Self-Diffusion in LiquidHe3

The Landau model of a Fermi liquid is employed to obtain an expression for the coefficient of self-diffusion, $D$, in liquid ${\mathrm{He}}^3$. It is found that $D=\frac{A}{T^2}$, where $A\approx 2\times {10}^{-6\mathrm{}}$ ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$ ${\mathrm{degree}}^2$, and $T$ is the temperature in degrees Kelvin. As this temperature dependence differs from that experimentally observed ($T^{-\frac{3}{2}}$), although the order of magnitude of the theoretical prediction agrees well with experiment, the possible effect of the 1% ${\mathrm{He}}^4$ impurity known to be present is investigated; it is found that the diffusion coefficient is essentially unaffected by the impurity (a result also obtained experimentally). It is estimated that the Landau model is applicable only well below 0.05°K. As even the most recent experiments have been carried out only down to 0.03°K, it is concluded that the transport properties of ${\mathrm{He}}^3$ should be investigated experimentally at lower temperatures in order to check the validity of the theory.