Second-Sound Velocity and Superfluid Density inHe4under Pressure nearTλ

The velocity of second sound was measured in superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ between vapor pressure and the melting pressure for $T\ge 1.6$ K. Particular emphasis was given to the temperature region near $T_{\lambda }$ with $2\times {10}^{-5\mathrm{}}\lesssim \epsilon \equiv 1-\frac{T}{T_{\lambda }\mathrm{}\left(P\right)\mathrm{}}\lesssim {10}^{-2\mathrm{}}$. Using these results, other existing thermodynamic information, and linear two-fluid hydrodynamics, the superfluid fraction $\frac{{\rho }_s}{\rho }$ was determined. The higher-pressure data at small $\epsilon$ revealed that $\frac{{\rho }_s}{\rho }$ along isobars cannot be described by a pure power law in $\epsilon$. Instead, singular corrections to the leading power-law term exist which are much larger than of order $\epsilon$. Therefore, the results were fitted to the expression $\frac{{\rho }_s}{\rho }=k\left(P\right)\mathrm{}{\epsilon }^{\zeta }\mathrm{}[1+a(P\left)\mathrm{}{\epsilon }^y\right]$. They yielded $0.66\lesssim \zeta \lesssim 0.68$ and $0.4\lesssim y\lesssim 0.6$, independent of the pressure $P$. These results for the exponents, and the existence of singular corrections, are consistent with scaling, universality, and recent explicit calculations.