The three-nucleon potential in a QCD based model

Abstract

Three-nucleon potentials are calculated in the Born-Oppenheimer approximation using a triple-well harmonic oscillator potential to confine the quarks. The model builds in some of the effects of local gauge invariance. Matrix elements of the hamiltonian are calculated in a basis consisting of fifteen gaussian functions centered at different locations so that they cover the appropriate are of a plane. The Born-Oppenheimer potentials is the energy of this system as a function of the three distances separating the potential wells, the three internucleonic separations. After subtraction of the two-body potentials, a pure three-body potential is revealed which is similar in magnitude to the two-body potentials but has shorter range. As expected, the lowest energy configuration is that of the equilateral triangle. The size of the potential barrier against passing through the linear trinucleon configuration is reported.