Level rearrangement in exotic-atom-like three-body systems

We study systems of three bosons bound by a long-range interaction supplemented by a short-range potential of variable strength. This generalizes the usual two-body exotic atoms where the Coulomb interaction is modified by nuclear forces at short distances. The energy shift due to the short-range part of the interaction combines two-body terms similar to the ones entering the Trueman-Deser formula, and three-body contributions. A sudden variation of the energy levels is observed near the coupling thresholds of the short-range potential. But the patterns of rearrangement are significantly modified as compared to the two-body case.