The dynamics of normal and fully spin-polarized ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are studied for momentum transfers below 2 A${\mathrm{̊}}^{\mathrm{-}1}$. 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, ${\mathit{I}}_{\mathrm{ph}}$, which is needed in the calculation of χ(Q,ω). The BK procedure yields an ${\mathit{I}}_{\mathrm{ph}}$ that conserves particle number, energy, and momentum. When the BK procedure is applied to the Galitskii-Feynman-Hartree-Fock (GFHF) self-energy, the resulting ${\mathit{I}}_{\mathrm{ph}}$ consists of direct and induced terms. Previous calculations using GFHF theory have neglected induced effects. For Q<2 A${\mathrm{̊}}^{\mathrm{-}1}$, the induced term contributes significantly to the strength of ${\mathit{I}}_{\mathrm{ph}}$. Landau parameters calculated with induced effects included are greatly improved. We compare our (static) ${\mathit{I}}_{\mathrm{ph}}$ to those obtained from other first-principles calculations, from polarization-potential theories, and from the available experimental data. In spin-polarized ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, we find that ${\mathit{I}}_{\mathrm{ph}}$ is strongly density dependent. In normal ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, 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 ${\mathit{I}}_{\mathrm{ph}}$, effective mass, Landau parameter ${\mathit{F}}_1^{\mathit{s}}$, and a polarization-potential form for the frequency dependence of ${\mathit{I}}_{\mathrm{ph}}$, we obtained a zero-sound dispersion that agrees well at low Q with the experimentally determined one. Finally, we comment on the relevance of the spin-fluctuation contribution observed in our ${\mathit{I}}_{\mathrm{ph}}$ for the case of normal ${}_{}{}^3{}_{}{}^{}\mathrm{He}$.

• Received 11 March 1991

DOI:https://doi.org/10.1103/PhysRevB.44.5216