Lectures on the properties of liquid and Solid 3He-4He mixtures at low temperatures

Abstract

We give a concise review of the empirical properties of liquid and solid 3He-4He mixtures and their phenomenological interpretation. The bulk of the paper is about dilute solutions of 3He in liquid 4He at temperatures well below the tricritical point, where the roton and phonon excitations are comparatively unimportant. We describe the thermodynamic properties in terms of the Landau-Pomeranchuk 3He quasiparticles and the effective interaction between them, introduced by Emery and Bardeen, Baym and Pines. The scattering amplitude, needed to fit the low temperature transport properties, and the effective interaction are related, provided the multiple virtual scattering calculated by Fu and Pethick is included. The multiple scattering should always be included, even for very small concentrations. We present the evidence for the velocity dependence of the effective interaction, and urge that this also be taken into account in the interpretation of experiments. We give a short description of spin-polarized liquid mixtures and of the possibility of pairing superfluidity in solutions of 3He in liquid 4He. The existence of supersaturated solutions may be a way to attain p-wave pairing at accessible temperatures. Beacause of phase separation, the concentration of 4He in dilute mixtures of 4He in liquid 3He becomes very small as the temperature is lowered, making it unlikely that a degenerate Bose gas of 4He quasiparticles can be produced. In addition, the superfluid 4He film on the walls of the vessel makes the achievement of a supersaturated solution very difficult. We briefly review the measurements of the phase separation, the density and specific heat, and show that the spectrum of the 4He quasiparticles and the role of their effective interactions are still in doubt. In solid 3He-4He mixtures the thermodynamic properties and the phase diagram, including the crystallographic transformation, fit the regular solution model very well. On the other hand, dilute solid solutions of either 3He or 4He in the other isotope have NMR relaxation times and spin diffusion which agree with the theory of impuritons (mass fluctuation waves) which tunnel more or less freely through the crystal. The reconciliation of these two theories and an explanation of the accuracy of the regular solution model remain mysteries. A deviation from the regular solution model, the fluctuation specific heat above the phase separation temperature, is discussed in detail. The review includes two tables which list most of the experiments on liquid and solid 3He-4He mixtures published between 1975 and 1990.