A simple model for the effects of polarization is introduced for the study of positron-atom interactions. The model is also used to study positronium-atom interactions by treatment of such systems as the interactions of positrons with polarizable anions. The model depends upon the average dipole polarizability of the atom (or ion) and one disposable parameter, an effective radius. The effective radius is determined by fitting calculated scattering lengths for H and He and the calculated positronium affinity of H to their well-established values, and by interpolating on the ionization potentials for other atoms. The model produces quite satisfactory phase shifts and cross sections for positrons scattering elastically off H, He, Ne, Ar, Kr, and Xe. The model appears to be equal or superior in predictive power to the much more elaborate polarized-orbital model recently formulated by McEachran et al. The model predicts that none of the rare-gas atoms studied will bind a positron. As a measure of how far from binding they are, negative values of the positron affinity are devised by appealing to effective-range theory and a heuristic argument involving the dependence of the calculated scattering length on the disposable parameter in the model.

Semiempirical polarization potential for low-energy positron-atom and positron-atomic-ion interactions. I. Theory: Hydrogen and the noble gases

Publisher Summary Positron–atom scattering experiments involve interactions of antimatter with matter and can help provide a better understanding of the scattering of electrons by atoms and molecules. The scattering of electrons is a subject of great importance to many different fields of science and technology such as plasma physics, laser development, gaseous electronics, astrophysics, and studies of the earth's upper atmosphere. Comparisons between e + -atom (molecule) and e – -atom (molecule) scattering reveal some interesting differences and similarities. The static interaction is attractive for electrons and repulsive for positrons, while the polarization interaction is attractive for both projectiles. The exchange interaction contributes to e – scattering but does not play a role in e + scattering. The combined effect of the static and polarization interactions is that they add to each other in e – scattering, whereas there is a tendency toward cancellation in e + scattering. There are four objectives of this chapter: (1) to point out the most significant developments in the first decade of e + -gas scattering experiments, (2) to search for some consistent patterns in the experimental results in cases where several different groups have investigated the same collision processes, (3) to present some puzzling questions raised by the new generation of experiments that go beyond Q T measurements, and (4) to indicate some experimental areas of e + -gas scattering that would be interesting and feasible to investigate in the near future.

Positron—Gas Scattering Experiments

The position and width of the lowest resonance in electron-hydrogen scattering have been calculated using a Hylleraas correlation function with up to 95 terms in the optical potential formalism. The results should be useful as calibration points for experimental electron scattering purposes. A formula relating the conventional (Breit-Wigner) width with the Feschbach formalism is derived.

Precision calculation of the lowest 1S resonance in e-H scattering

Absolute total cross section measurements are presented for e--Ne and e--Ar scattering. The covered energy range spans from 100 to 3000 eV. The overall systematic uncertainty was +or-2.4%, the random uncertainty was +or-1.5% and the angular resolution error was less than 0.5%. A comparison with existing experimental and theoretical data is given. This comparison suggests that the semi-empirical data of de Heer et al (1979) for Ne are possibly overestimated by 5% at 100 eV.

https://iopscience.iop.org/article/10.1088/0022-3700/20/19/025/pdf

Absolute total cross section measurements for intermediate energy electron scattering: III. Ne and Ar

Total cross sections for the scattering of 2--50-eV positrons by helium and neon atoms have been measured using the time-of-flight technique, and are compared with recent experimental and theoretical results. The measurement of positron energies and the flight path length is described and possible sources of systematic errors, including the effects of small-angle forward scattering, are fully discussed.

Scattering of low-energy positrons by helium and neon atoms

S-wave elastic collisions of positrons with helium have been studied using the method of models in an optical-potential formulation that gives lower bounds to the phase shifts within the accuracy of the helium-atom model. Four simple approximations to the helium ground-state wavefunction are used in a trial function with up to 84 correlation terms. The annihilation rate calculated from what is considered to be the best model treated (of analytic Hartree-Fock type with the correct polarizability) is in good agreement with the most recent experiment. The scattering results are compared with those of other recent calculations.

S-wave collisions of positrons with helium

S-wave phase shifts for the positron-helium elastic scattering problem are presented in the coupled static approximation ( i.e. the trial function contains the ground states of both the target atom and positronium but no other terms). Various models of the target atom wavefunction are employed, two of which confirm qualitatively the marked effect on the results as reported by Wardle (1973) for these models. While none of the target models used in this approximation appears to lead to an adequate description of the system, as is also the case in positron-hydrogen scattering in the same approximation, a qualitative comparison of the best results presented here and the corresponding approximation in the hydrogen case suggests a manageable calculation with two open channels (i.e. with real positronium formation) could produce meaningful results.

The S-wave elastic scattering of positrons by helium in the coupled static approximation

Evidence is presented, in the context of the positron-hydrogen atom zero-energy scattering problem treated with approximate (distorted) hydrogen wavefunctions, that it is important in a low energy scattering calculation involving an approximate target wavefunction that this target function should display the correct polarizability. The calculations have been carried out through 'variant IV' of Peterkop and Rabik (1971) and through the 'method of models' of Drachman (1972).

The importance of being correctly polarizable

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S-wave collisions of positrons with helium

The S-wave elastic scattering of positrons by helium in the coupled static approximation

The importance of being correctly polarizable