Atomic structure calculations for Tm2+ and Tm3+

Abstract

The self-consistent field (SCF) expansion method was employed to calculate accurate analytical SCF wave functions for the ground states of the ground configurations of two laser-active ions, Tm 2+, 4f13 , 2F and Tm3+, 4f12 , 3H, (Z=69). Calculations were also performed for the 3H-ground state of the excited configuration 4d9 4f13 of Tm3+. An amended computer program was used to accommodate atomic systems with 4f orbitals. All of the basis function exponents were optimized carefully and repeatedly. Convergent SCF results were obtained for the six excited states of the ground configuration 4f12 and for seven excited states of the excited configuration 4d9 4f13 of Tm3+. The calculated orbital wave functions for both ions are available for the first time. The analytical SCF wave functions for Tm2+ and Tm3+ were utilized to compute the free-ion energy levels of these two ions, without using any empirical or semi-empirical parameters. In these calculations energy matrices, which include the electrostatic, spin-orbit, orbit-orbit and spin-other-orbit interactions, were constructed and diagonalized. Spin-orbit coupling constants for Tm2+ and Tm3+ are presented. The free-ion energy level assignments are compared with experimental data extrapolated from solution and crystal spectra.