Singularity and nonlinearity in the Kapitza resistance between gold and superfluid sup 4 He near T sub. lambda

We report experimental results for the Kapitza resistance {ital R}{sub {ital K}} between gold and superfluid {sup 4}He, which were obtained by using very-high-resolution thermometry. The data imply that {ital R}{sub {ital K}} is singular at the superfluid transition temperature {ital T}{sub {lambda}}. Comparison with theory suggests that the singularity results from a hydrodynamic effect proposed by Landau, and that it is associated with the vanishing of the superfluid and normal-fluid currents at the boundaries. Recently a quantitative prediction of the singular part of this Kapitza resistance has been made based on dynamic renormalization-group theory. This theory requires no adjustable parameters and it agrees well with our data. The measurements of {ital R}{sub {ital K}} are independent of the heat flux {ital Q} only for reduced temperatures {ital t}=1{minus}{ital T}/{ital T}{sub {lambda}} greater than a characteristic value {ital t}{sub {ital c}}. We find that {ital t}{sub {ital c}} is approximately proportional to {ital Q}, and that for {ital t}{lt}{ital t}{sub {ital c}} the maximum value of ({partial derivative}{ital R}{sub {ital K}}/{partial derivative}{ital Q}){sub {ital t}} is approximately proportional to 1/{ital t}. The {ital Q}-dependent contribution {ital R}{sub {ital K}{ital Q}} to {ital R}{sub {ital K}} can be represented by a function of the single variable {ital Q}/{ital t}. For large {ital Q}/{ital t}, this function saturates at a value near 0.35 cm{sup 2} K/W. We know of no theory that predicts the dependence of {ital R}{sub {ital K}} on {ital Q}.