- Email: [email protected]
Antiparticle-atom collisions
536
Nuclear Instruments and Methods in Physics Research B42 (1989) 536-544 North-Holland, Amsterdam
ANTIPARTICLE-ATOM
COLLISIONS
H. KNUDSEN Institute
of Physics,
Wniversity of Aarhus, DK-8000 Aarhur C, Denmark
The production of beams of antiparticles useful for atomic-collision studies is discussed. The application of these beams in recent studies of single and multiple ionization of light atoms, as well as of the differential electron-emission cross section, is elaborated on. Finally, some future experiments with antiparticles are presented.
1. Introduction
Recently there has been a growing interest in antiparticle-atom collisions. The main reason for this interest is that since 1986, high-quality beams of useful velocity and intensity of all the particles, e+, e-, p+, and p- have become accessible. This means that experimentally, we can obtain data for atomic-collision phenomena for impact of particles with the same charge but of greatly different mass, or for impact of particles with the same mass but of opposite charge sign. We can therefore measure what happens when the force acting on the atomic electrons during the collision is inverted; we can change the number of accessible reaction channels (for example, turn on or off electron capture which happens only for positive particles), and we can investigate effects of projectile deflection which is a prerogative of the light particles. This gives us a unique tool to test the theoretical models for various phenomena and especially to probe the dynamics of the collisions. There exists already a large number of ion-atomcollision processes that have been studied with impact of antiparticles, either theoretically or experimentally. Most of these studies are concerned with the ionization phenomenon. Single ionization of outer [l-11] and inner [5,12-161 electrons has been investigated, as well as differential cross sections for electron ejection [9,17-221, multiple ionization [1,2,23-301, and energy loss in ionizing collisions [31-351. A few calculations of excitation cross sections exist for antiparticle impact [5,19]. Other investigations concentrated on the charge-exchange process, namely positronium formation in the case of positron impact [3,4,9,36-401, antiprotonic atom formation for p - impact on atoms [41], and antihydrogen formation for antiproton impact on positronium atoms [42-461. In this paper, I shall discuss experimental and theoretical results for total and differential single-ionization cross sections, as well as for total double-ionization 0168-583X/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
cross sections. In all cases, the main emphasis will be on a comparison between data for particle and antiparticle impact. Preceding this main part there is an introduction to the production of antiparticle beams suitable for atomic-collision studies. At the end, I shall present some possible future experiments that may be worthwhile.
2. Beams for antiparticle-atom
collision studies
Generally, antiparticles are produced in the laboratory in pair-creation processes. Initially they therefore have a large kinetic energy and a large spread in kinetic energy. In order to produce beams of these particles, which are useful for atomic-collision studies, we have to decelerate the particles and to “cool” them, i.e., to decrease their energy spread. At the Aarhus University magnetic positron facility, the positrons come out of a ,,Na source. Their initial energy distribution is shown in fig. 1. The positrons enter an annealed tungsten foil, in which they are slowed down to thermal velocities. A few (2-3 x 10e3) drift to the surface and exit from the foil with a narrow energy distribution, which is also shown in fig. 1 [47]. The positrons are then accelerated to the desired energy (10 eV-IO keV) and transported to the target area by a guiding magnetic field. Fig. 2 shows the experimental
0
02 p’ ENERGY
04 (MeV)
06
5
4
3
2
1
e’ ENERGY
0 -1 -2 -3 (A’)
Fig. 1. Energy distribution of positrons: a) produced in a ,,Na source; b) after moderation in tungsten foil.
H. Knuaken / Antiparticle- atom collisions
531
Fig. 2. The Aarhus positron accelerator with experimental scattering chamber. Insert: The target-gas cell for ionization measurements.
setup. Shown here is also the target arrangement used for measurements of single- and multiple-ionization cross sections [30]. The arrival time of each positron is registered by a detection of the annihilation 511 keV y ray by a large NaI crystal. The positrons pass through a dilute target gas, and the ions, which are created here, are extracted by a transverse electric field into a flight tube. The ion arrival time is registered by a ceramic channeltron. In the resulting ion time-of-flight spectrum, the peaks corresponding to the various ion charge states are well resolved and are readily integrated to give the cross section for n-fold ionization, (I”+, see, e.g., ref. [l]. For our measurements of u”+ for antiproton impact [1,2], we used basically the same target arrangement. In this case, the antiparticle beam was delivered by the CERN PS-LEAR accelerator facility. Here, protons are accelerated by a linear accelerator and the PSB-PS accelerators to a momentum of 26 GeV/c, see fig. 3. These protons then enter a thick solid target, where antiprotons are created. They leave the production target
AA.
with a broad momentum distribution centered around 3.5 GeV/c. The antiprotons are collected, accumulated, and cooled by the AA and ACOL synchrotrons and then sent back to the proton synchrotron PS in a pulse containing about lo9 particles. In the PS, the antiprotons are decelerated to 0.6 GeV/c and finally transferred to the low-energy antiproton ring LEAR. Here the antiprotons are further cooled and decelerated, and they are directed to the experimental setup, in our case as a dc beam of 5.3 MeV and 105-lo6 particles/s-‘. This kinetic energy is at present the lowest available directly from LEAR. Lower energies can be obtained, for example by foil degradation, with the obvious disadvantage of energy and angular broadening. The angular spread can be removed by collimation, but this decreases the beam intensity. The energy straggling can be compensated for by recording the velocity of each particle by a time-of-flight technique. Currently, antiprotons and positrons are the only antiparticles that can be obtained in beams usable for atomic-collision experiments. Meson factories around the world are able to produce beams of muons, but these are of a much lower quality than the e+, p- beams
ACOL
Table 1 Characteristic parameters of typical antiparticle rently available for atomic-collision studies
Source Velocity (a.u.) Intensity (s-l) Beam size (mm’) Divergence (mrad)2 AP/P
Fig. 3. The CERN PS-LEAR accelerator facility.
Lower velocities
beams cnr-
P-
s-
e+
LEAR 15 105-lo6 1x1 10x20 10K3 x1/10
SIN 25 lo*-lo3 20x30 30X60 4x1o-2 NO
5 mCi s,Na 15 lo4 3x3 “ 0” 10W2 x1/50
538
H. Knudsen / Antiparticle-atom
collisions
described above. In table 1, the properties of the SINmuon beam (see, e.g., ref. [48]) are compared to those of the e+, p- beams used in our experiment.
5
I
I
I,,,,
I
. protons
3. Total single ionization The process, which leads to the liberation of one target electron following the impact of a charged particle, is one of the most important and fundamental phenomena that are studied in the field of atomic collisions. In this section, we shall review what we can learn (or have learnt) about this process by comparing data for particle and antiparticle impact. We shall concentrate on outer-electron ionization and therefore focus on light target atoms. It is natural to divide the discussion into subsections, depending on whether the projectile velocity is much larger than, in the order of, or much smaller than that of the orbital velocity of the active target electron.
antiprotons i
q
2 I 10~‘6
t
t
“E Y
5
+ -b iJ
1 9
2
-+
44 Ne
T
10-17 1
t5L
3.1. The charge difference for heavy particles E (MeVI
At very high projectile velocity, the interaction with the atomic electron is short-lasting, and (for particles of unit charge) it can be described by first-order perturbation theory. The first Born result for the single-ionization cross-section scales as In V o+aq*-----, If* where q is the projectile charge in units of the elementary charge, and V is the projectile velocity. This means that the cross section is independent of the sign of the projectile charge in this approximation, and therefore fast protons and antiprotons should give the same single-ionization cross section. This is actually the case, as can be seen in fig. 4, where our data [l] for proton and antiproton impact on He, Ne, and Ar atoms are shown as a function of the projectile energy. At lower projectile velocities but still velocities larger than that of the atomic electron, we expect to see the first charge difference, as illustrated by the continuumdistorted wave calculations by Fainstein et al. [7] for proton and antiproton impact on He (see fig. 5). The proton cross section is predicted to be larger than that for antiprotons. This is due to a polarization effect: The target-electron cloud is attracted to the positive projectile but repelled by the negative projectile, this giving the proton a higher probability for ionizing the target. At projectile velocities below that of the target electron, this trend is reversed. There are two reasons for this: First, the proton can capture a liberated target electron. This additional final channel subtracts from the ionization channel, and this effect becomes the more important, the lower the projectile velocity, as can be
Fig. 4. Single-ionization cross sections for p+ and p- impact on He, Ne, and Ar from ref. [l]. c is an experimental efficiency which does not depend on the projectile charge.
seen in fig. 5. Second, during the rather slow collision, for close encounters, the proton adds to the binding of the target electron, whereas antiprotons reduce the binding force, this again reducing the proton cross section as compared to that for antiprotons. At very low projectile velocities, we can describe the collision through the quasimolecular model: During the approach of the projectile, the original atomic electron
-
CDW - EIS FaInsteIn &al
(87)
ld6 Hellurn
_
“E ,” b ,o” -:
I
16’
1
I
KY2
I
/
I
I
16’ E IMeVlamul
I loo
I
1 10’
Fig. 5. CDW calculations of p+- and p--impact single-ionization cross section for He [7]. Also shown (dashed curve) is the single-capture cross section for protons on He. The curve is based on the data of refs. [48] and [49].
H. Km&en
/ Antiparticle-atom
_ 0.4 s w , 0.6
1
B-H
1
Rhu)
Fig. 6. Electronic energy of the pseudomolecular orbital for the p+ + H and p- + H systems as a function of the internuclear distance R. Calculations by Rimura and Inokuti [8].
wave function evolves into a molecular orbital, the binding energy of which depends on the internuclear distance R. Fig. 6 shows such binding-energy curves calculated for p/p impact on atomic hydrogen by Kimura and Inokuti [PI. As the proton comes closer to the target nucleus, the electron initially occupying a H(ls) state becomes either more tightly bound, approaching the He+ groundstate wave function, or it is promoted to the first excited state corresponding to He(n = 2). In the second half of the collision, the quasimolecular orbital may evolve into the H(ls) state again, in which case we have either no reaction or resonant charge exchange. Alternatively, the electron is promoted to an excited H( n = 2) state. In this picture, there is no ionization exit channel. For antiprotons, on the other hand, there are no bound pseudomolecular states when the projectile is close to the target nucleus, and the dominant outcome of the collision is the so-called adiabatic ionization. Consequently, it is expected that very slow antiprotons have a much higher ionization probability than equivelocity protons.
collisions
539
ally, the ratio between the positron and the proton cross sections becomes zero at a positron energy equal to the target-ionization potential, see. fig. 7. The positron/ proton cross-section difference is primarily due to the fact that positrons, which have the same velocity as protons, carry 1836 times less kinetic energy into the collision. This means that the available phase space of final states shrinks with decreasing positron energy, thus decreasing the positron-ionization cross section. There are other reasons for the p+/e+ difference, however. For example, protons and positrons can both capture a target electron, but above 100 keV/amu, the positron-capture cross section is considerably larger than that for protons, and therefore relatively fewer free electrons are created by the positrons. Another mechanism, which makes positrons less efficient ionizers than protons, is projectile deflection. For those impact parameters that are typical for ionizing collisions and for the projectile velocities that we are concerned with here (see fig. 7) the protons pass virtually undeflected by the target. Positrons, on the other hand, may be strongly deflected away from the target nucleus, where the electron density is highest. This of course decreases the positron-ionization probability. The solid curve in fig. 7 represents the classicaltrajectory Monte Carlo calculations of Schultz and Olson [9]. It reproduces fairly well the experimental data, which shows that, surprisingly enough, such a calculation, which assumes the positron to be a “classical” 1.4
I
I
I
1.2
1.0
3.2. The mass difference If the single-ionization cross sections obtained for protons and equivelocity positrons are compared, the effect of the large mass difference between the two kinds of projectile can be studied. According to the first Born result, eq. (1) there should be no dependence on the projectile mass for very large projectile velocities. This is really the case, as discussed recently by Raith [51] who showed that there is no discernible difference between the proton and positron cross sections above 500 keV/amu (V - 4.5 a.u.) for impact
on He.
At lower velocities, creating
positrons
free target electrons
are not as efficient
as are protons,
in
and eventu-
0.4
02
2
3 VELOCITY
4
5
(a u.)
Fig. 7. Ratio of the total cross section for single ionization of He by positron to that for proton impact. The solid curve shows the CTMC calculation of ref. [9]. The experimental results were obtained from refs. [3] and (511.
540
H. Km&en
/ Antiparticle-atom
E [.eVl
Fig. 8. The single-ionization cross section for positrons impinging on He. The experimental data are from Fromme et al. [3]. The solid curve is a CDW calculation, including total screen-
ing, the dot-and-dashcurve without screening corrections. Both from Campeanu et al. [ll].
point-like particle, may yield reasonable results, even for positron velocities which correspond to de Broglie wavelengths larger than the target atom. The positron-impact ionization cross section for a He target has also been calculated recently by Campeanu et al. [ll]. These authors used the distorted-wave technique and found that it is very important to take into account the mutual screening of the residual target ion by the ionized electron and the ionizing positron. Their result is shown in fig. 8 and agrees very well with the experimental data of Fromme et al. [3]. We may conclude that we understand the general mechanisms of the single-ionization process fairly well, and that, based on this knowledge, we can calculate the associated total cross section - even for the light projectiles.
4. Differential single-ionization cross sections As we have seen, it is possible to test our understanding of atomic-collision phenomena by comparing experimental data and theoretical results for impact of particles and antiparticles. This technique is the more sensitive, the larger the difference between the measured quantities. Therefore we may get a very sensitive tool for probing the collision dynamics by looking at differential cross sections. One example of such quantities is the singly differential cross section for electron emission as a function of emission angle. This cross section has been calculated by the CTMC method for proton and antiproton impact on He by Olson and Gay [20] and is shown in fig. 9. For the impact velocity chosen here, 2.83 a.u., the total-ionization cross sections for p+ and p- differ by only 35%. Nevertheless, the differential cross section shows differences of more than an order of magnitude: For forward emission of electrons by proton impact, it
collisions
is 50 times larger than for antiproton impact. Olson and Gay ascribe this difference to the postcollision attraction/repulsion between the projectile and the ionized electron. Even more spectacular differences have been predicted for the cross section for electron emission differential in both electron energy and emission angle. Fig. 10 shows the continuum-distorted wave calculations of Fainstein et al. [18] for 1 MeV p+ and p- impact on He. In this case, the emission angle is 0 = 0 O. As can be seen, most electrons exit from the interaction region with very small kinetic energies. However, at an electron velocity equal to the projectile velocity, for proton impact, we see a strong enhancement of the cross section, the so-called “cusp”. It is due to electrons that were captured to nearly bound (so-called continuum) states around the projectile. Such states do not exist in the case of antiproton projectiles, and Fainstein et al. predict an “anticusp” - the doubly differential cross section goes exponentially towards zero with decreasing projectile-electron velocity difference. Quite recently, this anticusp was observed at LEAR. Yamazaki et al. [53] degraded the original 5.3 MeV pbeam to an energy close to 1 MeV and transmitted it through a carbon foil. The forward-emitted electrons were energy-analyzed by a parallel-plate spectrometer. At the electron energy, where the cusp is observed for proton impact, they saw a broad and deep anticusp, reaching a lowest value which was two orders of magnitude smaller than the proton-cusp value. This result confirms nicely the existence of the intrigueing anticusp which has also been predicted for electron impact [21].
-161
-19’ 0
I 30
I 60
I I 90 120 DEGREES
I 150
Fig. 9. The cross section for electron emission to angle 0 for p+ and p- colliding with He. The impact velocity is 2.83 a.u. Solid curves indicate the CTMC result. From ref. [20].
H. Km&en
/ Aniiparticle-
5. Double ionization The theoretical calculations mentioned until now have one thing in common with most theories on charged-particle-atom collisions: they assume the independent-electron model to give a good approximation. That is, instead of treating all the interactions between the atomic electrons, the atomic nucleus, and the projectile, the theories treat only the transitions of the so-called active electrons caused by the projectile impact. For each active electron, the other electrons and the nucleus are taken into account in such a way that they create an effective potential, in which the active electron moves. As an example of phenomena beyond the independent-electron model, in the following we shall discuss the two electron transitions leading to double ionization. For charged-particle impact, the energy transferred to a target electron is generally very small (see, e.g., fig. 10). This means that during the double-ionization transition, the two active electrons usually interact strongly. This interaction is clearly not describable in the independent-electron model. Most experimental and theoretical investigations of the double-ionization process have concentrated on the He target atom because double ionization caused by interactions between more than two electrons is ruled out in this case. Three basic mechanisms exist for double ionization of He by charged-particle impact [l]. In the first, one electron is removed from the atom directly by the passage of the projectile. Thereafter, the
atom collisions
other electron, originally occupying a ground-state He wave function, has to relax onto the set of He+ states. In doing so, there is a finite probability that it ends up in the ion continuum. This is the so-called shake-off (SO) mechanism. In the second mechanism, the first electron, which interacts directly with the projectile, then hits the second electron which is now also removed from the atom. This is a two-step process involving only one electron-projectile encounter, and it is denoted TS-1. In the third mechanism, the projectile interacts directly with the target electrons, one at a time, and hence it is denoted TS-2. For large projectile velocities, it is fairly straightforward to predict the dependence of the cross sections for these three mechanisms on the projectile velocity and charge. The SO and the TS-1 mechanisms both involve one encounter with the charged particle, and their cross section is therefore expected to be proportional to the single-ionization cross section, eq. (1). Contrary to this, the TS-2 mechanism involves two electron-projectile encounters, and its cross section goes approximately [27] as the square of the single-ionization cross section, i.e., as ( q/V)4. Frequently, the most accurately measured quantity is the ratio R between the double- and the single-ionization cross section. This ratio is then expected to be rather constant for the SO and TS-1 processes but to follow a q2/V2 In V dependence for the TS-2 mechanism. In fig. 11 are shown experimental R data for proton double ionization of He [l]. At the largest projectile energies, R is rather constant, as expected from the discussion above, being dominated by contributions from the SO and TS-1 mechanisms. At lower velocities, the TS-2 mechanism gives the largest contribution, and hence R increases with decreasing V. S. 1. The charge
ELECTRON
ENERGY
(eV)
Fig. 10. The double-differential cross section for electron emission in the forward direction for 1 MeV p+ (- --) and pcolliding with He. CDW-EIS calculations from Fain( -) stein et al. [18].
541
difference
for heavy projectiles
In the simple picture presented until now, for large ion velocities there should be no difference between the p+- and p--impact double-ionization cross sections. As can be seen in fig. 11, this is not at all the case. Even at very large projectile velocities, where the single-ionization cross sections are virtually identical, the antiproton double-ionization cross section is approximately a factor of 2 larger than the proton double-ionization cross section. This fact is quite surprising and has led a number of theorists to develop new and sophisticated theoretical models of the double-ionization phenomenon. Already in 1982, McGuire [27] suggested that the difference is due to interference: All the double-ionization mechanisms lead to the same final state with two free electrons, and hence their probability amplitudes should be added instead of their cross sections. Such a
calculations compiicated, is the problem of introducing a stable two-electron atom into such a classical model. As can be seen in fig. 11, the classical calculations reproduce the proton cross section and accounts for some of the p’/pdifference. The forced-impulse method gives a remarkably good agreement with the proton data and accounts for most of the p+/p- difference, although there is some discrepancy left at the higher projectile velocities.
. p-
this work p+ this work 0 P’ a e- this work 0 el
14 t
-
Reading and Ford (87)
(x 1.35) ----
Olson (87)
5.2. The mass difference
6-
A comparison between data for p’, p- and data for e+, e- impact reveals the effect of the low mass of the light projectiles. In fig. 12 is shown data for electron impact compared to the p+ and p- results [l]. The general trend of the electron data is that they agree with the antiproton data at very high projectile velocities, but at decreasing velocity, the double-ionization cross section for electron impact becomes smaller and smaller, and eventually it is zero at an electron energy equal to the target double-ionization potential. The electron-antiproton difference is probably mainly due to the much reduced energy that the electrons carry into the collision, as compared with the
‘\
4-
IO’
Fig. 11. The ratio between the cross sections for double and single ionization of He by p+ and p- impact as a function of the projectile energy. References to experimental data can be found in ref. [l].
procedure gives a contribution to the double-ionization cross section which is proportional to q3, and which stems from interference between one or both of the singe-proj~tile-electron encounter mechanisms and the TS-2 mechanism. The interference term clearly leads to a difference between the cross sections for p+ and pimpact. It can be calculated only through models that take into account the full electron-electron interaction. During the last two years, the first two of such theories were published. In their so-called forced-impulse method, FIM, Reading and Ford [23-251 solve the time-dependent Schrijdinger equation by the coupledchannels method, using a two-electron basis set constructed of s, p, and d single-particle states. The important new aspect is that their calculation includes the interaction between the two target electrons, a feature that greatfy complicates such quantal calculations. Contrary to the FIM, Olson’s recently developed model for double ionization is based on a purely classical solution of the four-body problem [26]. In his CTMC calculations, he follows each collision step by step, and the full electron-electron interaction is taken into account. Apart from the long computing time, what makes these
0 P’ e e0 e-
thts work
1
D
12 CT b = 10 -
00
0
b ;‘ “b
_
-t-
D
80 0
+
I
n
6-
4-
Z-
E(MeVlamu)
Fig. 12. The ratio between the cross sections for double and single ionization for p+. p-, and e- impact [l].
H. Km&m
/ Antiparticle - atom collisions
543
6. Future experiments
E
[ MeVlamul
Fig. 13. The ratio between the cross sections for double and single ionization of He for positron impact (30) compared to curves drawn through the data for p+, p- and e- impact of fig. 12. Dashed curve represents eq. (2). Its low-energy part is calculated from recently obtained p- data 1541.
energy of equivelocity antiprotons. This gives a reduced space for doubly ionized final states and a correspondingly diminished double-ionization cross section. In view of the above explanation of the e-/pdifference in double ionization, we should be able to “factorize” the ratio between the double- and singleionization cross sections into a “charge factor” (stemming from interference, as discussed above, and from the electron-capture channel for positive projectiles) and a “mass factor”. Hence we may express the ratio for positron impact as phase
R(e’)
=~~e-~~(p+)/~(p-~.
(2) There are a number of effects that are not taken into account by this simple approach. For example, the deflection of the positrons tends to decrease the double-ionization cross section, as compared to that of electron impact. Also, the electron-capture cross section is not of the same magnitude for equivelocity positrons and protons. Nevertheless, eq. (2) does give a prediction of the positron ratio which agrees rather well with the positron experimental data 1301,as can be seen in fig. 13 for a He target. A similarly good agreement was found recently for Ne and Ar targets by Charlton et al. [SS]. The approach embedded in eq. (2) towards a prediction of the positron double-ionization cross section is purely empirical. At the moment, no theoretical calculations exist of the double-ionization cross section for the light projectiles. Such calculations seem to be within reach at the present time, although of course they would be a great challenge to the theorists.
Currently, two experiments based on the LEAR antiproton beam have reached the stage where feasibility studies have been completed successfully, Firstly, the project of Yamazaki et al. [53] aims not only at measuring the anticusp for p’s traversing thin carbon foils, but also at detecting the so-called wake-riding electrons that are supposed to occupy bound states of the oscillating potential which is created in the solid target due to the projectile passage. Secondly, Andersen et al. 1541 have succeeded in detecting target K-X-rays produced by antiprotons traversing a thin Cu foil. The next step in this experiment is to measure the cross sections for K-shell excitation by proton and antiproton impact and thereby to test the theories concerned with this process [5,13-161. Other experiments are at the planning stage. For example, Gay and Olson [56] have suggested to measure the differential cross section for electron emission in e+ and e- collisions with He atoms in a gas jet. This experiment would primarily test the theoretical predictions shown in fig. 9. Initial work may start in 1989 on the Aarhus University electrostatic positron beam line. Another experiment is currently being designed by our group in which the absolute cross section for single ionization of rare-gas atoms by et and p- impact for velocities below 0.5 MeV/amu will be measured. This experiment will make possible a test of theories such as that of Fainstein et al. [7], see fig. 5. In some years, we may get access to useful beams of p- of energies in the few-keV range. At least two schemes exist for the production of such beams [57,58]. They are primarily aimed at the PS-200 experiment which will measure the gravitational force on the antiproton [S7], but keV beams of antiprotons would also make feasible the production of antihydrogen atoms through positron capture by antiprotons from positronium [46] and studies of, e.g., adiabatic ionization (81, see fig. 6. Clearly, we are just beginning to acknowledge the abundance of possibilities to learn about atomic collisions which the new antiparticle beams offer. It is a pleasure to thank all my colleagues who have been involved in our work with antiprotons, see e.g., [I], and positrons, see, e.g., ref. [30].
References [l] L.H. Andersen, P. Hvelplund, H. Kundsen, S.P. Moller, A.H. Sorensen, K. Elsener, K-G. Rensfelt and E. Uggerhoj, Phys. Rev. A36 (1987) 3612. [2] L.H. Andersen, P. Hvelplund, H. Knudsen, S.P. Moller, K-G. Rensfett and E. Uggerhoj, Phys. Rev. Lett. 57 (1986) 2147.
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H. Knudsen
/Antiparticle
[3] D. Fromme, G. Kruse, W. Raith and G. Sinapius, Phys. Rev. Lett. 57 (1986) 3031. [4] D. Fromme, G. Kruse, W. Raith and G. Sinapius, J. Phys. B21 (1988) L261. [5] M.H. Martir, A.L. Ford, J.F. Reading and R.L. Becker, J. Phys. B15 (1982) 1729. [6] A.M. Ermolaev, in: Atomic Physics with Positrons, eds. J.W. Humberston and E.A.G. Armour (Plenum Press, New York and London, 1987) p. 393. [‘?I P.D. Fainstein, V.H. Ponce and R.D. Rivarola, Phys. Rev. A36 (1987) 3639. [8] M. Kimura and M. Inokuti, Phys. Rev. A38 (1988) 3801. [9] D.R. Schultz and RE. Olson, Phys. Rev. A38 (1988) 1866. [lo] A.E. Wetmore and R.E. Olson, to be pubfished. Ill) R.I. Campeanu, R.P. McEachran and A.D. Stauffer, J. Phys. B20 (1987) 1635. [12] P.J. Schultz and J.L. Campbell, Phys. Lett. 112A (1985) 316. [13] P.A. Amundsen, J. Phys. BlO (1977) 2177. [14] D. Trautmann, F. R&e1 and G. Baur, Nucl. Instr. and Meth. 214 (1983) 21. [15] W. Brandt and G. Basbas, Phys. Rev. A27 $1983) 578; Phys. Rev. A28 (1983) 3142. 1161 G. Mehler, B. Miiller, W. Greiner and G. Soff, Phys. Rev. A36 (1987) 1454. [17] C.R. Garibotti and J.E. MiragIia, Phys. Rev. A21 (1980) 572. [18] P.D. Fainstein, V.H. Ponce and R.D. Rivarola, J. Phys. 821 (1988) 2989. [19] A. Miiller-Groeiing and G. Soff, 2. Physik D9 (1988) 233. [20] R.E. Olson and T.J. Gay, Phys. Rev. Lett. 61 (1988) 302. [21] M. Brauner and J.S. Brigs, J. Phys. B19 (1986) L325. [22] P. Mandal, K. Roy and N.C. Sil, Phys. Rev. A33 (1986) 756. [23] J.F. Reading and A.L. Ford, Phys. Rev. Lett. 58 (1987) 543. [24] J.F. Reading and A.L. Ford, J. Phys. B20 (1987) 3747. [25] A.L. Ford and J.F. Reading, submitted to J. Phys. B21 (1988) L685. 1261 R.E. Olson, Phys. Rev. A36 (1987) 1519. 1271 J.H. McGuire, Phys. Rev. Lett. 49 (1982) 1153. [28] J.H. McGuire and J. BurgdBrfer, Phys. Rev. A36 (1987) 4089. 1291 L. Vegh, Phys. Rev. A37 (1988) 992. 1301 M. Charlton, L.H. Andersen, L. Brun-Nielsen, B.I. Deutch, P. Hvelplund, F.M. Jacobsen, H. Knudsen, G. Laricchia, M.R. Poulsen and J.O. Pedersen, J. Phys. B21 (1988) L545. [31] W.H. Barkas, J.N. Dyer and H.H. Heckman, Phys. Rev. Lett. 11 (1963) 26. [32] J. Lindhard, Nucl. Instr. and Meth. 132 (1976) 1. [33] H.H. Andersen, J.F. Bak, H. Knudsen, P. Mlailer Petersen, and B.R. Nielsen, Nucl. Instr. and Meth. 140 (1977) 537. [34] L.H. Andersen, P. Hvelplund, H. Knudsen, S.P. MeIIer, J.O.P. Pedersen, E. Uggerhoj, K. Elsener and E. Morenzoni, Phys. Rev. Lett. 62 (1989) 1731.
- atom colitsions [35] F. Kottmann, Proc. Int. Symp. on Muon and Pion Interaction with Matter, Dubna (1987) p. 268. [36] J.H. McGuire and N.C. Deb, in: Atomic Physics with Positrons eds. J.W. Humberston and E.A.G. Armour (Plenum Press, New York and London, 1987) p. 83; see also Phys. Rev. A34 (1986) 685. [37] R.I. Campeanu, D. Fromme, G. Kruse, R.P. McEachran, L.A. Parcel& W. Raith, G. Sinapius and A.D. Stauffer, J. Phys. B20 (1987) 3557. [38] L.M. Diana, P.G. Coleman, B.L. Brooks, P.K. Pendleton and D.M. Norman, Phys. Rev. A34 (1986) 2731. [39] L.S. Fomari, L.M. Diana and P.G. Coleman, Phys. Rev. Lett. 51 (1983) 2276. [40] T.C. Griffith, in: Positron Scattering in Gases, eds. J.W. Humberston and M.R.C. McDowell (Plenum Press, New York, 1984) p. 53. 1411 L.M. Simon?., Phys. Scripta T22 (1988) 90. 1421 J.W. Humberston, M. Charlton, F.M. Jacobsen and B.I. Deutch, J. Phys. B20 (1987) L25. [43] A.M. Ermolaev, B.H. Bransden and C.R. Mandal, Phys. Lett. A12.5 (1987) 44. [44] J.W. Darewych, J. Phys. B20 (1987) 5917. [45] S.N. Nakov and J.M. Wadehra, Phys. Rev. A37 (1988) 4118. [46] B.I. Deutch, F.M. Jacobsen, L.H. Andersen, P. Hvelplund, H. Knudsen, M.H. Holzscheiter, M. Charlton and G. Laricchia, Phys. Scripta T22 (1988) 248. [47] F.M. Jacobsen, M. Charlton, J. Chevallier, B.I. Deutch, G. Laricchia and M.R. Paulsen, J. Phys. B, to be published. 1481 K. Elsener, submitted to Comments At. Mol. Phys. [49] M.E. Rudd, R.D. DuBois, L.H. Toburen, C.A. Ratcliffe and T.V. Goffe, Phys. Rev. A28 (1983) 3244. [50] M.B. Shah and H.B. Gilbody, J. Phys. B18 (1985) 899. [Sl] W. Raith, in: Atomic Physics with Positrons, eds. J.W. Humberston and E.A.G. Armour (Plenum Press, New York and London, 1987) p. 1. [52] Atomic Data for Controlled Fusion Research, eds. CF. Bamett et al., ORNL Report No 5206 (1977). [53] Y. Yamazaki, K. Kuroki, F. Fujimoto, L.H. Andersen, P. Hveiplund, H. Knudsen, S.P. Meller, E. Uggerhej and K. Elsener, CERN-PSCC/87-39, Proposal P 108 (1988). (541 L.H. Andersen, P. Hvelplund, H. Knudsen, S.P. Mailer, E. Uggerhej, K. Elsener, E. Morenzoni and K.G. Rensfelt, CERN-PSCC/86-47, Experiment PS 194/2 (1988). [55] M. Charlton, L.H. Andersen, L. Bnm-Nielsen, B.I. Deutch, P. Hvelplund, F.M. Jacobsen, H. Knudsen, G. Laricchia and M.R. Poulsen, to be submitted to J. Phys. B. [56] T.J. Gay and R.E. Olson, 10th Int. Conf. on Application of Accelerators in Research and Industry, Denton (1988) Nucl. Instr. and Meth. B40/41 (1989) 104. [57] N. Beverini et al., Los Alamos National Laboratory Report LA-UR-86-260; M.V. Hynes. Phys. Scripta T22 (1988) 19.5. [58] J. Eades and L.M. Simons, CERN/EF 88-13, submitted to Nucl. Instr. and Meth. A.
Nuclear Instruments and Methods in Physics Research B42 (1989) 536-544 North-Holland, Amsterdam
ANTIPARTICLE-ATOM
COLLISIONS
H. KNUDSEN Institute
of Physics,
Wniversity of Aarhus, DK-8000 Aarhur C, Denmark
The production of beams of antiparticles useful for atomic-collision studies is discussed. The application of these beams in recent studies of single and multiple ionization of light atoms, as well as of the differential electron-emission cross section, is elaborated on. Finally, some future experiments with antiparticles are presented.
1. Introduction
Recently there has been a growing interest in antiparticle-atom collisions. The main reason for this interest is that since 1986, high-quality beams of useful velocity and intensity of all the particles, e+, e-, p+, and p- have become accessible. This means that experimentally, we can obtain data for atomic-collision phenomena for impact of particles with the same charge but of greatly different mass, or for impact of particles with the same mass but of opposite charge sign. We can therefore measure what happens when the force acting on the atomic electrons during the collision is inverted; we can change the number of accessible reaction channels (for example, turn on or off electron capture which happens only for positive particles), and we can investigate effects of projectile deflection which is a prerogative of the light particles. This gives us a unique tool to test the theoretical models for various phenomena and especially to probe the dynamics of the collisions. There exists already a large number of ion-atomcollision processes that have been studied with impact of antiparticles, either theoretically or experimentally. Most of these studies are concerned with the ionization phenomenon. Single ionization of outer [l-11] and inner [5,12-161 electrons has been investigated, as well as differential cross sections for electron ejection [9,17-221, multiple ionization [1,2,23-301, and energy loss in ionizing collisions [31-351. A few calculations of excitation cross sections exist for antiparticle impact [5,19]. Other investigations concentrated on the charge-exchange process, namely positronium formation in the case of positron impact [3,4,9,36-401, antiprotonic atom formation for p - impact on atoms [41], and antihydrogen formation for antiproton impact on positronium atoms [42-461. In this paper, I shall discuss experimental and theoretical results for total and differential single-ionization cross sections, as well as for total double-ionization 0168-583X/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
cross sections. In all cases, the main emphasis will be on a comparison between data for particle and antiparticle impact. Preceding this main part there is an introduction to the production of antiparticle beams suitable for atomic-collision studies. At the end, I shall present some possible future experiments that may be worthwhile.
2. Beams for antiparticle-atom
collision studies
Generally, antiparticles are produced in the laboratory in pair-creation processes. Initially they therefore have a large kinetic energy and a large spread in kinetic energy. In order to produce beams of these particles, which are useful for atomic-collision studies, we have to decelerate the particles and to “cool” them, i.e., to decrease their energy spread. At the Aarhus University magnetic positron facility, the positrons come out of a ,,Na source. Their initial energy distribution is shown in fig. 1. The positrons enter an annealed tungsten foil, in which they are slowed down to thermal velocities. A few (2-3 x 10e3) drift to the surface and exit from the foil with a narrow energy distribution, which is also shown in fig. 1 [47]. The positrons are then accelerated to the desired energy (10 eV-IO keV) and transported to the target area by a guiding magnetic field. Fig. 2 shows the experimental
0
02 p’ ENERGY
04 (MeV)
06
5
4
3
2
1
e’ ENERGY
0 -1 -2 -3 (A’)
Fig. 1. Energy distribution of positrons: a) produced in a ,,Na source; b) after moderation in tungsten foil.
H. Knuaken / Antiparticle- atom collisions
531
Fig. 2. The Aarhus positron accelerator with experimental scattering chamber. Insert: The target-gas cell for ionization measurements.
setup. Shown here is also the target arrangement used for measurements of single- and multiple-ionization cross sections [30]. The arrival time of each positron is registered by a detection of the annihilation 511 keV y ray by a large NaI crystal. The positrons pass through a dilute target gas, and the ions, which are created here, are extracted by a transverse electric field into a flight tube. The ion arrival time is registered by a ceramic channeltron. In the resulting ion time-of-flight spectrum, the peaks corresponding to the various ion charge states are well resolved and are readily integrated to give the cross section for n-fold ionization, (I”+, see, e.g., ref. [l]. For our measurements of u”+ for antiproton impact [1,2], we used basically the same target arrangement. In this case, the antiparticle beam was delivered by the CERN PS-LEAR accelerator facility. Here, protons are accelerated by a linear accelerator and the PSB-PS accelerators to a momentum of 26 GeV/c, see fig. 3. These protons then enter a thick solid target, where antiprotons are created. They leave the production target
AA.
with a broad momentum distribution centered around 3.5 GeV/c. The antiprotons are collected, accumulated, and cooled by the AA and ACOL synchrotrons and then sent back to the proton synchrotron PS in a pulse containing about lo9 particles. In the PS, the antiprotons are decelerated to 0.6 GeV/c and finally transferred to the low-energy antiproton ring LEAR. Here the antiprotons are further cooled and decelerated, and they are directed to the experimental setup, in our case as a dc beam of 5.3 MeV and 105-lo6 particles/s-‘. This kinetic energy is at present the lowest available directly from LEAR. Lower energies can be obtained, for example by foil degradation, with the obvious disadvantage of energy and angular broadening. The angular spread can be removed by collimation, but this decreases the beam intensity. The energy straggling can be compensated for by recording the velocity of each particle by a time-of-flight technique. Currently, antiprotons and positrons are the only antiparticles that can be obtained in beams usable for atomic-collision experiments. Meson factories around the world are able to produce beams of muons, but these are of a much lower quality than the e+, p- beams
ACOL
Table 1 Characteristic parameters of typical antiparticle rently available for atomic-collision studies
Source Velocity (a.u.) Intensity (s-l) Beam size (mm’) Divergence (mrad)2 AP/P
Fig. 3. The CERN PS-LEAR accelerator facility.
Lower velocities
beams cnr-
P-
s-
e+
LEAR 15 105-lo6 1x1 10x20 10K3 x1/10
SIN 25 lo*-lo3 20x30 30X60 4x1o-2 NO
5 mCi s,Na 15 lo4 3x3 “ 0” 10W2 x1/50
538
H. Knudsen / Antiparticle-atom
collisions
described above. In table 1, the properties of the SINmuon beam (see, e.g., ref. [48]) are compared to those of the e+, p- beams used in our experiment.
5
I
I
I,,,,
I
. protons
3. Total single ionization The process, which leads to the liberation of one target electron following the impact of a charged particle, is one of the most important and fundamental phenomena that are studied in the field of atomic collisions. In this section, we shall review what we can learn (or have learnt) about this process by comparing data for particle and antiparticle impact. We shall concentrate on outer-electron ionization and therefore focus on light target atoms. It is natural to divide the discussion into subsections, depending on whether the projectile velocity is much larger than, in the order of, or much smaller than that of the orbital velocity of the active target electron.
antiprotons i
q
2 I 10~‘6
t
t
“E Y
5
+ -b iJ
1 9
2
-+
44 Ne
T
10-17 1
t5L
3.1. The charge difference for heavy particles E (MeVI
At very high projectile velocity, the interaction with the atomic electron is short-lasting, and (for particles of unit charge) it can be described by first-order perturbation theory. The first Born result for the single-ionization cross-section scales as In V o+aq*-----, If* where q is the projectile charge in units of the elementary charge, and V is the projectile velocity. This means that the cross section is independent of the sign of the projectile charge in this approximation, and therefore fast protons and antiprotons should give the same single-ionization cross section. This is actually the case, as can be seen in fig. 4, where our data [l] for proton and antiproton impact on He, Ne, and Ar atoms are shown as a function of the projectile energy. At lower projectile velocities but still velocities larger than that of the atomic electron, we expect to see the first charge difference, as illustrated by the continuumdistorted wave calculations by Fainstein et al. [7] for proton and antiproton impact on He (see fig. 5). The proton cross section is predicted to be larger than that for antiprotons. This is due to a polarization effect: The target-electron cloud is attracted to the positive projectile but repelled by the negative projectile, this giving the proton a higher probability for ionizing the target. At projectile velocities below that of the target electron, this trend is reversed. There are two reasons for this: First, the proton can capture a liberated target electron. This additional final channel subtracts from the ionization channel, and this effect becomes the more important, the lower the projectile velocity, as can be
Fig. 4. Single-ionization cross sections for p+ and p- impact on He, Ne, and Ar from ref. [l]. c is an experimental efficiency which does not depend on the projectile charge.
seen in fig. 5. Second, during the rather slow collision, for close encounters, the proton adds to the binding of the target electron, whereas antiprotons reduce the binding force, this again reducing the proton cross section as compared to that for antiprotons. At very low projectile velocities, we can describe the collision through the quasimolecular model: During the approach of the projectile, the original atomic electron
-
CDW - EIS FaInsteIn &al
(87)
ld6 Hellurn
_
“E ,” b ,o” -:
I
16’
1
I
KY2
I
/
I
I
16’ E IMeVlamul
I loo
I
1 10’
Fig. 5. CDW calculations of p+- and p--impact single-ionization cross section for He [7]. Also shown (dashed curve) is the single-capture cross section for protons on He. The curve is based on the data of refs. [48] and [49].
H. Km&en
/ Antiparticle-atom
_ 0.4 s w , 0.6
1
B-H
1
Rhu)
Fig. 6. Electronic energy of the pseudomolecular orbital for the p+ + H and p- + H systems as a function of the internuclear distance R. Calculations by Rimura and Inokuti [8].
wave function evolves into a molecular orbital, the binding energy of which depends on the internuclear distance R. Fig. 6 shows such binding-energy curves calculated for p/p impact on atomic hydrogen by Kimura and Inokuti [PI. As the proton comes closer to the target nucleus, the electron initially occupying a H(ls) state becomes either more tightly bound, approaching the He+ groundstate wave function, or it is promoted to the first excited state corresponding to He(n = 2). In the second half of the collision, the quasimolecular orbital may evolve into the H(ls) state again, in which case we have either no reaction or resonant charge exchange. Alternatively, the electron is promoted to an excited H( n = 2) state. In this picture, there is no ionization exit channel. For antiprotons, on the other hand, there are no bound pseudomolecular states when the projectile is close to the target nucleus, and the dominant outcome of the collision is the so-called adiabatic ionization. Consequently, it is expected that very slow antiprotons have a much higher ionization probability than equivelocity protons.
collisions
539
ally, the ratio between the positron and the proton cross sections becomes zero at a positron energy equal to the target-ionization potential, see. fig. 7. The positron/ proton cross-section difference is primarily due to the fact that positrons, which have the same velocity as protons, carry 1836 times less kinetic energy into the collision. This means that the available phase space of final states shrinks with decreasing positron energy, thus decreasing the positron-ionization cross section. There are other reasons for the p+/e+ difference, however. For example, protons and positrons can both capture a target electron, but above 100 keV/amu, the positron-capture cross section is considerably larger than that for protons, and therefore relatively fewer free electrons are created by the positrons. Another mechanism, which makes positrons less efficient ionizers than protons, is projectile deflection. For those impact parameters that are typical for ionizing collisions and for the projectile velocities that we are concerned with here (see fig. 7) the protons pass virtually undeflected by the target. Positrons, on the other hand, may be strongly deflected away from the target nucleus, where the electron density is highest. This of course decreases the positron-ionization probability. The solid curve in fig. 7 represents the classicaltrajectory Monte Carlo calculations of Schultz and Olson [9]. It reproduces fairly well the experimental data, which shows that, surprisingly enough, such a calculation, which assumes the positron to be a “classical” 1.4
I
I
I
1.2
1.0
3.2. The mass difference If the single-ionization cross sections obtained for protons and equivelocity positrons are compared, the effect of the large mass difference between the two kinds of projectile can be studied. According to the first Born result, eq. (1) there should be no dependence on the projectile mass for very large projectile velocities. This is really the case, as discussed recently by Raith [51] who showed that there is no discernible difference between the proton and positron cross sections above 500 keV/amu (V - 4.5 a.u.) for impact
on He.
At lower velocities, creating
positrons
free target electrons
are not as efficient
as are protons,
in
and eventu-
0.4
02
2
3 VELOCITY
4
5
(a u.)
Fig. 7. Ratio of the total cross section for single ionization of He by positron to that for proton impact. The solid curve shows the CTMC calculation of ref. [9]. The experimental results were obtained from refs. [3] and (511.
540
H. Km&en
/ Antiparticle-atom
E [.eVl
Fig. 8. The single-ionization cross section for positrons impinging on He. The experimental data are from Fromme et al. [3]. The solid curve is a CDW calculation, including total screen-
ing, the dot-and-dashcurve without screening corrections. Both from Campeanu et al. [ll].
point-like particle, may yield reasonable results, even for positron velocities which correspond to de Broglie wavelengths larger than the target atom. The positron-impact ionization cross section for a He target has also been calculated recently by Campeanu et al. [ll]. These authors used the distorted-wave technique and found that it is very important to take into account the mutual screening of the residual target ion by the ionized electron and the ionizing positron. Their result is shown in fig. 8 and agrees very well with the experimental data of Fromme et al. [3]. We may conclude that we understand the general mechanisms of the single-ionization process fairly well, and that, based on this knowledge, we can calculate the associated total cross section - even for the light projectiles.
4. Differential single-ionization cross sections As we have seen, it is possible to test our understanding of atomic-collision phenomena by comparing experimental data and theoretical results for impact of particles and antiparticles. This technique is the more sensitive, the larger the difference between the measured quantities. Therefore we may get a very sensitive tool for probing the collision dynamics by looking at differential cross sections. One example of such quantities is the singly differential cross section for electron emission as a function of emission angle. This cross section has been calculated by the CTMC method for proton and antiproton impact on He by Olson and Gay [20] and is shown in fig. 9. For the impact velocity chosen here, 2.83 a.u., the total-ionization cross sections for p+ and p- differ by only 35%. Nevertheless, the differential cross section shows differences of more than an order of magnitude: For forward emission of electrons by proton impact, it
collisions
is 50 times larger than for antiproton impact. Olson and Gay ascribe this difference to the postcollision attraction/repulsion between the projectile and the ionized electron. Even more spectacular differences have been predicted for the cross section for electron emission differential in both electron energy and emission angle. Fig. 10 shows the continuum-distorted wave calculations of Fainstein et al. [18] for 1 MeV p+ and p- impact on He. In this case, the emission angle is 0 = 0 O. As can be seen, most electrons exit from the interaction region with very small kinetic energies. However, at an electron velocity equal to the projectile velocity, for proton impact, we see a strong enhancement of the cross section, the so-called “cusp”. It is due to electrons that were captured to nearly bound (so-called continuum) states around the projectile. Such states do not exist in the case of antiproton projectiles, and Fainstein et al. predict an “anticusp” - the doubly differential cross section goes exponentially towards zero with decreasing projectile-electron velocity difference. Quite recently, this anticusp was observed at LEAR. Yamazaki et al. [53] degraded the original 5.3 MeV pbeam to an energy close to 1 MeV and transmitted it through a carbon foil. The forward-emitted electrons were energy-analyzed by a parallel-plate spectrometer. At the electron energy, where the cusp is observed for proton impact, they saw a broad and deep anticusp, reaching a lowest value which was two orders of magnitude smaller than the proton-cusp value. This result confirms nicely the existence of the intrigueing anticusp which has also been predicted for electron impact [21].
-161
-19’ 0
I 30
I 60
I I 90 120 DEGREES
I 150
Fig. 9. The cross section for electron emission to angle 0 for p+ and p- colliding with He. The impact velocity is 2.83 a.u. Solid curves indicate the CTMC result. From ref. [20].
H. Km&en
/ Aniiparticle-
5. Double ionization The theoretical calculations mentioned until now have one thing in common with most theories on charged-particle-atom collisions: they assume the independent-electron model to give a good approximation. That is, instead of treating all the interactions between the atomic electrons, the atomic nucleus, and the projectile, the theories treat only the transitions of the so-called active electrons caused by the projectile impact. For each active electron, the other electrons and the nucleus are taken into account in such a way that they create an effective potential, in which the active electron moves. As an example of phenomena beyond the independent-electron model, in the following we shall discuss the two electron transitions leading to double ionization. For charged-particle impact, the energy transferred to a target electron is generally very small (see, e.g., fig. 10). This means that during the double-ionization transition, the two active electrons usually interact strongly. This interaction is clearly not describable in the independent-electron model. Most experimental and theoretical investigations of the double-ionization process have concentrated on the He target atom because double ionization caused by interactions between more than two electrons is ruled out in this case. Three basic mechanisms exist for double ionization of He by charged-particle impact [l]. In the first, one electron is removed from the atom directly by the passage of the projectile. Thereafter, the
atom collisions
other electron, originally occupying a ground-state He wave function, has to relax onto the set of He+ states. In doing so, there is a finite probability that it ends up in the ion continuum. This is the so-called shake-off (SO) mechanism. In the second mechanism, the first electron, which interacts directly with the projectile, then hits the second electron which is now also removed from the atom. This is a two-step process involving only one electron-projectile encounter, and it is denoted TS-1. In the third mechanism, the projectile interacts directly with the target electrons, one at a time, and hence it is denoted TS-2. For large projectile velocities, it is fairly straightforward to predict the dependence of the cross sections for these three mechanisms on the projectile velocity and charge. The SO and the TS-1 mechanisms both involve one encounter with the charged particle, and their cross section is therefore expected to be proportional to the single-ionization cross section, eq. (1). Contrary to this, the TS-2 mechanism involves two electron-projectile encounters, and its cross section goes approximately [27] as the square of the single-ionization cross section, i.e., as ( q/V)4. Frequently, the most accurately measured quantity is the ratio R between the double- and the single-ionization cross section. This ratio is then expected to be rather constant for the SO and TS-1 processes but to follow a q2/V2 In V dependence for the TS-2 mechanism. In fig. 11 are shown experimental R data for proton double ionization of He [l]. At the largest projectile energies, R is rather constant, as expected from the discussion above, being dominated by contributions from the SO and TS-1 mechanisms. At lower velocities, the TS-2 mechanism gives the largest contribution, and hence R increases with decreasing V. S. 1. The charge
ELECTRON
ENERGY
(eV)
Fig. 10. The double-differential cross section for electron emission in the forward direction for 1 MeV p+ (- --) and pcolliding with He. CDW-EIS calculations from Fain( -) stein et al. [18].
541
difference
for heavy projectiles
In the simple picture presented until now, for large ion velocities there should be no difference between the p+- and p--impact double-ionization cross sections. As can be seen in fig. 11, this is not at all the case. Even at very large projectile velocities, where the single-ionization cross sections are virtually identical, the antiproton double-ionization cross section is approximately a factor of 2 larger than the proton double-ionization cross section. This fact is quite surprising and has led a number of theorists to develop new and sophisticated theoretical models of the double-ionization phenomenon. Already in 1982, McGuire [27] suggested that the difference is due to interference: All the double-ionization mechanisms lead to the same final state with two free electrons, and hence their probability amplitudes should be added instead of their cross sections. Such a
calculations compiicated, is the problem of introducing a stable two-electron atom into such a classical model. As can be seen in fig. 11, the classical calculations reproduce the proton cross section and accounts for some of the p’/pdifference. The forced-impulse method gives a remarkably good agreement with the proton data and accounts for most of the p+/p- difference, although there is some discrepancy left at the higher projectile velocities.
. p-
this work p+ this work 0 P’ a e- this work 0 el
14 t
-
Reading and Ford (87)
(x 1.35) ----
Olson (87)
5.2. The mass difference
6-
A comparison between data for p’, p- and data for e+, e- impact reveals the effect of the low mass of the light projectiles. In fig. 12 is shown data for electron impact compared to the p+ and p- results [l]. The general trend of the electron data is that they agree with the antiproton data at very high projectile velocities, but at decreasing velocity, the double-ionization cross section for electron impact becomes smaller and smaller, and eventually it is zero at an electron energy equal to the target double-ionization potential. The electron-antiproton difference is probably mainly due to the much reduced energy that the electrons carry into the collision, as compared with the
‘\
4-
IO’
Fig. 11. The ratio between the cross sections for double and single ionization of He by p+ and p- impact as a function of the projectile energy. References to experimental data can be found in ref. [l].
procedure gives a contribution to the double-ionization cross section which is proportional to q3, and which stems from interference between one or both of the singe-proj~tile-electron encounter mechanisms and the TS-2 mechanism. The interference term clearly leads to a difference between the cross sections for p+ and pimpact. It can be calculated only through models that take into account the full electron-electron interaction. During the last two years, the first two of such theories were published. In their so-called forced-impulse method, FIM, Reading and Ford [23-251 solve the time-dependent Schrijdinger equation by the coupledchannels method, using a two-electron basis set constructed of s, p, and d single-particle states. The important new aspect is that their calculation includes the interaction between the two target electrons, a feature that greatfy complicates such quantal calculations. Contrary to the FIM, Olson’s recently developed model for double ionization is based on a purely classical solution of the four-body problem [26]. In his CTMC calculations, he follows each collision step by step, and the full electron-electron interaction is taken into account. Apart from the long computing time, what makes these
0 P’ e e0 e-
thts work
1
D
12 CT b = 10 -
00
0
b ;‘ “b
_
-t-
D
80 0
+
I
n
6-
4-
Z-
E(MeVlamu)
Fig. 12. The ratio between the cross sections for double and single ionization for p+. p-, and e- impact [l].
H. Km&m
/ Antiparticle - atom collisions
543
6. Future experiments
E
[ MeVlamul
Fig. 13. The ratio between the cross sections for double and single ionization of He for positron impact (30) compared to curves drawn through the data for p+, p- and e- impact of fig. 12. Dashed curve represents eq. (2). Its low-energy part is calculated from recently obtained p- data 1541.
energy of equivelocity antiprotons. This gives a reduced space for doubly ionized final states and a correspondingly diminished double-ionization cross section. In view of the above explanation of the e-/pdifference in double ionization, we should be able to “factorize” the ratio between the double- and singleionization cross sections into a “charge factor” (stemming from interference, as discussed above, and from the electron-capture channel for positive projectiles) and a “mass factor”. Hence we may express the ratio for positron impact as phase
R(e’)
=~~e-~~(p+)/~(p-~.
(2) There are a number of effects that are not taken into account by this simple approach. For example, the deflection of the positrons tends to decrease the double-ionization cross section, as compared to that of electron impact. Also, the electron-capture cross section is not of the same magnitude for equivelocity positrons and protons. Nevertheless, eq. (2) does give a prediction of the positron ratio which agrees rather well with the positron experimental data 1301,as can be seen in fig. 13 for a He target. A similarly good agreement was found recently for Ne and Ar targets by Charlton et al. [SS]. The approach embedded in eq. (2) towards a prediction of the positron double-ionization cross section is purely empirical. At the moment, no theoretical calculations exist of the double-ionization cross section for the light projectiles. Such calculations seem to be within reach at the present time, although of course they would be a great challenge to the theorists.
Currently, two experiments based on the LEAR antiproton beam have reached the stage where feasibility studies have been completed successfully, Firstly, the project of Yamazaki et al. [53] aims not only at measuring the anticusp for p’s traversing thin carbon foils, but also at detecting the so-called wake-riding electrons that are supposed to occupy bound states of the oscillating potential which is created in the solid target due to the projectile passage. Secondly, Andersen et al. 1541 have succeeded in detecting target K-X-rays produced by antiprotons traversing a thin Cu foil. The next step in this experiment is to measure the cross sections for K-shell excitation by proton and antiproton impact and thereby to test the theories concerned with this process [5,13-161. Other experiments are at the planning stage. For example, Gay and Olson [56] have suggested to measure the differential cross section for electron emission in e+ and e- collisions with He atoms in a gas jet. This experiment would primarily test the theoretical predictions shown in fig. 9. Initial work may start in 1989 on the Aarhus University electrostatic positron beam line. Another experiment is currently being designed by our group in which the absolute cross section for single ionization of rare-gas atoms by et and p- impact for velocities below 0.5 MeV/amu will be measured. This experiment will make possible a test of theories such as that of Fainstein et al. [7], see fig. 5. In some years, we may get access to useful beams of p- of energies in the few-keV range. At least two schemes exist for the production of such beams [57,58]. They are primarily aimed at the PS-200 experiment which will measure the gravitational force on the antiproton [S7], but keV beams of antiprotons would also make feasible the production of antihydrogen atoms through positron capture by antiprotons from positronium [46] and studies of, e.g., adiabatic ionization (81, see fig. 6. Clearly, we are just beginning to acknowledge the abundance of possibilities to learn about atomic collisions which the new antiparticle beams offer. It is a pleasure to thank all my colleagues who have been involved in our work with antiprotons, see e.g., [I], and positrons, see, e.g., ref. [30].
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544
H. Knudsen
/Antiparticle
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