Multiple scattering in the Compton effect. I. Analytic treatment of angular distributions and total scattering probabilities

The probabilities of single and multiple Compton scattering and the angular distributions of scattered photons are analyzed in terms of the effects of sample geometry and details of the photon-electron interaction (form of the single-electron cross section). It is shown that the desired quantities may be calculated analytically if Thomson scattering and an appropriate geometry are assumed. Consideration of scattering using an isotropic cross section suggests that in most cases sample geometry is more important than the form of the cross section in determining the probability and angular distribution of single and multiple scattering