The hard-sphere model of strongly interacting fermion systems

TL;DR

This paper develops and tests a formalism based on Correlated Basis Functions to study strongly interacting fermion systems, focusing on hard-sphere models to analyze quasiparticle properties and transport coefficients relevant to nuclear matter and astrophysics.

Contribution

It introduces a novel approach combining perturbation theory with realistic short-range correlations, and applies it to hard-sphere fermion systems to evaluate quasiparticle and transport properties.

Findings

Second order self-energy corrections significantly affect quasiparticle effective mass.

Transport coefficients are highly sensitive to the effective mass and second order effects.

The formalism provides a realistic description of short-range correlations in fermion systems.

Abstract

The formalism based on Correlated Basis Functions (CBF) and the cluster-expansion technique has been recently employed to derive an effective interaction from a realistic nuclear Hamiltonian. One of the main objectives of the work described in this Thesis is establishing the accuracy of this novel approach--that allows to combine the flexibility of perturbation theory in the basis of eigenstates of the noninteracting system with a realistic description of short-range correlations in coordinate space--by focusing on the hard-sphere fermion system. As a first application of the formalism, the quasiparticle properties of hard spheres of degeneracy four have been determined from the two-point Green's function. The calculation has been performed carrying out a perturbative expansion of the self-energy, up to the second order in the CBF effective interaction. The main results of this study are the momentum distributions, the quasiparticle spectra and their description in terms of effective mass. The investigation of the hard-sphere fermion fluid has been extended to study the shear viscosity and thermal conductivity coefficients of the system with degeneracy two, that can be regarded as a model of pure neutron matter. The resulting transport coefficients show a strong sensitivity to the quasiparticle effective mass, reflecting the effect of second order contributions to the self-energy which are not taken into account in nuclear matter studies available in the literature. The difference between first and second order results is likely to play an important role in astrophysical applications and needs to be carefully investigated extending our analysis to nuclear matter.