The effect of the spin-orbit interaction in the bound excited I 4 states of the F center is investigated within the framework of the semicontinuum F-center model. Assuming the K band arises from allowed transitions, expressions for the K-band spin-orbit splitting and the F-K spin-orbit configuration interaction are found using vacancy-centered F-center model wave functions orthogonalized to the core states of neighboring ions. A simple physical picture for the variation of the spin-orbit splitting with state of excitation is developed and the spin-orbit splitting of the highly excited states is shown to vary as the inverse cube of the principal quantum number. A detailed numerical calculation for the RbC1 F center is carried out. The predictions include an F-band splitting of -15.3 x10 3 eV, a K-band splitting of -2.2 x10+ eV, and an F-K configuration interaction parameter of -3, 8x10 3 eV. These results are in good agreement with quantities derived from magneto-optic experiments.
%. INTRODUCTIONThe optical absorptions and emissions for electronic transitions of color centers in solids are generally broadened into bands by the electronphonon interaction. The typical optical spectrum of a color center consequently does not show any of the fine structure that may be present in the center's electronic energy levels. However, in the past few years it has been found that this fine structure may be resolved by external-field techniques. ' " These techniques were first applied to the F center in magneto-optical studies that disclosed an unexpectedly large and negative spinorbit splitting in the E band. ' ' In addition, these investigations yielded unrelaxed excited-state g factors, ' and the relative contribution of cubic and noncubic lattice vibrations to the broadening of the F band Spin-orbit structure has also been found in magneto-optic experiments" ' on the K-band absorption"' of the E center. This is of particular interest because of the controversy surrounding assignment of this band to specific transitions. In the present paper we shall investigate the theory of spin-orbit effects for this absorption.Briefly, the K band is a small absorption found in association with the F band in many alkali halides. Typically it lies a few tenths of an eV higher in energy than the F band, but has an oscillator strength roughly one-tenth as great. '~T he K band is best resolved in RbCl, and in those salts in which it is not resolved it probably comprises the long high-energy tail of the E band. There has been much speculation as to the nature of the K absorption, but Chiarotti and Grassano" established by modulation of the F-center ground-state population that the K band involves transitions from the F-center ground state. Independent evidence for this is given by the observations of d'Aubignd and Gareyte" and of Henry' that magneto-optic effects in the K band have the same spin-relaxation time as the F-center ground state. The situation with respect to the final excited state involved is not as clear. The two most widely disc...