Golden-rule approach to the soft-x-ray-absorption problem

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Abstract
The cross section of the soft-x-ray absorption is derived based on the Fermi golden rule, by summing the transition probabilities over all possible final states. It is shown that the factor connected with the Anderson orthogonality catastrophe is canceled in the process of summation, and the spectrum is finally expressed by the core-hole propagator times the open-line propagator, as shown by Nozières and De Dominicis. Our results are compared with the results obtained by Mahan and collaborators and are shown to improve over theirs in several respects, expecially in the core-hole propagator. With the use of the new integral kernel, the integral equation for the threshold region is treated and the exact form of the edge anomaly, including the analytical form of the prefactor of the power-law spectrum of Nozières and De Dominicis, is obtained.