Mary T. McAlinden

Positron scattering by atomic hydrogen

Cross sections for positron scattering by atomic hydrogen are calculated in the energy range 0 - 110 eV using a 33-state approximation which employs the 1s, 2s and 2p eigenstates of both positronium and hydrogen together with 27 hydrogen pseudostates. Cross sections are given for elastic scattering, H(2s) and H(2p) excitation, Ps(1s), Ps(2s), Ps(2p) and total positronium formation, ionization, and total scattering. The degree of agreement with an earlier 18-state calculation of Kernoghan et al, with sophisticated single-centre approximations, and with the available experimental data, strongly suggests that the main cross sections for positron scattering off ground-state atomic hydrogen are now known to quite a high degree of accuracy. Problems with the total cross section highlighted by Kernoghan et al are now resolved by new experimental data of Stein et al which give excellent agreement with theory for both positron and electron scattering. Suggestions are made for further experimental investigations.

Positron scattering by rubidium and caesium

We report results in the energy range 0.5 to 64 eV for positron scattering by ground state rubidium and caesium in and coupled-state approximations, respectively. The pattern of results is similar to analogous calculations made on potassium by McAlinden et al. Except at the lowest energies, positronium formation is found to be almost entirely into excited states, with there being a dramatic collapse of the Ps(1s) cross section in the case of caesium. Ps(n=2), Ps(n=3) and cross sections are predicted to be of comparable size. formation is estimated from the calculated Ps(n=3) results using the scaling rule. Good agreement in shape and magnitude is obtained with the recent lower bound measurements of total positronium formation in rubidium by Surdutovich et al, although there are differences in detail. Good agreement is also achieved with the total cross section measurements of Parikh et al on rubidium after these have been corrected for discrimination against forward elastic scattering and renormalized upwards by 5%. These total cross section measurements display a pronounced peak near 6 eV which is well reproduced by the present theory but is at variance with the earlier Rb(5s,5p,6s,6p,4d) calculations of McEachran et al which neglect positronium formation. This peak, which also appears in the calculations on potassium and caesium, is primarily associated with the maximum in the total positronium formation cross section. At low energies elastic scattering is dominant, this dominance being directly taken over by the resonance excitation of the atom with increasing impact energy. The next most important cross section is positronium formation, followed by excitation of the lowest atomic d-state. The and transitions in rubidium and the and transitions in caesium are of relatively minor importance.

Positron scattering by potassium

Coupled-state calculations in a K(4s,4p,5s,5p,3d) + Ps(1s,2s,2p,3s,3p,3d) approximation are reported for positron scattering by ground-state potassium in the energy range 0.5 - 60.0 eV. Comparison is made with the earlier work of Hewitt and co-workers in a K(4s,4p,5s,5p) + Ps(1s,2s,2p) approximation. For the first time cross sections for positronium formation in n = 3 states are obtained. We support the conclusion of Hewitt et al that above about 4 eV positronium formation is mainly into excited states, although we disagree significantly on the distribution of the excited state population. Fairly good agreement is obtained with the measurements of Zhou and co-workers for total positronium formation when scaling is used to estimate the amount of positronium in states with . Our cross sections for elastic scattering, 4s - 4p, 4s - 5s and 4s - 5p excitation of potassium are in relatively good agreement with those of Hewitt and co-workers but our calculations also emphasize the importance of the 4s - 3d excitation which is omitted in their approximation. Atom excitation to the n = 5 level is found to be a relatively minor process. Good agreement is obtained with the total cross section measurements of Kwan and co-workers and Parikh and co-workers when these are normalized upwards by 10% and corrections made for near forward elastic scattering. This upward normalization lies within the quoted overall 21% error on the measurements. Below 4 eV the calculated total cross section is dominated by elastic scattering while at high energies 4s - 4p excitation is the main contributor. In the vicinity of 6 eV, and consistent with the measurements of Parikh and co-workers, the total cross section displays a pronounced peak which derives largely, although not totally, from positronium formation. Positronium formation is not important above about 30 eV.

Positronium scattering by Ne, Ar, Kr and Xe in the frozen target approximation

A full-electron coupled-state treatment of positronium (Ps)-inert gas scattering is developed within the context of the frozen target approximation. Calculations are performed for Ps(1s) scattering by Ne and Ar in the impact energy range 0-40 eV using coupled pseudostate expansions consisting of nine and 22 Ps states. The purpose of the pseudostates is primarily to represent ionization of the Ps which is found to be a major process at the higher energies. First Born estimates of target excitation are used to complement the frozen target results. The available experimental data are discussed in detail. It is pointed out that the very low energy measurements (≤2 eV) correspond to the momentum transfer cross section σmom and not to the elastic cross section σel. Calculation shows that σmom and σel diverge very rapidly with increasing energy and consequently comparisons of the low-energy data with σel can be very misleading. Agreement between the calculations and the low-energy measurements of σmom, as well as higher energy (≥15 eV) beam measurements of the total cross section, is less than satisfactory. Results for Ps(1s) scattering by Kr and Xe in the static-exchange approximation are also presented.

Reply to Comment on ‘Positronium scattering by Ne, Ar, Kr and Xe in the frozen target approximation’

A numerical inaccuracy in the static-exchange calculation of Blackwood et al (2002 J. Phys. B: At. Mol. Opt. Phys. 35 2661) for Ps(1s)–Xe scattering is corrected. The corrected result now conforms to the same pattern as He, Ne, Ar and Kr.

Positron Collisions with Atoms

The past few years have seen considerable advances in the experimental and theoretical study of positron - atom collisions. On the theoretical side these advances have been associated primarily with the development of coupled — state methods for positron collisions with one — electron atoms, i.e., with atomic hydrogen and, in a frozen core approximation, the alkali metals. For these systems there now exist computer programs capable of using large numbers of eigenstates and pseudostates. It is the achievements of this coupled — state approach to which we shall confine our attention here. However, in celebrating these recent successes, we would not wish to forget the earlier pioneering work of Wakid1,2, Ghosh3–20, McEachran and Stauffer21–30, and their collaborators, using this form of approximation. Invaluable to the coupled — state work has been the existence of good variational calculations at low energies31–54, especially those which go beyond the positronium formation threshold34,41–45,47,48,50,52–54. Last, but not least, the theory has profited enormously from the stimulation provided by experiment, particularly, in the present context, the experimental work of Charlton, Laricchia and co-workers at University College London, of Kauppila, Stein and co-workers at Detroit, and of Raith and co-workers at Bielefeld.

Overview of the present theoretical status of positron‐atom collisions

Recent advances in the theoretical treatment of positron‐atom scattering are reviewed with particular emphasis on coupled‐state methods. Resonances appearing above the ionization threshold in positron‐atomic hydrogen collisions are shown to be artefacts of simple approximations. Reliable results can now be obtained for all the main transitions in positron scattering off ground state atomic hydrogen. Calculations now exist for all the alkali metals from Li to Cs. These show a pronounced growth in excited state positronium formation on going up the sequence but with a corresponding collapse in the Ps(1s) formation cross section. Despite a wealth of experimental data, coupled‐state calculations on the noble gases which include positronium formation are rather sparse.

The Scattering of Positrons and Positronium by Atomic Targets

We focus upon the coupled - state approach to positron - and positronium (Ps) - atom collisions. The concept of pseudostates as a way of including ionization channels is discussed. Examples are given from positron scattering by atomic hydrogen and the alkali metals. The present status of Ps - atom collisions is next considered with emphasis upon the Ps-H, He, Ne and Ar systems where large coupled - pseudostate calculations have been performed within the frozen target model. Discrepancies between theories and experiments are highlighted. It is argued that converged cross sections have been obtained within the frozen target model and that any remaining discrepancies must be associated with the neglect of target excitation, whether real or virtual.

Positronium—atom scattering

Results of recent large coupled-pseudostate calculations of Ps scattering by H and He are presented. The parlous state of both theory and experiment for He is highlighted.