Low Scale Saturation of Effective NN Interactions and Their Symmetries

Arriola, E. Ruiz

doi:10.3390/sym8060042

Cited by 20 publications

(17 citation statements)

References 73 publications

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“…A similar mapping of renormalization scale dependent counterterm coefficients to Skyrme-like couplings has been done in Ref. [55]. For example, the densitydependent contributions to the conventional Skyrme parameters t 0 and x 0 are given by the leading C 0 terms in the 1 S 0 and 3 S 1 channels, t 1 and x 1 are given by the leading C 2 terms in the 1 S 0 , 3 S 1 channels and C 0 terms in the 3 S 1 − 3 D 1 channel:…”

Section: Countertermsmentioning

confidence: 91%

Incorporating Brueckner-Hartree-Fock correlations in energy density functionals

2018

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Recently, a microscopically motivated nuclear energy density functional was derived by applying the density matrix expansion to the Hartree-Fock (HF) energy obtained from long-range chiral effective field theory two-and three-nucleon interactions. However, the HF approach cannot account for all many-body correlations. One class of correlations is included by Brueckner-Hartree-Fock (BHF) theory, which gives an improved definition of the one-body HF potential by replacing the interaction by a reaction matrix G. In this paper, we find that the difference between the G-matrix and the SRG evolved nucleon-nucleon potential V SRG can be well accounted for by a truncated series of contact terms. This is consistent with renormalization group decoupling generating a series of counterterms as short-distance physics is integrated out. The coefficients C n of the power series expansion C n q n for the counterterms are examined for two potentials at different renormalization group resolutions and at a range of densities. The success of this expansion for G−V SRG means we can apply the density matrix expansion at the HF level with low-momentum interactions and density-dependent zero-range interactions to model BHF correlations.

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Section: Countertermsmentioning

confidence: 91%

Incorporating Brueckner-Hartree-Fock correlations in energy density functionals

2018

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“…Ref. [2] and references therein) which is ultimately related to a high energy cut-off in the problem.…”

Section: Introductionmentioning

confidence: 99%

Coarse-grained short-range correlations

et al. 2017

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We develop a scheme to take into account the effects of short-range nucleon-nucleon correlations in the nucleon-pair wave function by solving the Bethe-Goldstone equation for a coarse grained delta shell potential in S-wave configuration. The S-wave delta shell potential has been adjusted to reproduce the 1 S0 phase shifts of the AV18 potential for this partial wave up to 2 GeV in the laboratory kinetic energy. We show that a coarse grained potential can describe the high momentum tail of the back-to-back correlated pairs and the G-matrix in momentum space. We discuss the easiness and robustness of the calculation in coordinate space and the future improvements and utilities of this model. This work suggests the possibility of using perturbation theory for describing the short-range correlations, and related to this, to substitute the G-matrix by an appropriate coarse-grained potential.

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“…This of course suggests that the implicit renormalization approach may be a better method to determine the effective interaction. This was the purpose of a previous analysis [16] where the Skyrme force parameters just deducible from the NN interaction were determined until a low-energy saturation was observed. The present discussion provides an a posteriori explanation of this observation.…”

Section: Discussionmentioning

confidence: 99%

“…This reflects both the lack of a unambiguous link to the fundamental two-body interaction as well as the quite disparate finite nuclei and nuclear matter observables which have been used to fix the effective Hamiltonian parameters. An effort has been made [16] (see e.g. Ref.…”

Section: Introductionmentioning

confidence: 99%

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Implicit and explicit renormalization: Two complementary views of effective interactions

2015

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We analyze quantitatively the interplay between explicit and implicit renormalization in Nuclear Physics. By explicit renormalization we mean to integrate out higher energy modes below a given cutoff scale using the similarity renormalization group (SRG) with a block-diagonal evolution generator, which separates the total Hilbert-space into a model space and its complementary. In the implicit renormalization we impose given conditions at low energies for a cutoff theory. In both cases we compare the outcoming effective interactions as functions of the cutoff scale. We carry out a comprehensive analysis of a toy-model which captures the main features of the nucleon-nucleon (NN) S -wave interaction at low energies. We find a wide energy region where both approaches overlap. This amounts to a great simplification in the determination of the effective interaction. Actually, the outcoming scales are within the expected ones relevant for the physics of light nuclei.

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Low Scale Saturation of Effective NN Interactions and Their Symmetries

Cited by 20 publications

References 73 publications

Incorporating Brueckner-Hartree-Fock correlations in energy density functionals

Incorporating Brueckner-Hartree-Fock correlations in energy density functionals

Coarse-grained short-range correlations

Implicit and explicit renormalization: Two complementary views of effective interactions

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