An experiment to measure the diffusion of4He in4He in the Fermi liquid region

The diffusion coefficient D and the thermal diffusion factor T, for⁴He in liquid³He at low temperatures T, have recently been calculated by solving the Boltzmann equation derived from Fermi-liquid theory. As T 0, T approaches a constant and D varies as 1/T. Both transport coefficients are determined solely by a₀³⁴, the l = 0 forward scattering amplitude. Because a₀³⁴ can be found from thermodynamic data, e.g. the solubility of⁴He in liquid³He, X₄^sat, a strict test of the theory is possible. We have built an apparatus to measure D and X₄^sat as functions of pressure and temperature. The ratio of the capacitances of two parallel plate capacitors measures the number of⁴He atoms diffusing out of the liquid into the superfluid film. A bellows initiates the diffusion by changing the pressure in the liquid and thus the equilibrium concentration. A change of 10^–8 in the⁴He concentration can be detected.