Superconductivity in Simple Metals

This paper reports an attempt to calculate directly from normal-state data the superconducting properties of a number of simple metals. Information about the lattice vibrations is taken from a Born-von K\'arm\'an force-constant fit to the dispersion curves measured by means of inelastic neutron scattering. The matrix element of the electron-ion potential, for electrons scattering at the Fermi surface, is taken from pseudopotential theory. From this information we evaluate the electron-phonon part entering the Eliashberg gap equations which are then solved numerically to obtain the gap in the excitation spectrum. The calculated gap for Pb as well as for Al is in close agreement with experiment. For Na and K it is predicted that the transition temperature is certainly much less than ${10}^{\ensuremath{-}5}$ \ifmmode^\circ\else\textdegree\fi{}K if, in fact, they superconduct at all.

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