Trajectory of virtual, bound and resonant Efimov states

The pole trajectory of Efimov states for a three-body $\alpha \alpha \beta$ system with $\alpha \alpha$ unbound and $\alpha \beta$ bound is calculated using a zero-range Dirac-$\delta$ potential. It is showed that a three-body bound state turns into a virtual one by increasing the $\alpha \beta$ binding energy. This result is consistent with previous results for three equal mass particles. The present approach considers the $n-n{-}^{18}C$ halo nucleus. However, the results have good perspective to be tested and applied in ultracold atomic systems, where one can realize such three-body configuration with tunable two-body interaction.