Anisotropy of the Fermi surface, Fermi velocity, many-body enhancement, and superconducting energy gap in Nb

The detailed angular dependence of the Fermi radius kF, the Fermi velocity vF(k), the many-body enhancement factor (k), and the superconducting energy gap (k), for electrons on the Fermi surface of Nb are derived with use of the de Haas van Alphen (dHvA) data of Karim, Ketterson, and Crabtree [J. Low Temp. Phys. 30, 389 (1978)], a Korringa-Kohn-Rostoker parametrization scheme, and an empirically adjusted band-structure calculation of Koelling. The parametrization is a nonrelativistic five-parameter fit allowing for cubic rather than spherical symmetry inside the muffin-tin spheres. The parametrized Fermi surface gives a detailed interpretation of the previously unexplained, , and orbits in the dHvA data. Comparison of the parametrized Fermi velocities with those of the empirically adjusted band calculation allow the anisotropic many-body enhancement factor (k) to be determined. Theoretical calculations of the electron-phonon interaction based on the tight-binding model agree with our derived values of (k) much better than those based on the rigid-muffin-tin approximation. The anisotropy in the superconducting energy gap (k) is estimated from our results for (k), assuming weak anisotropy.