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Based on an equations--of--motion approach for time--dependent paircorrelations in strongly interacting Fermi liquids, we have developed a theoryfor describing the excitation spectrum of these systems. Compared to the known``correlated'' random--phase approximation (CRPA), our approach has thefollowing properties: i) The CRPA is reproduced when pair fluctuations areneglected. ii) The first two energy--weighted sumrules are fulfilled implying acorrect static structure. iii) No ad--hoc assumptions for the effective massare needed to reproduce the experimental dispersion of the roton in 3He. iv)The density response function displays a novel form, arising from vertexcorrections in the proper polarisation. Our theory is presented here withspecial emphasis on this latter point. We have also extended the approach tothe 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 anaccuracy that has previously only been achieved for impurities in Bose liquids.Comment: to be published in: JLTP (2007) Proc. Int. Symp. QFS2006, 1-6 Aug.  2006, Kyoto, Japa

Pair Excitations and Vertex Corrections in Fermi Fluids