He3Spin Diffusion in DiluteHe3-He II Mixtures at Elevated Pressures in the Semiclassical Regime

Measurements of the spin-diffusion coefficient in dilute ${\mathrm{He}}^3$-He II mixtures are presented. The thermodynamic parameters of the samples are varied within the following limits: $0.3\le T\le 1.15$ °K, $\mathrm{saturated}\mathrm{vapor}\mathrm{pressure}\le P\le 24$ atm, $0.322\times {10}^{-4\mathrm{}}\le n_3\le 4.54\times {10}^{-4\mathrm{}}$ mole/${\mathrm{cm}}^3$. It is shown that all samples considered are within the limits of the semiclassical regime. The data are analyzed by considering the reciprocal of the diffusion to be the sum of two parts: $\frac{1}{D}(T,P,n_3)=\frac{1}{D_{3\rho }}\mathrm{}(T,P)+\frac{1}{D_{33}}(T,P,n_3)$, where $D(T,P,n_3)$ is an experimental measurement at ($T,P,n_3$), $D_{3\rho }\mathrm{}(T,P)\mathrm{}$ is the $n_3$-independent spin diffusion of a ${\mathrm{He}}^3$ quasiparticle as limited by interactions with rotons, and $D_{33}(T,P,n_3)$ is the spin diffusion of a ${\mathrm{He}}^3$ quasiparticle limited by interactions with other ${\mathrm{He}}^3$ quasiparticles. Since $D_{3\rho }$ is independent of $n_3$, and $D_{33}$ is shown to be proportional to $n_3^{-1\mathrm{}}$, a least-squares fit of the data to the above equation gives the experimentally determined values of $D_{3\rho }$ and $D_{33}$. A comparison of $D_{33}$ with the theoretical expression gives directly the moment of the effective ${\mathrm{He}}^3$-${\mathrm{He}}^3$ interaction measured by spin diffusion in the semiclassical regime: $〈V\left(k\right)\mathrm{}〉{|}_{T,P}=A\int e^{-ak2\mathrm{}}{k}^3{\left|V\right(\mathrm{bk}\left)\mathrm{}\right|}^2\mathrm{dk}$, where $A$, $a$, and $b$ are constants. The measurements are insufficient to determine $V\left(k\right)\mathrm{}$ uniquely. Calculations using an assumed interaction (which reduces to the interaction used by Ebner at saturated vapor pressure) show a remarkable similarity to the experimental data.