Positron-Hydrogen Scattering, Annihilation, and Positronium Formation

Anand Bhatia

doi:10.3390/atoms4040027

Abstract

In previous papers (Bhatia A.K. 2007, 2012) a hybrid theory for the scattering of electrons from a hydrogenic system was developed and applied to calculate scattering phase shifts, Feshbach resonances, and photoabsorption processes. This approach is now being applied to the scattering of positrons from hydrogen atoms. Very accurate phase shifts, using the Feshbach projection operator formalism, were calculated previously (Bhatia A.K. et al. 1971 and Bhatia et al. 1974a). The present results, obtained using shorter expansions in the correlation function, along with long-range correlations in the Schrödinger equation, agree very well with the results obtained earlier. The scattering length is also calculated and the present results are compared with the previous results. Annihilation cross-sections, and positronium formation cross-sections, calculated in the distorted-wave approximation, are also presented.

Highlights

Scattering by hydrogenic systems has been carried out using various approximations
Feshbach projection operators were used to carry out the positron-hydrogen scattering calculations of Bhatia et al (1971, 1974) [9,10] and the correction due to the effect of the target polarization was applied to the extrapolated variational results
Atoms 2016, 4, 27 correlations at the same time, as mentioned above. The details of this formalism have been given in previous publications of Bhatia (2007, 2008) [7,8] and we briefly describe the method

Summary

Introduction

Scattering by hydrogenic systems has been carried out using various approximations. Among them is the method of polarized orbitals of Temkin (1959) [1], which takes into account the distortion produced in the target by the incident particle in the ansatz for the wave function for the scattering process. The phase shifts calculated by Bhatia (2007, 2008) [7,8] have rigorous lower bounds We apply this approach to the scattering of positrons from hydrogen atoms. Feshbach projection operators were used to carry out the positron-hydrogen scattering calculations of Bhatia et al (1971, 1974) [9,10] and the correction due to the effect of the target polarization was applied to the extrapolated variational results. In the above equation ρ is the density in grams per cubic centimeter and M A is the atomic mass

Positronium Formation

Conclusions