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

Abstract

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 $1.5{m}_{ e}{c}^{2}$ in heavy elements ($Z>47$). For low-$Z$ elements, screening effects are always important. The ${n}^{3}$ 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 ${L}_{I}$ single-quantum pair-annihilation cross sections is well predicted by the square of the ratio of the $K$ and ${L}_{I}$ bound-electron wave-function normalizations.