Critical-region measurements of the mutual-friction parameters in rotating He II

Abstract

We report measurements of the two mutual-friction parameters $B$ and $B^{\prime }$ in rotating He II in the range of temperature from 1.75up to 6×${10}^{-4\mathrm{}}$ K below the $\lambda$ point. All results are obtained by investigating the second-sound response of a square resonator. The data previously reported in the literature reveal some marked discrepancies in the behavior of $B$ and $B^{\prime }$ as $T\to T_{\lambda }$, in spite of considerable scatter above 2.1 K. In this work we attempt to describe this behavior precisely, and at the same time we extend the measurements of $B^{\prime }$ above ${10}^{-2\mathrm{}}$ K from $T_{\lambda }$. Primarily because of good temperature stabilization using a second-sound controller, a close fit of both amplitude and phase of the resonance response to calculated values was possible, which greatly improved the precision of the results. Plotting $B$ and $B^{\prime }$ as a function of the reduced temperature $\epsilon =1-\frac{T}{T_{\lambda }}$, in the temperature range $2\times {10}^{-4\mathrm{}}<\epsilon <3\mathrm{}\times {10}^{-2\mathrm{}}$, we found the experimental data are well fitted by the following expressions, where $-\alpha$ is a critical exponent near $-\frac{1}{3}$: $B=b{e}^{-\alpha }$, $B^{\prime }=b^{\prime }{e}^{-\alpha }+b_{}^{\prime }{}_0{}^{}$ with $\alpha =0.330\mathrm{}\pm 0.015$, $b=0.470\mathrm{}\pm 0.033$, $b^{\prime }=-0.34\mathrm{}\pm 0.03$, $b_{}^{\prime }{}_0{}^{}=1.01\mathrm{}\pm 0.12$.