Theoretical study of ground-state configurations 4f^Nin Nd IV, Pr IV and Nd V

Abstract

Although the trivalent lanthanide ions embedded in compounds have a wealth of applications in laser physics and the lighting industry, the theoretical interpretation of their ground-state configurations 4fN in the free ion spectra was restricted by the lack of experimental data. In the first part of this paper, the present status of their group-theoretical description and prospects for improvement are given. In the second part, this description is applied for the first time to a truly isolated configuration 4f3 in Nd IV by performing a parametric fit of level energies, taking into account Coulomb and spin-dependent interactions beyond the first order of perturbation. A root mean square (rms) deviation 5.39 cm−1 (i.e. 1/13 000 of the energy spread of the configuration) is obtained with 23 free parameters and 41 newly determined levels. The contributions of all parameters to the level energies are detailed for the first time. It is shown that energy shifts caused by the effective electrostatic parameters related to the third order of perturbation amount to about 10−3 of the total energy spread of the configuration 4f3. As concerns spin-dependent operators, the relative contributions of the spin–orbit interaction (SO), of the combined effects of spin–other-orbit and configuration interaction (SOO + CI) and of the spin–spin interaction (SS) are in the ratios 571:12:1. The Marvin integrals derived from the experimental energies are in a very good agreement with Hartree–Fock estimates. The ground-state configurations 4f2 of Pr IV and of the newly analysed spectrum Nd V are studied with the same methods.

Parametrization of free ion levels of four isoelectronic 4f2 systems: Insights into configuration interaction parameters

“…The 4f 2 free ion energy level data were taken from Sugar [8] and they have previously been analyzed by Wyart et al [11] using 10 adjustable parameters. Other previous studies have been described by Yoca and Quinet [17], who also fitted the Pr 3+ data set.…”

“…The recent fit to Pr 3+ free ion data by Wyart et al [11] employed M 0 = 1.663 ± 0.061 cm À1 , with the ratios M 0 :M 2 :M 4 constrained to the values as herein, but using the additional freely-varied parameter P 0 (with P 2 also varied, but the ratios with P 4 and P 6 constrained). The fitted value of f 4f was 763.0 cm À1 .…”

“…Currently, there is renewed interest, both experimentally and theoretically, in free ion energy levels and the Wyart group has been particularly active in this respect [11][12][13][14][15]. Tabulations of atomic energy levels are available at the National Institute of Standards and Technology (NIST) web site [16].…”

Relativistic Hartree–Fock calculations of transition rates for allowed and forbidden lines in Nd IV

“…In this latter work, theoretical values of lifetimes and transition probabilities, computed with a rather limited relativistic Hartree-Fock (HFR) model, were reported. Furthermore, Wyart et al (2008) carried out a detailed theoretical investigation of the 4f 3 configuration in Nd IV by performing a parametric fit of level energies, taking into account Coulomb and spin-dependent interactions beyond the first order of perturbation. Note also that systematic Hartree-Fock and relativistic configurationinteraction studies of energy levels and lifetimes of some triply ionized lanthanides, including Nd 3+ , were published by Dzuba et al (2003).…”

Atomic structure calculations and beam-foil observations of La IV

“…Observations of inner-shell excited configurations in triply ionized cerium Ce 3+ have also been reported very recently by Reader and Wyart [9]. Theoretical investigations of 4f N ground-state configurations have been carried out in Nd IV and Pr IV [10].…”