Theory of Spin-Orbit Effects in theFBand in Alkali Halides

A calculation of the spin-orbit splitting of the first optically excited state of the $F$ center is reported. It is based on a tight-binding, static lattice model of the crystal and assumes a vacancy-centered electronic wave function for the $F$ center. To satisfy the Pauli principle, the $F$-center state must be orthogonalized to the occupied states of the crystal. This modifies the vacancy-centered wave function by introducing states localized about the ions. These states undergo a spin-orbit interaction in the fields of the ionic nuclei, causing a splitting of the $F$ band into two components. Explicit calculations for NaCl predict splittings of about 0.008 eV with the $P_{\frac{1}{2}}$ state lying above the $P_{\frac{3}{2}}$ state. This is in good agreement with the observed splittings. The calculations indicate that the spin-orbit splitting is determined primarily by the halide ion in the halides of light alkalies and generally increases with the atomic number of both ions. It further suggests that the structure in the $F$ band of the cesium salts is due, at least in part, to a spin-orbit splitting.