CXIV. X-ray transition probabilities with special reference to K absorption in lithium

Summary To interpret the position of x-ray absorption edges in monovalent metals, the author assumed in a previous paper that the positive hole created in an inner shell was screened by a bound electron. It is shown here that this assumption gives also a correct order for the magnitude of the absorption coefficient near the edge. In an introductory treatment we take the absorbing system to be the ejected electron alone. We use the hydrogenic wave-function for the bound state and the plane wave for the continuum. We thus obtain approximate formulae for the total jump in the absorption coefficients at the K, L and M edges, both for x-rays and in the optical region. In a further treatment, taking lithium as an example, we treat the absorbing atom and the Fermi electrons as a whole, and with this model analyse the fine structure of the edge. We show how the screening may be obtained from the conduction band. We analyse various possible types of transitions producing edges or lines in the absorption, and relate them to the structure observed near the edge. To avoid too much complexity in treating the Fermi electrons, we enclose the metal in a large but finite sphere. Quantitative agreement with experiment is not altogether satisfactory, possibly because of inaccuracies in the wave-functions used. Finally, we describe briefly the reverse process of K-emission in lithium, and discuss the possible presence of lines as well as bands in the x-ray spectra of monovalent metals.