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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 the normal and superconducting states. Transition temperatures calculated under the rule are accurate within a few per cent when compared with experimental data. Features of the Matthias relations are also explained. The high T c so far predicted for metallic hydrogen is probably overly optimistic.

Empirical rule to reconcile Bardeen–Cooper–Schrieffer theory with electron–phonon interaction in normal state