Viscous waves in 4He films

Abstract

A quartz crystal resonator has been used to excite shear waves at a frequency of 20.5 MHz in He films above and below the superfluid transition and just above the liquid-gas critical point. The wave has a viscous penetration depth 6-20 nm and the transverse acoustic impedance Z = R - iX of the film was found from changes in the quality factor and resonant frequency of the crystal. The thickness of a He I film was swept at constant temperature by creating a small temperature difference between the He film on the crystal and bulk liquid helium below it. Calculations of the impedance of a homogeneous film as a function of d/6 using transmission line theory show the film's thickness d could be swept from 1.5 to >60 nm . The impedance of six superfluid films of constant thickness in the range 14-23 nm has been measured for 0.4 T T . From the impedance in the ballistic limit, , the average probability of the quantum evaporation of a

He atom by a roton incident upon the liquid-vapourinterface is estimated to be ~0.35 . A resonance, the temperature of which was dependent on film thickness, was observed in the superfluid film and has tentatively been identified with the resonance in the A/4 Kelvin mode of vortices pinned to the crystal surface.The transverse acoustic impedance Z of helium has also been measured 49 mK above the liquid-gas critical point for pressures up to 2000 torr. In the highly compressible critical region, the impedance shows the effects of the large density gradients that develop close to the crystal surface under van der Waals1 forces. At low pressures, the transition to non-hydrodynamic behaviour is observed, and it is estimated that a fraction 0.2 of He atoms incident upon the crystal are diffusely scattered from it.