Binding and structure of tetramers in the scaling limit

Abstract

The momentum-space structure of the Faddeev-Yakubovsky (FY)components of weakly-bound tetramers is investigated at the unitary limit using a renormalized zero-range two-body interaction. The results, obtained by considering a given trimer level with binding energy $B_3$, provide further support to a universal scaling function relating the binding energies of two successive tetramer states. The correlated scaling between the tetramer energies comes from the sensitivity of the four-boson system to a short-range four-body scale. Each excited $N-$th tetramer energy $B_4^{(N)}$ moves as the short-range four-body scale changes, while the trimer properties are kept fixed, with the next excited tetramer $B_4^{(N+1)}$ emerging from the atom-trimer threshold for a universal ratio $B_4^{(N)}/B_3=B_4^{(N)}/B_4^{(N+1)}\simeq 4.6$, which does not depend on $N$. We show that both channels of the FY decomposition [atom-trimer ($K-$type) and dimer-dimer ($H-$type)] present high momentum tails, which reflect the short-range four-body scale. We also found that the $H-$channel is favored over $K-$channel at low momentum when the four-body momentum scale largely overcomes the three-body one.

To appear in PRA

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Cited by in corpus (16)

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• Universality in Four-Boson Systems
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• Effective range from tetramer dissociation data for cesium atoms
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• Efficient calculation of trion energies in monolayer transition metal dichalcogenides
• Three-Body Bound State Calculations by Using Three-Dimensional Low Momentum Interaction $V_{low-k}$
• Four-Body Systems at Large Cutoffs in Effective Field Theory
• The Four-Boson First-Excited State Near Two-Body Unitarity
• Relativistic Faddeev 3D Equations for Three-Body Bound States Without Two-Body $t-$Matrices
• A Novel Regularization Scheme for Nucleon-Nucleon Lattice Simulations with Effective Field Theory
• Universal prohibited zones in the coordinate space of few-body systems
• Four-body bound states in momentum space: the Yakubovsky approach without two-body $t-$matrices
• Comment on "Three-dimensional study of the six-body bound-state for the case of effective three-body configuration model" [Int. J. Mod. Phys. E 25, 9 (2016) 1650072]
• Fixed-Point Few-Body Hamiltonians in Quantum Mechanics
• Three-boson stability for boosted interactions towards the zero-range limit