New approach to the x-ray-absorption problem

We present a simple numerically stable procedure for calculating frequency-dependent response functions for a fermion system in the presence of localized perturbations over all frequency scales. In the case of the x-ray singularity problem, the asymptotic result of Nozieres and De Dominicis can be extended to excitation energies comparable to the bandwidth. The range of this extension depends on the structure of the localized perturbation.