PROPAGATION OF 2ND SOUND NEAR T-LAMBDA

Superfluid hydrodynamics for second sound, expanded to first order in del rho(s) and including second-sound damping and finite-amplitude effects, are cast into a boundary-value-problem format, suitable for calculating the resonant frequency in a second-sound cavity operating near the lambda point. This model is applied to the data of Marek, Lipa, and Philips, which showed deviations from a simpler model in the region close to the transition. We find that our model by itself cannot explain the deviations, but if a shift in the estimated location of T(lambda) is included, a significant improvement can be obtained. The critical exponent zeta, describing the divergence of rho(s), was found to be zeta=0.6708+/-0.0004, in good agreement with the renormalization-group prediction 0.672+/-0.002. The range for the reduced temperature parameter was extended to epsilon=2 x 10(-7), substantially closer to the transition than in the previous analysis of this data. The shift in T(lambda) can be considered acceptable if the data very near T(lambda) are reinterpreted. The effect of the del rho(s) term is shown to be important for epsilon < 10(-6).