Microscopic theory of3He—4He solutions

The ring diagram contribution to the grand partition function of a mixture of fermions and bosons is obtained from a rigrous 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 of³He with⁴He. For a small mass difference parameter, the ground state energy is shown to be expressed as a linear function of³He 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.This work was supported by ONR under Contract No. N00014-79-C-0451