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

References in corpus (11)

• Chiral effective field theory and nuclear forces
• Improved nuclear matter calculations from chiral low-momentum interactions
• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• Neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory
• Local chiral effective field theory interactions and quantum Monte Carlo applications
• Minimally non-local nucleon-nucleon potentials with chiral two-pion exchange including $\Delta$'s
• Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory
• Neutron matter from chiral two- and three-nucleon calculations up to N${}^3$LO
• Quantum Monte Carlo Calculations of Light Nuclei Using Chiral Potentials
• Convergence of the Born Series with Low-Momentum Interactions
• Weinberg Eigenvalues and Pairing with Low-Momentum Potentials

Cited by in corpus (1)

• Quantum Monte Carlo calculations of light nuclei with local chiral two- and three-nucleon interactions