The attenuation $\ensuremath{\alpha}$, the velocity $u$, and the dispersion $D=u(\ensuremath{\omega})\ensuremath{-}u(0)$ of first sound have been measured in pressurized liquid $^{4}\mathrm{He}$ ($P=0.06, 5.01, 9.21, 15.24, 20.38, 25.46, 29.33$ bar) near the superfluid transition. The frequency range was $4.6 \mathrm{kHz}\ensuremath{\le}\frac{\ensuremath{\omega}}{2\ensuremath{\pi}}\ensuremath{\le}1.0 \mathrm{MHz}$, the temperature range was $1 \ensuremath{\mu}\mathrm{K}\ensuremath{\le}|T\ensuremath{-}{T}_{\ensuremath{\lambda}}|\ensuremath{\le}3 \mathrm{mK}$. From the measured velocities we calculate the thermodynamic velocity $u(0)$, as well as ${(\frac{\ensuremath{\partial}S}{\ensuremath{\partial}P})}_{\ensuremath{\lambda}}$ and ${(\frac{\ensuremath{\partial}V}{\ensuremath{\partial}P})}_{\ensuremath{\lambda}}$. The attenuation and the dispersion at constant ${T}_{\ensuremath{\lambda}}\ensuremath{-}T$ are only weakly pressure dependent. They are interpreted as arising from a relaxation process occurring only below ${T}_{\ensuremath{\lambda}}$, and a fluctuation process occurring on both sides of the $\ensuremath{\lambda}$ transition; both contributions have about equal strength. The strength ${A}_{R}$ of the relaxation process and the amplitude ${\ensuremath{\tau}}_{0}^{\ensuremath{'}}$ of the relaxation time ${\ensuremath{\tau}}^{\ensuremath{'}}={\ensuremath{\tau}}_{0}^{\ensuremath{'}}{t}^{\ensuremath{-}{x}^{\ensuremath{'}}}$ are independent of pressure to within 10%; ($t=\frac{|T\ensuremath{-}{T}_{\ensuremath{\lambda}}|}{{T}_{\ensuremath{\lambda}}}$). The latter result seems to be inconsistent with the pressure independence of the correlation-length amplitude ${\ensuremath{\xi}}_{0}^{\ensuremath{'}}=1.0\ifmmode\pm\else\textpm\fi{}0.05$ \AA{} (which was confirmed in this work), and the known pressure dependence of the amplitude ${u}_{2,0}$ of second-sound velocity, if the relation ${\ensuremath{\tau}}^{\ensuremath{'}}=\frac{{\ensuremath{\xi}}^{\ensuremath{'}}}{{u}_{2}}$ is correct. For $T>{T}_{\ensuremath{\lambda}}$, where only critical fluctuations contribute, our absorption and dispersion data for all $\ensuremath{\omega}$ and $P$ can be scaled with functions of $\ensuremath{\omega}\ensuremath{\tau}$ for ${10}^{2}>\ensuremath{\omega}\ensuremath{\tau}>{10}^{\ensuremath{-}2}$. This scaling analysis shows that the time $\ensuremath{\tau}$ characterizing the critical order-parameter fluctuations at $T>{T}_{\ensuremath{\lambda}}$ has the same temperature and pressure dependence as the relaxation time ${\ensuremath{\tau}}^{\ensuremath{'}}$ at $T<{T}_{\ensuremath{\lambda}}$; these two times differ at most by a constant multiplicative factor. Below ${T}_{\ensuremath{\lambda}}$, the data are represented by the sum of the contribution represented by the scaling function plus the contribution from order-parameter relaxation. The weak pressure dependence of $\ensuremath{\alpha}$ and $D$, and the pressure independence of ${A}_{R}$, ${\ensuremath{\xi}}_{0}^{\ensuremath{'}}$, ${\ensuremath{\tau}}_{0}^{\ensuremath{'}}$, and ${\ensuremath{\tau}}_{0}$ contrasts with the strong concentration dependence of these quantities in $^{3}\mathrm{He}$-$^{4}\mathrm{He}$ mixtures. The scaling functions determined from our data are identical in form to those determined earlier from the mixture data. The frequency dependences of the attenuation and of the dispersion for $\ensuremath{\omega}\ensuremath{\tau}\ensuremath{\gtrsim}1$ scale as $\ensuremath{\alpha}\ensuremath{\propto}{\ensuremath{\omega}}^{1+y}$ and $D\ensuremath{\propto}{\ensuremath{\omega}}^{y}$, respectively, with $y=0.15\ifmmode\pm\else\textpm\fi{}0.03$.
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Nov 1, 2001
M E Guzhva + 2
Open Access