High-resolution thermal-conductivity measurements near the lambda point of helium.

Abstract

We report measurements of the thermal conductivity of helium in the region from 6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ to 6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$ K above the lambda point at the vapor pressure. Primarily because of uncertainties in the Kapitza boundary resistance, reliable results were obtained only in the region from 6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}7}$ to 6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$ K above the transition. Within 5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$ K of the transition we find conductivity values significantly lower than expected on the basis of theoretical extrapolations from previous experiments. When the parameter ${\mathrm{R}}_{\mathrm{K}}$ is calculated, we find a maximum about 2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$ K above the transition, in disagreement with the predictions of the two-loop dynamic renormalization-group theory. The uncertainties in our results in this region are discussed in detail.