Effects of ${\mathrm{He}}^3$-${\mathrm{He}}^3$ Interactions in Dilute Solutions of ${\mathrm{He}}^3$ in ${\mathrm{He}}^4$

Using the classical gas expression for the diffusion coefficient and experimental measurements of the spin diffusion coefficient of a 5% solution of ${\mathrm{He}}^3$ in ${\mathrm{He}}^4$ at temperatures up to 1°K, we have extended the effective interaction between ${\mathrm{He}}^3$ quasiparticles, as derived by Bardeen, Baym, and Pines, to larger values of the momentum. This potential is then used in first-order perturbation theory to calculate the high-temperature magnetic susceptibility of dilute solutions and the variation in the ${\mathrm{He}}^3$ chemical potential with concentration. From the latter, and from measurement of the phase-separation curve at finite temperature, the maximum solubility of ${\mathrm{He}}^3$ in ${\mathrm{He}}^4$ is determined down to $T=0\mathrm{}$. Agreement with experiment is good.