Effects of binding energy on exchange contributions in the stopping of electrons

Abstract

We describe a theoretical treatment of the exchange contributions in Bethe's theory of the stopping of electrons. Starting with the first Born approximation, we obtain an expansion in powers of the ratio of the electronic energy of the target atom to the incident electron's kinetic energy. The binding of the electron within the atom is systematically taken into account, and the leading contribution recovers Bethe's results. The approach involves the use of sum rules that are generalizations of the Bethe sum rule, specifically dealing with the contributions from electron exchange. Though we restrict our discussion to the stopping power here, the method is quite general and may also be used to find the exchange contributions to other quantities related to cross sections of electron-atom scattering. Our results indicate that there may be significant corrections when one accounts for the binding energy.