Bound state energies of three self-gravitating Bose-Einstein condensates

The bound state energies of a system consisting of three identical bosons bound to each other by gravitational forces are investigated using highly correlated exponential basis functions. The bound states energy levels of two Rydberg series converging to the dissociation threshold (the (2+1) threshold) for such a three-body self-gravitating Bose-Einstein condensates are reported. Our results show high degree of accuracy, with one of the Rydberg series lying below those reported in the literature, and the other Rydberg series representing bound states for the three self-gravitating fermions are new calculations.