Effective interaction in the Rayleigh–Schrödinger perturbation theory

Takayanagi, Kazuo

doi:10.1016/j.aop.2014.08.002

Cited by 7 publications

(5 citation statements)

References 21 publications

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“…For example, when calculating ab|H eff |cd , E (ν) 0 takes ǫ c +ǫ d . The explicit calculations of the folded diagrams up to a certain order are complicated, especially for a nondegenerate model space [36]. Fortunately, the folded diagrams start to appear in the third order expansions.…”

Section: A Perturbation Frameworkmentioning

confidence: 99%

“…It is worth noting that the cancellation of unlinked diagrams holds for both degenerate and nondegenerate model spaces [15,17]. For a nondegenerate model space, however, the evaluations of the folded diagrams are more complicated [28,29] than the degenerate case. In the RS perturbation, the energy-independent effective Hamiltonian is…”

Section: Perturbation Frameworkmentioning

confidence: 99%

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Perturbation calculations of nucleon–nucleon effective interactions in the Hartree–Fock basis

Fang

et al. 2019

J. Phys. G: Nucl. Part. Phys.

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We perform two types of ab initio perturbation calculations of effective interactions in the Hartree-Fock (HF) basis instead of the harmonic-oscillator basis: one is called the Brillouin-Wigner (BW) perturbation and another is called the Rayleigh-Schrödinger (RS) perturbation. It is shown that the HF basis provides good convergences. We also benchmark the perturbation calculations with the in-medium similarity renormalization group (IM-SRG) which is a nonperturbative method. In the HF basis some-type perturbation diagrams can be cancelled out, while the cancellation does not happen in the harmonic-oscillator basis. We have investigated the sd shell using the chiral N 3 LO potential softened by V low-k . With the low-momentum N 3 LO potential, we first perform the spherical HF calculations for the 16 O core of the sd shell, and the realistic effective two-body interactions for the HF sd-shell space can be derived by the perturbation calculations.The calculations give simultaneously effective single-particle energies and excitation spectra of two valence particle systems (i.e., 18 O, 18 F, and 18 Ne in the sd shell). Convergences have been analyzed order by order. The perturbation calculations are in fairly good agreement with nonperturbative method IM-SRG. We find that the HF RS perturbation gives even better results compared with the BW perturbation. The HF realistic effective interactions derived by the perturbations can be used for further shell-model calculations. *

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Section: A Perturbation Frameworkmentioning

confidence: 99%

Section: Perturbation Frameworkmentioning

confidence: 99%

Perturbation calculations of nucleon–nucleon effective interactions in the Hartree–Fock basis

Fang

et al. 2019

J. Phys. G: Nucl. Part. Phys.

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“…In the Rayleigh-Schrödinger perturbation theory [10], it can be shown that the matrix element i ⟨v⟩ j in the P-space is conveniently expressed in the bracketing form as…”

Section: Effective Interaction In the Rayleigh-schrödinger Perturbatimentioning

confidence: 99%

“…Our proof here shows a clear contrast with the existing proof sketched in the above; we have derived the theorem in a coherent manner using the RS energy denominators only. We first eliminate the energy dependence of the effective interaction using the general theory of the folded diagram [10], and then eliminate the unlinked diagrams. This is not, however, the whole story of the present proof.…”

Section: Linked Diagram Theorem -Imentioning

confidence: 99%

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Linked Diagram Theorem for Effective Interaction

Takayanagi

2018

Proceedings of the Ito International Research Center Symposium "Perspectives of the Physics of Nuclear Structure"

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We revisit the so-called linked diagram theorem for the effective interaction in open systems. First, we outline a novel proof of the linked diagram theorem, which is much simpler than the existing proof and leads naturally to a new form of the theorem. Second, we show that the linked diagram theorem in its known form gives many redundant diagrams which cancel among themselves in the exact perturbation expansion, while the new form is free of such redundant diagrams. At the end, we point out that all existing microscopic effective interactions suffer from such redundant contributions, and outline the way out of such difficulties.

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Effective interaction in unified perturbation theory

Takayanagi

2016

Annals of Physics

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Effective interaction in the Rayleigh–Schrödinger perturbation theory

Cited by 7 publications

References 21 publications

Perturbation calculations of nucleon–nucleon effective interactions in the Hartree–Fock basis

Perturbation calculations of nucleon–nucleon effective interactions in the Hartree–Fock basis

Linked Diagram Theorem for Effective Interaction

Effective interaction in unified perturbation theory

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