Quantum Statistics and Liquid Helium-3—Helium-4 Mixtures
E. G. D. Cohen 1
1 Professor at The Rockefeller University, New York 10021
I have argued, following Einstein and London, that Bose-Einstein statistics is important for understanding the behavior of superfluid 4He, while Fermi-Dirac statistics is important for understanding that of 3He. In order to understand qualitatively the general behavior of 3He-4He mixtures at constant pressure, the interaction between the helium atoms cannot be neglected. A very simple model of 3He-4He 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 4He 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 3He 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.
