Note on Compton scattering

Calculations on the energy exchange between free electrons and electromagnetic radiation are presented. The full Klein-Nishina cross section is used to evaluate 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 given. A Fokker-Planck equation which includes induced scattering is used to derive a generalized diffusion equation in frequency for multiple scattering of photons off nonrelativistic electrons. The relationship of the Klein-Nishina cross section with that of classical electromagnetic radiation theory is also elucidated