Crystalline Field Selection Rules: The Effect of Vibration-Electronic Interaction

Abstract

It is pointed out that the selection rules for stationary ions in crystalline electric fields are violated for many transitions in the neodymium bromate and ethylsulfate absorption spectra, making it impossible consistently to assign irreducible representations to crystalline levels. The appearance of spectral lines not obeying the usual crystalline field selection rules is assumed to be due to the interaction of the vibration of the rare earth ion or ion-water complex with its electronic motion about the nucleus. The theory of such an interaction is presented and selection rules derived for D3h, C3v, D3, C3, and C3h local symmetries about the equilibrium position. It is found that the vibration interaction can account for the type of violations seen and with intensities that are probably comparable to some allowed pure electronic transitions. A satellite structure, which is a consequence of the vibration-electronic interaction, is predicted for all spectral lines except transitions between upper and lower J = ½ or J = 0 levels. Such a structure may be manifested experimentally as a high-temperature ``line width.'' Such satellites of pure electronic transitions should obey the same selection rules and have the same Zeeman effect as the ``parent'' pure electronic transition. The intensity of the individual satellite components of a line does not depend on the strength of the vibration-electronic interaction but only on the Boltzmann factors of their lower state and on the intensity of the parent line.