Spin-Orbit Effects in theFandKBands of Colored Alkali Halides

The effect of the spin-orbit interaction in the bound excited ${\Gamma }_4^{-}$ 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 RbCl $F$ center is carried out. The predictions include an $F$-band splitting of -15.3×${10}^{-3\mathrm{}}$ eV, a $K$-band splitting of -2.2×${10}^{-3\mathrm{}}$ eV, and an $F-K$ configuration interaction parameter of -3.8×${10}^{-3\mathrm{}}$ eV. These results are in good agreement with quantities derived from magneto-optic experiments.