Model Fermi liquid interacting via a hard-core repulsive potential and an attractive tail

In this paper we present an extensive microscopic study of the collective and single-particle properties of a model Fermi liquid whose particles interact via a repulsive hard-core potential and an attractive tail. The model system is intended to simulate liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. The study is based on an approximate theoretical scheme of Singwi, Tosi, Land, and Sjölander, which was devised to treat correlations in Coulomb Fermi liquids. The primary aim of this study is to learn how far the model system is capable of reproducing some of the salient features observed in normal liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, and about the role of the repulsive and attractive parts of the bare potential in the determination of the properties of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. We have calculated the Landau parameters $F_0^s$ and $F_0^a$ and their variation with pressure, the wave-number and pressure dependence of the spin-symmetric and spin-antisymmetric polarization potentials, pressure dependence of the dispersion of the zero sound, the static structure factors, and the quasiparticle mass. It is our belief that this study has provided us with some physical insight into the nature of liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ although much remains to be done for its quantitative understanding.