Multiple scattering in the Compton effect. II. Analytic and numerical treatment of energy profiles

Energy profiles are calculated for photons scattered twice from stationary electrons in a cylindrical sample of infinite radius. Both double-Compton (inelastic) and one-Rayleigh (elastic), one-Compton events are treated. Klein-Nishina, Thomson, and isotropic differential cross sections are employed. It is found that at the energies typically used in $\gamma$-ray experiments, the different cross sections result in significantly different energy profiles and angular distributions, while at x-ray energies the form of the cross section is (as expected) considerably less important. Sample thickness and choice of primary scattering angle are found to have major effects on the shapes of the double-scattered profiles.