  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.
