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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 rₒ5. Comparison is made with similar calculations made using the static random-phase-approximation and Hubbard interactions.
Crowell et al. (Fri,) studied this question.