Infrared catastrophy and excitons in the X-ray spectra of metals

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Abstract
The singularities near the edges of X-ray spectra in metals are investigated by a new method, using a description of initial and final states in terms of Slater determinants. The calculation of line and band spectra is reduced to that of a single determinant, for which an asymptotic approximation is developed. Special attention is paid to the case in which the final potential is strong enough to bind an electron : the absorption spectrum then possesses two thresholds, whose characteristics are found. The position of the threshold, as well as the nature of the singularities agree completely with the predictions of Hopfield [3]. When the number of electrons decreases, the spectrum goes continuously into that of an insulator, the infrared catastrophy divergence turning into an Auger broadened exciton line