Longitudinal Polarization of Bremsstrahlung and Pair Production

The Born approximation bremsstrahlung (and pair production) cross sections, valid at all energies and angles, are given for all possible states of longitudinal polarization of the particles involved.When the photon-incoming electron angle (θ₀) and the photon-outgoing electron angle (θ) are both zero, a cancellation of Feynman diagrams causes all cross sections to vanish in Born approximation. Further, if both θ₀ and θ are small compared to m²E₀², the "spin-flip" cross sections are small (of order θ²) relative to the "non-spin-flip" ones. When account is taken of the above cancellation, angular momentum conservation is sufficient to determine this small-angle behavior, but it explains neither the sign nor the magnitude of the bremsstrahlung circular polarization.