Comments on Screening and Shell-Ratio Effects in Single-Quantum Pair Annihilation

We show that atomic-electron screening and subshell-ratio effects in single-quantum pair annihilation, reported by Broda and Johnson and by Sheth and Swamy, have a simple origin observed also in pair production and atomic photoelectric effect. In all three processes, the characteristic distances are small on an atomic scale, but large on a nuclear scale; wave functions have a point-Coulomb shape, but not the point-Coulomb normalization. Atomic-electron screening effects cause appreciable modifications of the total pair-annihilation cross section for positron energies below 1.5mₑc² in heavy elements ($Z>47$). For low-Z elements, screening effects are always important. The n³ rule of Bethe for subshell ratios is good only for low-Z elements (where n is the prinicipal quantum number); we find that the subshell ratio between the K and LI single-quantum pair-annihilation cross sections is well predicted by the square of the ratio of the K and LI bound-electron wave-function normalizations.