SPECIFIC-HEAT AND SUPERFLUID DENSITY OF BULK AND CONFINED HE-4 NEAR THE LAMBDA-TRANSITION

The specific heat and superfluid density of liquid He-4 are calculated using a vortex-ring renormalization group theory, both for the bulk fluid and for confinement in a sphere of diameter L. In the finite geometry the superfluid density remains finite and universal at T-lambda, in agreement with Monte Carlo simulations and with finite-size scaling. The specific-heat peak is flattened in the finite geometry, and the onset temperature of the deviation from bulk behavior approaches T-lambda more closely as L is increased.