Scaling limit of weakly bound triatomic states

Abstract

The usefulness of a scale-independent approach to identify Efimov states in three-body systems is shown by comparing such an approach with a realistic calculation in the case of three helium atoms. We show that the scaling limit is realized in practice in this case, and suggest its application to study other similar systems, including the case where two kinds of atoms are mixed. We also consider the observed large scattering length of $\mathrm{the}{ }^{87}\mathrm{Rb}$ dimer to estimate the critical value of the ground-state energy of the corresponding trimer $(>~1.5 \mathrm{mK})$, in order to allow for one Efimov state above the ground state.