STRUCTURE PROPERTIES OF THE HE-3-HE-4 MIXTURE AT T=0-K

The spatial structure properties of He-3-He-4 mixtures at T = 0 K are investigated using the hypernetted-chain formalism. The variational wave function used to describe the ground-state of the mixture is a simple generalization of the trial wave functions for pure phases and contains two- and three-body correlations. The elementary diagrams are taken into account by means of an extension of the scaling approximation to the mixtures. The two-body distribution (g(alpha, beta) (r)) and the structure functions (S(alpha, beta) (k)) together with the different spin-spin distribution functions of the He-3 component in the mixture are analyzed for several concentrations of He-3. Two sum-rules, for the direct and the exchange part of the g(3, 3) (r), are used to ascertain the importance of the full treatment of the Fermi statistics in the calculation. The statistical correlations are found responsible for the main differences between the several components of the distribution function. Due to its low concentration, He-3 behaves as a quasi-free Fermi gas, as far as the statistical correlations are concerned, although it is strongly correlated with the He-4 atoms through the interatomic potential.