The Fermi Liquid theory of4He in3He

The Zharkov-Silin Fermi Liquid theory of solutions of⁴He in normal (non-superfluid) liquid³He is reviewed and slightly extended. The theory is expected to be valid only below 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 the⁴He concentration X₄ is so small that there is no macroscopic phase separation, only a gradual thickening of the⁴He-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 the⁴He effective mass m₄^* is close to, and may be equal to, the bare mass m₄. The difference in binding at zero pressure between⁴He in liquid⁴He and in liquid³He is (E₄₄–EE₄₃)/k_B=(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 11 atm. This implies that the solubility of⁴He in³He 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 of⁴He in liquid³He are also discussed.