Universality of excited three-body bound states in one dimension

Abstract

We study a heavy-heavy-light three-body system confined to one space dimension in the regime where an excited state in the heavy-light subsystems becomes weakly bound. The associated two-body system is characterized by (i) the structure of the weakly-bound excited heavy-light state and (ii) the presence of deeply-bound heavy-light states. The consequences of these aspects for the behavior of the three-body system are analyzed. We find a strong indication for universal behavior of both three-body binding energies and wave functions for different weakly-bound excited states in the heavy-light subsystems.

Proof of universality in one-dimensional few-body systems including anisotropic interactions

“…As a result, we can provide approximate expressions for the three-body binding energies valid in the case of small potential magnitude v 0 , that is when the pair-interactions are tuned to support a weakly-bound ground state in the heavy-light subsystems. The universality of energies and wave functions of threebody bound states for finite-range interactions that are tuned to support a weakly-bound excited state in the heavy-light subsystems has been demonstrated numerically in reference [16]. An analytical proof as presented in this work would be desirable and might explain the reported [16] differences and similarities compared to the situation of a weakly-bound heavy-light ground state.…”

“…The universality of energies and wave functions of threebody bound states for finite-range interactions that are tuned to support a weakly-bound excited state in the heavy-light subsystems has been demonstrated numerically in reference [16]. An analytical proof as presented in this work would be desirable and might explain the reported [16] differences and similarities compared to the situation of a weakly-bound heavy-light ground state.…”