Superconductivity and phonon softening. III. Relation between electron bands and phonons in Nb, Mo, and their alloys

Calculations are presented by ${\chi }_1\left(\overrightarrow{\mathrm{Q}}\right)$ and ${\chi }_2(\overrightarrow{\mathrm{Q}},\omega )$ for Nb, Mo, and alloys in the rigid-band model. The matrix elements are set to 1. The results for Nb agree with a previous calculation by Cooke, Davis, and Mostoller. An empirical linear relation is found between ${\chi }_1\left(\overrightarrow{\mathrm{Q}}\right)$ and $\frac{d{\chi }_2(\overrightarrow{\mathrm{Q}},0)}{d\omega }$. This relation leads to a simple formula relating the superconducting coupling constant ($\lambda$) to the phonon frequencies. However, we are unable to evaluate the terms in this formula with sufficient accuracy to calculate $\lambda$.