A note on Compton scattering

Abstract

Calculations are presented on the energy exchange between free electrons and electromagnetic radiation. The full Klein-Nishina cross section is used in evaluating average scattering coefficients for an electron moving with arbitrary velocity. A number of useful series expansions for the mean energy and mean square energy transfer rates are presented. A Fokker-Planck equation that includes induced scattering is used in deriving a generalized diffusion equation in frequency for multiple scattering of photons of nonrelativistic electrons. The relationship of the Klein-Nishina cross section to that of classical electromagnetic radiation theory is elucidated.