LECTURES ON THE PROPERTIES OF LIQUID AND SOLID HE-3-HE-4 MIXTURES AT LOW-TEMPERATURES

We give a concise review of the empirical properties of liquid and solid He-3- He-4 mixtures and their phenomenological interpretation. The bulk of the paper is about dilute solutions of He-3 in liquid He-4 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 He-3 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 He-3 in liquid He-4. The existence of supersaturated solutions may be a way to attain p-wave pairing at accessible temperatures. Because of phase separation, the concentration of He-4 in dilute mixtures of He-4 in liquid He-3 becomes very small as the temperature is lowered, making it unlikely that a degenerate Bose gas of He-4 quasiparticles can be produced. In addition, the superfluid He-4 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 He-4 quasiparticles and the role of their effective interactions are still in doubt. In solid He-3- He-4 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 He-3 or He-4 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 He-3- He-4 mixtures published between 1975 and 1990.