Diffusion Constant Measurement of Dilute $^3$He in Superfluid $^4$He for UCN Experiments

Ultra cold neutrons (UCNs) are commonly employed in precise measurements of fundamental neutron properties such as in the neutron electric dipole moment experiment at ORNL. High densities of UCN’s can be attained by down-scattering cold neutrons in superfluid $^4$He, but $^3$He impurities in the superfluid absorb neutrons, making it desirable to control the relative fraction of $^3$He to $^4$He in these experiments. The $^3$He diffusion constant at concentrations at or below that of natural $^4$He, around 1 ppm, is important for this control and determined by microscopic scatterings between $^3$He and phonon excitations in the superfluid. This talk discusses a planned measurement of the $^3$He spin diffusion constant using free induction decay for concentrations around 1 ppm and temperatures between 150 to 550 mK. This phase space covers both $^3$He-phonon and $^3$He-$^3$He dominated diffusion, providing a check against theory and a complement to previous measurements.