Compton Scattering From Hydrogen And Helium Atoms

We develop an approach to describing Compton scattering of photons in the keV energy range from hydrogen and helium atoms based on a relativistic version of the AA-approximation within the standard perturbative S-matrix formalism. The resulting formulas for the cross section take into account the effects of the electron boundness and correctly reproduce the behavior of the cross section with the growth of photon energy, as it goes to the Thomson cross section, which coincides with the Klein-Nishina-Tamm formula for the cross section in the non-relativistic limit.