Spectral characteristics of zero-phonon transitions in crystal impurities: A diagrammatic approach

The zero-phonon line shape of a localized transition in a crystal is treated by use of a general interaction between the local transition and the lattice phonons with the harmonic approximation. The theory is carried out to infinite order perturbation by diagrammatic techniques and is thus valid for arbitrarily large phonon coupling. Within our model it is found that the spectral characteristics of the zero phonon line and their temperature dependence are due to resonant Raman-ike phonon scattering processes which cause a decay of the phase coherence of the excitation. The line shape due to this mechanism is found to be lorentzian, and its width increases with temperature, but is zero at 0 K. The line position is also a function of temperature.