Quasiparticle interaction in the Fermi liquidHe3

Abstract

The Fermi-liquid interaction and the quasiparticle scattering amplitude on the Fermi surface for liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are calculated by solving the pair of coupled Bethe-Salpeter equations in the two particle-hole channels. The method of solution preserves exchange symmetry by employing the eigenfunctions of the exchange operator as a basis set. The quasiparticle effective mass and the totally particle-hole irreducible direct interaction needed as an input are taken from available microscopic calculations. It is found that a small nonlocal part is necessary in the direct interaction in order to obtain a large backflow parameter $F_1^s$, as observed in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. The origin of this contribution is traced back to screening effects on the interaction in the particle-particle channel. Upon including a phenomenological nonlocal part into the direct interaction, good agreement is found with available thermodynamic and transport data.