Pseudopotential Calculation of the Mass Enhancement and Superconducting Transition Temperature of Simple Metals

A calculation is presented of the electron-phonon mass-enhancement parameter $\lambda$ and the superconducting transition temperature $T_c$ for sixteen simple metals plus Ca, Sr, and Ba. Empirical pseudopotentials and phonon spectra are used to calculate the electron-phonon coupling in a one-orthogonalized-plane-wave approximation using a spherical model of the phonons and the Fermi surface. Umklapp processes are explicitly evaluated. Calculated values of $\lambda$ are compared with values of $\lambda$ extracted from $T_c$ and with values of the enhancement of the density of states at the Fermi surface as measured by the low-temperature specific heat. Excellent agreement is found for the divalent hexagonal metals, using empirical nonlocal pseudopotentials. Satisfactory agreement is found for the other simple metals. It is predicted that Li and Mg should be superconducting at low temperatures. The calculated results are also compared with a simple model for $\lambda$ due to McMillan, and the simple model is used to discuss the occurrence of superconductivity in the Periodic Table.