Scattering of polarized photons by protons

We derive the differential cross section for the scattering of plane polarized photons by protons below pion threshold. The contributions from the charge, spin, and anomalous magnetic moment is calculated with no approximation in the photon energy, ω. The contribution from the proton structure is included only to lowest order [viz., O((ω/M${)}^2$) ], and comes from the electric and magnetic dipole polarizabilities.