Multiple scattering of charged particles byNatoms

Abstract

The scattering of charged particles by $N$ atoms is investigated theoretically. We derive the scattering equations by applying the approach of Faddeev that was originally developed to study quantum mechanically the scattering of three particles. We focus on the case in which the distance between the $N$ target atoms is sufficiently large to allow the interactions between the atoms to be neglected. The Faddeev equations can then be reduced to a linear system whose solution is valid from the low-energy diffusive scattering regime, where the Foldy-Lax approach is often applied, to the ballistic regime, where multiple-scattering effects are small. To illustrate the method, results of calculations of the scattering of electrons by random configurations of 250 atoms, modeled by spherical potential wells, are presented. As an additional application, the solution obtained by Mott for the inelastic scattering of $\ensuremath{\alpha}$ particles by two atoms is extended to $N$ atoms.