Rare-Earth Ions in the Alkali Halides. III. Electron-Lattice Coupling and the Details of the Vibronic Spectra

Electron-lattice interaction is discussed for the case of rare-earth ions in the alkali halides. A selection rule is derived to show that for the present defect electronic transitions can be coupled only to vibrational modes of $A_1$ symmetry. Under the assumption of electrostatic coupling between the electron and the lattice vibrations, a coupling function is derived which is proportional to the projection of the field of the electron under-going a transition on to the eigenvectors of the vibrations. It is further shown that this coupling function can be determined from the details of the structural form of the vibronic spectra. A number of other features of the vibronic spectra are accounted for through the properties of Franck-Condon integrals.