Y. Dewulf

Long-range correlations, which are partially responsible for the observed fragmentation and depletion of low-lying single-particle strength, are studied in the Green's function formalism. The self-energy is expanded up to second order in the residual interaction. We compare two methods of implementing self-consistency in the solution of the Dyson equation beyond Hartree-Fock, for the case of the 16O nucleus. It is found that the energy-bin method and the BAGEL method lead to globally equivalent results. In both methods the final single-particle strength functions are characterized by exponential tails at energies far from the Fermi level.

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.

A fully self-consistent treatment of short-range correlations in nuclear matter is presented. Different implementations of the determination of the nucleon spectral functions for different interactions are shown to be consistent with each other. The resulting saturation densities are closer to the empirical result when compared with (continuous choice) Brueckner-Hartree-Fock values. Arguments for the dominance of short-range correlations in determining the nuclear matter saturation density are presented. A further survey of the role of long-range correlations suggests that the inclusion of pionic contributions to ring diagrams in nuclear matter leads to higher saturation densities than empirically observed. A possible resolution of the nuclear matter saturation problem is suggested.