Calculations of Scattering Cross Sections and Annihilation Rates in Low Energy Collisions of Positrons with Molecular Hydrogen

Abstract

An analysis of the requirements for an accurate calculation of Z_eff, the effective number of electrons per molecule available to the positron for annihilation, for low energy e⁺H₂ scattering using the Kohn method shows the importance of including basis functions which contain the positron-electron distance as a linear factor, i.e. Hylleraas-type functions. Such functions are very complicated to include as they are not separable, i.e. they cannot be expressed as a finite expansion of one particle functions. However, I have been able to extend the calculation of the lowest partial wave for low energy e⁺H₂ scattering using the Kohn method and basis sets involving only separable functions, which I described at the last Workshop at Detroit in 1985, to include Hylleraas-type basis functions. The results for Z_eff at very low energies are much closer to the experimental value than any that have been obtained previously. The inclusion of Hylleraas-type functions also has a very significant effect on the low energy phase shift and total cross section, bringing the cross section into agreement with experiment for incident positron energies up to about 2 eV. As far as I am aware, this is the first time that Hylleraas-type functions have been used in a molecular scattering calculation.