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 B4(N) moves as the short-range four-body scale changes, while the trimer properties are kept fixed, with the next excited tetramer B4(N+1) emerging from the atom-trimer threshold for a universal ratio B4(N)/B 3=B4(N)/B4(N+1)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. © 2012 American Physical Society.