Properties of Dilute Mixtures ofHe3in LiquidHe4at Low Temperatures

Abstract

Properties of dilute mixtures of ${\mathrm{He}}^3$ in liquid ${\mathrm{He}}^4$ are calculated on the assumption that, for the most part, they behave as low-density fermion systems with an effective ${\mathrm{He}}^3$ Hamiltonian. Expressions for ${\mathrm{He}}^3$ scattering amplitudes in terms of phase shifts are obtained, and the measured spin diffusion coefficient $D$ for temperature $T$ below 1°K is used to determine the effective interaction between ${\mathrm{He}}^3$ atoms. It is found to have a strong repulsive region with a longer-range attraction which is deeper but of shorter range than the corresponding part of the Van der Waals force. At low momenta, the phase shifts are small, and at low temperatures, the effects are weak. At higher temperatures, larger momenta are probed, and the scattering is more significant. The phase-separation curve and the low-temperature viscosity, thermal conductivity, spin susceptibility, compressibility, and specific heat are calculated and agree with existing experimental evidence. It is found that the mixtures should undergo a fermion superfluid phase transition, but the maximum transition temperature is ${10}^{-6\mathrm{}}$ °K. Evidence for the transition should be found in a 4% decrease of D${\mathrm{T}}^2$ between ${10}^{-2\mathrm{}\mathrm{°}}$ and 2×${10}^{-3\mathrm{}}$ °K.