On the Theory of LiquidHe3—He4Mixtures

An asymptotic theory of liquid ${\mathrm{He}}^3$—${\mathrm{He}}^4$ mixtures is presented, in which the component fluids are described, approximately, in terms of ideal symmetric and antisymmetric fluids. The theory yields results in at least semiqualitative agreement with the data if the antisymmetric fluid is taken to be of negligible degeneracy. The computed isothermal mixing energies and entropies are good approximations to the preliminary data on these quantities obtained in this Laboratory. The present model exhibits complete miscibility at all temperatures together with a vanishing total and mixing entropies, in all possible mixtures, at the approach of the absolute zero. It is shown that the mixtures undergo third-order phase changes along their transition line, where their constant-volume and constant-pressure heat capacities have sharp peaks, with lambda-point type discontinuities of their temperature derivatives. On mixing the ideal symmetric fluid with an ideal antisymmetric or classical fluid the original first-order phase change of the former, as a result of its momentum space condensation, has thus been modified.