Abstract
There is wide disagreement over which parameter describing the electron-phonon interaction is most important in determining the transition temperature of a strong-coupling superconductor. This role has been claimed for three different frequency moments of the electron-phonon spectral function alpha 2F( omega ). The Eliashberg theory is used to derive some rigorous upper bounds on Tc that are helpful in clearing up the confusion. It is found that the zeroth moment is the most important moment for the strong-coupling materials so far encountered in practice. In the limit of very strong electron-phonon coupling (a situation that appears not to occur in nature because of lattice instabilities) it is the first moment which is important. The mass enhancement parameter lambda appears to play a secondary role for strong-coupling superconductors.
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