The Klein–Nishina formula gives the differential cross section of photons scattered from a single free electron in lowest order of quantum electrodynamics. At low frequencies (e.g., visible light) this yields Thomson scattering; at higher frequencies (e.g., x-rays and gamma-rays) this yields Compton scattering.
For an incident photon of energy , the differential cross section is:
where is a differential cross section, is an infinitesimal solid angle element, is the fine structure constant (~1/137.04), is the scattering angle; is the "reduced" Compton wave length of the electron (~0.38616 pm); is the mass of an electron (~511 keV); and is the ratio of photon energy after and before the collision: