Compton scattering of polarized light: scattering matrix for isotropic electron gas

The scattering matrix for the scattering of radiation by isotropic monoenergetic relativistic electron gas is found. The expression for the absorption coefficient by such gas is also given. The relativistic kinetic equation is obtained which describes the Compton scattering of radiation with arbitrary energy and polarization for random electron directions. The Compton scattering matrix (C SM) contains five redistribution functions (RFs) describing the redistribution of radiation on frequency and depending also on the scattering angle. The expressions for these functions are reduced to the forms free of cancellations.