Ultrasonic Attenuation of Pure Strong-Coupling Superconductors

The low-frequency longitudinal ultrasonic attenuation of strong-coupling superconductors is discussed. The starting point is a formula due to Kadanoff and Falko which expresses the attenuation in terms of various correlation functions. These functions were evaluated in the ladder approximation. The results are valid for all values of $\mathrm{ql}$ ($l$=electron mean free path, $q$=phonon wave number). In the limit $\mathrm{ql}\gg 1$, the contribution of the density-density correlation function is dominant and we obtain Ambegaokar's result for the reduced attenuation (ratio of attenuation in superconducting to normal states). In the limit $\mathrm{ql}\ll 1$, all correlation functions are equally important. The reduced attenuation is a function of $q$ and differs from the results of the BCS isotropic model. Numerical calculations for the reduced attenuation in lead were performed for various values of $q$ which satisfy $\mathrm{ql}\ll 1$. The results are in rough agreement with those of Deaton's experiment.