The spin diffusion coefficient of3He in3He-4He solutions

The transport properties of³He in³He-⁴He solutions with molar concentrations of 5, 9, 14, and 24% have been studied for 0.9 KT2.5 K. The spin diffusion coefficientD_s and the longitudinal relaxation timeT₁ were measured by the spin-echo method for temperatures both above and below the solution lambda temperatureT. The spin-echo method measures the diffusion coefficient for magnetizationD_s, which differs from the usual diffusion coefficient for particlesD belowT.D_s depends on the³He-³He scattering cross section_FF and the³He-roton/phonon cross section_FB, whileD depends only on_FB. The distinction betweenD_s andD is elaborated in terms of a simple mutual-friction model for diffusion. The two scattering mechanisms are clearly evident in the behavior ofD_s as a function of concentrationx and temperature. The contribution due to the³He-³He scattering is inversely proportional tox, indicating that the³He can be treated in first approximation as a classical gas (the Pomeranchuk model). The predictions of various theoretical models are compared with the results, where possible, but most of the previous theoretical work is not applicable to the concentration range and temperatures of these measurements.Supported in part by the National Science Foundation and the U.S. Office of Naval Research.