Simple model for the quasiparticle interactions in He3. II. Transport coefficients and the superfluid free energy

We explore the consequences of a phenomenological model for the low-frequency interaction (vertex function) in He3 of the form k -J(q)S S +V(q). 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 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, 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 2+ 4 is in nearly exact agreement with high-pressure data, |5| is about 30% too large. We have also considered models for k in which J is of the spindensity wave form and in which J=0. In both these cases the transport coefficients and the 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 He3 and all properties derived from them.