The Rayleigh-Schrodinger perturbation and the linked-diagram theorem for a multi-configurational model space

Lindgren, Ingvar

doi:10.1088/0022-3700/7/18/010

Cited by 449 publications

(272 citation statements)

References 25 publications

(20 reference statements)

Supporting

Mentioning

270

Contrasting

Order By: Relevance

“…The theoretical basis of the RMBPT method, as implemented in the FAC code, is based on the Rayleigh-Schrödinger perturbation theory [47] and allows for a combination of configuration interaction and second-order many-body perturbation theory (Gu [33]). The approach is built on the H DCB , which is split up into a zero-order, model Hamiltonian, H 0 , and a perturbation, V , defined as,…”

Section: The Fac Relativistic Many-body Perturbation Theory Methodsmentioning

confidence: 99%

Energy levels and radiative data for Kr-like W³⁸⁺from MCDHF and RMBPT calculations

Guo¹,

Grumer²,

Brage³

et al. 2016

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

View full text Add to dashboard Cite

Abstract. Energies, transition rates, line strengths and lifetimes have been computed for all levels of the 4p 6 and 4p 5 4d configurations of W 38+ by using the multiconfiguration Dirac-Hartree-Fock method as well as relativistic many-body perturbation theory. We investigate systematically correlation, relativistic and QED effects on different properties, including excitation energies and transition rates. We demonstrate that it is important to include core-valence correlation of rather deep subshells (including 3d and 3p) to reach close to spectroscopic accuracy for the transition energies. We also show that high multipole transitions (E3, M2) are important for the lifetime of some metastable levels of 4p 5 4d ( 3 F 3 , 1 D 2 , 3 D 2 ). The present results are in good agreement with experiments and of considerable higher accuracy than what has been reached in previous theoretical works.

show abstract

Section: The Fac Relativistic Many-body Perturbation Theory Methodsmentioning

confidence: 99%

Energy levels and radiative data for Kr-like W³⁸⁺from MCDHF and RMBPT calculations

Guo¹,

Grumer²,

Brage³

et al. 2016

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

View full text Add to dashboard Cite

show abstract

“…The second-order MBPT approach (Lindgren 1974;Safronova et al 1996), implemented by Gu (2005Gu ( , 2006 in FAC has been used successfully to calculate atomic parameters with high accuracy (Gu 2007;Gu et al 2011;Wang et al 2014;Fei et al 2014;Guo et al 2015;Wang et al 2015;Si et al 2015a,b). Here we briefly describe the theory.…”

Section: Mbptmentioning

confidence: 99%

Energy levels and transition rates for helium-like ions withZ = 10–36

Guo

Wang

et al. 2016

A&A

View full text Add to dashboard Cite

Aims. Helium-like ions provide an important X-ray spectral diagnostics in astrophysical and high-temperature fusion plasmas. An interpretation of the observed spectra provides information on temperature, density, and chemical compositions of the plasma. Such an analysis requires information for a wide range of atomic parameters, including energy levels and transition rates. Our aim is to provide a set of accurate energy levels and transition rates for helium-like ions with Z = 10-36. Methods. The second-order many-body perturbation theory (MBPT) was adopted in this paper. To support our MBPT results, we performed an independent calculation using the multiconfiguration Dirac-Hartree-Fock (MCDHF) method. Results. We provide accurate energies for the lowest singly excited 70 levels among 1snl (n ≤ 6, l ≤ (n − 1)) configurations and the lowest doubly excited 250 levels arising from the K-vacancy 2ln l (n ≤ 6, l ≤ (n − 1)) configurations of helium-like ions with Z = 10−36. Wavelengths, transition rates, oscillator strengths, and line strengths are calculated for the E1, M1, E2, and M2 transitions among these levels. The radiative lifetimes are reported for all the calculated levels. Conclusions. Our MBPT results for singly excited n ≤ 2 levels show excellent agreement with other elaborate calculations, while those for singly excited n ≥ 3 and doubly excited levels show significant improvements over previous theoretical results. Our results will be very helpful for astrophysical line identification and plasma diagnostics.

show abstract

“…To determine S < σ (3), we draw a horizontal dashed line just above 3 and we gather the segments of L crossing the dashed line from above. In our case the segments are (1, 0), (2,4) , (3,1), (4,3) and (5, 2), (6,5) . S < σ (3) is the set of abscissae of the first point of each segment:…”

Section: Lemma 7 (I) S < σ (K) Cannot Be Empty and (Ii) S < σ (K) Andmentioning

confidence: 73%

Tree expansion in time-dependent perturbation theory

Brouder

Mestre

Patras

2010

Journal of Mathematical Physics

View full text Add to dashboard Cite

The computational complexity of time-dependent perturbation theory is well-known to be largely combinatorial whatever the chosen expansion method and family of parameters (combinatorial sequences, Goldstone and other Feynman-type diagrams...). We show that a very efficient perturbative expansion, both for theoretical and numerical purposes, can be obtained through an original parametrization by trees and generalized iterated integrals. We emphasize above all the simplicity and naturality of the new approach that links perturbation theory with classical and recent results in enumerative and algebraic combinatorics. These tools are applied to the adiabatic approximation and the effective Hamiltonian. We prove perturbatively and non-perturbatively the convergence of Morita's generalization of the Gell-Mann and Low wavefunction. We show that summing all the terms associated to the same tree leads to an utter simplification where the sum is simpler than any of its terms. Finally, we recover the time-independent equation for the wave operator and we give an explicit non-recursive expression for the term corresponding to an arbitrary tree.

show abstract

The Rayleigh-Schrodinger perturbation and the linked-diagram theorem for a multi-configurational model space

Cited by 449 publications

References 25 publications

Energy levels and radiative data for Kr-like W³⁸⁺from MCDHF and RMBPT calculations

Energy levels and radiative data for Kr-like W³⁸⁺from MCDHF and RMBPT calculations

Energy levels and transition rates for helium-like ions withZ = 10–36

Tree expansion in time-dependent perturbation theory

Contact Info

Product

Resources

About

The Rayleigh-Schrodinger perturbation and the linked-diagram theorem for a multi-configurational model space

Cited by 449 publications

References 25 publications

Energy levels and radiative data for Kr-like W38+from MCDHF and RMBPT calculations

Energy levels and radiative data for Kr-like W38+from MCDHF and RMBPT calculations

Energy levels and transition rates for helium-like ions withZ = 10–36

Tree expansion in time-dependent perturbation theory

Contact Info

Product

Resources

About

Energy levels and radiative data for Kr-like W³⁸⁺from MCDHF and RMBPT calculations

Energy levels and radiative data for Kr-like W³⁸⁺from MCDHF and RMBPT calculations