Calculation of the Phonon Sideband of theRLine in MgO:Cr3+

A calculation of the phonon sideband associated with the ${}_{}{}^2{}_{}{}^{}E_g^{}{}_{}{}^{}\to {}_{}{}^4{}_{}{}^{}A_{2g}^{}{}_{}{}^{}$ transition of a ${\mathrm{Cr}}^{3+}$ ion at a cubic site in MgO is presented. The short-range coupling model used and the method of calculation follow closely those used in a previous calculation of the sidebands for MgO: ${\mathrm{V}}^{2+}$ and MgO: ${\mathrm{Ni}}^{2+}$. Satisfactory agreement with experiment is obtained by assuming that only displacements of the impurity ion and its nearest neighbors are coupled to the electronic transition. Differences between the coupling for the ${\mathrm{Cr}}^{3+}$ ion and that for the divalent ions are discussed as is the validity of the assumption of short-range coupling.