Quantum-Mechanical Formulas for the Inelastic Scattering of Fast Electrons and their Compton Line Shape. Nonrelativistic Approximation

Abstract

A critical discussion is presented on the various ways to calculate the total inelastic electron scattering in the Born approximation. It is shown that the Morse approximation, the simplest and most frequently used, fails at small and large scattering angles. An improvement can be obtained by use of the “quasi-free-scattering” approximation first proposed by Bethe. An attempt is made to take into account the binding of the target electrons through their momentum distributions and in this way to correct Bethe's approximation for Doppler effects. This quantum-mechanical treatment shows the contribution of exchange terms to the Compton profile of the scattered electrons.