Electron-phonon spectral function and mass enhancement of niobium

The electron-phonon spectral distribution function ${\alpha }^2\left(\omega \right)F\left(\omega \right)$ has been calculated for niobium. The electron energy bands and wave functions were obtained from a self-consistent augmented-plane-wave muffin-tin potential, and the electron-phonon matrix elements were evaluated using the so-called rigid-ion approximation. With this approximation, it is found that ${\alpha }^2\left(\omega \right)$ is constant over the whole energy spectrum. The electron-phonon mass enhancement has also been calculated for local regions of the Fermi surface and found to be anisotropic. The calculated local values of the enhancement do not agree with experimental values available for different orbits from de Haas—van Alphen measurements. The discrepancy seems to arise because the bare-rigid-ion matrix elements are relatively small between states with nearly pure $l=2\mathrm{}$ character.