Cross section for double compton scattering

Employing elementary methods in nonrelativistic quantum electrodynamics, the cross section for γ0+e →e+γ+γ' is computed for arbitrary energy in the spectrum of the outgoing photons. The final result is given, differential in the energy of one of these photons, for the case where the incident photon is unpolarized and has energy E0<<mc2, a polarization sum and angular integration being performed for the final-state photons. The cross section has a simple algebraic form resulting from contributions from the sum of squared direct and exchange amplitudes; interference terms from these amplitudes do not contribute to the angular-integrated cross section