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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 li4l i+2lfN →li4l i+1lfN+1, which yields the integrated strength of observed absorption spectra.