Electronic susceptibility of niobium

The static electronic susceptibility χ(→q) is calculated for niobium along the [100] direction both with and without matrix elements. The energy bands are generated by a fitted second neighbor, s-p-d Slater-Koster model, and matrix elements are approximated by using the Slater-Koster wave-function coefficients with radial integrals of Fermi-level Korringa-Kohn-Rostoker wave functions within the muffin tin. The Brillouin-zone integration is carried out by the combined linear-quadratic method of Cooke and Wood. Contrary to the work of Evenson, Fleming, and Liu our constant-matrix-element calculation yields a result for χ(→q), which is relatively featureless. The major effects of including the band and momentum dependence of the matrix elements are to make χ(→q) a generally decreasing function of |→q|, and to bring out some structure not seen in the constant-matrix-element calculation. The static susceptibility has a noticeable hump around the same wave vector as the observed [100] LA-phonon anomaly. The frequency dependence of the real part of the dynamic susceptibility appears to be small for ω in the phonon-frequency range.