Effect of Electron-Damped Dislocations on the Determination of the Superconducting Energy Gaps of Metals

When account is taken of the damping of dislocations by electrons—i.e., by electron viscosity—it is shown that the energy losses due to this source are appreciable and are different in the normal and in the superconducting states. By subtracting off these two losses for the acoustic attenuation measured for these two states, and using the relation between the residual attenuations for the two states determined from the BCS theory, a much better determination of the energy gaps for superconductors is obtained. For lead the value is $2{\epsilon }_0=(4.1\mathrm{}\pm 0.1)k{T}_c$, in good agreement with other methods for measuring the gap. The electron damping of dislocations accounts also for the amplitude effect in the superconducting range first observed by Love and Shaw. Theoretical calculations by Tsuneto have indicated that the ratio of the attenuation in the superconducting to that in the normal state for longitudinal waves should be the same for the region $q\overline{l}\ll 1$ as that which has been found by BCS in the region $q\overline{l}\gg 1$. When account is taken of the dislocation damping effect, it is shown that existing data confirm this calculation.