Semiempirical potentials for positron scattering by atoms

Abstract

We report calculations of differential and integral cross sections for positron scattering by noble gas and alkaline-earth atoms within the same methodology. The scattering potentials are constructed by scaling adiabatic potentials so that their minima coincide with the covalent radii of the target atoms. Elastic differential and integral cross sections are calculated for Ne, Ar, Be, and Mg, and the results are very close to experimental and best theoretical data. Particularly, elastic differential cross sections for Be and Mg at low energies are reported.

A rigid sphere approach to positron elastic scattering by noble gases, molecular hydrogen, nitrogen and methane

“…For example, many-body theory [19] requires an inclusion of virtual positronium, convergent-close-coupling formalism takes into account coupling effects to virtual positronium formation channels [20], whereas polarized-orbital [13][14][15][16][17][18], DFT [10,12] and model-potential [21,22] approaches need higher multipole terms (quadrupole, octupole, hyperpolarizability) in long-range polarization in order to get good agreement with experiments. The present results show that the lack of attractive virtual effects, short-range correlations and higher long-range multipoles can be effectively compensated by very deep minimum of dipole polarization potential (for example −α/2R 4 0 ≈ −49 eV for Ar, see Fig.…”

“…For positrons the repulsive static potential is counterbalanced solely by an attractive polarization potential making computational approaches very sensitive to the short-range positron -target's electrons (nonadiabatic) correlations. High quality (but computationally expensive) models have been developed to challenge this problem including, for example, approximate density functional theory (DFT) by Gianturco et al [12], polarizedorbital calculations by McEachran and Stauffer [13] and McEachran et al [14][15][16][17][18], many-body theory with virtual positronium formation by Green et al [19], convergent close-coupling (CCC) method by Fursa and Bray [20] and semi-empirical potential model for ab initio calculations by Assafrão et al [21] and Poveda et al [22]. All these approaches were able to successfully reproduce shapes and magnitudes of experimental elastic scattering cross-sections for most noble gases, though they are not fully consistent, particularly in the prediction of scattering lengths.…”

Comment on “Semiempirical potentials for positron scattering by atoms”

“…[9], this minimum is an artifact which comes about from a lack of discrimination against forward-scattered positrons in the measurement of the total scattering cross section, and thus reproducing it is not a strong point of the model approach. Furthermore, the large discrepancy between the approach presented by Assafräo et al [1] and the experimental data from Jones et al [8] (shown in Fig. 4 of [1]) is not discussed, despite this most recent data being the only experimental result to take account of the missing forward-angle effect in the scattering measurement.…”

“…A brief examination of the recent literature on this subject demonstrates, however, that comparisons with several important and recent results have not been made, and that such comparisons clearly affect the accuracy of their conclusions. In a recent paper, Assafräo et al have performed positronatom scattering calculations using an adiabatic potential which is scaled to the covalent radius of the atom in question to calculate low-energy scattering of positrons from Ne, Ar, Be, and Mg [1]. In introducing their work, they claimed that their approach might be useful in positron scattering as "diverging results have been presented even for the simplest problems, such as the total elastic cross section (TECS) from helium target.…”

“…2. Calculation from [1] compared to CCC results from [15], with inaccurate data between the positronium formation threshold (dotted line; E Ps ) and the ionization potential (short-dashed line; E Ion ) removed.…”