Role of short range potentials in solving the eigenvalue problem for the three body Dirac equation

The eigenvalue problem for a bound state solution of three quarks requires deep analysis to even start a numerical attempt. A power series solution to the three body Dirac equation solved in hypercentral approximation is soug ht. A scalar linear flux tube three body string potential is used to confin e the quarks. In addition one gluon exchange potentials (OGEP) between quar k pairs are considered to model the short range interactions. The angular m omentum barrier is found to dominate the wave function behavior at the orig in when including only the magnetic part of the OGEP. This occurs when the Coulomb part of the OGEP is neglected, or canceled by terms of opposite sig n from the scalar potential. Recurrence relations for the power series coef ficients are determined. When the Coulomb part of the OGEP is included, the initial ratios of the composite three quark wave function components are a lso determined. In this case, the Coulomb strength of the OGEP combines wit h the angular momenta to determine the wave function behavior near the orig in.