Structure of Heavy Atoms: Three-Body Potentials

Mittleman, Marvin H.

doi:10.1103/physreva.4.893

Cited by 155 publications

(37 citation statements)

References 3 publications

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“…The non-linear terms give no additional contributions to the matrix element formula (31). However, the values of the matrix elements change when NL terms are added owing to modified values of the excitation coefficients.…”

Section: Recent Developments In the Calculations Of Monovalent Systemmentioning

confidence: 99%

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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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Section: Recent Developments In the Calculations Of Monovalent Systemmentioning

confidence: 99%

“…[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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“…A well-known problem of any such formalism is the correct treatment of negative-energy states, which, if included improperly, lead to the continuum dissolution problem discussed by Sucher [1]. This problem can be avoided by using the no-pair Hamiltonian [1,2], which excludes negative-energy states. In reference [3], configuration interaction (CI) techniques were used to carry out accurate calculations of energies of n=1 and n=2 states along the helium isoelectronic sequence starting from the no-pair Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

Relativistic Calculations of Transition Amplitudes in the Helium Isoelectronic Sequence

Johnson

Plante

Sapirstein

1995

Advances in Atomic, Molecular, and Optical Physics

195

171

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Exact relativistic wave functions for n=1 and n=2 states of heliumlike ions are used to calculate single-photon transition amplitudes for 2 S0.Particular attention is given to the role of negative-energy states in bringing length and velocity forms into agreement, and related quantum electrodynamics issues. This is a reprinted version of an article with the same title published in Advances in Atomic, Molecular and Optical Physics 35, 225-329 (1995). Figures included in the original article are omitted here.

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“…It is rather complicated to restore the effect of negative energy states, which are usually omitted from Hamiltonian treatments in order to avoid the continuum dissolution problem [8], and in addition the treatment of retardation is problematical [9]. These issues can be avoided altogether if the Hamiltonian formalism is simply abandoned, and replaced with the Feynman diagram oriented approach offered by S-matrix theory [10], which will be used here, or the essentially equivalent Green's function techniques used by the St. Petersburg group [11].…”

Section: Introductionmentioning

confidence: 99%

S-matrix calculations of energy levels of the lithium isoelectronic sequence

Sapirstein

Cheng

2011

Phys. Rev. A

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A QED approach to the calculation of the spectra of the lithium isoelectronic sequence is implemented. A modified Furry representation based on the Kohn-Sham potential is used to evaluate all one-and two-photon diagrams with the exception of the two-loop Lamb shift. Three-photon diagrams are estimated with Hamiltonian methods. After incorporating recent calculations of the two-loop Lamb shift and recoil corrections a comprehensive tabulation of the 2s, 2p 1/2 and 2p 3/2 energy levels as well as the 2s − 2p 1/2 and 2s − 2p 3/2 transition energies for Z = 10 − 100 is presented.

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Structure of Heavy Atoms: Three-Body Potentials

Cited by 155 publications

References 3 publications

All-Order Methods for Relativistic Atomic Structure Calculations

All-Order Methods for Relativistic Atomic Structure Calculations

Relativistic Calculations of Transition Amplitudes in the Helium Isoelectronic Sequence

S-matrix calculations of energy levels of the lithium isoelectronic sequence

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