On the modification of the Efimov spectrum in a finite cubic box

Abstract

Three particles with large scattering length display a universal spectrum of three-body bound states called "Efimov trimers''. We calculate the modification of the Efimov trimers of three identical bosons in a finite cubic box and compute the dependence of their energies on the box size using effective field theory. Previous calculations for positive scattering length that were perturbative in the finite volume energy shift are extended to arbitrarily large shifts and negative scattering lengths. The renormalization of the effective field theory in the finite volume is explicitly verified. Moreover, we investigate the effects of partial wave mixing and study the behavior of shallow trimers near the dimer energy. Finally, we provide numerical evidence for universal scaling of the finite volume corrections.

21 pages, 8 figures, published version

References in corpus (21)

• Observation of an Efimov spectrum in an atomic system
• Collisional stability of a three-component degenerate Fermi gas
• Three-body recombination in a three-state Fermi gas with widely tunable interactions
• Observation of universality in ultracold 7Li three-body recombination
• Observation of an Efimov-like resonance in ultracold atom-dimer scattering
• Observation of heteronuclear atomic Efimov resonances
• Hyperon-Nucleon Scattering from Fully-Dynamical Lattice QCD
• Multi-Pion States in Lattice QCD and the Charged-Pion Condensate
• n-Boson Energies at Finite Volume and Three-Boson Interactions
• High Statistics Analysis using Anisotropic Clover Lattices: (II) Three-Baryon Systems
• Three-boson problem at low energy and Implications for dilute Bose-Einstein condensates
• Efimov physics in a finite volume
• Universal properties and structure of halo nuclei
• Low-Energy Universality in Atomic and Nuclear Physics
• The Energy of n Identical Bosons in a Finite Volume at O(L^{-7})
• Hadronic Interactions from Lattice QCD
• The Delta-resonance in a finite volume
• Three fermions in a box at the unitary limit: universality in a lattice model
• Pion-mass dependence of three-nucleon observables
• More on the infrared renormalization group limit cycle in QCD
• Kaon Condensation with Lattice QCD

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