Zero Sound and Spin Fluctuations in Liquid Helium-3

Abstract

The density fluctuation spectrum of $^{3}\mathrm{He}$ is calculated using a generalized polarization potential approach and shown to yield both zero sound and quasiparticle spectra in good agreement with the recent neutron scattering experiments. Landau Fermi-liquid theory is used to calculate the spin density fluctuation spectrum; and sum-rule arguments are presented which enable us to establish the qualitative nature of this spectrum at larger wave vectors with results in good qualitative agreement with the recent experiment of Sk\"old et al.