Quantum statistics and liquid helium-3--helium-4 mixtures.

I have argued, following Einstein and London, that Bose-Einstein statistics is important for understanding the behavior of superfluid (4)He, while Fermi-Dirac statistics is important for understanding that of (3)He. In order to understand qualitatively the general behavior of (3)He-(4)He mixtures at constant pressure, the interaction between the helium atoms cannot be neglected. A very simple model of (3)He-(4)He mixtures is then a binary mixture of two kinds of hard spheres that follow Bose-Einstein and Fermi-Dirac statistics, respectively. This model correctly predicts the most striking features of the phase diagrams of helium mixtures in the temperature-concentration plane. In particular, the Bose-Einstein statistics of (4)He is responsible for the occurrence of a phase separation of the mixture at low temperatures that starts at an unusual type of critical point, while the Fermi-Dirac statistics of (3)He leads to an incomplete phase separation near the absolute zero of temperature, which makes possible the successful operation of a powerful cooling device, the helium dilution refrigerator.