Potential-Barrier Effects in Photoabsorption. I. General Theory

Abstract

This paper combines parts of the theories of spectroscopy, collisions, and autoionization to provide a unified framework for a quantitative theory of experimental data on $4d$-shell photoabsorption in rare earths. The calculations by atomic theory are intended for tentative application to solids. The theory should also apply to $3p$-shell photoabsorption in the transition metals and to other cases where the effect of a potential barrier is crucial. A prescription is given for the ab initio numerical calculation of total and partial photoabsorption cross sections, as well as of the profiles, energies, and widths of resonances. A sum rule is derived for transitions of the type ${{l}_{i}}^{{4l}_{i}+2}{l}_{f}^{N}\ensuremath{\rightarrow}{{l}_{i}}^{{4l}_{i}+1}{l}_{f}^{N+1}$, which yields the integrated strength of observed absorption spectra.