The soft X-ray spectra of metals near the emission edge

A theoretical investigation is made of the behaviour of soft X-ray emission spectra near the high-energy (Fermi) edge, where divergencies have been reported in previous many-body theoretic calculations, and a spike has been observed in the L-emission spectra of several metals. We use a simplified, but for our purposes sufficiently general, model Hamiltonian and introduce a calculational method which overcomes difficulties associated with previous treatments. The results of the calculation up to second order confirm general arguments leading to the conclusion that the divergence will prevail in the exact solution of the model problem. The effect will, however, be blurred by initial- and final-state effects neglected in the model.