Positron Effective Mass in an Electron Gas

A calculation is made of the positron effective mass in an electron gas at the sodium electron density, emphasizing terms which are nonlinear in the electron-positron interaction. We exploit a close similarity between the perturbation expansions for the lifetime and the self-energy. Both quantities are approximated by a $t$-matrix equation, using a two-parameter static effective interaction. The parameters are restricted to values which give agreement with the experimental annihilation rate. It is shown to be possible to obtain agreement with the experimental effective-mass value calculated from the thermal smearing of the $2\gamma$ angular correlation by Stewart and co-workers. However, if, in addition, we impose the screening requirement that the total displaced electron charge should exactly compensate the positron charge, we obtain effective-mass values that are too low. This result indicates that the observed thermal smearing of the angular-correlation curves cannot be explained from the effective mass of positrons in an electron gas.