Pair Excitations and Vertex Corrections in Fermi Fluids

Based on an equations--of--motion approach for time--dependent pair correlations in strongly interacting Fermi liquids, we have developed a theory for describing the excitation spectrum of these systems. Compared to the known ``correlated'' random--phase approximation (CRPA), our approach has the following properties: i) The CRPA is reproduced when pair fluctuations are neglected. ii) The first two energy--weighted sumrules are fulfilled implying a correct static structure. iii) No ad--hoc assumptions for the effective mass are needed to reproduce the experimental dispersion of the roton in 3He. iv) The density response function displays a novel form, arising from vertex corrections in the proper polarisation. Our theory is presented here with special emphasis on this latter point. We have also extended the approach to the single particle self-energy and included pair fluctuations in the same way. The theory provides a diagrammatic superset of the familiar GW approximation. It aims at a consistent calculation of single particle excitations with an accuracy that has previously only been achieved for impurities in Bose liquids.