Phonon transmission across interfaces and the Kapitza resistance

The transmission of phonons across an interface between a classical solid and liquid helium is calculated. Several simple models of the helium system are considered. Calculations for a solid with a clean and perfect surface give a transmission coefficient for low-energy phonons. ($\epsilon <20\mathrm{}$ K), which is very small (typically ≤0.1), and which decreases with decreasing energy. At energies above 30 K the transmission is predicted to have a larger value which is slowly varying with energy, and to be inversely proportional to the acoustical impedance of the solid. Possible mechanisms which increase the transmission for damaged or dirty surfaces are briefly discussed.