Role of matrix elements in the theoretical determination of generalized susceptibilities in metals

The role of matrix elements in the calculation of the generalized susceptibilities $\chi \left(\overrightarrow{\mathrm{q}}\right)$ of metals is discussed using the results of an augmented-plane-wave energy-band calculation for the eigenvalues and eigenfunctions of Sc metal. The inclusion of the oscillator strength matrix elements is found to significantly alter the structure obtained for $\chi \left(\overrightarrow{\mathrm{q}}\right)$ in the constant-matrix-element approximation. The effect of local-field corrections on the phonon anomaly in Sc and the observed magnetic ordering of dilute rare-earth Sc alloys are described; in the latter case, a crude estimate of this effect is found to restore a (broad) peak in $\chi \left(\overrightarrow{\mathrm{q}}\right)$ at $\overrightarrow{\mathrm{q}}\approx [0,0,0.5(\frac{\pi }{c}\left)\right]$, in good agreement with experiment.