SIMPLE-MODEL FOR THE QUASI-PARTICLE INTERACTIONS IN HE-3 .1. SUPERFLUID TRANSITION-TEMPERATURES

Taking as a basis both the s-p and paramagnon approximations, we explore the consequences of a phenomenological model for the low-frequency effective interaction (vertex function) in He3 of the form (unsymmetrized) k-J(q)S S+V(q). Here q represents the magnitudes of the momentum and energy transfer and S=12. Using the known Landau scattering amplitudes, we demonstrate that within this ansatz it is possible to (i) understand the magnitude and pressure dependence of the superfluid transition temperature Tc, (ii) give a partial justification for the validity of the s-p approximation as applied to transport properties, and (iii) understand qualitatively the stabilization of the superfluid A phase within a more general framework than the paramagnon model. The present ansatz yields the same expression for the scattering amplitudes A(,), as does the s-p approximation at =, which limit is most significant for transport properties. We find that the values of the Landau scattering amplitudes, (i) and (iii) are consistent with the picture that J(q) is peaked around q=0 and that J(0) is larger than the potential term, V. This description is similar to that used in spin-fluctuation theories. Choosing the parameters in k to yield reasonable fits to the measured {Als,a}, we find by numerical solution of the Eliashberg equations that Tc 0.1TFe-9A1s. This expression which is in good agreement with experiment at all pressures provides confirmation of the importance of spin fluctuations in Tc. Numerical examples of the pressure dependent {Als,a} and Tc are given for a number of different models for the functions J and V. © 1979 The American Physical Society.