Spectroscopy of the three-heavy-quark system

We describe a way to include asymptotic freedom in the potential energy for a baryon composed of three heavy quarks, which is based on the Born-Oppenheimer approximation to the MIT bag model. The running coupling constant appears in both the two-body Coulomb terms and the three-body confining term of the potential energy. The Schroedinger equation with this potential is solved using a hyper-spherical expansion, and spectra are obtained for the baryons b/sup 3/, c/sup 3/, and ..cap omega../sup -/(s/sup 3/). Comparisons of these systems with the corresponding qq-bar systems are made using the same running coupling constant and bag parameters for the baryons and the mesons.