Vibrational Coupling of Nearly Degenerate Electronic States

An anomalously large interval between lines of a vibrational series has been observed in the vibronic part of the absorption spectra of NaCl, KCl, and RbCl containing ${\mathrm{Eu}}^{2+}$ ions. Many details of these anomalous spectra can be accounted for through a vibrational coupling of two nearly degenerate excited electronic states, each belonging to a different electronic configuration. The analysis of the vibrational coupling is simplified by the fact that the point symmetry of the rare-earth defect admits only nondegenerate states. Consequently, a theorem by Neumann and Wigner requires that any two electronic states may not cross each other under variations of one vibrational coordinate, although they may approach each other. Furthermore, the Born-Oppenheimer approximation applies, if it is assumed that the states do not approach each other by less than a typical vibrational quantum. Under these circumstances, the vibrational potential can be defined for each of the pertinent electronic states, and the corresponding vibronic spectra determined in detail. It is shown that one of the coupled states has associated with it a strongly increased vibrational frequency. In addition, the selection rule $\Delta m=0, \pm 2\cdots$ applies for absorptive transitions to the vibrational components of this state. Together these facts account for the observed anomalous line interval. The other coupled state has associated with it a decreased vibrational frequency. However, the transition probability to this state is shown to be very small, in agreement with the fact that the corresponding transitions are not observed experimentally. The observed emission spectrum is also accounted for in the analysis.