Discrete approach to self-consistent GW calculations in an electron gas

Recent debate considering the importance of combining the GW approach to the electron gas with vertex corrections urges a calculation that can deal with both concepts in a self-consistent way. A major difficulty is the complicated energy dependence of the electron spectral function. We therefore propose an approximation for the Green's function that may be very useful for tackling a more complete treatment of the electron gas problem. The key concept in this approach is the representation of the Green's function by a limited number of carefully chosen poles. In this paper we present results for self-consistent GW calculation and find that they compare quite well to other self-consistent approaches. This legitimizes the use of this scheme as a practical tool for more involved calculations