Dynamic screening and interference effects in X-ray and auger emission spectra

We study X-ray and Auger emission spectra from initial core holes which are strongly influenced by many-electron effects of giant Coster-Kronig type. In particular we include the dynamics of relaxation and decay processes in a systematic manner both in the spectral function of the initial-state core-hole (self-energies) and in the emission matrix elements (vertex corrections). We explicitly demonstrate that proper dressing of the emission matrix element guarantees that the sum of all branching ratios become unity (conservation of probability). Finally, we present numerical calculations of the 4p ^?1?4d ^?1 X-ray emission spectrum in Xe, illustrating the importance of a systematic treatment of self-energy and vertex corrections.