Analysis of the off-center effect ofCu+in alkali halides using crystal-field theory

We have found that the relative intensity of the ${}_{}{}^1{}_{}{}^{}\mathrm{A}_{1\mathrm{g}}^{}{}_{}{}^{}$ ${\to }^1$ ${\mathrm{E}}_{\mathrm{g}}$ and ${}_{}{}^1{}_{}{}^{}\mathrm{A}_{1\mathrm{g}}^{}{}_{}{}^{}$ ${\to }^1$ ${\mathrm{T}}_{2\mathrm{g}}$ crystal-field components of the 3$d^{10}$→3$d^9$4s transition of ${\mathrm{Cu}}^{+}$ in alkali halide hosts provides a measure of the ${\mathrm{Cu}}^{+}$ ground-state off-center displacement along the [111] axis. This is shown by deriving the crystal- field potential that describes the off-center effect of ${\mathrm{Cu}}^{+}$, and then calculating the transition moments to the ${}_{}{}^1{}_{}{}^{}\mathrm{E}_{\mathrm{g}}^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}\mathrm{T}_{2\mathrm{g}}^{}{}_{}{}^{}$ final states. By analyzing the spectra of ${\mathrm{Cu}}^{+}$ in numerous alkali halide hosts, it is found that the degree of off-center displacement increases with the lattice constant of the alkali halide.