Numerical asymptotic functions in variational scattering theory

Abstract

A procedure for explicitly incorporating the effects of long range potentials in variational trial functions for electron-atom and electron-ion scattering is outlined. The component of the wavefunction that represents the asymptotic solution consists of two parts. Outside a certain boundary radius, the asymptotic solutions are generated numerically. The total trial wavefunction is made everywhere smooth and continuous by matching these asymptotic solutions at the boundary with two fixed analytical linearly independent functions, defined within the radius in each channel. Two choices of the fixed internal functions are considered. The numerical feasibility of this approach is investigated by application to the problem of scattering of electrons from atomic hydrogen in the static exchange approximation and from the positive He ion in the static approximation.