Polarization Phenomena in the One-Quantum Annihilation of Positrons and the Photoelectric Effect

Cross sections are derived for the one-quantum annihilation of longitudinally-polarized positrons and for the photoelectric effect with longitudinally-polarized photons. Simple expressions, quantitatively reliable for light elements, are obtained by considering only K-shell electrons and describing the outgoing electron (incoming positron) by plane waves. In both cases, the incoming and outgoing particles have predominantly the same helicity if the free Dirac particle is relativistic.In a note added in proof, these calculations are extended to the case of elliptically polarized radiation. For linearly polarized photons, the results are compared with those obtained by including lowest-order Coulomb corrections to the continuum wave function of the electron, as given by Sauter in 1931. The difference in the angular distribution is very marked, and indicates a sensitive dependence on the degree of screening of the Coulomb field.