Range Corrections to Universal Tetramer Properties

The universal properties of weakly-bound tetramers close to the scaling limit are investigated by solving a subtracted set of Faddeev–Yakubovsky (FY) equations for identical bosons with a zero-range interaction. The solution demands a four-body scale independent of the trimer properties. Furthermore, the effect of a finite effective range is introduced in the FY equations, which we show produces results that are distinct from the scale variation. In particular range effects to two universal scaling functions for the tetramers are investigated. The correlation between successive tetramer energies corresponding to states within two Efimov trimer energies, proposed before and studied close to the unitary limit; and the correlation between the position of the four-atom recombination peaks. In this case, we found a shift in the scaling function due to the range, which can be associated to the shift of the data found for caesium atoms, with respect to zero-range calculations, due to a nonvanishing range in the actual experimental setups. (author)