The Fermi liquid theory of [sup 4]He in [sup 3]He

The Zharkov-Silin Fermi Liquid theory of solutions of [sup 4]He in normal (non-superfluid) liquid [sup 3]He is reviewed and slightly extended. The theory is expected to be valid only below [approximately] 0.1 K, and it predicts that there should be a hundred-fold increase in the diffusion coefficient as the temperature is lowered into this region. The limited range of validity explains the apparent disagreement between the recent very low temperature measurements of the phase separation line by Nakamura et al. and extrapolations from higher temperatures. In the low temperature experiments the [sup 4]He concentration X[sub 4] is so small that there is no macroscopic phase separation, only a gradual thickening of the [sup 4]He-rich film on the walls. The authors confirm that the phase separation temperature T[sub ps](X[sub 4]) including the new data show that the [sup 4]He effective mass m[sub 4][sup *] is close to, and may be equal to, the bare mass m[sub 4]. The difference in binding at zero pressure between [sup 4]He in liquid [sup 4]He and in liquid [sup 3]He is (E[sub 44]-E[sub 43])/k[sub B] = (0.21 + 0.03/[minus]0.01) K. Using the volume measurements of Laheurte to calculate the pressure dependence of E[sub 43] indicates that the difference in binding has a minimum of (0.0 [plus minus] 0.2) K near [approximately] 11 atm. This implies that the solubility of [sup 4]He in [sup 3]He is enhanced in this region of pressure. The behavior of the spinodal line at low temperature, and the possibility of observing Bose condensation in a metastable solution of [sup 4]He in liquid [sup 3]He are also discussed. 31 refs., 6 figs.