Self-consistent GW(0) results for the electron gas: Fixed screened-potential W-0 within the random-phase approximation

With the aim of properly understanding the basis for and the utility of many-body. perturbation theory as applied to extended metallic systems, we have calculated the electronic self-energy of the homogeneous electron gas within the CW approximation. The calculation has been carried out in a self-consistent way; i.e., the one-electron Green function obtained from Dyson's equation is the same as that used to calculate the self-energy. The self-consistency is restricted in the sense that the screened interaction W is kept fixed and equal-to that of the random-phase approximation for the gas. We have found that the final results are margin ally affected by the broadening of the quasiparticles, and that their self-consistent energies are still close to their free-electron counterparts as they are in non-self-consistent calculations. The reduction in strength of the quasiparticles and the development of satellite structure (plasmons) gives, however, a markedly smaller dynamical self-energy leading to, e.g., a smaller reduction in the quasiparticle strength as compared to non-self-consistent results. The relatively bad description of plasmon structure within the non-self-consistent GW approximation is marginally improved. A first attempt at including W in the self-consistency cycle leads to an even broader and structureless satellite spectrum in disagreement with experiment.