Efimov universality with Coulomb interaction

The universal properties of charged particles are modified by the presence of a long-range Coulomb interaction. We investigate the modification of Efimov universality as a function of the Coulomb strength using the Gaussian Expansion Method. The resonant short-range interaction is described by Gaussian potentials to which a Coulomb potential is added. We calculate binding energies and root mean square radii for the three- and four-body systems of charged particles and present our results in a generalised Efimov plot. We find that universal features can still be discerned for weak Coulomb interaction, but break down for strong Coulomb interaction. The maximum root mean square radius of the system decreases as the strength of the Coulomb interaction is increased and the probability distributions of the states become more concentrated inside the Coulomb barrier. As an example, we apply our universal model to nuclei with an α cluster substructure. Our results point to strong non-universal contributions in that sector.