Forcing Conservation of Particle Flux in Perturbation-Theory Calculations of Inelastic Scattering

Abstract

Two approximations to Seaton's unitarization scheme are described which make it possible to impose the conservation-of-particle-flux requirements on an approximate calculation of inelastic scattering without making calculations of elastic scattering in the two channels which the transition connects. One approximation is based on the black-sphere model of Feshbach and Weisskopf. Another approximation corrects only for back coupling and can be equivalent to a method of Levine. The methods are illustrated by applying them to the Born approximation for the $1s-2s$ excitation of the hydrogen atom by electron impact.