Dynamics and particle-hole interactions in liquid 3He: A Green's-function approach

The dynamics of normal and fully spin-polarized 3He are studied for momentum transfers below 2 A-1. This study is based on a first-principles calculation of the dynamic susceptibility, χ(Q,ω). We invoke the Baym and Kadanoff (BK) procedure for generating an approximate particle-hole irreducible interaction, Iph, which is needed in the calculation of χ(Q,ω). The BK procedure yields an Iph that conserves particle number, energy, and momentum. When the BK procedure is applied to the Galitskii-Feynman-Hartree-Fock (GFHF) self-energy, the resulting Iph consists of direct and induced terms. Previous calculations using GFHF theory have neglected induced effects. For Q<2 A-1, the induced term contributes significantly to the strength of Iph. Landau parameters calculated with induced effects included are greatly improved. We compare our (static) Iph to those obtained from other first-principles calculations, from polarization-potential theories, and from the available experimental data. In spin-polarized 3He, we find that Iph is strongly density dependent. In normal 3He, the same behavior is observed for the spin-symmetric contribution. In contrast, the spin-antisymmetric contribution is nearly independent of density. This finding is in agreement with experiment. For both systems a well-defined zero-sound mode was determined. Using our microscopically determined Iph, effective mass, Landau parameter F1s, and a polarization-potential form for the frequency dependence of Iph, we obtained a zero-sound dispersion that agrees well at low Q with the experimentally determined one