Abstract
Nonmagnetic impurities change the electron-phonon interaction in a metal and therefore they influence the superconducting properties. This is demonstrated for an impure simple metal by deriving the Eliashberg equation. It turns out that (1) this equation is of the same formal structure as in the clean case, (2) there exists an additional coupling of low-frequency transverse phonons to the electrons, whereas (3) the interaction between longitudinal phonons and electrons is reduced. Since the former effect is much larger than the latter, the effective phonon density of states α2F(ω) is considerably enlarged in the low-frequency regime, which generally leads to an increased transition temperature and energy gap. Calculated values of the change in the transition temperature are compared for various impurity concentrations with experimental results and satisfactory agreement is obtained.
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