Positron - hydrogen scattering in the vicinity of the positronium formation threshold

Abstract

An analysis is made of the behaviour of the elastic scattering and positronium formation cross sections for s-, p- and d-wave low-energy positron - hydrogen scattering in the vicinity of the positronium formation threshold. The accurate cross sections, obtained using the Kohn variational method with elaborate trial functions containing many Hylleraas correlation functions, reveal interesting threshold structures which arise from the coupling between the positronium formation and the elastic scattering channels. Wigner's R-matrix method is used to provide a qualitative analysis of these structures. One of the most interesting features of the present results is the presence of a `rounded cusp' in the s-wave elastic scattering cross section at the threshold itself, as predicted by Wigner's threshold theory. Remarkably good fits to the partial-wave cross sections for elastic scattering, positronium formation and Ps - p elastic scattering are obtained using a five-parameter fit for each partial wave.