Superfluid Density of He II in the Critical Region

The superfluid density of liquid ${\mathrm{He}}^4$ near the $\lambda$ point has been measured using the oscillating-disk-pile technique. From accurate measurements of the period of oscillation as a function of the temperature difference $T_{\lambda }-T$, the superfluid density ${\rho }_s$ is found to obey the power-law expression ${\rho }_s=1.43\mathrm{}\rho {(T_{\lambda }-T)}^{\zeta }$ with $\zeta =0.666\mathrm{}\pm 0.006$. This power-law dependence closely resembles that found in other systems near a symmetry-breaking higher-order phase transition. In particular, Josephson has shown for He II that the value $\zeta =\frac{2}{3}$ is a direct consequence of a logarithmically divergent specific heat ($\sim \ln |T_{\lambda }-T|$). Thermodynamic and scaling arguments suggest that the coherence length in He II varies as ${(T_{\lambda }-T)}^{-\zeta }$. Our result for the superfluid critical exponent $\zeta$, together with the superfluid-specific-heat data of Kellers, Fairbank, and Buckingham, are consistent with the validity of the Widom-Kadanoff-Josephson scaling laws.