Form Factors of Truncated Atomic Potentials

Abstract

The effect on pseudopotential form factors of a step in the atomic potential is investigated. From an analytic approximation to such muffin-tin potentials, $V\left(q\right)\mathrm{}$ curves are calculated for Al and several semiconductors. Although a cutoff at the Wigner-Seitz radius leads to form factors surprisingly close to experimental values, the results are rather poor for a step at the inscribed-sphere radius. By adjusting the step parameter $U_0$, one may obtain rough agreement either with the Friedel sum rule at $q=0\mathrm{}$ or near the first reciprocal lattice vectors. But no satisfactory approximation is found over as wide a range of $q$ as required e.g., in the calculation of electron-phonon interactions for the determination of phonon spectra.