The Effectiveness of Variational Methods for Inelastic Scattering Problems

Abstract

The calculation of a partial cross section in atomic collision theory requires the solution of a pair of coupled integro-differential equations when the collision is inelastic and there is a possibility of particle exchange. A discussion is given of some variational procedures available for obtaining approximate solutions of such equations. These procedures are applied to the solution of two sets of model equations which simulate the equations of real problems but permit of exact solution. A comparison of exact and variational solutions enables the effectiveness of the variational methods to be assessed. It is found that a good approximation may be expected when trial functions are used which allow for the mixing of inelastically and elastically scattered waves, but that if only crude trial functions are used the approximation will be poor in cases where coupling is strong.