Three-body systems with attractive 1/r potentials
  We have used the hyperspherical adiabatic representation to describe the system of three identical bosons in an spin stretched state interacting by an attractive 1/r potential. A proposal has been made how such a system might be realized experimentally in cold trapped atoms using extremely off-resonant laser fields [Phys. Rev. Lett. 84, 5687 (2000)]. We have obtained effective potentials, channel functions, and nonadiabatic couplings for this gravity-like interaction, allowing us to calculate the ground state energy with accuracy that substantially improves upon previous results. We have similarly calculated the energies for the first four 0^+ excited states. These results show that the simple adiabatic hyperspherical approximation offers an accurate description for such a system. 
J. P. D'Incao, S. C. Cheng, H. Suno and B. D. Esry