THE DAMPING OF A VIBRATING WIRE RESONATOR IN 0.003-PERCENT AND 0.1-PERCENT HE-3-HE-4 SOLUTIONS BELOW 120-MK - THE EFFECTIVE VISCOSITY OF A 0.1-PERCENT SOLUTION

We have measured the damping of a 13-μm diameter vibrating wire resonator in 0.1% and 0.003%3He-4He solutions at temperatures between 7 and 120 mK. This is a particularly interesting system since it involves a transition from Fermi-Dirac to Maxwell-Boltzmann statistics and also a transition from viscous to ballistic behavior. Contributions to the damping on the wire from sources other than the3He quasiparticle component in the solutions are determined by measurements in pure4He. The viscosity inferred from the data for the 0.1% solution spans the quantum to classical transition, with a minimum at around 13 mK. The temperature dependence of the viscosity is in close agreement with that obtained from recent measurements of the damping of second sound, although the absolute values differ by about 25%. In the 0.003% solution the quasiparticle mean free path is much larger than the wire radius, so that momentum density rather than viscosity is the determining physical quantity. Nevertheless the measured damping on the wire is to found be in excellent agreement with the predictions of a simple kinetic approach, with no adjustable parameters. © 1990 Plenum Publishing Corporation.