Threshold Behavior of the Soft-X-Ray Spectra in Metals

The behavior of soft-x-ray emission and absorption spectra near the Fermi-limit threshold is considered. Realistic parameters have been calculated for the Nozières-de Dominicis solution to a simplified model for the soft-x-ray process which is valid near the threshold. It is shown that for simple metals these parameters are only weakly dependent upon the particular metal and that it is the symmetry of the x-ray transition matrix element which is of essential importance in determining the threshold behavior. It is found that $L_{2,3}$ spectra tend to be enhanced near the threshold, whereas $K$ spectra tend to fall smoothly to zero. This result is in accord with the observed emission spectra of the light elements, and appears to explain the "anomalous" $K$ spectrum of Li as well as the high-energy peak in the $L_{2,3}$ spectrum of Na.