Velocity Dependence of the Superfluid Density in HELIUM-4 Near T

An understanding of the thermodynamic state of liquid helium in a temperature region near the superfluid transition (lambda point) at present remains incomplete. The thermodynamic state can be described by the variables P (pressure), T (temperature), and (v_{ rm s}-v_{rm n})^2. The functional dependence of the superfluid density on the relative velocity (v _{rm s}-v_ {rm n}) between the superfluid and normal fluid is an independent equation of state. We measured this dependence (as a function of temperature) with a superfluid Helmholtz resonator, whose resonant frequency is related to the square root of the superfluid density by a geometric factor. Measurements were made by recording the dependence of the resonant frequency on amplitude of oscillation at discrete temperatures, which were concentrated near the lambda point, closest being within 14 mK. We tried to minimize other effects that might contribute to the variation of resonant frequency with velocity amplitude. The principal ones are nonlinearity in the normal fluid flow, nucleation of vortices in the superfluid, and temperature drift of the system during the measurement process. To limit the normal fluid flow, a Nuclepore filter was installed in the Helmholtz resonator in series with and very close to the flow channel. The apparatus parameters crucial for estimating the contribution of normal fluid flow nonlinearity to the frequency shift are determined from the Q-factor measurements. Our measurements of the velocity effect on the superfluid density were found to be in agreement with the Khalatnikov model for HeII at temperatures between 1.25 and 1.90 K, within the uncertainty of a multiplicative factor which includes a geometric constant for the HR flow channel and a velocity calibration constant. Our experimental results are close to the roton interaction model of Mishra and Bedell at intermediate temperatures and the apparent difference nearer the lambda point may be due to parameters used in this model, which were based on data that extend only up to 2.10 K. The temperature dependence of the velocity effect near the transition does not yield the expected critical exponent, but it is reasonable to believe that the scaling region may begin closer to lambda transition. (Abstract shortened with permission of author.).