All-Order Methods for Relativistic Atomic Structure Calculations

Abstract

All-order extensions of relativistic atomic many-body perturbation theory are described and applied to predict properties of heavy atoms. Limitations of relativistic many-body perturbation theory are first discussed and the need for all-order calculations is established. An account is then given of relativistic all-order calculations based on a linearized version of the coupled-cluster expansion. This account is followed by a review of applications to energies, transition matrix elements, and hyperfine constants. The need for extensions of the linearized coupled-cluster method is discussed in light of accuracy limits, the availability of new computational resources, and precise modern experiments. For monovalent atoms, calculations that include nonlinear terms and triple excitations in the coupled-cluster expansion are described. For divalent atoms, results from second-and third-order perturbation theory calculations are given, along with results from configuration-interaction calculations and mixed configuration interaction-many-body perturbation theory calculations. Finally, applications of all-order methods to atomic parity nonconservation, polarizabilities, C 3 and C 6 coefficients, and isotope shifts are given.

Electric quadrupole moments of metastable states ofCa+,Sr+, andBaJiang1, Arora2, Safronova3 2008Phys. Rev. A344400View full textAdd to dashboardCite

“…The relativistic all-order method is one of the most accurate methods used for the calculation of atomic properties of monovalent systems (see Ref. [21] for a review and references therein). The lifetimes of the 3d levels in Ca + calculated in this approach and estimated to be accurate to 1% were found to be in agreement with the high-precision experiment [22].…”

Relativistic effects on the hyperfine structures of2p4(3P)3p2Do,<

“…When both methods produce similar results, the first approach (MCHF-BP) offers some advantages compared with the second one (MCDHF). The analysis of the relative orbital, spin-dipole and contact contributions, that is difficult in the MCDHF framework [66,67] and that becomes impossible when using the simple form of the magnetic dipole operator (27), sheds indeed some light in the origin of the large J-dependency of relativistic effects, as we explicitly illustrate in the present work.…”

“…As a nine-electron atom, it definitely lies outside the "few"-electron systems domain for which the elaborate variational calculations in Hylleraas coordinates can be successfully applied, usually giving rise to the most reliable expectation values [23][24][25]. Moreover, taken in its 2p 4 3p excited configuration, neutral fluorine consitutes a difficult target for many-body approaches that are often restricted to single-or two-valence atoms or ions [26][27][28]. The coupled-cluster theory is promising [29][30][31] but investigation of hyperfine structures in more complex systems remains scarce [32].…”

Black-body radiation shifts and theoretical contributions to atomic clock research

“…The relativistic all-order method including single, double, and partial valence triple excitations (or LCCSDpT) was applied to accurate calculations of energies, transition amplitudes, hyperfine constants, static and dynamic electricdipole polarizabilities, quadrupole and octupole polarizabilities, magic wavelengths, atomic quadrupole moments, C 3 and C 6 coefficients, isotope shifts and other properties of monovalent atoms (Li, Na, Mg II, Al III, Si IV, P V, S VI, K, Ca II, In, In-like ions, Ga, Ga-like ions, Rb, Cs, Ba II, Tl, Fr, Ra II, Th IV, other Fr-like ions, Ra II ) as well as the calculation of parity-violating amplitudes in Cs, Fr, and Ra + . We refer the reader to review [29] and references therein for a detailed description of this method, its extensions, and applications. The relativistic all-order method is applicable to the calculation of the monovalent systems, i.e.…”

“…The scaling procedure is described in Ref. [29]. Briefly, the single valence excitation coefficients are multiplied by the ratio of the corresponding experimental and theoretical correlation energies, and the matrix element calculation is repeated with the modified excitation coefficients.…”