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

Tomona Kinugawa, Tetsuo Hyodo

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.

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

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.
Paper Structure (4 sections, 5 equations, 1 figure)

This paper contains 4 sections, 5 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Formulation
  3. Pole trajectories and compositeness
  4. Summary

Figures (1)

  • Figure 1: Left panel: Pole trajectories of the eigenstates originated from the short-range interaction in the complex momentum $a_{B}k$ plane as the inverse scattering length $1/a_{s}^{C}$ is varied. The effective range is fixed at $r_{e}^{C}/a_{B} = -0.1$. Right panel: Compositeness $X$ of the bound state as functions of $a_{B}/a_{s}^{C}$ for $r_{e}^{C}/a_{B} = -10$ (solid line), $-1$ (dashed line), and $-0.1$ (dotted line).