Finite temperature effects in the Fermi liquid theory of the diffusion of ⁴He in ³He

Abstract

The diffusion coefficient D and the thermal diffusion ratio kT for dilute ⁴He in liquid ³He are calculated from Fermi liquid theory. The collision integral assumes a scattering amplitude a³⁴ expanded in scalar combinations of the quasiparticle momenta. As T→0, D varies as 1/T and kT/c, where c is the concentration, approaches a constant. As shown previously, the limits for DT and kT/c are determined by thermodynamic properties, the ⁴He effective mass and partial volume, and properties of pure ³He. We have decreased kT/c by a few percent, by including the effect of ∇T on the ³He distribution function. The temperature dependence of DT and kT/c is linear and related to the coefficients in the expansion of a³⁴. Two coefficients can be found from thermodynamics. A conjecture about the remainder suggests that DT may have a maximum between 0 and 0.5 K.