Bound-Electron-Lattice Coupling and Vibronic Spectra

The radial extent of the coupling between the bound electronic states of a defect ion in a crystal and the vibrations of the lattice ions is investigated. An electrostatic-coupling model is used to evaluate the electronlattice interaction. It is found that those electronic transitions which involve a change in configuration are coupled primarily to the vibrations of ions in the immediate vicinity of the defect. Consequently, if there exist local or pseudolocalized vibrations, the resultant vibronic spectra are dominated by transitions to vibrational modes which have high local amplitude. In contrast, it is found that in general, electronic transitions within a configuration are coupled to nonlocalized vibrations as well as to the localized vibrations. In the special case of the transition ${}_{}{}^5{}_{}{}^{}D_0^{}{}_{}{}^{}\to {}_{}{}^7{}_{}{}^{}F_0^{}{}_{}{}^{}$ of ${\mathrm{Sm}}^{2+}$, the coupling is primarily to nonlocalized vibrations, so that the vibrations resemble those of ions of the undisturbed lattice. The observed vibronic structure accompanying this transition of ${\mathrm{Sm}}^{2+}$ in the alkali halides is presented. A comparison is made for ${\mathrm{Sm}}^{2+}$: KBr between the singularities in the phonon density of states as observed in the vibronic structure, and those predicted from the published dispersion curves of KBr obtained from neutron-scattering data. The agreement is found to be very good. The vibronic structure accompanying the same transition of ${\mathrm{Sm}}^{2+}$ in the alkaline-earth halides is also discussed.