X-ray-edge singularities with nonconstant density of states: A renormalization-group approach

We present the results of a calculation of the x-ray absorption and photoemission spectra of metals based on the Wilson renormalization group (RG) (Wilson and co-workers) using free-electron, Lorentzian, and semicircular density of states. The deviation from the asymptotic singular behavior is studied. This illustrative calculation introduces an algorithm for obtaining a tridiagonalized (hopping) Hamiltonian from the logarithmically discretized conduction band. We provide a detailed description of the algorithm which renders the study of problems of impurities in metals with nonconstant conduction electron density of states using the RG method feasible.