We report new measurements in four cells of the thermal boundary resistance $R$ between copper and ${}^4\mathrm{He}$ below but near the superfluid-transition temperature $T_{\lambda }$. For ${10}^{-7\mathrm{}}\le t\equiv {1-T/T}_{\lambda }\le {10}^{-4\mathrm{}}$ fits of ${R=R}_0{t}^{{-x}_b}{+R}_B$ to the data yielded $x_b\simeq 0.18$, whereas a fit to theoretical values based on the renormalization-group theory yielded $x_b=0.23\mathrm{}$. Alternatively, a good fit of the theory to the data could be obtained if the amplitude of the prediction was reduced by a factor close to 2. The results raise the question whether the boundary conditions used in the theory should be modified.

• Received 1 August 2001

DOI:https://doi.org/10.1103/PhysRevLett.88.095702