Theory of the soft-x-ray edge problem in simple metals: historical survey and recent developments

In the first half of this article, theoretical treatments of the infrared divergence involved in the edge problem of soft-x-ray absorption, emission, and photoemission spectra of simple metals are reviewed historically. In the second half, recent developments in the work of the present authors using the Fermi golden rule are described to show that the method permits an analytical treatment and provides exact results for various aspects of the edge problem.