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 Nth 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)) similar or equal to 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 that reflect the short-range four-body scale. We also found that the H channel is favored over the K channel at low momentum, when the four-body momentum scale largely overcomes the three-body scale.