Radiative Corrections to Compton Scattering

Corrections of order $e^6$ to the differential cross section for Compton scattering of unpolarized radiation by electrons are computed. The results for corrections ascribable to virtual photons are finite, relativistically invariant, and valid at all energies, but contain a term which depends logarithmically on an assumed small photon mass $\lambda$. A cross section of the same order has also been obtained for double Compton scattering in which one of the emitted photons has an energy small compared to the rest mass of the electron (with the electron initially at rest). This contains a term depending on $\ln \lambda$ which exactly compensates the similar term arising from virtual quanta in all observable cases. Approximations for low and high energies, as well as numerical results, are given. These disagree with results obtained previously by Schafroth.