THE FERMI-LIQUID THEORY OF HE-4 IN HE-3

The Zharkov-Silin Fermi Liquid theory of solutions of He-4 in normal (non-superfluid) liquid He-3 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 He-4 concentration X4 is so small that there is no macroscopic phase separation, only a gradual thickening of the He-4-rich film on the walls. We confirm that the phase separation temperature T(ps)(X4) estimated from the thickening is close-to the values which would be observed in an ideal experiment with a macroscopic phase. Fits to T(ps)(X4) including the new data show that the He-4 effective mass m4* is close to, and may be equal to, the bare mass m4. The difference in binding at zero pressure between He-4 in liquid He-4 and in liquid He-3 is (E44- E43)/kB = (0.21 + 0.03/ - 0.01)) K. Using the volume measurements of Laheurte to calculate the pressure dependence of E43 indicates that the difference in binding has a minimum of (0.0 +/- 0.2) K near approximately 11 atm. This implies that the solubility of He-4 in He-3 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 He-4 in liquid He-3 are also discussed.