Variational solution of the T-matrix integral equation

Departamento de F´isica de Materiales, Facultad de Ciencias Qu´imicas,UPV/EHU and Centro Mixto CSIC-UPV/EHU, Apdo. 1072, 20080 San Sebasti´an, Basque Country, Spain(Dated: February 2, 2008)We present a variational solution of the T-matrix integral equation within a local approximation.This solution provides a simple form for the T matrix similar to Hubbard models but with the localinteraction depending on momentum and frequency. By examining the ladder diagrams for irre-ducible polarizability, a connection between this interaction and the local-field factor is established.Based on the obtained solution, a form for the T-matrix contribution to the electron self-energy inaddition to the GW term is proposed. In the case of the electron-hole multiple scattering, this formallows one to avoid double counting.