Thermal-conductivity measurements in liquid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>below 0.7 K

High-precision steady-state heat-flow measurements were made in pure liquid $^{4}\mathrm{He}$ under pressures of up to 25 bar. The data cover the temperature range between 0.1 and 0.7 K and were obtained using sample containment tubes which ranged in diameter from 0.14 to 1.4 cm. The data yield information about $\ensuremath{\Lambda}$, the phonon mean free path for large-angle scattering. At the higher pressures phonon-roton scattering plays a significant role in limiting $\ensuremath{\Lambda}$. However, at low pressures and temperatures the $\ensuremath{\Lambda}$ results show evidence that three-phonon processes become dominant. This permits inferences to be made concerning the phonon dispersion relation. In the temperature regime for which $\ensuremath{\Lambda}$ is comparable with the tube diameter, a phenomenon was observed which is analogous to the Knudsen minimum observed in ordinary-gas flow measurements. These data are compared with the recent calculations of Benin and Maris.

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