Theory of relativistic effects on atoms: Configuration-space Hamiltonian

Mittleman, Marvin H.

doi:10.1103/physreva.24.1167

Cited by 314 publications

(173 citation statements)

References 12 publications

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“…[31][32][33][34]. In this Hamiltonian, the electron kinetic and rest energies are from the Dirac equation and the potential energy is the sum of Coulomb and Breit interactions.…”

Section: Relativistic Many-body Perturbation Theorymentioning

confidence: 99%

All-Order Methods for Relativistic Atomic Structure Calculations

Safronova¹,

Johnson²

2008

Advances in Atomic, Molecular, and Optical Physics

116

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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.

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“…[31][32][33][34]. In this Hamiltonian, the electron kinetic and rest energies are from the Dirac equation and the potential energy is the sum of Coulomb and Breit interactions.…”

Section: Relativistic Many-body Perturbation Theorymentioning

confidence: 99%

All-Order Methods for Relativistic Atomic Structure Calculations

Safronova¹,

Johnson²

2008

Advances in Atomic, Molecular, and Optical Physics

116

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“…In order to obtain a correct relationship between many-body methods and quantum electrodynamics (QED) [17,18,19,20], one should start from the no-pair Hamiltonian…”

Section: Calculation Of Atomic Wave Functions and Energiesmentioning

confidence: 99%

Relativistic calculation of two-electron one-photon and hypersatellite transition energies for 12 Z 30 elements

Martins

Costa

Santos

et al. 2004

J. Phys. B: At. Mol. Opt. Phys.

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“…In the no virtual-pair approximation, the excitations are limited to positive-energy eigenstates of H. [17,18,19,20] The eigenstates of a divalent system having angular momentum (J, M ) are described by the coupled states…”

Section: Theoretical Methodsmentioning

confidence: 99%

Third-order many-body perturbation theory calculations for the beryllium and magnesium isoelectronic sequences

Johnson

Blundell

et al. 2006

Phys. Rev. A

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Relativistic third-order MBPT is applied to obtain energies of ions with two valence electrons in the no virtual-pair approximation (NVPA). A total of 302 third-order Goldstone diagrams are organized into 12 one-body and 23 two-body terms. Only third-order two-body terms and diagrams are presented here, owing to the fact that the one-body terms are identical to the previously studied third-order terms in monovalent ions. Dominant classes of diagrams are identified. The model potential is a Dirac-Hartree-Fock V N−2 potential, and B-spline basis functions in a cavity of finite radius are employed in the numerical calculations. The Breit interaction is taken into account through second order of perturbation theory and the lowest-order Lamb shift is also evaluated. Sample calculations are performed for berylliumlike ions with Z = 4-7, and for the magnesiumlike ion P IV. The third-order energies are in excellent agreement with measurement with an accuracy at 0.2% level for the cases considered. Comparisons are made with previous second-order MBPT results and with other calculations. The third-order energy correction is shown to be significant, improving second-order correlation energies by an order of magnitude.

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Theory of relativistic effects on atoms: Configuration-space Hamiltonian

Cited by 314 publications

References 12 publications

All-Order Methods for Relativistic Atomic Structure Calculations

All-Order Methods for Relativistic Atomic Structure Calculations

Relativistic calculation of two-electron one-photon and hypersatellite transition energies for 12 Z 30 elements

Third-order many-body perturbation theory calculations for the beryllium and magnesium isoelectronic sequences

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