Structure of theA,B, andCAbsorption Bands in KCl: Tl

Abstract

A twelvefold dengenerate perturbation technique is used to determine wave functions and eigenenergies of the first excited state of ${\mathrm{Tl}}^{+}$ in an $O_h$ field. The governing Hamiltonian includes exchange, spin-orbit, static $O_h$, and dynamic electron-lattice interactions. This dynamic interaction is approximated by a term linear in the lattice coordinates. The resulting 12 × 12 interaction matrix is numerically diagonalized, yielding eigenfunctions and eigen-energies as functions of lattice coordinates. These results are used to determine transition probabilities and oscillator strengths for transitions from the $6s^2$ ground state to the $6s6p$ excited state. The main conclusions reached are (a) the $A$, $B$, and $C$ bands are composed of subsidiary temperature-dependent bands. The $A$ band is a doublet at low temperature and a triplet at higher (300°K) temperatures. The $C$ band is a triplet at all temperatures, and the $B$ band is a strongly temperature-dependent doublet. (b) The $C$- and $A$-band oscillator strengths are almost constant over a wide range of temperature. However, the $C$-band oscillator strength decreases at very high temperatures. (c) The $B$-band oscillator strength is a rapidly increasing function of temperature, and its shape is not Gaussian or near-Gaussian at higher temperature. (d) No transitions occur from the ground state to the ${}_{}{}^2{}_{}{}^{}P_0^{}{}_{}{}^{}$ (i.e., $|{}_{}{}^3{}_{}{}^{}A_1^{}{}_{}{}^{}u〉$) state.