%0 Journal Article
%T Self-Consistent Green Function Method in Nuclear Matter
%A Khaled S. A. Hassaneen
%J Physics Research International
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/415605
%X Symmetric nuclear matter is studied within the Brueckner-Hartree-Fock (BHF) approach and is extending to the self-consistent Green¡¯s function (SCGF) approach. Both approximations are based on realistic nucleon-nucleon interaction; that is, CD-Bonn potential is chosen. The single-particle energy and the equation of state (EOS) are studied. The Fermi energy at the saturation point fulfills the Hugenholtz-Van Hove theorem. In comparison to the BHF approach, the binding energy is reduced and the EOS is stiffer. Both the SCGF and BHF approaches do not reproduce the correct saturation point. A simple contact interaction should be added to SCGF and BHF approaches to reproduce the empirical saturation point. 1. Introduction The correct treatment of short-range correlations when performing nuclear matter calculations using the basic nucleon-nucleon interaction (NN) is of great importance [1]. One of these correlations has been studied using Brueckner-type resummation of ladder diagrams. This resummation allows to rewrite the ground-state energy of nuclear matter, using as an effective interaction the -matrix, which takes care of the short-range repulsive core in the nucleon-nucleon interaction [2, 3]. Calculations using realistic interactions lead to results, which lie along a line (the Coester line) shifted with respect to the phenomenological saturation point ( , ) [4]. The remaining discrepancy can be attributed to relativistic effects and three-body forces contributions [5]. Self-consistent approaches based on the in-medium -matrix approximation for nuclear matter have been studied [6]. In this way, a spectral function for nucleons in nuclear matter including two-particle correlations is obtained. The ladder diagrams involved in the calculation of the in-medium -matrix include also hole-hole ( ) propagation. The -matrix approximation takes into account some of the higher-order hole line contributions as compared to the -matrix approach. It would be instructive to study the saturation properties of nuclear matter for the self-consistent -matrix approximation with realistic interactions. Strictly speaking, however, the Bethe-Brandow-Petschek theorem [7] only defines the energy variable to be used in the calculation of self-energy or single-particle potential for the hole states. The choice for the propagator of the particle states is not defined on this level of the hole-line expansion and, therefore, has been discussed in a controversial way. The conventional choice has been to ignore self-energy contributions for the particle states completely and
%U http://www.hindawi.com/journals/physri/2013/415605/