Weinberg eigenvalues for chiral nucleon-nucleon interactions

Abstract

We perform a comprehensive Weinberg eigenvalue analysis of a representative set of modern nucleon-nucleon interactions derived within chiral effective field theory. Our set contains local, semilocal, and nonlocal potentials, developed by Gezerlis, Tews et al. (2013); Epelbaum, Krebs, and Meißner (2015); and Entem, Machleidt, and Nosyk (2017) as well as Carlsson, Ekström et al. (2016), respectively. The attractive eigenvalues show a very similar behavior for all investigated interactions, whereas the magnitudes of the repulsive eigenvalues sensitively depend on the details of the regularization scheme of the short- and long-range parts of the interactions. We demonstrate that a direct comparison of numerical cutoff values of different interactions is in general misleading due to the different analytic form of regulators; for example, a cutoff value of $R=0.8$ fm for the semilocal interactions corresponds to about $R=1.2$ fm for the local interactions. Our detailed comparison of Weinberg eigenvalues provides various insights into idiosyncrasies of chiral potentials for different orders and partial waves. This shows that Weinberg eigenvalues could be used as a helpful monitoring scheme when constructing new interactions.

14 pages, 17 figures, published version

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• Three-Nucleon Forces: Implementation and Applications to Atomic Nuclei and Dense Matter
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• Auxiliary field diffusion Monte Carlo calculations of light and medium-mass nuclei with local chiral interactions
• Probing the core of the strong nuclear interaction
• Properties of nuclei up to $A=16$ using local chiral interactions
• Quantum Monte Carlo calculations of light nuclei with local chiral two- and three-nucleon interactions
• Towards grounding nuclear physics in QCD
• Few- and many-nucleon systems with semilocal coordinate-space regularized chiral nucleon-nucleon forces
• Improved many-body expansions from eigenvector continuation
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• Natural orbitals for many-body expansion methods
• Neutron stars and the dense matter equation of state: from microscopic theory to macroscopic observations
• Bogoliubov many-body perturbation theory under constraint
• Single- and two-nucleon momentum distributions for local chiral interactions
• Double-folding potentials from chiral effective field theory
• Exploring the relationship between nuclear matter and finite nuclei with chiral two- and three-nucleon forces
• Analysis of the neutron matter equation of state and the symmetry energy up to fourth order of chiral effective field theory
• Neutron-deuteron scattering cross-sections with chiral $NN$ interactions using wave-packet continuum discretization
• The Equation of State of Neutron-Rich Matter at Fourth Order of Chiral Effective Field Theory and the Radius of a Medium-Mass Neutron Star
• Bayesian Analysis of $\chi$EFT at Leading Order in a Modified Weinberg Power Counting Approach
• Neutron matter from local chiral effective field theory interactions at large cutoffs
• Low-rank matrix decompositions for ab initio nuclear structure
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• The quasi-deuteron model at low RG resolution
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• Renormalization group evolution of optical potentials: explorations using a toy model
• An overview of symmetric nuclear matter properties from chiral interactions up to fourth order of the chiral expansion
• A quadratic-scaling algorithm with guaranteed convergence for quantum coupled-channel calculations