Generalized Bruckner-Hartree-Fock theory and self-consistent RPA

Self-consistent RPA (SCRPA) theory is developed in the particle-particle (pp) channel. It is pointed out that in this way vertex and self-energy corrections are taken into account on an equal footing whereas in Bruckner-Hartree-Fock (BHF) this is not the case. We discuss in detail the interconnection between both theories and apply them to a model case. Excellent agreement with the exact solution is found for SCRPA where as BHF gives somewhat poorer results. In an appendix it is demonstrated how SCRPA connects to a variational principle and how, for the particle-hole case, sum rules and conservation laws are fulfilled. (C) 1998 Elsevier Science B.V.