Embedding nuclear physics inside the unitary window

Abstract

The large values of the singlet and triplet scattering lengths locate the two-nucleon system close to the unitary limit, the limit in which these two values diverge. As a consequence, the system shows a continuous scale invariance which strongly constrains the values of the observables, a well-known fact already noticed a long time ago. The three-nucleon system shows a discrete scale invariance that can be observed by correlations of the triton binding energy with other observables as the doublet nucleon-deuteron scattering length or the alpha-particle binding energy. The low-energy dynamics of these systems is universal; it does not depend on the details of the particular way in which the nucleons interact. Instead, it depends on a few control parameters, the large values of the scattering lengths and the triton binding energy. Using a potential model with variable strength set to give values to the control parameters, we study the spectrum of $A=2,3,4,6$ nuclei in the region between the unitary limit and their physical values. In particular, we analyze how the binding energies emerge from the unitary limit forming the observed levels.

References in corpus (15)

• Minimally non-local nucleon-nucleon potentials with chiral two-pion exchange including $\Delta$'s
• Universal Properties of the Four-Body System with Large Scattering Length
• No-core shell model in an effective-field-theory framework
• Essential elements for nuclear binding
• Four-Body Scale in Universal Few-Boson Systems
• Energy spectra of small bosonic clusters having a large two-body scattering length
• Non-symmetrized hyperspherical harmonic basis for $A$-bodies
• $N$-boson spectrum from a Discrete Scale Invariance
• Implications of Efimov physics for the description of three and four nucleons in chiral effective field theory
• The harmonic hyperspherical basis for identical particles without permutational symmetry
• Fate of the neutron-deuteron virtual state as an Efimov level
• More on the infrared renormalization group limit cycle in QCD
• Comment on "Is a Trineutron Resonance Lower in Energy than a Tetraneutron Resonance?" [arXiv:1612.01502]
• Saturation properties of helium drops from a Leading Order description
• More on the universal equation for Efimov states

Cited by in corpus (20)

• Nuclear effective field theory: status and perspectives
• Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
• Efimov Physics and Connections to Nuclear Physics
• Two- and three-nucleon contact interactions and ground-state energies of light- and medium-mass nuclei
• Naturalness in Nuclear Effective Field Theories
• A Comprehensive Study of the Three- and Four-Neutron Systems at Low Energies
• Clustering of Four-Component Unitary Fermions
• Nuclear Effective Field Theories: Reverberations of the early days
• From few to many bosons inside the unitary window: a transition between universal to non-universal behavior
• Nuclear Structure at the Crossroads
• The $p\Lambda$ and $pp\Lambda$ correlation functions
• Multi-fermion systems with contact theories
• A Vision for the Science of Rare Isotopes
• ${}^7$H ground state as a ${}^3$H+4n resonance
• Mass-Energy Equivalence in Bound Three-Nucleon Systems
• The excited state of the $\alpha$-particle: a benchmark study
• Quantum Monte Carlo studies of a trimer scaling function with microscopic two- and three-body interactions
• The role of the effective range in strongly-interacting few-body systems
• Gaussian characterization of two-neutron halo nuclei
• Improved Actions for Nuclear Effective Field Theories