Independent electron approximation for atomic scattering by heavy particles

TLDR

Scattering of a heavy particle from a multielectron target is approximated by treating each electron independently. The paper derives the link between the multi‑electron excitation/ionization amplitude and the scattering amplitude, and evaluates the validity of the independent‑electron approximation. The method treats the projectile classically, neglects electron correlations, and represents the system wave function as a product of single‑electron states, yielding scattering amplitudes and cross sections as products of single‑electron amplitudes and a binomial distribution of probabilities.

Abstract

Scattering from a multielectron target by a heavy particle is approximated in terms of amplitudes for scattering from individual target electrons. By treating the motion of the projectile classically and ignoring correlations, the wave function for the system is expressed as a product of single-electron wave functions. The probability amplitude for scattering into specific states is then a product of single-electron scattering amplitudes. In this approximation, cross sections for excitation and ionization involving many electrons are expressed in terms of a binomial distribution of single-electron probabilities. The standard connection of this amplitude for multiple excitation and ionization, ${A}^{\mathrm{if}}(B)$, to the corresponding scattering amplitude, $f(\ensuremath{\theta})$, is given, and the validity of this approximation is discussed.