Positron-annihilation characteristics in an electron gas from low to high densities

Abstract

The approach to the ${\mathit{e}}^{+\mathrm{\ensuremath{-}}}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ interaction in jellium developed recently by Stachowiak and used to calculate annihilation characteristics for metallic densities (2\ensuremath{\le}${\mathit{r}}_{\mathit{s}}$\ensuremath{\le}6) is applied to determine these quantities also at high (${\mathit{r}}_{\mathit{s}}$2) and low densities (${\mathit{r}}_{\mathit{s}}$>6). The calculations are done self-consistently. The results are reasonable for all investigated values of ${\mathit{r}}_{\mathit{s}}$. It is shown that the theoretical momentum dependence of the partial annihilation rates is well described by one parameter, giving no theoretical support to the two independent parameters (b/a and c/a) usually determined with such a great effort in experimental papers. A simple formula is proposed for the total annihilation rate as a function of the electron density.