Thermal expansion coefficient, scaling, and universality near the superfluid transition ofHe4under pressure

Experimental results for the isobaric-thermal-expansion coefficient ${\beta }_P$ of pressurized ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ near the superfluid transition temperature $T_{\lambda }$ are reported. Near $T_{\lambda }$, ${\beta }_P$ is an asymptotically linear function of the specific heat at constant pressure $C_P$. Therefore these measurements yield some of the same critical-point parameters as those derivable from $C_P$. The measurements were made with high-temperature resolution over the range $2\times {10}^{-5\mathrm{}}\lesssim \mathrm{}\left|t\right|\mathrm{}\equiv |\frac{T}{T_{{\lambda }^{\prime }}}-1|<\mathrm{}7\mathrm{}\times {10}^{-2\mathrm{}}$, along nine isobars. They span the pressure interval $5\lesssim P\lesssim 30$ bar. A new experimental technique was employed which yielded a temperature resolution of two parts in ${10}^7$ and a pressure stability of 1 × ${10}^{-7\mathrm{}}$ bar. The results for each isobar were fitted with the equation ${\beta }_P=\left(\frac{A}{\alpha }\right)t^{-\alpha }(1+D{t}^x)+B$ above $T_{\lambda }$, and with the same expression with primed coefficients below $T_{\lambda }$. When the amplitudes $D$ and $D^{\prime }$ of the confluent singularity are assumed to be equal to zero (i.e., the data are fitted with a pure power law), the leading exponents are pressure dependent and vary from 0.00 at low $P$ to 0.06 at high $P$. This analysis also yields $B^{\prime }>B$. The inequality between $B$ and $B^{\prime }$, and the pressure dependence of $\alpha$ and ${\alpha }^{\prime }$, are contrary to the predictions of the phenomenological and renormalization-group theories of critical phenomena. When $D$ and $D^{\prime }$ are permitted to assume nonzero values, it is statistically allowed by the data to impose the theoretically predicted relations $\alpha ={\alpha }^{\prime }$, $x=x^{\prime }$, and