Wave-functions overlap in stoichiometric lanthanide laser crystals

Two-center overlap integrals (TCOIs), 〈4f|4f〉 of symmetry types σ, π, δ, φ, 〈2s|4f〉, 〈2p|4f〉σ, and 〈2p|4f〉π, have been computed for 11 stoichiometric lasing lanthanide compounds: PrP4O15, NdP5O14, NdLiP4O12, NdAl3(BO3)4, NdNa5(WO4)4, NdK3(PO4)2, NdKP4O12, HoF3, Ho3Al5O12, Er3Al5O12, and ErP5O14. Four-term (4-t) and six-term (6-t) SCF Slater-type orbitals have been employed for Ln3+ at mean distances Ln3+-Ln3+ and Ln3+-ligand. Different results for ion pair overlap have been obtained by using 4-t or 6-t wave functions of Pr3+ and Nd3+. The TCOIs have been correlated with measured lifetimes of laser transitions of Pr3+, Nd3+, Ho3+, and Er3+ in the mentioned crystals.