In this paper, we solve the eigen solutions to the Dirac equation with local parabolic potential which is approximately equal to the short distance potential generated by spinor itself. The energy spectrum is quite different from that with Coulomb potential. The mass spectrum of some bary-ons is similar to this one. The angular momentum-mass relation is quite similar to the Regge trajectories. The parabolic potential has a structure of asymptotic freedom near the center and confinement at a large distance. So, the results imply that, the local parabolic potential may be more suitable for describing the nuclear potential. The procedure of solving can also be used for some other cases of Dirac equation with complicated potential.
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