Polarization effects in incoherent scattering of light by relativistic electrons

The quantum and classical cross sections for the scattering of light by a relativistic electron are derived for arbitrary polarization states of the incident and scattered light. The cross sections are derived in a form which permits direct averaging over the electron velocity distribution, in contrast with other cross sections which have been derived. An explanation is offered for the discrepancy (mentioned previously) between two forms of the scattering cross section for linear polarizations of the light which have been reported in the literature: the purely classical cross section and the classical limit of the quantum cross section