Persistent-Current Measurements of the Superfluid Density and Critical Velocity

Gyroscopic measurements of superfluid persistent currents in liquid helium below and near the $\lambda$ transition are presented here. Measurements were conducted in a variety of sizes of porous material from 0.05- to 150-μaverage size. Near the $\lambda$ transition, both the superfluid density $\frac{{\rho }_s}{\rho }$ and the critical velocity ${\omega }_c$ exhibit a $\frac{2}{3}$-power dependence on the temperature difference from the transition. A depression of the $\lambda$ transition is observed for both $\frac{{\rho }_s}{\rho }$ and ${\omega }_c$ in the smallest pores. Data for $\frac{{\rho }_s}{\rho }$ and ${\omega }_c$ away from the transition and down to about 1.25°K are given and are in agreement with measurements made by other methods.