Compositeness of near-threshold states in charged hadronic systems

We quantify the internal structure of near-threshold bound, virtual, and resonance states in systems where Coulomb and short-range interactions coexist by evaluating the compositeness. Using the Coulomb-modified effective range expansion, we derive an expression for the compositeness in terms of the eigenenergy and Coulomb effective range in the weak-binding limit. We then apply the formulation to several near-threshold states in hadronic and nuclear systems, including $pp$, $\alpha \alpha$, ${\mathrm{\Omega }}^{-}{\mathrm{\Omega }}^{-}$, ${\mathrm{\Omega }}_{ccc}^{++}{\mathrm{\Omega }}_{ccc}^{++}$, ${\mathrm{\Xi }}^{-}\alpha$, and ${\mathrm{\Omega }}^{-}p$.