Two-centre wavefunctions in the theory of electron scattering by hydrogen atoms

Abstract

The scattering wavefunctions of the H – ion are expanded in a basis of two-centre wavefunctions with radial components. Two expansions are considered characterized by the charge ratio q being either – 1 or + 1. These expansions may be regarded as an extension of the polarized-orbital method. The q = + 1 expansion has some novel features. The radial components are determined as the solutions of a set of coupled radial differential equations. Imposition of exchange antisymmetry transforms these equations into integro-differential equations for the q = - 1 expansion, but for the q = + 1 expansion the equations remain simply differential. The cross-sections are determined by partial wave analysis, utilizing the Mathieu function form of the radial wavefunctions at moderately large values of R. Numerical work is reported based upon truncation of the q = + 1 expansion after two terms. Phase shifts derived from static and adiabatic q = + 1 potentials for the l = 0 - 7 partial waves are presented for 59 values of the energy between 0 and 13.6eV. The corresponding differential and total cross-sections are compared with experimental, and other theoretical results.