Heat Transfer between Phonons and Quasiparticles in a Dilute Mixture of<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>3</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>in<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>

A description is given of a novel technique for measuring the thermal resistance (${R}_{\mathrm{p}\mathrm{h}\ensuremath{-}\mathrm{q}\mathrm{u}}$) between phonons and quasiparticles in a bulk sample of dilute mixture of $^{3}\mathrm{He}$ in liquid $^{4}\mathrm{He}$. For 0.1% $^{3}\mathrm{He}$ we find $V{R}_{\mathrm{p}\mathrm{h}\ensuremath{-}\mathrm{q}\mathrm{u}}{T}^{6.5}=3.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ ${\mathrm{m}}^{3}$${\mathrm{K}}^{7.5}$ ${\mathrm{W}}^{\ensuremath{-}1}$ for $35&lt;T&lt;60$ mK, in fair agreement with known interactions between phonons and quasiparticles. The discrepancy, however, suggests an additional, unidentified, inelastic scattering process.

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