Correlation and Relativistic Effects in Spin-Orbit Splitting

Relativistic many-body perturbation theory based on the no-pair Dirac-Coulomb-Breit Hamiltonian: Relativistic correlation energies for the noble-gas sequence through Rn (Z=86), the group-IIBatoms through Hg, and the ions of Ne isoelectronic sequence

“…In c-number theory, the projection operator takes into account the field-theoretic condition that the negative energy states are filled. Because the electron-electron interaction is approximated by the classical instantaneous Coulomb interactions, the no-pair DC Hamiltonian is deficient in that it is both noncovariant and inaccurate for precision calculation of fine-structure separations and binding energies of the inner-shell electrons [33,34]. A higher approximation involves modification of the instantaneous Coulomb interaction V, -.…”

“…The addition of the low-&equency Breit interaction to the instantaneous Coulomb interaction provides covariance of the efFective many-body Hamiltonian to first order and increases the accuracy in fine-structure splittings and inner-shell binding energies [33,34].…”

Atomic spectroscopy of trapped, highly charged, heavy ions

“…However, these results are close to experiment only up to Z = 36, and then they also deviate systematically. Near Z = 40, calculations by Huang et al [14] and by Vilkas et al [15] are doing well, but they do not extend to high Z. Much closer to experiment also in this high-Z range -though not in full agreement Fig.…”

“…In a, the deviation of the MCDF results obtained by Cheng et al [11] is most notable. In b, this trace has been left out, since the calculation by Huang et al [14] explicitly represents a numerical improvement over the CKD work. For further explanations, see the text compared to data recorded by the Chandra and XMM-Newton spacecrafts) and of plasma physics interest to precision determinations of the structure of few-electron ions.…”

Bromine iso-electronic sequence: Lifetimes of the 4p44d metastable level

“…Even if, in the relativistic case, the gauge independence cannot be achieved without including the negative energy states [14], it is unlikely that their contribution will be significant for the valence electrons considered here. Known from a long time [15], but explained only recently [16], relativistic LSJ levels will not always reduced to the same LS level in the formal limit of the speed of light going to infinity, thus leading to a potential bias in the fine structure splittings. For the present calculations this is a negligible contribution in the error of the transition energies since the offset in the LS levels is 13 cm −1 for the 4s 2 4p 5 configuration and 15 cm −1 for the 4s 2 4p 4 4d one.…”