SUPERCONDUCTIVITY IN THE HOMOGENEOUS ELECTRON-GAS - EXCHANGE AND CORRELATION-EFFECTS

We examine the influence of exchange and correlation effects on normal-state and superconducting properties of the homogeneous electron gas. Our investigations extend an earlier paper by Rietschel and Sham (RS) on exact solutions of Eliashbergs equations for the random-phase-approximation (RPA)-screened Coulomb interaction between the electrons. We do this in two steps: In a first step, the dielectric function is modified by including local-field corrections, while in a second step, the spin dependence of the electron-electron interaction is taken into account explicitly within a phenomenological model first proposed by Kukkonen and Overhauser. This latter step is synonymous with consideration of vertex corrections. Our main result is the following: Local-field corrections alone are not able to remove the artifact of plasmon-induced superconductivity in the RPA-screened electron gas as reflected by negative values for the Coulomb pseudopotential *(RS). Only additional consideration of spin-dependent vertex corrections leads to values for * which are positive throughout and of order 0.05-0.10 for electronic densities 1rs5. © 1990 The American Physical Society.