We introduce a simple empirical rule wherein the pairing interaction in superconductors is cancelled when normal and umklapp phonon scattering coexist. Superconductivity then arises solely from the residual umklapp contribution. As a result the deduced electron-phonon interactions in niobium, tantalum, lead and aluminum become virtually identical in both the normal and superconducting states. Transition temperatures calculated under the rule are accurate within a few percent when compared with experimental data. Features of the Matthias relations are also explained. The high Tc so far predicted for metallic hydrogen is probably overly optimistic.
- superconductivity, BCS theory, Tc prediction, Matthias relations