Detailed calculations on low-energy positron-hydrogen-molecule and helium-antihydrogen scattering

In this paper, we consider two scattering processes: low-energy positron-hydrogen-molecule and helium-antihydrogen scattering. In the positron-hydrogen-molecule scattering calculations, we use the Kohn variational method to calculate Zeff, the number of target electrons available to the positron for annihilation. In the helium-antihydrogen scattering calculations, we use the Rayleigh-Ritz variational method to calculate a wave function for the leptons as a function of the distance between the helium and the antihydrogen. This is used, together with the associated nuclear wave function and the wave function for α p-bar + Ps-, to calculate the cross section for the rearrangement reaction He + H-bar → α p-bar + Ps-, using the T-matrix and a form of the distorted wave approximation. For both processes, positron-electron correlation is taken into account accurately using Hylleraas-type functions.