KX-Ray Emission from KCl

Details of the $K$ x-ray emission spectra of ${\mathrm{K}}^{+}$ and ${\mathrm{Cl}}^{-}$ in KCl are discussed. It is shown that the valence hole is effectively localized to one atomic site during the lifetimes of both the potassium and chloride $1s$ holes. This localization is found to be an appreciable factor in the processes contributing to the emission. Calculations of the relative intensity of the cross-transition lines, of the type $1{s_K}^{-1\mathrm{}}\to 3{p_{C1\mathrm{}}}^{-1\mathrm{}}$, $K{\beta }_5$, are reported. The results of the calculations agree, to within 40%, with the observed values. The widths of the valence emission lines, due to the transitions $1{s_K}^{-1\mathrm{}}\to 3{p_{C1\mathrm{}}}^{-1\mathrm{}}$ and $1{s_{C1\mathrm{}}}^{-1\mathrm{}}\to 3{p_{C1\mathrm{}}}^{-1\mathrm{}}$, $K{\beta }_{1,3}$ are considered. Because of the localization of the final hole state, both initial and final hole states of the $K{\beta }_{1,3}$ transition see the same crystal potential, and thus there is no first-order broadening due to spatial variation of that potential. This is not the case for the cross-transition line $K{\beta }_5$. A model due to Dexter is then used to show that the corrected width of the $K{\beta }_5$ line should be about 0.5 eV greater than that for $K{\beta }_{1,3}$. This corresponds to the observations made by Deslattes.