Lifetime of Positrons in an Electron Gas

Abstract

New estimates of the lifetime of a positron in an electron gas are presented. The discussion is based on a modified ladder-type approximation to the electron-positron Green's function chosen so that the displaced-charge sum rule is identically satisfied. This constitutes a refinement of the simple ladder sum used by Kahana which leads to a large unphysical accumulation of charge about the positron. While this violation of the displaced-charge sum rule is, to say the least, annoying, reasons are given why it may not be very serious if one is concerned only with the computation of annihilation rates. We find, in fact, that the rates obtained in the more consistent modified ladder scheme are not very different from those quoted by Kahana although they represent a distinct improvement.