Universal Correlations in Pion-less EFT with the Resonating Group Model: Three and Four Nucleons

Abstract

The Effective Field Theory "without pions" at next-to-leading order is used to analyze universal bound state and scattering properties of the 3- and 4-nucleon system. Results of a variety of phase shift equivalent nuclear potentials are presented for bound state properties of 3H and 4He, and for the singlet S-wave 3He-neutron scattering length a_0(3He-n). The calculations are performed with the Refined Resonating Group Method and include a full treatment of the Coulomb interaction and the leading-order 3-nucleon interaction. The results compare favorably with data and values from AV18(+UIX) model calculations. A new correlation between a_0(3He-n) and the 3H binding energy is found. Furthermore, we confirm at next-to-leading order the correlations, already found at leading-order, between the 3H binding energy and the 3H charge radius, and the Tjon line. With the 3H binding energy as input, we get predictions of the Effective Field Theory "without pions" at next-to-leading order for the root mean square charge radius of 3H of (1.6\pm 0.2) fm, for the 4He binding energy of (28\pm 2.5) MeV, and for Re(a_0(3He-n)) of (7.5\pm 0.6)fm. Including the Coulomb interaction, the splitting in binding energy between 3H and 3He is found to be (0.66\pm 0.03) MeV. The discrepancy to data of (0.10\mp 0.03) MeV is model independently attributed to higher order charge independence breaking interactions. We also demonstrate that different results for the same observable stem from higher order effects, and carefully assess that numerical uncertainties are negligible. Our results demonstrate the convergence and usefulness of the pion-less theory at next-to-leading order in the 4He channel. We conclude that no 4-nucleon interaction is needed to renormalize the theory at next-to-leading order in the 4-nucleon sector.

24 pages revtex4, including 8 figures as .eps files embedded with includegraphicx, leading-order results added, calculations include the LO three-nucleon interaction explicitly, comment on Wigner bound added, minor modifications

References in corpus (35)

• An accurate nucleon-nucleon potential with charge-independence breaking
• Modern Theory of Nuclear Forces
• Universality in Few-body Systems with Large Scattering Length
• Quantum Monte Carlo calculations of nuclei with A \leq 7
• Effective Field Theory for Few-Nucleon Systems
• Renormalization of the Three-Body System with Short-Range Interactions
• Realistic models of pion-exchange three-nucleon interactions
• The Three-Boson System with Short-Range Interactions
• Effective Field Theory of Nuclear Forces
• Effective Field Theory for Halo Nuclei: Shallow p-Wave States
• Low Energy Expansion in the Three Body System to All Orders and the Triton Channel
• Rearranging Pionless Effective Field Theory
• How short is too short? Constraining zero-range interactions in nucleon-nucleon scattering
• Charge Symmetry Breaking and QCD
• Precision Calculation of n+p->d+gamma Cross Section for Big-Bang Nucleosynthesis
• On the correlation between the binding energies of the triton and the alpha-particle
• Four-nucleon scattering: Ab initio calculations in momentum space
• No-core shell model in an effective-field-theory framework
• Improved Convergence in the Three-Nucleon System at Very Low Energies
• Range Corrections to Doublet S-Wave Neutron-Deuteron Scattering
• Simultaneous measurement of the photodisintegration of 4He in the giant dipole resonance region
• Low-Energy Universality in Atomic and Nuclear Physics
• Two-body Photodisintegration of ${}^4$He with Full Final State Interaction
• The Three-Boson System at Next-To-Next-To-Leading Order
• 4He experiments can serve as a database for determining the three-nucleon force
• The Three-Nucleon System at Next-To-Next-To-Leading Order
• Building light nuclei from neutrons, protons, and pions
• Charge-Symmetry-Breaking Three-Nucleon Forces
• From Hadrons to Nuclei: Crossing the Border
• Universality in the triton charge form factor
• Determination of bound state wave functions by a genetic algorithm
• Pion-less Effective Field Theory on Low-Energy Deuteron Electro-Disintegration
• Photodisintegration of three- and four- nucleon systems
• The $A_y$-Problem in Refined Resonating Group Model calculations for ($p{-}^3\mathrm{He}$) Scattering
• Chiral effective field theory for few-nucleon systems

Cited by in corpus (44)

• Nuclear effective field theory: status and perspectives
• Three-body forces: From cold atoms to nuclei
• Quantum Monte Carlo Calculations with Chiral Effective Field Theory Interactions
• Effective field theory description of halo nuclei
• Efimov States in Nuclear and Particle Physics
• Effective Field Theory for Lattice Nuclei
• Nuclear Physics Around the Unitarity Limit
• Pion-less effective field theory for atomic nuclei and lattice nuclei
• Quark mass variation constraints from Big Bang nucleosynthesis
• Four-Body Scale in Universal Few-Boson Systems
• Correlations imposed by the unitary limit between few-nucleon systems, nuclear matter and neutron stars
• Spectra and Scattering of Light Lattice Nuclei from Effective Field Theory
• The Theory of Parity Violation in Few-Nucleon Systems
• Three and Four Harmonically Trapped Particles in an Effective Field Theory Framework
• Effective field theory of 3He
• Parity-violating neutron spin rotation in hydrogen and deuterium
• Power counting in chiral effective field theory and nuclear binding
• Low-energy p-d scattering and He-3 in pionless EFT
• Two and Three Nucleons in a Trap and the Continuum Limit
• The Triton Charge Radius to Next-to-next-to-leading order in Pionless Effective Field Theory
• Two- and three-nucleon contact interactions and ground-state energies of light- and medium-mass nuclei
• Naturalness in Nuclear Effective Field Theories
• Efimov physics from a renormalization group perspective
• The proton-deuteron system in pionless EFT revisited
• Charge and Magnetic Properties of Three-Nucleon Systems in Pionless Effective Field Theory
• Second-order perturbation theory for 3He and pd scattering in pionless EFT
• Electromagnetic characteristics of $A\le 3$ physical and lattice nuclei
• Clustering of Four-Component Unitary Fermions
• Description of light nuclei in pionless effective field theory using the stochastic variational method
• The Tjon Band in Nuclear Lattice Effective Field Theory
• Five-body calculation of $s$-wave $n$-${}^4$He scattering at next-to-leading order pionless effective field theory
• Few nucleons scattering in pionless effective field theory
• The Coulomb interaction in Helium-3: Interplay of strong short-range and weak long-range potentials
• Constraining the neutron-neutron scattering length with \eftnopi
• Effective field theory for deformed odd-mass nuclei
• Three-body systems in pionless effective field theory
• Ab Initio Theory of Light-ion Reactions
• Exactness of the normal-ordered two-body truncation of three-nucleon forces
• Four-Body Systems at Large Cutoffs in Effective Field Theory
• Few-Nucleon Systems within Finite-Cutoff Pionless EFT
• Matching effective few-nucleon theories to QCD
• Toward scalable quantum computations of atomic nuclei
• NuLattice: Ab initio computations of atomic nuclei on lattices
• Two-Body Triton Photodisintegration and Wigner-SU(4) Symmetry