Tomonaga's Model and the Threshold Singularity of X-Ray Spectra of Metals

Singularities near the threshold of the soft x-ray spectra of metals have been predicted by Mahan and have recently been calculated by Nozi\`eres et al. using the model of a localized core hole. We show that the singular behavior can be understood in terms of density waves of the conduction electrons which are excited when, in the absorption process, the core hole is created, providing an attractive potential for the conduction electrons. For the description of the conduction electrons in terms of density waves, Tomonaga's model is adopted.