Calculations of positron binding and annihilation in polyatomic molecules

TL;DR

This paper introduces a versatile model-potential method for calculating positron binding energies and annihilation rates in various polyatomic molecules, extending applicability beyond strongly polar molecules to include weakly polar and nonpolar systems.

Contribution

The authors develop a new model-potential approach that can be applied to both polar and nonpolar molecules for positron binding and annihilation calculations, unlike previous ab initio methods.

Findings

Results for HCN binding energy agree with existing calculations.

Predicted annihilation rate for HCN is 0.1–0.2 × 10^9 s⁻¹.

Method successfully extends to weakly polar and nonpolar molecules.

Abstract

A model-potential approach to calculating positron-molecule binding energies and annihilation rates is developed. Unlike existing ab initio calculations, which have mostly been applied to strongly polar molecules, the present methodology can be applied to both strongly polar and weakly polar or nonpolar systems. The electrostatic potential of the molecule is calculated at the Hartree-Fock level, and a model potential that describes short-range correlations and long-range polarization of the electron cloud by the positron is then added. The Schrodinger equation for a positron moving in this effective potential is solved to obtain the binding energy. The model potential contains a single adjustable parameter for each type of atom present in the molecule. The wave function of the positron bound state may be used to compute the rate of electron-positron annihilation from the bound state. As a first application, we investigate positron binding and annihilation for the hydrogen cyanide (HCN) molecule. Results for the binding energy are found to be in accord with existing calculations, and we predict the rate of annihilation from the bound state to be $\Gamma=0.1$--$0.2 \times 10^9~\text{s}^{-1}$.