Theory for resonant X-ray emission of core excitons with lattice relaxation: changeover from shallow to deep level

A simple model is proposed for the X-ray emission of core excitons which is accompanied by a strong lattice relaxation. The effect of electron itinerancy in the conduction band is taken into account in addition to that of a local attractive potential and the lattice deformation. The X-ray absorption and the emission spectra are calculated exactly. It is shown that, as the lattice deformation goes on, the wave function of the exciton shrinks and the effective electron-phonon interaction changes from the weak coupling regime to the strong coupling regime