The Dirac oscillator and its contribution to the baryon mass formula

There are very few potentials for which the Dirac equation can be solved exactly, particularly if the authors do not want to go through a series expansion whose coefficients may involve complex recurrence relations. One of these potentials was discussed recently by Moshinsky and Szczepaniak and was based on the idea that as the ordinary oscillator is quadratic in both momenta and coordinates, one should explore a Dirac equation in which both are linear. They give to this problem the name of Dirac oscillator. In the present paper the authors generalize the concept of Dirac oscillator interaction to an n-body system for which the center of mass is at rest. The authors particularize the authors' discussion to n = 3 and define a mass operator whose eigenvalues we can determine with the help of finite secular equations