Note on the Generalization of the Burnett-Kroll Soft-Photon Theorem to Polarized Cross Sections

Burnett and Kroll have shown from the Low soft-photon theorem that an unpolarized radiative cross section is given by an operator acting on the corresponding unpolarized nonradiative cross section. Tarasov has generalized this result to cases when all spins are not summed. We rederive his result here and are able to express it in a substantially simpler and more useful way. Specifically we show that the cross section for a radiative process in which the particles involved have some particular polarization configuration is given through the first two orders in the photon momentum $k$ by a simple operator acting on the cross section for the nonradiative process with arbitrary polarization.