Phase-Shift Pseudopotentials and the Electron-Phonon Interaction: Theory and Results for Alkali Metals

The electronic properties of the alkali metals are interpreted by using augmented-plane-wave (APW) pseudopotentials derived from phase-shift analyses of experimental Fermi-surface data. The APW-pseudopotential form factors are found to be consistent with the results of local-pseudopotential interpretations of the experimental data, and with the energy gaps predicted by model-potential and band-structure calculations. It is shown that the matrix elements of the electron-phonon interaction can be deduced from the empirical phase shifts. The result is a form factor for electron-phonon coupling that is very similar to the APW form factor derived from the secular equation. The form factors for electron-phonon coupling are used to estimate the electrical resistivities and electron-phonon mass enhancements of the alkali metals. The trend of resistivities within the alkali-metal series is predicted correctly, and the renormalization factors are generally consistent with the experimental data, although the strength of the electron-phonon interaction in sodium is significantly overestimated, apparently because the experimental Fermi-surface data yield no information about $V_{200}$ and higher pseudopotential coefficients.