Sound Absorption in Liquid Helium II,T<0.5°K

The expression $\Gamma =\frac{A\Omega T^4}{\rho {c_0}^3}$ for the absorption of sound in liquid ${\mathrm{He}}^4$ II for $T<\mathrm{}0.5\mathrm{}°$K, where $T$ is the absolute temperature, is shown to be a simple consequence of the principles of the excitation theory of a Bose liquid and a few other reasonable postulates. ($\Gamma$ is the absorption, $\frac{\Omega }{2\pi }$ is the frequency and $c_0$ the velocity of the sound, and $\rho$ is the density.) As in the work of Woodruff and Ehrenreich on sound absorption in insulating crystals, the analysis is based on the linearized Boltzmann transport equation and the Blount formula for the energy loss from a system of interacting excitations driven by a sound wave. It is valid for frequencies such that $\Omega \tau \gg 1$ and $\Omega \ll \frac{\mathrm{KT}}{\hslash }$, where $\tau$ is the relaxation time for the thermal phonons and $K$ is Boltzmann's constant. The coefficient $A$ is related to the rate of change of the sound velocity with density. An attempt is made to determine the exact magnitude of $A$ within the framework of the present considerations by postulating a relative motion of the normal and superfluid components, but this approach leads to new difficulties.