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 deg. and 45 deg., 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 4f7 5d 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)A1g → (5D4)A1g 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)A1g → (5D4)Eg TPA transition line strength have been separated, and the latter effect is shown to be more important for the transition investigated