Effect of Short-Wavelength Components of the Electronic Polarizability on the Transition Temperature of Superconductors

It is argued that the "local" electric polarizability (or, in the band picture, its "interband" component) has major effects on the top of the phonon spectrum of certain superconductors. This causes interesting pressure and isotopic dependences of $T_c$ and might furnish and explanation for the variation of $T_c$ with electron number in these superconductors.