Theory of Photochromic Centers in CaF2

On the basis of recent optical and EPR work, it has been suggested that the ionized and thermally stable photochromic centers in Ca${\mathrm{F}}_{2}$ consist of one and two electrons bound at an anion vacancy adjacent to a trivalent impurity cation. For the ionized center, we have shown that the energy levels and wave functions of the isolated $F$ center are not strongly perturbed by the introduction of the impurity ion. Since the divalent ions of the impurities which are found to form these centers, i.e., Y, La, Ce, Gd, Tb, and Lu, have low-lying $s$ and $d$ valence orbitals which overlap the $F$-center wave functions, we have investigated the defect-impurity orbitals which may be formed from a linear combination of $F$ electron orbitals and these impurity orbitals. The predictions based on this defect-impurity orbital description are found to be consistent with the optical and EPR data for the stable and ionized photochromic centers.