Quantum-Lattice-Gas Model forHe3-He4Mixtures

A quantum-lattice-gas model of ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures is proposed which includes the effects of the Bose and Fermi statistics. The effect of the hard-core interaction between all particles is included by altering the commutation relations of the field operators. The phase diagram of the model is obtained within mean-field theory under conditions of constant normal density and constant pressure. The diagram shows many of the features of the physical system. However, within mean-field theory, the phase separation is complete at the absolute zero of temperature.