Arbitrarily polarized model Fermi liquid

We study the effects of spin polarization on the collective and single-particle properties of a model Fermi liquid–a model which is designed to simulate liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. The study is based on an approximate theoretical scheme of Singwi, Tosi, Land, and Sjölander. Using this scheme, we have calculated the Landau parameters $F_{\sigma \sigma \mathcal{’}}$ as a function of polarization for various densities, the so-called polarization potentials, the compressibility and magnetic susceptibility, and the zero-sound dispersion. This study of a model system may provide some guidance for future experimental and theoretical works on a more realistic system such as partially polarized liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$.