Compton scattering of photons by inner-shell electrons

We have developed an exact second-order S-matrix code for the relativistic numerical calculation of cross sections for Compton scattering of photons by bound electrons within the independent-particle approximation. We find good agreement with less exact treatments in regions where such theories are valid, recovering the impulse approximation and the soft-photon infrared divergence. We do not find agreement with an earlier calculation of Whittingham. We compare with recent scattering experiments in the regime Z{α}({}ωᵢ){~}EB, where we find that the impulse approximation is not adequate.