Trajectory of virtual, bound and resonant Efimov states

TL;DR

This paper investigates the evolution of Efimov states in a three-body system with specific unbound and bound pairs, using a zero-range potential, and discusses implications for nuclear and ultracold atomic systems.

Contribution

It provides a detailed analysis of Efimov state trajectories in a non-symmetric three-body system with potential applications to nuclear and atomic physics.

Findings

A three-body bound state becomes virtual as the $eta$ binding energy increases.

Results are consistent with previous studies on equal mass particles.

The approach can be applied to halo nuclei and ultracold atomic systems.

Abstract

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.