We present two methods for solving the Stoneley equation for lightly loaded surfaces, which we apply to interfaces between, on the one hand, copper and quartz, and, on the other hand, liquid and solid 4He, solid hydrogen, deuterium, and neon. We look for solutions with velocities near the Rayleigh wave on the free surface of the heavy medium. The methods for solving the equation are, respectively, a first-order expansion near the Rayleigh velocity and a computer iteration. We show that both methods give nearly identical results for the damping, and therefore the first-order approximation gives a useful analytical expression for the damping of loaded Rayleigh waves. The approximate result for the velocity increment is poor. By applying the results to the Kapitza conductance problem we are able to put forward an explanation for some of the experimental features, and to make suggestions for further experimental and theoretical work.
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van der Sluijs, J.C.A., van der Sluijs, M.J. Damping of loaded Rayleigh waves on lightly loaded interfaces: Application to the Kapitza conductance. J Low Temp Phys 44, 223–245 (1981). https://doi.org/10.1007/BF00120774
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DOI: https://doi.org/10.1007/BF00120774