Electronic Transitions of theFCenter in Alkali Halides

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Topological wave functions, in the form of localized free-electron orbitals, are used to describe the $F$ center in alkali halides of the NaCl structure. Previous calculations on the $F$-band transition energies are extended to the $K$ and $L$ bands, confirming that these are higher-energy trnasitions of the $F$ center. Oscillator strengths are calculated for the $F$ and $K$ bands. The model treats these bands as tangential excitations of the free-electron orbitals, and shows that the allowed radial transition correlates well with the $\ensuremath{\beta}$ band. The low transition energy and long lifetime of $F$ emission follows directly from the theory.