Potential energy of three heavy quarks in the MIT bag model

In the Born-Oppenheimer approximation to the MIT bag model the color-singlet $n$-quark (and/or antiquark) system is studied. Analytic approximations to the spin-independent $n$-quark potential energy are developed, based on spherical and cylindrical trial bag shapes. The domain of validity of these results is established in the $q\overline{q}$ case through tests against a numerical solution. The resulting three-quark potential contains Coulomb-type and confining parts. The Coulomb-type terms are purely two-body in nature, and the confinement term is a three-body potential.