P-Wave Positron-Hydrogen Scattering, Annihilation, and Positronium Formation

Anand Bhatia

doi:10.3390/atoms5020017

Abstract

In a previous paper (Bhatia A.K. 2016), a hybrid theory for the scattering of positrons from hydrogen atoms was applied to calculate S-wave phase shifts, annihilation, and positronium formation cross sections. This approach is now being applied to calculate P-wave positron-hydrogen scattering. The present results, obtained using short-range correlation functions along with long-range correlations in the Schrödinger equation at the same time, agree very well with the results obtained in an earlier calculation by Bhatia et al. (1974), using the Feshbach projection operator formalism. In these earlier calculations, the correction due to the long-range correlations was applied to the variational results. In spite of the fact that this ad hoc correction destroyed the variational bound, the final results have been considered accurate. Annihilation cross-sections, positronium formation cross-sections, calculated in the distorted-wave approximation, are also presented.

Highlights

Various approximations have been used to study scattering of electrons and positrons by hydrogenic systems
Various experiments carried out on the formation of positronium are given in Bhatia (2016) [4] and are not repeated here
The integrals occurring in the positronium formation calculation have been carried out using the Fourier transforms, as indicated in [4]

Summary

Introduction

Various approximations have been used to study scattering of electrons and positrons by hydrogenic systems. The phase shifts obtained are rigorous lower bounds to the exact phase shifts We apply this approach to the P-wave scattering of positrons by hydrogen atoms. Ψ0 is the wave function given in Equation (1) without the correlation term. Calculations have been carried out to N = 84 for all values of k, the incident momentum, in order to have converged results and to use the resulting wave functions for the calculation of Ze f f. The present results include short-range and long-range correlations at the same time and have variational lower bounds to the exact phase shifts. A: Bhatia et al (1977) [18], B: Humberston (1977), quoted in Bhatia et al (1977) [18]

Positronium Formation

Conclusions