The Four-Boson First-Excited State Near Two-Body Unitarity

Abstract

Near two-body unitarity, the three-boson system is characterized by an approximate discrete scale invariance manifest in a geometric tower of bound states (the Efimov effect). In the absence of a strong four-body force, the four-boson system has two states associated with each Efimov state, one very nearly unstable, the other several times deeper. We study correlations between the excited- and ground-state properties, such as binding energies and radii, up to next-to-leading order in an effective field theory for short-range forces. We obtain the parameters in these correlations from similar correlations arising from existing precise calculations based on short-range potentials. We also derive correlations among excited-state properties that emerge from the proximity of the state to the break-up threshold into a boson and a three-boson bound state, using an effective field theory for "halo" states.

31 pages, 6 figures

References in corpus (10)

• Universal Properties of the Four-Body System with Large Scattering Length
• Efimov physics in bosonic atom-trimer scattering
• Description of ${}^4$He tetramer bound and scattering states
• Energy spectra of small bosonic clusters having a large two-body scattering length
• Linear correlations between 4He trimer and tetramer energies calculated with various realistic 4He potentials
• Effective Field Theory for Few-Boson Systems
• $N$-boson spectrum from a Discrete Scale Invariance
• Ground-state properties of unitary bosons: from clusters to matter
• Few nucleons scattering in pionless effective field theory
• Universal bosonic tetramers of dimer-atom-atom structure

Cited by in corpus (2)

• Improved Actions for Nuclear Effective Field Theories
• Bound-like State in a 1D Self-Similar Delta-Barrier Array