Two- and three-nucleon contact interactions and ground-state energies of light- and medium-mass nuclei

Abstract

Classes of two-nucleon ($2N$) contact interactions are developed in configuration space at leading order (LO), next-to-leading order (NLO), and next-to-next-to-next-to-leading order (N3LO) by fitting the experimental singlet $np$ scattering length and deuteron binding energy at LO, and $np$ and $pp$ scattering data in the laboratory-energy range 0--15 MeV at NLO and 0--25 MeV at N3LO. These interactions are regularized by including two Gaussian cutoffs, one for $T$=$0$ and the other for $T$=$1$ channels. The cutoffs are taken to vary in the ranges $R_0$=$(1.5$--2.3) fm and $R_1$=$(1.5$--3.0) fm. The 780 (1,100) data points up to 15 (25) MeV energy, primarily differential cross sections, are fitted by the NLO (N3LO) models with a ${\chi }^2$/datum about 1.7 or less (well below 1.5), when harder cutoff values are adopted. As a first application, we report results for the binding energies of nuclei with mass numbers $A$=$3$--6 and 16 obtained with selected LO and NLO $2N$ models both by themselves as well as in combination with a LO three-nucleon ($3N$) contact interaction. The latter is characterized by a single low-energy constant that is fixed to reproduce the experimental ${}^3$H binding energy. The inclusion of the $3N$ interaction largely removes the sensitivity to cutoff variations in the few-nucleon systems and leads to predictions for the ${}^3$He and ${}^4$He binding energies that cluster around 7.8 MeV and 30 MeV, respectively. However, in ${}^{16}$O this cutoff sensitivity remains rather strong. Finally, predictions at LO only are also reported for medium-mass nuclei with $A$=$40$, 48, and 90.

arXiv comment23 pages, 6 figures

References in corpus (50)

• An accurate nucleon-nucleon potential with charge-independence breaking
• The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)
• Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory
• Construction of high-quality Nucleon-Nucleon potential models
• Universality in Few-body Systems with Large Scattering Length
• Effective Field Theory for Few-Nucleon Systems
• A New Expansion for Nucleon-Nucleon Interactions
• Two-Nucleon Systems from Effective Field Theory
• The two-nucleon system at next-to-next-to-next-to-leading order
• Renormalization of the Three-Body System with Short-Range Interactions
• The Two-Nucleon Potential from Chiral Lagrangians
• Nuclear Energy Density Optimization
• Accurate nuclear radii and binding energies from a chiral interaction
• Nuclear effective field theory: status and perspectives
• Efimov Physics: a review
• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• The Three-Boson System with Short-Range Interactions
• Precision nucleon-nucleon potential at fifth order in the chiral expansion
• High-quality two-nucleon potentials up to fifth order of the chiral expansion
• Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order
• Nucleon-Nucleon Effective Field Theory Without Pions
• A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states
• 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
• Generalized Dimensional Analysis
• Local chiral potentials and the structure of light nuclei
• Covariant spectator theory of np scattering: Phase shifts obtained from precision fits to data below 350 MeV
• Coarse grained Potential analysis of neutron-proton and proton-proton scattering below pion production threshold
• Subleading contributions to the three-nucleon contact interaction
• Auxiliary field diffusion Monte Carlo calculations of light and medium-mass nuclei with local chiral interactions
• Properties of nuclei up to $A=16$ using local chiral interactions
• Ground-State Properties of ${}^4$He and ${}^{16}$O Extrapolated from Lattice QCD with Pionless EFT
• Nuclear Physics Around the Unitarity Limit
• Statistical Error analysis of Nucleon-Nucleon phenomenological potentials
• Atomic nuclei from quantum Monte Carlo calculations with chiral EFT interactions
• From the lightest nuclei to the equation of state of asymmetric nuclear matter with realistic nuclear interactions
• Universal Correlations in Pion-less EFT with the Resonating Group Model: Three and Four Nucleons
• Coarse grained NN potential with Chiral Two Pion Exchange
• Correlations imposed by the unitary limit between few-nucleon systems, nuclear matter and neutron stars
• Wilsonian renormalization group versus subtractive renormalization in effective field theories for nucleon--nucleon scattering
• Calculation of the ${}^6$Li ground state within the hyperspherical harmonic basis
• Short-range three-nucleon interaction from A=3 data and its hierarchical structure
• Embedding nuclear physics inside the unitary window
• Implications of Efimov physics for the description of three and four nucleons in chiral effective field theory
• Efimov physics with $1/2$ spin-isospin fermions
• Unitary ambiguity of NN contact interactions and the 3N force
• Saturation properties of helium drops from a Leading Order description
• Description of light nuclei in pionless effective field theory using the stochastic variational method
• From few to many bosons inside the unitary window: a transition between universal to non-universal behavior
• Wilsonian renormalization group and the Lippmann-Schwinger equation with a multitude of cutoff parameters

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