Analytic wave functions and oscillator strengths for Ce3+, Pr3+, Nd3+, and Cu2+

Abstract

Accurate analytical self-consistent field (SCF) wave functions are presented for the ground state and some excited states of Ce3+ (Z=58), Pr3+ (Z=59), and Nd3+ (Z=60). The accurate results for the excited states are available for the first time. The wave functions for these ions were used to compute the total weighted electric dipole oscillator strength gtf for optical transitions between various states of these ions. The oscillator strengths were calculated so as to include the entire relaxation effect of the charge cloud. We expect that these results will be helpful in the specification of the intensities of the lines present in the free-ion spectra of the above lanthanides. It was found that the formulae for the relative line and multiplet strengths, as derived by use of Racah's algebra of tensor operators, apply rigorously even when one includes the relaxation effect due to the overlap between the transiting and non-transiting electrons. To test our results for oscillator strengths, the analytical SCF procedure was also employed in the calculation of the wave functions and energies for the 1s, 2p, and 3p hole states of Cu+ (Z=29); the resulting wave functions were applied in a theoretical determination of the K_alpha/K_beta X-ray intensity ratio in Cu2+; very good agreement with experiment was obtained .