Convergence in the no-core shell model with low-momentum two-nucleon interactions

Bogner, S. K.; Furnstahl, R. J.; Maris, Pieter; Perry, Robert J.; Schwenk, A.; Vary, James P.

doi:10.1016/j.nuclphysa.2007.12.008

Cited by 151 publications

(206 citation statements)

References 34 publications

Supporting

Mentioning

198

Contrasting

Order By: Relevance

“…The first application of the SRG for the transformation of a nuclear Hamiltonian was presented by Bogner et al [64,65] and the SRG in connection to the UCOM approach was first discussed in Refs. [66,67].…”

Section: Similarity Renormalization Group (Srg)mentioning

confidence: 99%

Nuclear structure in the framework of the Unitary Correlation Operator Method

Roth¹,

Neff²,

Feldmeier³

2010

Progress in Particle and Nuclear Physics

162

217

View full text Add to dashboard Cite

Correlations play a crucial role in the nuclear many-body problem. We give an overview of recent developments in nuclear structure theory aiming at the description of these interactioninduced correlations by unitary transformations. We focus on the Unitary Correlation Operator Method (UCOM), which offers a very intuitive, universal and robust approach for the treatment of short-range correlations. We discuss the UCOM formalism in detail and highlight the connections to other methods for the description of short-range correlations and the construction of effective interactions. In particular, we juxtapose UCOM with the Similarity Renormalization Group (SRG) approach, which implements the unitary transformation of the Hamiltonian through a very flexible flow-equation formulation. The UCOM-and SRG-transformed interactions are compared on the level of matrix elements and in many-body calculations within the no-core shell model and with Hartree-Fock plus perturbation theory for a variety of nuclei and observables. These calculations provide a detailed picture of the similarities and differences as well as the advantages and limitations of unitary transformation methods.

show abstract

Section: Similarity Renormalization Group (Srg)mentioning

confidence: 99%

Nuclear structure in the framework of the Unitary Correlation Operator Method

Roth¹,

Neff²,

Feldmeier³

2010

Progress in Particle and Nuclear Physics

162

217

View full text Add to dashboard Cite

show abstract

“…The size of these matrices increases rapidly with particle number. V low k requires drastically fewer matrix elements to accurately reproduce all low-energy NN scattering data, and this reduction exponentiates as we move to the many-nucleon problem [7]. In contrast to conventional NN interactions, which are highly nonperturbative, V low k leads to nearly converged nuclear matter calculations at second order in many-body perturbation theory.…”

Section: Discussionmentioning

confidence: 99%

“…The three-nucleon interaction is an essential ingredient in saturating nuclear matter close to the empirical density and binding energy [15]. Even more, the problem is not well-posed until consistent few-body interactions are found, as the nucleon-nucleon interaction on its own does not maintain unitarity in even the three-nucleon problem and violations are comparable to nuclear level spacings [7].…”

Section: Discussionmentioning

confidence: 99%

“…This transformation is a simplified version of Wegner's flow equations [5] and one of a much larger class of Similarity Renormalization Group (SRG) transformations developed by Glazek and Wilson [6]. The transformation leads to NN potentials for which calculations of few-nucleon binding energies and other observables converge rapidly [2,3,7] . However, further progress will require the consistent treatment of at least the three-nucleon interaction.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Three-body forces produced by a similarity renormalization group transformation in a simple model

Bogner¹,

Furnstahl²,

Perry³

2008

Annals of Physics

Self Cite

View full text Add to dashboard Cite

A simple class of unitary renormalization group transformations that force hamiltonians towards a band-diagonal form produce few-body interactions in which low-and high-energy states are decoupled, which can greatly simplify many-body calculations. One such transformation has been applied to phenomenological and effective field theory nucleon-nucleon interactions with success, but further progress requires consistent treatment of at least the three-nucleon interaction. In this paper we demonstrate in an extremely simple model how these renormalization group transformations consistently evolve two-and three-body interactions towards band-diagonal form, and introduce a diagrammatic approach that generalizes to the realistic nuclear problem.

show abstract

“…We also see a dramatic difference in convergence rate: the strongly bound nucleus 4 He converges more rapidly than the weakly bound nucleus 6 Li; furthermore, up to N 2 LO convergence is rapid, but at N 3 LO and N 4 LO our results for 6 Li are far from being converged, even at N max = 18. In order to improve the convergence of the many-body calculations we apply the Similarity Renormalization Group (SRG) at the three-body level to 'soften' the chiral NN interaction [8][9][10][11]. Indeed, at SRG evolution values of α = 0.04 fm 4 and α = 0.08 fm 4 we do find rapid convergence of the many-body calculation, and, including induced 3N interactions, only very weak dependence on the SRG evolution.…”

Section: No-core Configuration Interaction Calculationsmentioning

confidence: 99%

Properties of⁴He and⁶Li with improved chiral EFT interactions

Maris

Binder

Calci

et al. 2016

EPJ Web of Conferences

Self Cite

View full text Add to dashboard Cite

Abstract. We present recent results for 4 He and 6 Li obtained with improved NN interactions derived from chiral effective field theory up to N 4 LO. The many-body calculations are performed order-by-order in the chiral expansion. At N 3 LO and N 4 LO additional renormalization using the Similarity Renormalization Group is adopted to improve numerical convergence of the many-body calculations. We discuss results for the ground state energies, as well as the magnetic moment and the low-lying spectrum of 6 Li. Nuclear potential from chiral EFTChiral effective field theory (EFT) allows one to derive nuclear forces (and corresponding electoweak currents) in a systematical way [1]. In particular, the leading order (LO) and next-to-leading order (NLO) contributions to the interaction are given solely by nucleon-nucleon (NN) operators while three-nucleon forces (3NFs) appear first at next-to-next-to-leading order (N 2 LO) [2] in the chiral expansion. Four-nucleon forces are even more suppressed and start contributing at N 3 LO. The chiral power counting thus provides a natural explanation of the observed hierarchy of nuclear forces.In Refs. [3, 4] a new generation of chiral EFT NN potentials up to N 4 LO was developed, using local regulators for the long-range terms and with reduced finite-cutoff artefacts by employing a novel ultraviolet regularization scheme; in addition, a procedure to estimate the theoretical uncertainties due to the truncation of the chiral expansion was proposed (see also [5]). Here we present results for 4 He and 6 Li obtained with these improved chiral NN potentials using a regulator of R = 1.0 fm [6]. a

show abstract

Convergence in the no-core shell model with low-momentum two-nucleon interactions

Cited by 151 publications

References 34 publications

Nuclear structure in the framework of the Unitary Correlation Operator Method

Nuclear structure in the framework of the Unitary Correlation Operator Method

Three-body forces produced by a similarity renormalization group transformation in a simple model

Properties of⁴He and⁶Li with improved chiral EFT interactions

Contact Info

Product

Resources

About

Convergence in the no-core shell model with low-momentum two-nucleon interactions

Cited by 151 publications

References 34 publications

Nuclear structure in the framework of the Unitary Correlation Operator Method

Nuclear structure in the framework of the Unitary Correlation Operator Method

Three-body forces produced by a similarity renormalization group transformation in a simple model

Properties of4He and6Li with improved chiral EFT interactions

Contact Info

Product

Resources

About

Properties of⁴He and⁶Li with improved chiral EFT interactions