Many-body perturbation-theory formulas for energy levels of excited states of closed-shell atoms

Avgoustoglou, E.; Wr, Johnson; Dr, Plante; Sapirstein, J.; Sheinerman, S.; Sa, Blundell

doi:10.1103/physreva.46.5478

Cited by 36 publications

(59 citation statements)

References 11 publications

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“…In Table 3, we present results for the zeroth-, first-, and second-order Coulomb contributions, E (0) , E (1) , and E (2) , and the first-and second-order Breit-Coulomb corrections, B (1) hf and B (2) . It should be noted that corrections for the frequency-dependent Breit interaction [23] are included in the first order only.…”

Section: Example: Energy Matrix For W 46+mentioning

confidence: 99%

“…Relativistic many-body perturbation theory (RMBPT) was used recently to study atomic characteristics of particle-hole excitations of closed-shell ions [1][2][3][4][5][6]. In the first of these studies, energies [1][2][3] and oscillator strengths [4] in Ne-like ions were considered by Avgoustoglou et al Reduced matrix elements, oscillator strengths, and transition rates into the ground state for all allowed and forbidden electric-and magnetic-dipole and electric-and magnetic-quadrupole transitions (E1, M1, E2, M2) in Ne-like ions were presented by Safronova in ref.…”

Section: Introductionmentioning

confidence: 99%

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E1, E2, M1, and M2 transitions in the nickel isoelectronicsequence

Hamasha¹,

Shlyaptseva

Safronova³

2004

Can. J. Phys.

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A relativistic many-body method is developed to calculate energy and transition rates for multipole transitions in many-electron ions. This method is based on relativistic many-body perturbation theory (RMBPT), agrees with MCDF calculations in lowest order, includes all second-order correlation corrections, and includes corrections from negative-energy states. Reduced matrix elements, oscillator strengths, and transition rates are calculated for electric-dipole (E1) and electric-quadrupole (E2) transitions, and magneticdipole (M1) and magnetic-quadrupole (M2) transitions in Ni-like ions with nuclear charges ranging from Z = 30 to 100. The calculations start from a 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 Dirac-Fock potential. First-order perturbation theory is used to obtain intermediate-coupling coefficients, and second-order RMBPT is used to determine the matrix elements. The contributions from negative-energy states are included in the second-order E1, M1, E2, and M2 matrix elements. The resulting transition energies and transition rates are compared with experimental values and with results from other recent calculations.Résumé : Nous développons une méthode relativiste à N corps pour calculer l'énergie et les taux de transitions multiples dans les atomes multi-électroniques. Cette méthode, qui est basée sur la théorie perturbative relativiste (RMBPT), est en accord avec les calculs MCDF à l'ordre le plus bas, inclut toutes les corrections de corrélation du second ordre et les corrections pour les états d'énergie négative. Nous calculons les éléments de matrice réduits, les forces d'oscillateur et les taux de transition pour les transitions dipolaires électriques (E1), dipolaires magnétiques (M1), quadripolaires électriques (E2) et quadripolaires magnétiques (M2) dans les ions de type Ni avec charges nucléaires dans le domaine Z = 30-100. Le calcul démarre avec un potentiel Dirac-Fock 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 . Nous utilisons les perturbation au premier ordre pour obtenir les coefficients de couplage intermédiaire et au deuxième ordre RMBPT pour obtenir les éléments de matrice. Les contributions des états d'énergie négative sont inclues dans les éléments de matrice E1, M1, E2 et M2. Nous comparons nos énergies et taux de transition avec les résultats expérimentaux et avec les résultats calculés par d'autre sauteurs.[Traduit par la Rédaction]

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Section: Example: Energy Matrix For W 46+mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

E1, E2, M1, and M2 transitions in the nickel isoelectronicsequence

Hamasha¹,

Shlyaptseva

Safronova³

2004

Can. J. Phys.

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“…[33,42] for calculation of radiative electric-dipole, electric-quadrupole, magneticdipole, and magnetic-quadrupole rates in Ne-and Ni-like systems. We will present here only the model space for Ni-like ions without repeating the detailed discussions given in [38,39], [40], [41], and [33,42]. The calculations are carried out using sets of basis Dirac-Hartree-Fock (DHF) orbitals.…”

Section: Methodsmentioning

confidence: 99%

“…[38,39] for calculation of energies of hole-particle states, in Ref. [40] for calculation of energies of particle-particle states, in Ref.…”

Section: Methodsmentioning

confidence: 99%

Relativistic many-body calculations of multipole (E1, M1, E2, M2, E3, and M3) transition wavelengths and rates between 3l−14l′ excited and ground states in nickel-like ions

Safronova

Hamasha

et al. 2006

Atomic Data and Nuclear Data Tables

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“…(3) and used in the order-by-order RayleighSchrödinger perturbation expansion of the atomic state energies E and other properties such as oscillator strengths. An example of the reduction of the perturbation expansion to MBPT formulas using Feynman diagrams and second-quantization method is given in Avgoustoglou et al (1992) for closed-shell atoms. For processes involving the continuum, the continuum atomic state function Ψ(ε) for the (N +1)-electron system has to be evaluated,…”

Section: Fig 6 Fit To a 3×10mentioning

confidence: 99%

Atomic data for x-ray astrophysics

2007

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We review the available atomic data used for interpreting and modeling X-ray observations. The applications for these data can be divided into several levels of detail, ranging from compilations which can be used with direct inspection of raw data, such as line finding lists, to synthetic spectra which attempt to fit to an entire observed dataset simultaneously. This review covers cosmic sources driven by both electron ionization and photoionization and touches briefly on planetary surfaces and atmospheres. We review all of this, the applications to X-ray astronomy, the available data, recommendations for astronomical users, and attempt to point out the applications where the shortcomings are greatest.

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Many-body perturbation-theory formulas for energy levels of excited states of closed-shell atoms

Cited by 36 publications

References 11 publications

E1, E2, M1, and M2 transitions in the nickel isoelectronicsequence

E1, E2, M1, and M2 transitions in the nickel isoelectronicsequence

Relativistic many-body calculations of multipole (E1, M1, E2, M2, E3, and M3) transition wavelengths and rates between 3l−14l′ excited and ground states in nickel-like ions

Atomic data for x-ray astrophysics

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