Impulse Approximation in Compton Scattering

Abstract

Calculations of the core contributions to the Compton profiles for lithium ($1{s}^{2}$), carbon ($1{s}^{2}$), and aluminum ($2{s}^{2}2{p}^{6}$) were made employing excited-state one-electron continuum wave functions evaluated in the ground-state Hartree-Fock-Slater potential of the nucleus and remaining electrons. Good agreement with the impulse approximation is obtained. Measurements of the Compton profiles of lithium metal, graphite, and aluminum metal were made with Mo $K\ensuremath{\alpha}$ radiation and the core contributions were separated from the valence electron contributions. The Compton profiles for the core electrons [$1{s}^{2}$ for lithium and carbon, $2{s}^{2}2{p}^{6}$ for aluminum ($1{s}^{2}$ not excited)] were in fair agreement with the calculations. Total Compton cross sections (integrated over the Compton profile) were calculated in the impulse approximation and compared to the Waller-Hartree theory with and without the Bonham corrections. The agreement can be quite poor, differing at low angles by as much as a factor of 3.