Dynamics of matter-, antimatter-atom collisions

Nuclear Instruments and Methods in Physics Research B42 (1989) 527-535 North-Holland, Amsterdam

DYNAMICS

OF MATTER-,

ANTIMATTER-ATOM

D.R. SCHULTZ, C.O. REINHOLD

527

COLLISIONS

and R.E. OLSON

Department of Physics and Laboratory for Atomic and Molecular Research, University of Missouri-Rolla, Rolla, Missouri 65401, USA

Dynamical effects which lead to differences in the cross section for single- or multi-electron removal from atoms by singly-charged particle, (e, e, p. p) impact are caused by the differences in mass and sign of the charge of the projectile. This fact, often masked by simple first order theories, has now been demonstrated both experimentally and by more appropriate and sophisticated theoretical methods. Here we summarize our recent work elucidating these effects using the classical trajectory Monte Carlo technique to examine the total cross sections, and various cross sections differential These cross sections have been calculated for intermediate velocity (1 to 6 a.u.) collisions been compared with other theoretical results and experimental measurements.

1. Introduction The study of ion-atom collisions involving members of the singly-charged family of particles e, 8, p and p (electron, positron, proton and antiproton) provides a fundamental testing ground for theoretical approaches which go beyond simple first order theories. The more strenuous test of theoretical treatments arises, in particular, from what has recently been understood to be the manifestation of dynamical effects caused by the magnitude of the projectile’s mass and the sign of its charge [l-11]. Furthermore, the advent of experimental measurements of electron-removal cross sections using antimatter projectiles has allowed, and prompted, a critical comparison between theory and experiment. These new experiments reflect the recent availability of intense low energy antiproton [12] and positron [13-141 beams and their application to the study of inelastic ion-atom collisions. Differences in collision dynamics due to differences in projectile mass and sign of charge may be explored both theoretically and experimentally by comparing the cross sections for impact of the singly-charged particles e, e, p and p at equal collision velocities. The study of these processes allows the variation of a single collision parameter at a time. Comparisons using electrons and protons vary not only the mass but also the sign of the charge and therefore the number of open channels. Thus comparisons including positrons and protons allow a superior discrimination of the mass effect. To these ends we have calculated classical trajectory Monte Carlo (CTMC) [15,16] cross sections for a number of electron-removal processes in electron, positron, proton and antiproton collisions with hydrogen and helium. We find that the differences in the cross sections for these collisions may be explained by a relatively few dynamical effects. 0168-583X/89/$03.50 Q Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

in angle and energy, for electron removal. of e, e, p and p with H and He, and have

By its nature, the CTMC method is well suited for this program since it includes an explicit description of the collision dynamics. Furthermore, it represents a step beyond simple first order theories since the forces between all bodies are included, not only electron-target and electron-projectile interactions. In addition, the CTMC method treats all the projectiles (e, e, p and p) within the same theoretical framework, thus isolating the dynamical effects from differences in the level or nature of approximation. The CTMC technique has been demonstrated to yield extremely good results for electron removal by heavy particle impact [15-211 and reasonable agreement with experiment for light particle impact (electrons [22] and positrons [7]) in the intermediate collision velocity range, a regime in which perturbative approaches have not, in general, had so much success. Thus, the relative ease with which it may be used to illuminate the differences in collision mechanisms, coupled with its demonstrated validity, justify the application of the CTMC technique. Finally, once identified, the effects elucidated by this method may provide direction for more exact fully quantum mechanical treatments. In section 3.1 we discuss the collision mechanisms responsible for the differences in the double-ionization cross sections for protonand antiproton-impact of helium [4). Single electron-removal processes in collisions of pOsitrons and protons with helium [7] and of electrons, positrons, protons an antiprotons with hydrogen [23] are discussed in sections 3.2 and 3.3, respectively. The conclusions drawn in these sections rest primarily on examination of total cross sections and their ratios, a limited number of differential cross sections and analysis of individual CTMC trajectories, so in section 3.4 we report on more detailed studies of ionization cross sections differential in the angle and the energy of the ejected electrons [24,25]. The favorable

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comparison of these differential cross sections with experimental measurements, as well as that of the total cross sections, constitutes considerable evidence for the validity of the model of the collision dynamics that we propose.

processes the same have been experiment six atomic

2. Theory

3. Discussion

In brief, the CTMC technique is a method in which a large ensemble of projectile-target configurations is sampled to simulate the ion-atom collision, and has been fully described by Abrines and Percival 1151, Olson and Salop [16] and others. The basis of its ability to accurately model such collisions rests in the technique of preparing the target ensemble so as to reproduce on average the initial quantum mechanical electronic distribution. This procedure was described in detail originally by Abrines and Percival [15] using the microcanonical distribution and subsequently by others in various forms [26-283. The treatments of single- and double-electron removal from helium require two different procedures of target ensemble initialization before the classical trajectories of the colliding particles may be computed. Single-electron removal from a multielectronic target is treated by calculating the probability of removing the electron from an atom with only one active electron and then using the independent electron model [29] to account for the increased probability due to the presence of other electrons. In this model the active electron moves in the screened Coulomb field of the atomic core and is initialized in position and vector momentum subject to the microcanonical ensemble [15]. In the case of double-electron removal from helium, where twoelectron processes are expected to be significant, we have used the so-called Bohr model of helium. In this model the electron-electron interaction is explicitly included and static correlation is enforced by placing both electrons initially in circular orbits 180” out of phase. This treatment has been demonstrated [18-211 to yield qualitative agreement with experiment for singleand double-ionization. The requirements of static correlation and electronelectron interactions limit the Bohr model’s ability to mimic the quantum mechanical helium electronic distribution and the stability of the classical atom. Therefore, the results of this model are intended to provide quantitative predictions only over a limited regime where these restrictions are not too severe. While the results are only qualitative elsewhere, the collision mechanisms that have been brought to light using this model do, however, confirm the importance of the electron-electron interaction in double-ionization and illustrate the sign of the charge dependence of the reaction. We note for completeness that the single-electron removal

collisions

in hydrogen and helium do not suffer from limitations as those of the Bohr model and demonstrated to be in good agreement with over the collision velocity range of one to units.

According to the Bethe-Born approximation, the ionization cross section for the charged particle impact of an atom is dependent upon the collision velocity and the square of the projectile charge. Therefore, within this framework, the cross section for equivelocity electrons and positrons, and for protons and antiprotons should be identical. For sufficiently large collision velocities this is indeed true. However, for smaller velocities, single ionization by e, e, p and i?i impact show marked differences in both the total and differential cross sections. Perhaps even more striking are the differences existing in the double ionization cross section, which persist to very high velocities. In fact, in the energy range of two to five MeV/u the cross section for the double ionization of helium by electrons is approximately twice as large as that for double ionization by protons [2]. Also evident in experimental results is the difference in the cross section for single charge transfer in protonand positron-atom collisions. These results show that variations in the projectile mass alone are sufficient to change the collision dynamics and the reaction cross section. Similarly, recent experiments comparing proton and antiproton cross sections indicate that a change in the sign of the charge alone is also sufficient to cause significant differences. Clearly, theoretical approaches which distinguish processes on the basis of the projectile mass and sign of charge are required to explain this behavior. Below we discuss the recent developments which have lead to an understanding of the origins of these differences. 3.1. (p, jj) + He: double ionization Much of the recent interest in matter-, antimatteratom collisions has centered about the observation in 1986 of proton and antiproton double ionization of helium by a group from Aarhus (Andersen and coworkers [12]) utilizing the low-energy antiproton ring (LEAR) facility at CERN. This investigation was itself stimulated [30] by the findings of Puckett and Martin [31] in 1970 that at about 2 MeV/u the cross section for the double ionization of helium by electron impact was about twice that for proton impact. This factor of 2 difference between equivelocity electron- and proton-induced double ionization of helium was again noted in

D. R. Schultz et al. / Dynamics of matter -, antimatter - atom coNisions

1982 by the Aarhus group (Haugen et al. [2]) in their measurements of multiple-el~tro~ transitions in noble gas targets, and by McGuire [l] in his proposed explanation of the effect in terms of the interference of two scattering amplitudes. By comparing p and p cross sections rather p and e cross sections, the new experiments conducted at CERN allowed the separation of the sign of the charge effect from the mass effect. In fact, it was found that the antiproton cross section for the double ionization of helium is larger by a factor of about 2 than that for protons for collision velocities in the range of 4.5 to 13 a.u. (corresponding to energies from 0.5 to 5 MeV/u). Above velocities of about 10 a.u. the antiproton cross sections were found to be about equal to the corresponding electron cross sections, indicating that a relatively high collision velocities, the enhancement of the double ionization process is due primarily to the sign of the projectile charge. At lower velocities, the antiproton cross sections are significantly larger than those for electrons, indicating the importance of the mass effect for lower collision energies, caused by significant energy loss and deflection of the electron. It should be noted that the results are not peculiar to helium and that similar effects have been found for molecular hydrogen, neon and argon [32,33]. Various theoretical explanations for this observed behavior have been put forth. However, as of yet no strong concensus as to the detailed explanation of the processes involved has been reached. What is agreed upon, though, is the fact that the correlation of the target electrons is of great importance. Unlike single ionization, which can be well described in terms of the independent electron model and requires only a single projectile-target interaction, double ionization requires a second interaction which may depend in detail on the correlated motion of the target electrons. McGuire’s 1982 paper [l] proposed that the difference in double ionization in the high velocity regime could be interpreted in terms of the coherent sum of the amplitudes for two different mechanisms. The first is a two step mechanism in which the projectile interacts first with one target electron and then with the second, known as TS-2. The second is the process of shakeoff (SO) in which one electron is removed quickly with the second electron “shaken off”. This occurs since in the quick removal of the first electron, the final state wavefunction of the second electron is not orthogonal to the continuum of the residual ion and therefore there is some probability for emission. Since the TS-2 amplitude is proportional to the square of the projectile charge, and the SO amplitude is proportional to the projectile charge, the resulting interference term is proportional to the cube of the projectile charge. Thus, the double ionization cross section should depend on the sign of the projectile charge and consequently the difference

529

between the e-p results (as well as those for the p-p experiments). This interference was shown by McGuire to yield a reasonable fit to the e-p data, however, subsequently, it has been argued [34] that the proposed interference may be not be allowed because of the different symmetries of the final states of the target in the TS-2 and SO processes. Additionally, it has been suggested 112,321 that another two step process could be more significant than TS-2 at high velocities. In this process the projectile interacts only once with an electron which it removes from the target, and which then collides with a second electron removing it also from the target. The amplitude for this process known as TS-1, is proportionai to the projectile charge and thus the interference resulting from the coherent sum of TS-1 and TS-2 amplitudes should also yield the required cubic dependence on projectile charge. Clearly, a conclusive statement as to the precise role of each of these mechanisms must await more complete treatments, since each process has a different velocity dependence; (for low velocities TS-1 and TS-2 are significant with TS-2 vanishing at high velocities and SO dominating at extremely high velocities). In another theoretical approach, Reading and Ford have used their novel method, the force-impulse method, which is a procedure for including electron-electron interactions into their ab initio solution of the time-dependent S&r&linger equation for two-electron targets, to also predict the helium double ionization cross sections for proton- and antiproton-impact [5,35,36]. Their results predict correctly the enhancement of the antiproton cross section over that for protons and the velocity dependence of the behavior. However, the cross sections are uniformly approximately 35% below the experimental measurements. They have attributed this discrepancy to the lack of inclusion of d-states in the basis used and report [36] that convergence in angular momentum is currently being tested. Significantly, their calculations indicate that another m~hanism, namely one in which the projectile interacts twice with a target electron which then collides with the other electron, should be important. Prompted by these indications that target electronelectron interactions should be important in double ionization, Olson [4] has performed CTMC calculations to elucidate the collision dynamics. Because the CTMC simulation follows the classical motion of each of the particles in the collision, examination of the individual trajectories allows observation of the mechanisms responsible for double ionization. The CTMC calculations were limited to the energy range of 1 to 5 MeV/u where the classical two-electron model has been demonstrated to yield reasonable results. In fact, the CTMC ratio of double to single ionization for protons was found to agree with experiment to within about 5 to

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D. R. Schultz et al. / Dynamics of matter - , antimatter - atom collisions

10% and for antiprotons to within about 25 to 35%. Furthermore, the calculations indicate that the enhancement of the cross section for antiprotons arises due to two major dynamical effects. In the first, there is a significant difference in the impact parameter dependence of the double ionization mechanism in which one electron collides with the other. It is found that antiprotons preferenti~ly scatter one electron into the other from larger impact parameters than do protons. This occurs since the negatively charged antiproton may repel one electron into the other from large impact parameters as it passes the target. In contrast, the positively charged proton must have a smaller impact parameter so as to attract an electron into such an orbit that it will collide with the other electron. This difference in impact parameter dependence significantly increases the double ionization cross section for antiprotons relative to protons. The second effect, which is found to dominate at small impact parameters and for relatively low velocities where the collision time is longest, involves the mechanisms of screening and antiscreening. For small impact parameter collisions, the antiproton effectively reduces (or screens) the nuclear charge resulting in a so-called Coulomb explosion. That is, since the binding of the two electrons to the nucleus is reduced, their mutual repulsion may become sufficient to free them from the atom. For protons, small impact parameter collisions transiently increase rather than decrease the binding of the electrons. It is found that this effect is even more important than the first since it does not require the relatively infrequent event of electron-electron collision. Thus the CTMC results, as well as those of the other studies, indicate that the correlated motion of the target electrons, their mutual interaction and the sign of the projectile-electron interaction all play a critical role in the double ionization process in helium. 3.2. (2, p) + He: single electrorr removal As we have noted above, the comparison of proton and antiproton collisions has lead to the separation of the effects of the sign of the projectile’s charge from those of its mass. Similarly, comparison of positron and proton collisions has lead to a superior discri~nation of the effects of the varying projectile mass. Schultz and Olson [7] have made CTMC calculations in order to explore the differences in the processes which lead to the removal of an electron, via ionization or charge transfer, in positronand proton-helium collisions. This work has been motivated in large part not only by the p-p investigations, but also by the recent experiments of Fromme and coworkers [X3] at Bielefeld and of Diana and coworkers [14] at the University of Texas - Arlington. These intermediate velocity (1.5 < u c 4.5

-18’ ’ 1

’

I

I

z 3 4 Velocity (a. u. J

I 5

Fig. 1. The total cross section for single ionization of helium by positron- and proton-impact (lower section): CTMC [7] (solid curves), experiment& measurements for positrons [13] (triangles) and for protons [46] (squares). The ratio of the positron and proton cross sections (upper section): CTMC (solid curve), ratio of experimental measurements (inverted triangles).

a.u.) positron-helium experiments reflect the recent advent of the availability of intense low energy positron beams for ion-atom collision studies. These experiments indicate that there are significant differences between positron- and proton-impact ionization of helium at velocities lower than about 3 a.u., the cross sections becoming about equal at high velocity. Also, perhaps even more conspicuously, they indicate that differences in the charge transfer cross sections persist to even higher velocities. These features are displayed in figs. 1 and 2 where we plot the ionization and charge transfer total cross sections as a function of velocity. Thus, single electron removal, either through ionization or charge transfer, clearly depends on the projectile mass in this velocity range. Furthermore, the CTMC studies and calculations by Deb, McGuire and Sil [6] using a second Born treatment, indicate that the difference between positron and proton charge transfer cross sections persists to asymptotic~ly large velocities. In fig. 1 we also present the ratio of the ionization cross sections for positrons and protons as a function of collision velocity. At very small velocities this ratio is much less than one due to a simple dynamical effect. That is, due to its smaller mass and therefore smaller energy, low velocity positrons have much less energy above the helium io~~tion threshold. Consequently, fewer positrons of low velocity succeed in ionizing the target than do equal velocity protons. As the collision velocity is increased, this effect decreases in importance

D. R Schultz et al. / Dynamics of matter -, antimatter-atom

1

4 3 2 Velocity (a. U. 1

5

Fig. 2. The total cross section for single charge transfer in the collision of positrons with helium (lower section): CTMC [7] (solid curves), experimental measurements for positrons [13] (triangles) and [14] (circles) and for protons [46] (squares). The ratio of the positron and proton cross sections (upper section): CTMC (solid curve), ratio of the experimental measurements (inverted triangles and circles).

as the positron acquires a greater amount of energy in excess of the ionization threshold. Therefore the ratio increases. At large velocities, as indicated by both experiment and theory, the ratio becomes one. In other words, for sufficiently large velocities, positrons and protons are equally likely to singly ionize helium. A similar dynamical effect occurs in low velocity charge transfer collisions as the ratio of the positron and proton cross sections in fig. 2 reflects. At low velocity, positrons have little energy above the capture threshold and accordingly the ratio of positron and proton cross sections is less than one. This effect, as in the case of ionization, diminishes in importance as velocity is increased and at a velocity of about 2 a.u. the positron and proton cross sections become equal. However, as velocity is further increased positrons become more likely than protons to capture an electron from helium. In fact, asymptotically this ratio is at least several times greater than 1. Explanation of this effect has come from examining the differential cross section as a function of projectile scattering angle for the two projectiles and from detailed examination of the individual trajectories which lead to charge transfer using the CTMC method. For example, in fig. 3 we present the differential cross section as a function of the projectile scattering angle for both ionization and charge transfer in the collision of positrons and protons with helium at a

collisions

531

velocity of 2.0007 a.u. As this figure indicates, positrons are deflected to very large angles, due to their relatively small mass and momentum, whereas protons remain nearly undeflected in the collisions. Also, positrons may be decelerated by the target due to their smaller momentum corresponding to their smaller mass. In rare events positrons may even be accelerated temporarily in the pseudomolecule which is transiently created in the collision. In contrast, protons follow a nearly straight line trajectory, suffering very little energy loss in the charge transfer collisions. Consequently, positrons are much more readily deflected and braked into trajectories which more readily vector momentum match with, and therefore capture, an orbital electron. In the velocity range of 1.5 to 4.5 a.u. the CTMC calculations indicate that positrons should become approximately five times as likely to remove an electron by charge transfer as equivelocity protons. At even larger velocities (u > 50 a.u.) the second Born and Brinkmar-Kramers treatments of Deb, McGuire and Sil[6] indicate that this trend of enhancement continues and that the ratio may become as large as about 12 to 15. It is important to note that there exists some disagreement between theory and experiment however, as evidenced in fig. 2. The experimental measurements of the charge transfer cross sections for positrons decrease as a function of energy as about E-’ to E-‘.5 whereas there is a general agreement among theories that the rate of decrease should be between Ee3 and Ee5. Schultz and Olson [7] have proposed a resolution of this disagreement. In each of the experiments an axial magnetic field is used to confine the positron beam to the forward direction as it passes through the target gas. Any positron flux removed from the beam is then

F+He

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I,

0. 05

0.10 SCATTERING

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1

I 0 ANGLE

45

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(deq)

Fig. 3. The single differential cross section as a function of the projectile scattering angle for proton- and positron-impact of helium at velocity of 2.0007 a.u.: CTMC result [7] for single ionization (broken curve) and for single charge transfer (solid curve), experimental measurements of charge transfer for protons [47] (squares).

D. R. Schultz et al. / Dynamics of matter -, antimatter - atom collisions

532

inferred to have gone to positronium formation. However, if in the ionization channel, positrons are scattered to sufficiently large angles for high velocity collisions, then some of the loss of flux may be due to ionization rather than charge transfer. Since the ionization cross section at high velocities is much greater than the charge transfer cross section, the measured charge transfer cross section will be swamped by the contribution by ionization and will decrease as approximately E-r, the behavior displayed by the ionization cross section. CTMC calculations indicate that such scattering to large angles does in fact persist to high velocities and estimates of the effect show rough agreement with the expe~mental behavior. This argument is presented in more detail and its plausibility defended in refs. [7] and 1371.

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3.3. (e, 2, p, F) + H: single electron removal

2

3

Velocrty

To explore the effects on single ionization when not only the mass but also the sign of the charge is varied Schultz [23] has calculated CTMC cross sections for e, E, p and iY collisions with atomic hydrogen. The results of these calculations are summarized in figs. 4 and 5 where the total cross section for ionization and charge transfer are plotted as a function of collision velocity. Also displayed are the ratios of the electron, positron and antiproton cross sections to that for protons.

1

2

3 Velocity

4

5

6

7

(0. U. 1

Fig. 4. Tbe total cross section for single ionization of hydrogen by electron-, positron-, proton- and antiproton-impact (lower section): CTMC [23] (solid curves). The ratio of the electron, positron and antiproton to proton cross sections (upper section): CTMC (solid curves), ratio of the experimental measurements for electrons 1461 and protons 1461 (triangles).

4

5

6

7

(a. U.)

Fig. 5. The total cross section for single charge transfer in the collision of positrons and protons with hydrogen (lower section): CTMC (231 (solid curves), experimental measurements for protons 1461 (squares). The ratio of the positron and proton cross sections (upper section): CTMC (solid curve).

Comparison of the ionization cross sections for e, 6, p and p immediately indicates that at small velocities (1.2 < u i 3 au.) there exist substantial differences on the basis of projectile mass and sign of charge, but that at larger velocities the differences di~~sh. So we conclude that the four singly-charged particles are equally likely to ionize hydrogen at high velocity, mass and sign of the charge effects becoming negligible. However, closer inspection of the relative magnitudes of the cross sections at high velocity indicates that the positively charge particles (E, p) while having very nearly the same cross section, have a slightly larger cross section than the negatively charged particles (e, B) which themselves have very nearly the same cross section. For example, at a velocity of 3.16 a.u., corresponding to an energy of 250 keV/u, the positron and proton cross sections are equal to within 4% but are greater than the electron and antiproton cross sections by nineteen percent. Similarly, at v = 4.33 a.u. (1 MeV/u) the positron and proton cross sections differ by less than 1% but are 5% greater than the electron and antiproton cross sections. Thus, an effect of the sign of the projectile charge persists to high velocities in the single ionization of hydrogen. This effect was predicted by Olson [4] in his calculation of the ratio of double to single ionization of helium by protons and antiprotons, and can be explained in terms of the difference in the ejected electron spectra for positively and negatively charged projectiles. These differences occur due to the fact that the positively

D.R. Schultz et al. / Dynamics of matter -, antimatter-atom charged particles create a region of reduced net charge on the atomic electron which is not present with the negatively charged particles. This region, centered about the midpoint between the atomic core and the projectile, has come to be known as the saddle-point region and electrons which are ionized there originate with velocities approximately one half of that of the projectile, and thus have come to be called v/2 electrons

P8,W. It is found that at high velocities the direct-impact ionization partial cross sections for positively and negatively charged particles are the same within the statistical uncertainties of the CTMC treatment, whereas the saddle-point ionization partial cross section is greater for positively charged particles. Thus, owing to the positive sign of their charge, positrons and protons may remove electrons by creating a region of reduced binding energy, a mechanism not possible for the negatively charged electrons and antiprotons, which accounts for their greater efficacy in single ionization at relatively large velocities. At low velocities, the differences due to the sign of the charge effect also exist, but superimposed on them are the effects of varying projectile mass and of the branching between the ionization and charge transfer channels, itself a sign of the charge effect. The mass effect is manifested in the fact that at very small velocities, electrons and positrons possess very little energy above the ionization threshold and consequently it is much more likely that equivelocity protons and antiprotons, with their much greater energy, will cause ionization. Thus, as indicated in fig. 4, the electron and positron cross sections are smaller than the proton and antiproton cross sections for velocities smaller than above 2 a.u. At high velocities the charge transfer cross sections for positrons and protons are orders of magnitude smaller than the ionization cross section. Therefore, this channel is relatively unimportant to ionization at high velocities. But at low velocities the charge transfer cross section for positrons and protons is comparable to or larger than the ionization cross section and may not be neglected. This occurs since at low velocities the collision time is relatively long, and if a positron or proton removes an electron from the target it has a relatively high probability of capturing it. Also, since the positively charged particles present an attractive potential, the threshold for charge transfer is lower than that for ionization, and therefore at extremely small velocities charge transfer dominates ionization. Consequently, the electron removal cross section is partitioned between ionization and charge transfer for positrons and protons. This partitioning accounts for the drastic drop in the positron and proton ionization cross sections at low velocity and their relative magnitudes with respect to the electron and antiproton cross

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sections. Thus, the detailed shape of the ionization cross sections in this velocity range is due to the subtle interplay of mass and sign of the charge effects. As in the case of charge transfer collisions with helium targets, CTMC calculations indicate an enhancement of the positron cross section relative to that for protons in collisions with atomic hydrogen (see fig. 5). In the very low velocity regime the ratio of the positron to proton charge transfer cross sections is less than one due to the small energy above the ionization threshold of positrons relative protons. As velocity is increased this effect rapidly diminishes in importance and positrons become much more likely to capture an electron from hydrogen than protons due to the positron’s greater ability to vector momentum match with an orbital electron. At large velocities it is expected that the positron cross section is approximately seven times as large as the corresponding proton cross section. In agreement with this is the high velocity limit of the Brinkman-Kramers approximation in which McGuire [3] calculates the ratio to be 6.6. Interestingly, and perhaps even surprisingly, the effect of varying projectile mass remains important even as the charge transfer cross section decreases by five orders of magnitude in this velocity regime. 3.4. (e, t?, p, j) f He: electronic spectra Variations in electronic spectra caused by a change in the projectile’s sign of charge or mass provide a deeper insight into the ionization dynamics than do total cross sections alone. Large differences in the ionization cross sections differential in energy and/or angle of the ejected electrons have been recently reported by several authors [11,24,25,39-421. In this section we summarize the conclusions obtained in these works. Most of the previous works have analyzed the behavior of those electrons that are ejected at very small angles in collisions of e, e, p and p projectiles with H and He targets. As is well known, the electronic spectra arising from collisions of positive heavy ions with atoms exhibit a sharp peak when the electrons are ejected at zero degrees with post-collision velocities close to the projectile velocity, which is called capture to the continuum (CTC) peak [43]. Theoretical studies [11,25,39] of collisions of antiprotons with He targets have revealed that, instead of the divergence predicted for the case of positive incident ions, a deep dip or “anticusp” is observed at small electron angles. Experimental evidence of this structure has been recently reported by Knudsen [40]. This behavior may be easily explained in terms of the projectile’s charge sign. That is, owing to their positive charge sign, protons focus the ejected electrons in the direction of their velocity, while antiprotons repel them. Recent studies [24,42] have also found that the

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Fig. 6. The single differential ionization cross section as a function of the angle of the ejected electron for collisions of electrons, positrons, protons and antiprotons with helium at a velocity of 2.83 a.u.: CTMC [24] (solid curves), sum of the CTMC spectra for target and projectile electrons (dashed curves), experimental measurements for protons [44] (solid triangles) and for electrons [45] (open triangles).

same structures observed for protons and antiprotons (i.e. cusp and anticusp) are also present in the triple differential ionization cross sections arising from collisions of positrons and electrons with H targets. However, these authors found that the position of the structures in the electronic spectra is shifted to lower electron energies with respect to the predictions for heavy ions. This shift is due to a mass effect since the final velocity of a light projectile can be very different from the initial one. Work including the study of electrons ejected at several different angles from 0 to 180” have been reported at intermediate velocities by Olson et al. [24,25] for the (e, E, p, p) + He systems and by Fainstein et al. [ll] for the (p, p) + He systems at high impact velocities. While these authors used different theoretical approximations in different impact velocity ranges, they agree in the global effects observed. These effects can be summarized by figs. 6 and 7, in which we present CTMC singly differential ionization cross sections at a velocity of 2.83 a.u. for the (e, E, p, B) + He collisions. In order to test the validity of the CTMC method, the theoretical results for e and p projectiles are compared with experimental data. The addition of the calculated electronic spectra resulting from both the target and the incident electrons for the e + He system are in good agreement with the experimental data of Rudd and DuBois [44]. The theoretical results for incident protons are in reasonable agreement with the experimental data of Rudd, Toburen and Stolterfoht [45], except,at large ejection angles. However, a comparison with new experimental data at impact velocities of 2 a.u. and 1.41 au. [25] suggests that the large-angle data of ref. [45] may be too high.

antimatter - atom collisions

Fig. 6 shows that the angular distributions of the ejected electrons are primarily determined by the sign of the projectile charge. In particular we note that, while electrons are mostly ejected at small angles in collisions with positive projectiles, they are ejected at larger angles by negative projectiles. Analysis of CTMC trajectories has indicated that while electrons are pulled out to small angles by positive projectiles, they are pushed either to the continuum or toward the target nucleus and scattered by this center to large angles in collisions with negative projectiles. In addition, the difference between the small-angle cross sections for incident antiprotons and electrons is due to a mass effect. As antiprotons are scattered to very small angles, any electron ejected at a small angle will be repelled to a larger angle. Due to the large mass of the antiprotons in comparison with the electron mass, this post-collision interaction does not alter their trajectories significantly. On the other hand, as incident electrons can be deflected to large angles due to their small mass, there is no constraint for the target electrons to be ejected at small angles and their distribution is more isotopic. Fig. 7 shows that different shapes are obtained for the energy distributions of the ejected electrons for different projectiles. While positive projectiles produce more soft electrons than negative projectiles, the opposite result is obtained at higher electron energies. This behavior is related to the different mechanisms that can lead to either slow or fast electrons. While fast electrons are usually obtained after a very close interaction with the projectile, slow electrons involve distant interactions with both the projectile and the target nucleus. The differences in the electronic distributions at small electron energies illustrates the fact that positive projectiles are more effective than negative projectiles in ionizing electrons due to cancellation of the target nucleus and

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-20050laoo ELECTRON

ENERGY

kV)

Fig. 7. The single differential ionization cross section as a function of the energy of the ejected electron for collisions of electrons, positrons, protons and antiprotons with helium at a velocity of 2.83 a.u.: symbols the same as in fig. 6.

D.R. Schultz et al. / Dynamics

of matter-, antimatter-

the projectile Coulombic fields, (i.e. the saddle-point mechanism). The reasons for the different behavior at higher ejected electron energies is due to different mechanisms. For example, some of the head-on collisions between the projectile and the target electrons may end in charge transfer reactions for the case of positive projectiles, removing flux from the high energy electronic spectra. For the case of incident positrons, a mass effect is also responsible for the fall off of the cross section. It is observed that before the close e-e collision a significant part of the available impact energy is dissipated in the e-He+ Coulomb repulsion. Thus, some insight has recently been gained into the fundamental differences in collision dynamics which manifest themselves in the differences in electron-, positron-, protonand antiproton-atom collisions through new experiments involving antimatter projectiles and by new theoretical treatments. The authors wish to gratefully acknowledge the support of the Office of Fusion Research, US Department of Energy.

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