Inelastic positron scattering in an electron gas

Abstract

The positron inelastic scattering rate $\ensuremath{\gamma}$ in an electron gas is calculated in the full positron energy range within the random-phase approximation (RPA) using the Green's-function approach. Both particle-hole pair and plasmon excitation are taken into account. It is found that, for positron energy $E$ much less than the Fermi energy ${E}_{0}$, particle-hole scattering gives $\ensuremath{\gamma}\ensuremath{\simeq}{E}^{2}$, whereas, for $E$ much greater than ${E}_{0}$, plasmon scattering dominates and $\ensuremath{\gamma}\ensuremath{\simeq}(\frac{1}{{E}^{\frac{1}{2}}})\mathrm{ln}(\frac{E}{{E}_{0}})$. Interestingly, the plasmon excitation threshold energy for the positron is found to be the same as that for an electron. These results for a positron are compared with those for an electron obtained by Quinn.