Approximate translation of screened spherical waves

Abstract

We develop and discuss a Taylor-series expansion of the addition theorem for screened spherical waves, $i^l$ $h_l$(kr)$Y_{\mathrm{lm}}$(r^). The expansion is designed for orderly progression in the addition of curved–wave-front corrections to multiple scattering of electrons in solids, but it applies to any wave-scattering problem based on the addition theorem for spherical waves. We relate one of the expansion indices to a magnetic quantum number in a coordinate system rotated to align the quantization and translation axes.