Atomic Many-Body Theory

Lindgren, Ingvar; Morrison, John C.

doi:10.1007/978-3-642-61640-2

Cited by 409 publications

(139 citation statements)

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“…The reader may find more detailed descriptions of what follows in Refs. [19][20][21]. In our treatment of the atomic Hamiltonian for one valence electron systems, we employ the frozen-core Dirac-Hartree-Fock (DHF) potential.…”

Section: Methodsmentioning

confidence: 99%

“…Here k 1 , k 2 are integer coupling momentum numbers and h is a half integer coupling angular momentum. As an example, the relationship between the ordinary and the reduced triples maybe represented as [22] ρ mnrvab = k1k2h ρ k1k2h (mnr vab) , (18) where the diagram subsumes various 3j symbols [19]. Interested readers can find complete discussions of angular reduction in Refs.…”

Section: Methodsmentioning

confidence: 99%

“…Interested readers can find complete discussions of angular reduction in Refs. [19] and [24], for single and double term reductions, and Ref. [22] for triple term reductions.…”

Section: Methodsmentioning

confidence: 99%

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Coupled-cluster calculations of properties of the boron atom as a monovalent system

Gharibnejad

Derevianko

2012

Phys. Rev. A

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We present relativistic coupled-cluster (CC) calculations of energies, magnetic-dipole hyperfine constants, and electric-dipole transition amplitudes for low-lying states of atomic boron. The trivalent boron atom is computationally treated as a monovalent system. We explore performance of the CC method at various approximations. Our most complete treatment involves singles, doubles and the leading valence triples. The calculations are done using several approximations in the coupledcluster (CC) method. The results are within 0.2-0.4% of the energy benchmarks. The hyperfine constants are reproduced with 1-2% accuracy.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Coupled-cluster calculations of properties of the boron atom as a monovalent system

Gharibnejad

Derevianko

2012

Phys. Rev. A

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“…As an introduction to the formal treatment, we shall review the standard nonrelativistic many-body perturbation theory (MBPT). [32] We consider a number of "target states," satisfying the Schr€ odinger equation, …”

Section: Formal Developmentmentioning

confidence: 99%

Development of many‐body perturbation theory: How to combine with quantum electrodynamics

Lindgren

2014

Int J of Quantum Chemistry

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In the first part, a review is made of the development of the many-body perturbation theory for the last half century. The development of methods for quantum electrodynamics (QED) calculations, which have occurred essentially in parallel, is also briefly reviewed. In the second part, an effort of unifying the two is discussed. The covariant-evolution-operator method, developed primarily for QED calculations by the Gothenburg group, can be combined with atomic/molecular many-body perturbation theory (MBPT) and for the first time making it possible to combine full QED with electron correlation of arbitrary order. The basic idea is to extend the standard procedure of MBPT to a time-or energy-dependent formalism, which makes it possible to include QED perturbations in a rigorous fashion. The procedure has been implemented and as a first test applied to helium like ions. The method can also be applied to dynamical processes.

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“…In the case of quasi-degeneracy some of the energy denominators become very small, which can lead to convergence problems in the traditional perturbation treatment, using a single reference function [3]. In more refined MBPT it is possible to work with several reference functions, based on an effective hamiltonian, H eff , and an extended model space [4,9,10]. This leads to the secular equation…”

Section: Many-body Perturbation Theorymentioning

confidence: 99%

Treatment of atomic quasi-degeneracy in bound-state QED. Application to the 1s2p states of He-like ions

Lindgren¹,

Pendrill²,

Salomonson³

et al. 2001

AIP Conference Proceedings

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In the case of quasi-degeneracy, i.e., when there are states close in energy to the state considered, standard perturbation theory may lead to convergence problem. A typical example is the relativistic treatment of the fine structure of light heliumlike ions. In Many-BodyPerturbation Theory (MBPT) this problem can be treated by including the quasi-degenerate states in an extended model space. The mixing is then treated to all orders already in the zeroth-order wave function by diagonalizing an effective hamiltonian in this subspace. Only non-quasi-degenerate states are treated by perturbation.Standard QED treatment of bound systems is based upon the S -matrix formalism. Here an extended model space cannot be used, the reason being that only matrix elements diagonal in energy can be determined, while the effective hamiltonian needed contains also non-diagonal elements between the states in the model space. In the present paper a modification of the bound-state QED procedure is described, based upon a covariant form of the time-evolution operator, rather than the S -matrix. In this way also elements non-diagonal in energy can be evaluated. The operator appearing in the final procedure is free from singularities, and no special procedure is needed for evaluating the so-called Model-Space Contribution, caused by model-space states appearing as the intermediate states.The procedure has been applied to the fine structure of helium-like ions, and numerical second-order QED results, including quasi-degenerate levels, are presented for the first time. The formalism is closely related to MBPT and may open the possibility to combine QED and MBPT in a more systematic fashion.

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Atomic Many-Body Theory

Cited by 409 publications

References 0 publications

Coupled-cluster calculations of properties of the boron atom as a monovalent system

Coupled-cluster calculations of properties of the boron atom as a monovalent system

Development of many‐body perturbation theory: How to combine with quantum electrodynamics

Treatment of atomic quasi-degeneracy in bound-state QED. Application to the 1s2p states of He-like ions

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