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__ li!B Nuclear Instruments and Methods in Physics Research B 99 (1995) 363-367

EL+SEVlER

Beam Interactions with Materials 6 Atoms

Positron and positronium collisions

G. Laricchia *

Department of Physics and Astronomy, University College London, Gower Street. London WClE 6BT. UK

Abstract Recent results concerning the interaction of positrons with atoms and molecules are presented. In this context, progress in

the study of ionization, including electron capture, by positron impact is discussed, in particular with respect to channel-coupling, near threshold and correlation effects. Novel advances in the field of atomic collisions involving

positronium as a projectile are also reported.

1. Introduction

The study of atomic collisions using positrons (e+) and a light neutral projectile such as positronium (Ps), the

bound state of an electron (e-) and a e+, may enhance the understanding of basic physical interactions and elucidate, when compared to other projectiles, the role played by

their masses and charges in the collision. Over the years, progress in the production of e+ beams has enabled the

examination of scattering processes in increasing detail. In this paper, recent advances in Ps formation,

beam and scattering are discussed.

2. Near-threshold positronium formation

ionization, Ps

Positron-matter encounters may result in the formation

of Ps. If the target is an atom (or a molecule) A, the reaction may be represented as

e’+A+Ps+A+.

It has a threshold at E,, = I - 6.8 eV, where I is the

ionization energy of A, and 6.8 eV is the binding energy of

a Ps atom in its ground-state.

The near-threshold behaviour of the Ps formation cross-section (Qr,), and its interplay with other scattering channels, has recently been investigated and revealed a

number of interesting effects [l-4]. The adopted experi- mental technique is based on measuring the total ion yield

y(E)=Ni(E)/N+(E)aQ:<E>,

where N,(E) is the number of ions produced by N,

* Tel. f44 71 387 7050, fax +44 71 380 7145, e-mail

ucapp6d@uk.ac.ucI.

positrons of incident energy E and the total ionization

cross-section is

Q: =Qp,+Qi+ + CQ,‘,,

where Qps includes contributions from excited states, QT is the cross-section for direct single ionization and ZQ,‘, is

the sum over higher-order processes. Assuming that the annihilation probability is negligible

in the energy range here considered, Q: = Qps for E + < 1.

Detailed measurements of Qps were performed by detect-

ing the ions produced by a e+ beam (energy spread = 0.8

eV FWHM) passing through a gas cell which incorporated

an ion extractor [I]. In order to prevent perturbations during the collision, the beam and the ion extractor were

pulsed periodically on and off in anticoincidence. Some of the results for He are shown in Fig. 1 where

they are compared with other measurements [5] with which excellent agreement is found. Total cross-section measure-

ments (Q,) [6,7] are also shown in the figure together with the quantity Qdirr = Q, - Q:. At energies below I, Qdin =

Qe, + Qe, where Q,, is the cross-section for elastic scatter- ing and Q,, that for excitation. In the inset, Qdirf is compared with other measurements [8]. Both indicate that

Qdirr varies smoothly across E,,, decreasing only slightly

above it. Measurements with improved energy resolution (spread

= 0.5 eV FWHM) have recently been performed and

extended to all the inert gases [4]. These are shown in Fig. 2 according to the main energy dependence of QPs ex- pected near-threshold, namely

Qrs a (E,)l’+r”, (1)

where E’ is the outgoing (cm) Ps energy and 2’ is the dominant outgoing (Ps) angular momentum. It has been found that I’-values of 1 for He and 0 for Ne, Ar, Kr and Xe predominate near threshold.

0168-583X/9.5/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0168-583X(94)00572-9 VI. POSITRON SOURCES

364 G. Laricchia /Nucl. Instr. and Meth. in Phys. Res. B 99 (1995) 363-367

(I.8 -

0.6 -

0.1~ ” ’ ” ’ ! J - 121416182022242628

Impact energy in eV I I I I I 1

10 15 20 25 .w 35 40 45 50 55 60

Impact energy in eV

Fig. 1. Cross-sections for e+-He scattering. Q:, circles: filled [l]; hollow [5]. Q,, squares: filled 161; hollow [7] with respective Qdift in triangles. Also large triangles in the inset [8]. From Ref. [l].

Cusps may be expected to occur in Q,, at E,, if Qps starts at threshold with an infinite slope (i.e. if 1’ = 0 in Eq. (1)). The dominance of the p-wave contribution to Qps in He, at least from _ 1 eV above threshold, explains the observation [1,8] of a smooth variation, within experimen- tal resolutions, of Q,, across E,. Interestingly however, the data also suggest that, whilst a pronounced Wigner cusp in Q,, would not be expected for He, one might be manifest in the heavier inert atoms [4].

E’(eV)

101, ,,..,, 8; .,.,I

100 * E'(eV)

1”

I i’o

The findings on the dominant [‘-values in Eq. (1) are in qualitative agreement with results from theory [9] and measurements of the efficiency for collimated Ps produc- tion from He, Ar and Xe [IO]. The reason for the observed target dependence of 1’ might be related to the e+-atom interaction strength, resulting in progressively broader an- gular distributions of the Ps produced from targets of increasing atomic number. This conjecture is also sup- ported by recent findings, discussed in Section 4, on the

lo@ * 10’

E’(eV)

6

5

4

3

2

1 0’

I

t

E’(eV) E’(eV)

Fig. 2. The dependence of up, on the excess energy E’ for (a) He, (b) Ne, (c) Ar, (d) Kr and (e) Xe [4].

G. Laricchia /Nucl. Instr. and Meih. in Phys. Res. B 99 (1995) 363-367 365

high degree of collimation of the Ps produced from H,

[11,12], and the importance of the p and d partial wave Ps

formation cross-sections near-threshold in H [13].

3. Differential ionization studies

A special case of ionization by positive ion impact

results in the ejected e- moving with a small velocity

relative to the scattered projectile. The phenomenon, known as Electron Capture to the Continuum (ECC) is manifested

by a cusp in the energy spectrum of the electrons ejected in a narrow angular range about the direction of the

scattered projectile [14]. Since the latter is almost unde- fleeted by the collision, the ECC peak is confined around

0”.

It has been found [15] that an ECC cusp should appear in the triply differential cross-section (TDCS) for ioniza-

tion of H by e + impact. Further calculations on the same

system [16] suggested that cusps should even be manifest in the doubly differential cross-sections (DDCS) over a broad angular range, although in some cases the magnitude

of these structures had originally been overestimated [17]. Contrasting results arose from a Classical Trajectory

Monte-Carlo (CTMC) calculation [18] where the lack of any cusp in the DDCS was attributed to large projectile

deflections.

In recent experimental studies of the energy spectra of

the electrons ejected from an Ar target [19,20] by e+ impact, no ECC cusp has been observed. Some of these

results are shown in Figs. 3 and 4. The energy spectra deduced from ejected e- time-of-flights at e+ impact

energies of 50. 100 and 150 eV are shown in Fig. 3. At these energies, the ECC electrons would possess energies

of around 17, 42 and 67 eV respectively. At the highest impact energies, a small ridge was found which could be

compatible with ECC. In this experiment, a magnetic beamline was used and the angular acceptance was esti-

mated to extend, at most energies, to angles > f 10”. This was reduced to < k6” by employing an electrostatic

beamline in conjuction with a double-pass parallel-plate

spectrometer which measured the energy distribution of e +

or e- projectiles after scattering inelastically around 0”. Little difference was observed in the shape of the spectra at 100, 150 and 250 eV incident energy. The study has been further extended to the DDCS for 100 eV incident

energy e _ and e+ scattered at 30” and 45”. The 30” results

for e+ impact are shown in Fig. 4 where they are com- pared with results of a CTMC calculation on the same target [21]. As partially illustrated in Fig. 4, these calcula- tions agree well with the measured ejected e- spectra [19,20] but poorly with the spectra of the scattered positrons 1201. Small ECC effects have also been predicted in the DDCS of 500 eV e + incident on H at 0” [22].

In conclusion, it appears that the large deflections

suffered by the light e+ diffuse the ECC process over a

1.2 / 1 I /

1.0

1 I

0.8 50eV impact

0.6 i

0.4

_;,zi )*I l ..,...,... 1

0 10 20 30 40 50

i;ected electron energy an eV

1 2 / 1

,

lo- i i

08 - I i ooev ,mpact

06 -

I 04 - I

!

0.2 - II . i

q l .

****.*a.. I

-02’ I I I / 1

0 ZD 40 EO 80 100 120

fyxted electron enerqy 1” eV

-0.2 1 I / I 1 I / 1 I 0 20 40 60 80 100 120 140 160

Ejected electron energy in eV

Fig. 3. Ejected e- energy spectra deduced from time-of-flights at

various e+ impact energies [19].

Fig. 4. Doubly differential cross-section of ejected e- (triangles)

and scattered projectile (diamonds) as a function of energy at 30”

for 100 eV e+ impact on Ar [20]. The solid line is from a CTMC

calculation [21].

VI. POSITRON SOURCES

366 G. Laricchia /Nucl. Instr. and Meth. in Phys. Res. B 99 (1995) 363-367

Table 1 4. Positronium beams and scattering Comparison of R = (DDCS) e+/(DDCS) e- for the secondary

e- ejected at 1.5 eV from 100 eV e * -atom collision at 30”

References Target Rcxp R theory

Kover et al. [20] Ar 2.7+ 1

Schmidt et al. [24] Ar 16 +ll

Sparrow and Olson [21] Ar -2

Schultz et al. [25] He 6.5

Klar and Berakdar [22] H - 15

broad range of angles with the effect being “washed out” at any given angle. The large impact parameters involved in ionization events by e + impact [23] also would reduce the strength of the final state e--e+ Coulomb interaction which gives rise to the ECC phenomenon. The pronounced structure predicted in the TDCS [15] awaits experimental confirmation.

At medium and high energies Ps may be produced efficiently as a projectile by the neutralization of a e+ beam. Techniques have used primarily gases as the neutral- izing medium but solids have also been employed [26]. The Ps beam characteristics depend on the neutralizer and the quality of the e+ beam. In the case of gases, the production efficiency is related to the differential cross- section for Ps production, integrated over a suitably small angular range, as well as the Ps-gas total cross-section which limits the usefulness of increasing the neutralizer pressure.

The projectile-ejected e- final state interaction results in observable differences between the angular distributions of the e- ionized by e+ and e- impact. This is illustrated in Table 1 where values of the ratio (R) of the intensities of 15 eV e- ejected at 30” by e+ and e- incident at 100 eV are compared. In all cases, the final state Coulomb attraction results in a larger intensity of the secondary e- ejected at forward angles by ef impact. However, discrep- ancies exist between the two experiments on Ar [20,24], the experimental results of Ref. [20] agreeing with calcula- tions [21] for the same target. The differing predictions from theory might instead reflect the dependence of R on the target atomic number, the heavier targets resulting in broader deflections of the e+ projectiles.

The Ps beam energy spread is related to the e+ beam energy resolution, the relative magnitude of the cross-sec- tion for Ps formation in its ground state to that in higher quantum states [10,26,27] as well as to that for other simultaneous processes [2,28]. The Ps beam energy and, partially, quantum states may be monitored via a timing method [29,10]. A characterized Ps beam has been applied to the study of energetic Ps scattering from atomic targets [30]. The total cross-section for Ps-Ar, in the range 16-95 eV incident energy, is shown in Fig. 5. It was measured via the attenuation of a timed Ps beam, produced in a gas cell containing Ar or Hz, passing through a second cell containing, in this case, Ar gas.

Comparison with theory [31] suggests that projectile ionization might be the dominant channel in the collision. These measurements represent the first controlled study of the atomic interactions of energetic Ps. It is expected that such studies may enhance our understanding of atomic

01 4 I I I I 6 I I I 0 10 20 30 40 50 60 70 60 90 100

Positronium Energy (eV)

Fig. 5. Total cross-section for Ps-Ar scattering [30].

G. Laricchia /Nucl. Instr. and Meth. in Phys. Res. B 99 (1995) 363-367 367

collision in general as well as helping the description of Ps

scattering from complex system [32].

Investigations into the efficiency for Ps beam produc-

tion [lo] had concluded that, despite its high ionization energy, a He target resulted in a higher degree of collima-

tion than other inert atoms. As discussed above, this might reflect the relatively weak (repulsive) static interaction between the projectile and the He atom. In the context of Ps beams, however, Ar was found to be a better neutralizer

than He since at their maximum Q,,(Ar) = lOQ,,(He).

More recently, H, has been found to be over twice as efficient as Ar for the production of collimated Ps [ll].

This might arise from both the magnitude of Qps, since

Qp,(H,> = 0.75Q,,(Ar) around the peak, and its forward

collimation arising from the low Z of the molecule. Addi-

tionally, the dependence of the production efficiency with neutralizer pressure suggests a total cross-section for Ps-H,

scattering lower than that from Ar. Further investigations are in progress.

5. Conclusions

Recent advances in the investigation of Ps formation and direct ionization by e+ impact as well as of Ps beams and scattering have been discussed. In the former case, the

emphasis has been on near-threshold and differential stud-

ies, respectively, where the light mass of the positron

results in marked differences in comparison to other posi- tive projectiles. It is anticipated that the controlled study of atomic interactions with energetic Ps will aid the under-

standing of atomic scattering phenomena and be of rele- vance in other fields in physics [26].

Acknowledgements

I am grateful to my coworkers for their contribution to

the research discussed above. Thanks are also due to The Engineering and Physical Sciences Research Council for

supporting this work under grant No. GR/44948 and to The Nuffield Foundation for the award of a Science Re- search Fellowship.

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VI. POSITRON SOURCES