Three-body systems with attractive 1∕r potentials

We have used the hyperspherical adiabatic representation to describe the system of three identical bosons in a spin stretched state interacting through an attractive 1∕r potential. A proposal has been forwarded to enable the experimental realization of such a system in cold trapped atoms using extremely off-resonant laser fields Phys. Rev. Lett., 84 5687 (2000). We have obtained the effective potentials, channel functions, and nonadiabatic couplings for this gravitylike 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. Further, since the effective potentials have a long-range 1∕R attraction, the properties of the excited states follow from the well-known results for Rydberg states. We have also analyzed the possible geometries and vibrational modes for this system.