J. Berakdar, O. Artamonov, and J. Kirschner, Phys. Rev. Lett., 85 1746(2000).
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5. S. Samarin, O. Artamonov, J. Berakdar, A. Morozov and J. Kirschner, Surf. Sci. 482 (Part 2) 1015 (2001). 6. J. Berakdar, A. Ernst, A. Morozov, S.N. Samarin, F.U. Hillebrecht, J. Kirschner, Novel imaging technique of the magnetic Brillouin zone of thin films and magnetic surfaces, in Photonic, Electronic, and Atomic Collisions. Ed., Sheldon Datz, Rinton Press, Santa Fe, NM, USA (2002). 7. A. Morozov, J. Berakdar, S.N. Samarin, F.U. Hillebrecht, J. Kirschner, Phys. Rev. B65 104425 (2002). 8. S. Samarin, O. M. Artamonov, A.D. Sergeant, and J.F. Williams, Twoelectron spectroscopy versus single-electron spectroscopy for studying secondary emission from surfaces, In: Correlation Spectroscopy of Surfaces, Thin Films and Nanostructures, Eds. Berakdar J. and Kirschner J., WILEY-VCH, Weinheim, Germany 2004 9. S. Samarin, O. M. Artamonov, A.D. Sergeant, and J.F. Williams, Surf. Sci. 579/2-3 166 (2005). 10. S. Samarin, O. M. Artamonov, A. D. Sergeant, J. Kirschner, A. Morozov, J. F. Williams, Phys. Rev. B70 073403/1-4 (2004). 11. J. Berakdar, Phys. Rev. Lett, 83 5150 (1999). 12. J. Berakdar, Nucl. Instr. & Methods in Physics Research, Section BBeam Interactions with Materials & Atoms. 193 609 (2002). 13. H. Gollisch, Xiao Yi, T. Scheunemann, and R. Feder, J. Phys.: Condens Matter 11 9555 (1999). 14. R. Cortenraada, S.N. Ermolov, V.N. Semenov, A.W. Denier van der Gon, V.G. Glebovsky, S.I. Bozhko, H.H. Brongersma, J. Crystal Growth, 222 154(2001). 15. M. Donath, J. Phys. C: Condens. Matter 11 9421 (1999).
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119 421 270 526 225 593, 601 593,601 405 159 405 405 195, 209 209 593, 601 123 98 429 466 601 458 209 195, 373 209 345 421, 552 131 90 298, 543 209 506 421 159 659 163 195 274 561 413 225
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601 30 601 609 543 123 298, 543 329 337 413,535 433 593 115 282 337 329 561 373 498 443 506 454 518 123 155 593, 601 345 466 397 139, 585, 627 306 571 609 235 454 535 593, 601 123 518
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679 Schiwietz, G SchlathOlter, T. Schmidt, E. W. Schmidt, H. T. Schmidt-Bocking, H Schnell, M Schoffler, M Schossler, S Schroter, C D Schuch, R Schultz, D. R Schulz.M Scofield,J. H Sergeant, A. D Sevic, D Shah, M. B Shibata, M Shigeta, W. Shiromaru, H Sierpowski, D Sigaud, G. M Simonet, J Skog, P. Solleder, B Solov'yov, A. V. Soria Orts, R Souza Melo, W. de Spillmann.U Srigengan, B Starace, A. F. Starrett, C Staudte, A Stebbings, S. L Stelbovics, A. T. Stia, C. R Stockl, J Stohlker, Th Stolterfoht, N Sullivan, J. P.
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30 466 179 609 147 262, 270 593, 601 482 60 90 421
Photonic, Electronic and Atomic Collisions Proceedings of the XXIV International Conference
This book contains a series of scientific contributions corresponding to the invited talks to the XXIV International Conference on Photonic, Electronic and Atomic Collisions. A wide range of subjects comprising a balanced mix of topics is covered. It includes the collisions of heavy particles and electrons with atoms, molecules and clusters, the coherent control of reaction dynamics using lasers and electromagnetic fields with molecules, clusters and liquids, the collisions of electrons and heavy particles with surfaces, the transport of particles through solids, the interaction of multicharged ions with metallic and insulating nanocapillaries, the recent experimental progress in the synthesis of antihydrogen, the interaction of solar winds with cometary atmospheres, the physical interpretation of reactions in biological systems, and cold-atom/ molecules collisions, among other themes.
6329 he ISBN 981-270-412-4
orld Scientific YEARS O I 8 1 -
PUBl SUING 2 0 D 6
