Fermi-Liquid Parameters ofHe3in the Brueckner Theory

Functional differentiation of the Brueckner-theory equations gives a prescription for calculating the effective interaction in a Fermi liquid. The many terms that result from the differentiation are calculated for the liquid-${\mathrm{He}}^3$ system using Østgaard's reaction matrices. ${\mathrm{He}}^3$ is strongly interacting in the sense that the defect wave-function probability $\kappa$ is large, of the order 0.56. As a result, many of the terms contribute substantially to the total. Of the Landau parameters $f_0$, $f_1$, and $z_0$, only $z_0$ is in reasonable agreement with experiment. The parameter $f_0$ is too small. This is known to be due in part to the neglect of three-body clusters. We find a small value for $f_1$, implying that the effective mass $m^{*}$ is close to one. Larger effective masses could be obtained by treating low-momentum-transfer processes more carefully and by summing higher-order diagrams.