The velocities of first and second sound in dilute solutions of3He in superfluid4He at very low temperatures

Abstract

A unified theory of first and second sound in dilute solutions of 3 He in superfluid 4 He at very low temperatures is presented. The theory is based on the detailed semimicroscopic model for the 3 He quasiparticle excitations described by Disatnik and Brucker a few years ago. In contrast with Khalatnikov's macroscopic theory, the application of this model enables the derivation of relatively simple expressions for the sound velocities in which no omissions of terms representing contributions due to the thermal expansion are made. The sound velocities are given in the final expressions in terms of various parameters of the 3 He quasiparticle spectrum and effective interaction. These expressions are both highly accurate and easy to use over a wide temperature regime spanning from the quantum limit to temperatures of the order of the 3 He quasiparticle degeneracy temperature. The actual application of the theory to measurements of the sound velocities is described in detail. Numerical values or estimates for various characteristic parameters of the 3 He quasiparticle system, including in particular the 3 He quasiparticle effective mass, are obtained from the comparison between the theory and the experiment. The example of the second sound velocity is used to illustrate a procedure for analyzing data from very low-temperature measurements of the equilibrium properties of the solutions, which is expected to produce meaningful information regarding the parameters of the basic model. In practice, the theory is found to be in a very good accord with the measurements of the sound velocities. The result obtained for the zero concentration limit of the 3 He quasiparticle effective mass (m 0 =2.19m 3 ) is somewhat lower than the empirical estimates reported in the past. On the other hand, this result is in very good agreement with variational calculations based on the detailed microscopic theory of the solutions. A discussion of this and other results obtained from the comparison between theory and experiment is included.