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Short-range correlations in nuclear matter using Green's functions within a discrete pole approximation

Dewulf, Yves, Van Neck, Dimitri, Michel Waroquier

Published Jan 1, 2001• 9 citations
OpenAlex

Abstract

We treat short-range correlations in nuclear matter, induced by the repulsive core of the nucleon-nucleon potential, within the framework of a self-consistent Green's function theory. The effective in-medium interaction sums the ladder diagrams of both the particle-particle and hole-hole type. The demand of self-consistency results in a set of nonlinear equations which must be solved by iteration. We explore the possibility of approximating the single-particle Green's function by a limited number of poles and residues.

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We treat short-range correlations in nuclear matter, induced by the repulsive core of the nucleon-nucleon potential, within the framework of a self-consistent Green's function theory. The effective in-medium interaction sums the ladder diagrams of both the particle-particle and hole-hole type. The demand of self-consistency results in a set of nonlinear equations which must be solved by iteration. We explore the possibility of approximating the single-particle Green's function by a limited number of poles and residues.
The self-consistent Green’s function method within the ladder approximation provides a microscopic description of correlated nuclear systems which properly treats the nucleon-nucleon correlations induced by the short-range and tensor components present in any realistic interaction. These correlations produce a sizable depletion of low momenta below the Fermi surface as well as the occupation of high momenta in the nuclear ground state. A few representative results for nuclear matter are presented to illustrate the present progress in the application of this method to nuclear systems.
The properties of symmetric nuclear matter are investigated within Green's functions approach. We have implemented an iterative procedure allowing for a self-consistent evaluation of the single-particle and two-particle propagators. The in-medium scattering equation is solved for a realistic (nonseparable) nucleon-nucleon interaction including both particle-particle and hole-hole propagation. The corresponding two-particle propagator is constructed explicitly from the single-particle spectral functions. Results are obtained for finite temperatures and an extrapolation to T=0T=0T=0 is presented.
Recent developments in the many-body theory of interacting fermions are discussed employing a self-consistent Green function approach. This scheme is outlined and its application to nuclear systems is presented. Special attention is paid to the consistent inclusion of short-range and long-range correlations induced by realistic nucleon-nucleon interactions. Such correlations lead to occupation probabilities which deviate from the simple mean-field or shell-model description. The scheme is extended to incorporate relativistic effects. Also applications of field theoretical models for hadrons in a nuclear medium and their relation to QCD are discussed.
The equation of state of symmetric nuclear matter is addressed starting both from a realistic interaction derived from nucleon-nucleon scattering processes and from a low-momentum effective potential. The approach is based on finite temperature Green’s functions. The internal energy per particle is estimated from the summation of diagrams and through the Galitskii-Koltun’s sum rule. At present, there is not a unique and reliable theory of nuclear interactions. From the study of nucleon-nucleon scattering processes different models for the basic interaction between nucleons have been developed, but difficulties arise when they are used in calculations which aim to reproduce the properties of bound nuclei. These models all reproduce the experimental N-N phase shifts up to the threshold for pion production with high accuracy, but differ in the short-wavelength region, where less experimental constraints are available. In deriving the properties of dense nuclear matter, if we start from a bare N-N potential we have to take into account the complex correlations induced
We propose a new method to calculate the particle-hole Green's function for an infinite system of fermions in the long-wavelength limit of the random-phase approximation. Contrary to the standard approach the present method does not require approximating the residual particle-hole interaction by a sum of separable terms. The method can also be applied to the Landau theory of Fermi liquids. We illustrate the method by evaluating the response function of nuclear matter in the long-wavelength limit for two different isospin channels.