Differential Cross Sections in the Multistate Impact-Parameter Description of Heavy-Particle Collisions

Abstract

Differential cross sections are derived from a multistate impact-parameter treatment of heavy-particle collisions. Various approximations are suggested and their relationship with previous expressions are discussed. The equivalence between the differential cross sections in the impact-parameter and wave versions of the Born approximation is established for elastic and inelastic scattering and is illustrated explicitly for the $1s$, $2s$, $2{p}_{0}$, and $2{p}_{\ifmmode\pm\else\textpm\fi{}1}$ excitations of atomic hydrogen by proton and hydrogen-atom impact.