An equilibrium theory of the dilute solutions of3He in superfluid4He at very low temperatures

Abstract

An equilibrium theory of the dilute solutions of 3 He in superfluid 4 He is derived systematically. The theory is based on a model which (a) goes beyond the parabolic Landau-Pomeranchuk approximation for the 3 He quasiparticle energy by taking into account the fourth-order term in the momentum expansion of this quantity, (b) disregards contributions to the 3 He quasiparticle effective interaction whose order in the momentum is higher than two, and (c) allows the effective interaction to be nonlocal. The simplicity of the model enables the development of a unified parametrization of the various equilibrium properties of the solutions. The expressions obtained for these properties are both easy to apply and highly accurate over a wide temperature range spanning from T=0 to temperatures of the order of the 3 He quasiparticle degeneracy temperature. It is shown that the parameters appearing in the expression for the 3 He quasiparticle effective interaction at fixed 4 He number density are replaced in the fixed-pressure, low-temperature expansions of the equilibrium properties by other parameters whose appearance in the theory seems to be due to the renormalization of this interaction by the interactions between the 3 He quasiparticles and the virtual fluctuations of the 4 He number density Finally, a comparison is made between theory and experiment. Three quantities are considered in detail : the 3 He osmotic pressure and the 3 He quasiparticle inertial and specific heat effective masses. The analysis of the experimental data makes it possible to determine the parameters associated with the effective interaction at several pressures. It is found that the theory is, in general, in a very good accord with the experimental situation and that, within its framework, the experimental values of the osmotic pressure and the two effective masses are indeed consistent with one another.