The transverse acoustic impedance of dilute solutions of3He in superfluid4He

Abstract

The transverse acoustic impedanceZ=R−iX of dilute solutions of3He in superfluid4He has been measured at a frequency (ω/2π) of 20.5 MHz at temperaturesT from 30 mK to the λ transition at Tλ. The3He concentrations studied werec=0.014, 0.031, 0.053, 0.060, and 0.092 below 1 K, thoughc decreased slightly near the λ point. The impedance was found from the temperature dependence of the quality factor and the resonant frequency of anAT-cut quartz crystal resonator immersed in the liquid. Below 1 K,Z is due to the Fermi gas of3He quasiparticles, and in the collisionless limit, ωτ≫1 (τ is a relaxation time),R remains constant whileX goes to zero. Measurements ofR(c, T) andX(c, T) were analyzed to determine the momentum accommodation coefficient α(c, T) and τ(c, T). The relaxation times were in good agreement with previous work, while α(c, T) was independent ofc, but increased from 0.29±0.03 below 0.1 K to 1.0±0.1 above 0.8 K. Various mechanisms are suggested to explain this. Between 1.0 and 1.5 K the3He quasiparticles and the thermally excited rotons are in the hydrodynamic region, ωτ≪1. Values of the total viscosity η(c, T) were obtained and analyzed to give the3He gas viscosity and the3He-3He and roton-3He scattering rates, both of which were energy-dependent. The superfluid healing length a was also measured. Near the λ point we founda=(0.1±0.03)e−2/3 nm, where e=1−T/Tλ, proportional to the phase coherence length ξ. Our data are consistent with the hypothesis that ξρs/T is a universal constant for superfluid dilute solutions, where ρ s is the superfluid density. Between 1.0 and 1.8 K we found thata(c, T) was comparable to measurements in3He-4He films.