When $F$ light is absorbed by $F$ centers it is assumed that electrons leave negative-ion vacancies and are transferred to the conduction band. Conduction electrons may be captured by holes and by negative ion vacancies. It is assumed that the cross sections for the latter two processes are equal and that the conduction electron concentration is small and stationary. Under these conditions the local $F$-center concentration, $n$, is specified by the equation $\frac{\partial n}{\partial t}=-bI{n}^2$, where $I$ is the local $F$-light intensity assumed to be given by the Beer-Lambert law and $b$ is a constant. Exact expressions for $n$ and $I$ have been obtained for the case of a uniform initial $F$-center distribution. The theoretical results are compared with quantitative measurements of the $F$-center concentration as a function of $F$-light irradiation time in x-rayed NaCl for a range of incident light intensities and initial $F$-center concentrations. It is found that the behavior of the model is consistent with experimental data in lightly x-rayed crystals having initial concentrations in the range ∼${10}^{16}$-∼${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$. In more heavily x-rayed crystals, appreciable growth of $M$ and $R$ bands occurs during the bleaching and deviations from the behavior of the model are observed.

• Received 24 March 1955

DOI:https://doi.org/10.1103/PhysRev.99.435