Violation of electronic optical selection rules in x-ray emission by nuclear dynamics: Time-dependent formulation

The resonant photon emission following the excitation of a highly symmetric system to core-excited electronic states is discussed within a time-dependent formulation. Two types of vibrational modes—localizing modes and symmetry breaking but nonlocalizing modes—are considered, named according to their impact on dynamical symmetry breaking and localization accompanying the process. The decay rates are proportional to the population of a coherent superposition of the relevant core states vibronically coupled via the appropriate vibrational modes. This population is essentially a product of partial contributions of the two types of vibrational modes mentioned above. The general arguments are illustrated on the CO2 molecule. Here, the bending mode is the symmetry breaking but nonlocalizing mode and the asymmetric stretching mode is the localizing mode. The decay rates and total resonant photon emission intensities are calculated in the leading terms approximation of the potential matrix Hamiltonian. The impact of the asymmetric mode on localization and hence on the optical selection rules as a function of time is discussed in detail. It is shown that the vibronic coupling via the bending mode changes the polarization of the emitted light and exerts an impact on the effect of vibronic coupling via the asymmetric stretching mode.