The shapes of baryons in constrained potential models

We examine the equilibrium shapes of the system of 3 quarks subject to a potential and to a variety of constraints, some of which have been used in the literature. Both relativistic and nonrelativistic dynamics are considered. The results indicate that realistic calculations of the baryon spectrum should be arranged so as to allow for considerable departures from the spherical shape of the system. The results of the assumption that quarks move in a potential of constant volume are compared with those of some other assumptions. Although the models used are very simple they do show the tendency to produce some of the observed level patterns of the baryon mass spectrum.