The approximate form of the effective interaction between ${\mathrm{He}}^3$ atoms in superfluid ${\mathrm{He}}^4$ is derived from the experimental data on spin diffusion and phase seperation in dilute mixtures of ${\mathrm{He}}^3$ in ${\mathrm{He}}^4$. The interaction is weak, and attractive at long wavelengths. Calculations of the Fermi-liquid parameters for the normal state of ${\mathrm{He}}^3$ in solution yield results for the effective mass and spin susceptibility in agreement with experiment. The temperature for a superfluid transition associated with the ${\mathrm{He}}^3$ is estimated to be ∼2×${10}^{-6\mathrm{}}$ °K; the maximum solubility of ${\mathrm{He}}^3$ in ${\mathrm{He}}^4$ is found to be ∼6% at $T=0\mathrm{}$. Thermodynamic and microscopic arguments are used to calculate the long-wavelength part of the effective interaction between the ${\mathrm{He}}^3$ atoms. The contribution arising from the exchange of a virtual ${\mathrm{He}}^4$ phonon is shown to be large and attractive, while the remaining part of the interaction is almost as large but repulsive; the calculated interaction at long wavelengths is thus weak and attractive and is in excellent agreement with that determined empirically; the physical origin of the weakness of the interaction is that ${\mathrm{He}}^3$ is an isotopic impurity. Finally, it is estimated that the application of pressure serves to weaken the effective interaction.

• Received 10 November 1966

DOI:https://doi.org/10.1103/PhysRev.156.207