Single-Collision-Time Theory of Sound Propagation in LiquidHe4below 0.6°K

A unified derivation of expressions for the velocity and the attenuation of sound in liquid ${\mathrm{He}}^4$ at $T<\mathrm{}0.6\mathrm{}$°K is presented. The derivation, which is valid for both the hydrodynamic and the collisionless regions, is carried out within the framework of the simple conserving collision-time model. It is shown that using this model one can reproduce the results obtained by Khalatnikov and Chernikova under the assumption of the existence of an equilibrium of collinear phonons. Since applying the collision-time approximation does not involve any assumption of this kind, it is argued that the assumption is in fact unnecessary. The theoretical derivation is accompanied by a discussion of the experimental results obtained by Abraham et al. for the attenuation of collisionless sound. Special emphasis is placed on the effects of scattering of phonons from boundaries. It is shown on the basis of these results that the parameter $\gamma$ which determines the dispersion of the phonon spectrum is likely to be smaller than 2×${10}^{35}$ ${\mathrm{g}}^{-2\mathrm{}}$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\sec }^2$.