Universality and scaling limit of weakly-bound tetramers
M. R. Hadizadeh 1*, M. T. Yamashita 1, L. Tomio 1,2, A. Delfino 2, T. Frederico 3
1 Instituto de Fsica Teorica, Universidade Estadual Paulista, 01140-070, Sao Paulo, SP, Brazil
2 Instituto de Fsica, Universidade Federal Fluminense, 24210-346, Niteroi, RJ, Brazil
3 Instituto Tecnologico de Aeronautica, 12228-900, Sao Jose dos Campos, SP, Brazil
The occurrence of a new limit cycle in few-body physics, expressing a universal scaling function relating the binding energies of two successive tetramer states, is revealed by considering a renormalized zero-range two-body interaction in bound state of four identical bosons. The tetramer energy spectrum is obtained by adding a boson to an Efimov bound state with energy B3 in the unitary limit (for zero two-body binding energy or infinite two-body scattering length). Each excited Nth tetramer energy B4(N) is shown to slide along a scaling function as a short-range four-body scale is changed, emerging from the 3+1 threshold for a universal ratio 4(N)/B3 = 4.6, which does not depend on N. The new scale can also be revealed by a resonance in the atom-trimer recombination process.