Parametrization of transition-metal Fermi-surface data

The phase shifts associated with a muffin-tin approximation of the crystal potential were used as parameters to represent the Fermi surface of the body-centered-cubic transition metals molybdenum and tungsten. The band-structure formalism employed was the relativistic Korringa-Kohn-Rostoker method and the phase-shift parameters were determined by a least-squares fit to extremal cross-sectional areas obtained from de Haas-van Alphen data. Five-parameter fits which employed the $s_{\frac{1}{2}}$, $p_{\frac{1}{2}}$, $p_{\frac{3}{2}}$, $d_{\frac{3}{2}}$, and $d_{\frac{5}{2}}$ phase shifts had root-mean-square errors which exceeded the estimated experimental error. Inclusion of the $f$ phase shifts did not significantly reduce the discrepancy. Therefore, a formalism was developed and applied to include the nonspherical (inside-muffin-tin) corrections of the potential with the fits truncated at $d$-wave scattering. With the additional two parameters thus introduced an rms error consistent with the experimental error was obtained. As in the earlier work on noble metals, the rms error was found to be quite insensitive to the value of the Fermi energy used.