Simple model for the quasiparticle interactions inHe3. II. Transport coefficients and the superfluid free energy

We explore the consequences of a phenomenological model for the low-frequency interaction (vertex function) in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ of the form ${\Gamma }^k\sim -J\left(q\right)\mathrm{}\overrightarrow{\mathrm{S}}·\overrightarrow{\mathrm{S}}+V\left(q\right)\mathrm{}$. Here $q$ represents the magnitude of the momentum and energy transfer. This is the second in a series of two papers and is concerned primarily with transport properties and the superfluid free energy. In Paper I we demonstrated that for spin-fluctuation-like models, in which $J$ is peaked at $q=0\mathrm{}$ and $V$ is relatively small, we obtain good agreement between theory and experiment for the magnitude and pressure dependence of the superfluid transition temperature. In the present paper we show that these spin-fluctuation-like models yield reasonably good agreement with the measured zero-temperature transport coefficients at all pressures. They, therefore, represent a considerably better description of the high-pressure scattering amplitudes than the $s-p$ approximation. The five fourth-order superfluid Landau-Ginzburg free-energy invariants, ${\beta }_i$, are computed using the Ranier-Serene formalism. At high and low pressures, paramagnonlike theories yield results essentially equivalent to those obtained in the $s-p$ approximation. As in all previous calculations, while the combination ${\beta }_2+{\beta }_4$ is in nearly exact agreement with high-pressure data, $\left|{\beta }_5\right|$ is about 30% too large. We have also considered models for ${\Gamma }^k$ in which $J$ is of the spindensity wave form and in which $J=0\mathrm{}$. In both these cases the transport coefficients and the ${\beta }_i$ are inconsistent with experiment. The evidence strongly suggests that it is the proximity to the ferromagnetic instability which governs the behavior of the scattering amplitudes in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and all properties derived from them.