Impact parameter treatment of atomic collisions

Abstract

A generalized impact parameter formalism for heavy-particle collisions is developed in a rigorous way from a purely quantal formalism in which all quantities, which tend uniformly to a limit as the mass of the atomic nuclei becomes infinite, are replaced by that limit. Subsequently, an expression for the differential scattering cross section is derived in terms of quantities obtained from impact parameter calculations. In particular, this expression is used to calculate the probability of charge exchange at large angles of scattering for protons in hydrogen. It is shown that our formalism predicts the correct damping of the oscillations in the probability at low energies of impact.