Ladder Corrections to the Static Random-Phase-Approximation Dielectric Constant and to Positron Annihilation in Metals

Abstract

A calculation of the static dielectric constant of a free-electron gas is made in which account is taken of repeated (ladder) electron-hole interactions. An analytic approximation is given for the results. The effective interaction thus obtained is used in a high-order (ladder) perturbation calculation of the two-photon annihilation rate of positrons in an electron gas. The results agree quite well with experimental data for $r_s\le 5$. Comparison is made with similar calculations made using the static random-phase-approximation and Hubbard interactions.