Tseng's calculations of low energy pair production

Abstract

We review the theoretical work 1971–1997 of H.K. Tseng on low energy pair production. In this work numerical calculations were performed in independent particle approximation in a screened self-consistent central potential, expanding the S-matrix element in partial waves and multipoles. Sampling techniques in partial waves and multipoles were used to extend the calculations to higher energies (up to 10 Mev). Total cross sections, the positron energy spectrum, the positron angular distributions, and the positron–photon polarization correlations were studied. Agreement was obtained with most experiments, although some anomalies remained at the lowest energies (particularly at 1082 keV). Atomic screening of the nuclear charge decreases cross sections at higher energies, as described by a form factor in the momentum transfer to the nucleus. In an intermediate energy regime point Coulomb results in a shifted energy spectrum may be used. At low energies screening increases cross sections, and this is characterized in terms of a normalization screening factor which describes the change in magnitude of electron and positron wave functions at small distances. In this low energy regime angular distribution shapes and polarization correlations are independent of screening.