Theoretical analysis of the two-photon absorption spectrum of Tb³⁺ in Cs₂NaTbCl₆

Eighteen selected two-photon absorption (TPA) transition line strengths with polarization angles θ = 0° and 45°, spanning several orders of magnitude, have been calculated for the Tb³⁺ ion in the cubic host Cs₂NaTbCl₆. The results are in reasonable agreement with experimental results in the literature. The calculation utilized the crystal field (CF) wavefunctions for the initial and final states of the 4f⁸ configuration, and utilized free ion or CF wavefunctions (with the corresponding energies) for 4f⁷ core states of the whole intermediate 4f⁷5d configuration comprising 34 320 states. The intensities of certain transitions were found to be very sensitive to the inclusion of the CF interaction within the 4f⁷ core. In contrast to previous fourth- or third-order calculations of the TPA transition line strength of the strong transition (⁷F₆)A_1g → (⁵D₄)A_1g using pure Russell-Saunders (RS) wavefunctions for the |⁷F₆> initial and <⁵D₄| final states, our second-order direct calculation shows that the admixed RS wavefunctions |[⁷F₆]> and <[⁵D₄]| must be used to account for its high intensity. The effects of CF interactions within the 4f⁷ core, i.e. J-mixing and CF energy level splitting, upon the (⁷F₆)A_1g → (⁵D₄)E_g TPA transition line strength have been separated, and the latter effect is shown to be more important for the transition investigated.