Structure of near-threshold states in systems with Coulomb and short-range interactions

TL;DR

This paper investigates the properties of near-threshold states in systems with both Coulomb and short-range interactions, revealing how Coulomb forces influence the internal structure and pole trajectories of bound states and resonances.

Contribution

It introduces a Coulomb-modified effective range expansion to analyze pole trajectories and compositeness, highlighting differences from systems with only short-range interactions.

Findings

Bound state and resonance poles are disconnected with Coulomb attraction.

Near-threshold bound states are nearly purely composite.

The interplay between Coulomb and short-range forces affects compositeness near unity.

Abstract

We study the nature of near-threshold eigenstates in systems with the attractive Coulomb plus short-range interactions. Using a model providing the Coulomb-modified effective range expansion, we analyze pole trajectories and the internal structure of near-threshold states characterized by the compositeness. We find that bound state and resonance poles are disconnected in the presence of the attractive Coulomb interaction, in contrast to the repulsive Coulomb force. Near the threshold, bound states become almost purely composite, while the behavior of the compositeness near unityis controlled by the competition between the Coulomb and short-range interactions, characterized by the Bohr radius and the Coulomb effective range.