A systematic investigation of the optical properties of several ions with the $s^2$ configuration (${\mathrm{In}}^{+}$, ${\mathrm{Sn}}^{2+}$, ${\mathrm{Tl}}^{+}$) dissolved in KCl, KBr, and KI has shown that the $B$ band, which is the weakest of the three bands that are clearly separated from the fundamental absorption edge, generally has observable structure, particularly at low temperatures. Whereas no structure could be detected for KBr:${\mathrm{Tl}}^{+}$, a doublet structure was observed for KCl:${\mathrm{In}}^{+}$, KBr:${\mathrm{In}}^{+}$, and KCl:${\mathrm{Sn}}^{2+}$, and a triplet structure for KBr:${\mathrm{Sn}}^{2+}$ and KI:${\mathrm{Sn}}^{2+}$. As the temperature is raised the $B$ band shifts to longer wavelengths in KBr:${\mathrm{Sn}}^{2+}$, KI:${\mathrm{Sn}}^{2+}$, and KBr:${\mathrm{Tl}}^{+}$, while it shifts to shorter wavelengths in KBr:${\mathrm{In}}^{+}$ and KCl:${\mathrm{In}}^{+}$, the magnitude of these shifts being proportional to $T$. In all the crystals examined the $B$-band intensity increases with temperature as expected for vibration-induced transition. The theoretical line shape for the $B$ band is discussed on the basis of various models, and it is concluded that the transition responsible is ${}_{}{}^1{}_{}{}^{}A_{1g}^{}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}T_{2u}^{}{}_{}{}^{}$ assisted principally by modes of $T_{2g}$ symmetry, but that $A_{1g}$ and $E_g$ modes also play a part. It is also concluded that mixing of the $|A〉$ and $|C〉$ states with ${}_{}{}^3{}_{}{}^{}T_{2u}^{}{}_{}{}^{}$ is the cause of the observed asymmetry in the $B$ band. The position of the $B$ band with respect to the $A$ and $C$ bands is related to the dipole strengths of these bands and the shift of the $B$-band maximum with temperature is due to the quadratic term in the Hamiltonian which is the second-order perturbation from the $A$ and $C$ states.

• Received 26 February 1973

DOI:https://doi.org/10.1103/PhysRevB.8.1698