Microscopic theory of 3He - 4He solutions

The ring diagram contribution to the grand partition function of a mixture of fermions and bosons is obtained from a rigorous formula which extends the single component formula of Montroll and Ward. Together with the contributions from some other relevant graphs, it is applied to a dilute solution of 3He with 4He. For small mass difference parameter, the ground state energy is shown to be expressed as a linear function of 3He concentration. The coefficients of this energy expression are obtained explicitly for soft and hard-sphere potential models. From the energy, the differential volume coefficient is obtained also. (orig.)