Model-potential calculations of positron binding, scattering, and annihilation for atoms and small molecules, using a Gaussian basis

TL;DR

This paper introduces a model-potential approach using Gaussian basis functions to calculate positron interactions, including binding, scattering, and annihilation, for various atoms and small molecules, aligning well with existing data.

Contribution

The study develops a novel model-potential method with adjustable parameters to accurately reproduce positron binding energies and scattering phase shifts for atoms and molecules.

Findings

Good agreement with experimental data for binding energies and annihilation rates.

Prediction that Cl₂ may support a positron bound state with a few meV binding energy.

Identification of a discrepancy in the $Z_{eff}$ value for Cl₂ compared to historical experimental data.

Abstract

A model-potential method is employed to calculate binding, elastic scattering, and annihilation of positrons for a number of atoms and small nonpolar molecules, namely, Be, Mg, He, Ar, H$_2$, N$_2$, Cl$_2$, and CH$_4$. The model potential contains one free parameter for each type of atom within the target. Its values are chosen to reproduce existing ab initio positron-atom binding energies or scattering phase shifts. The calculations are performed using a Gaussian basis for the positron states, and we show how to obtain values of the scattering phase shifts and normalized annihilation rate $Z_{\rm eff}$ from discrete positive-energy pseudostates. Good agreement between the present results and existing calculations and experimental data, where available, is obtained, including the $Z_{\rm eff}$ value for CH$_4$, which is strongly enhanced by a low-lying virtual positron state. An exception is the room-temperature value of $Z_{\rm eff}$ for Cl$_2$, for which the present value is much smaller than the experimental value obtained over 50 years ago. Our calculations predict that among the molecular targets studied, only Cl$_2$ might support a bound state for the positron, with a binding energy of a few meV.