Theory of thermal boundary resistance between small particles and liquid helium. II. Normal liquidHe3

The previous theory on the thermal boundary resistance between small particles and liquid He II [Phys. Rev. B 24, 6421 (1981)] is extended to the case for normal liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in terms of Landau Fermi-liquid theory. It is shown that the toroidal-mode phonons in small particles contribute to the heat flow through the excitation of transverse zero sound in contrast to the case of liquid He II. The calculated resistances exhibit a $T^{-3\mathrm{}}$ behavior above some temperature which depends on the size and elastic property of the small particle. In this temperature regime, the calculated results for silver and copper particles agree well with the observed resistances in both magnitude and temperature dependence. At lower temperatures the theory predicts exponentially increasing resistances with decreasing temperature as in the case for liquid He II. The relative contributions to the heat flow due to longitudinal and transverse zero sound are obtained as a function of temperature.