Ultrasonic Attenuation in Superconductors forql<1

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Abstract
A derivation is given for the attenuation of both transverse and longitudinal ultrasonic waves in the superconducting state for the case when the product of the ultrasonic wave vector times the electron mean free path is smaller than one. It is assumed that the effect of electromagnetic fields is negligible in this frequency range. For transverse waves it is found that the ratio of the ultrasonic attenuation coefficient in the superconducting state and the normal state is equal to twice the Fermi function of the temperature-dependent superconducting energy gap, in agreement with experimental results obtained by Levy, Kagiwada, and Rudnick. The same result is obtained for longitudinal waves.

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