Trimer–Tetramer Interwoven States in the Scaling Limit

Abstract

We report here some results we have obtained on the scale dependence of tetramer energies at the unitary limit, considering the number of tetramer energy levels appearing between the ground and the excited Efimov trimers. Our numerical investigation is done by solving a renormalized set of Faddeev–Yakubovsky equations for identical bosons with zero-range interaction, requiring a four-body scale, which in principle can be independent of the trimer properties. The ratio between the three- and four-body scales is introduced by considering the two lower trimer states and corresponding associated tetramers. We conclude that at least three tetramers are possible to exist between two Efimov states by varying the relation between such scales, and considering the relation between three-body Efimov states in the unitary limit. The results for the trimer–tetramer interwoven states are shown through a correlation between tetramers attached to consecutive Efimov trimer states.