Compositeness of near-threshold states with repulsive Coulomb interaction combined with short-range potential

We investigate the internal structure of near-threshold states in a system with a repulsive Coulomb interaction combined with a short-range potential, using the compositeness. We construct a model in which the eigenmomentum is expressed in terms of three observables: the Coulomb scattering length, the Coulomb effective range, and the Bohr radius. In the presence of the Coulomb interaction, a bound state directly goes into a resonance as parameters are varied, bypassing a virtual state, in contrast to the case with only the short-range interaction. We show that the compositeness of near-threshold states can be expressed solely in terms of these observables. When the magnitude of the Coulomb effective range is much smaller than that of the Bohr radius, both shallow bound states and near-threshold resonances exhibit common structures with large compositeness, reflecting the remnant of the low-energy universality.