Calculation of the energy levels and sizes of baryons with a noncentral harmonic potential

Abstract

It is considered that the effective interaction between any two quarks in a baryon can be approximately described by a simple harmonic potential. Also, it is made use of the nonrelativistic approximation. The problem is firstly solved in Cartesian coordinates in order to find the energy levels irrespective of their angular momenta and then it is also solved in polar cilindrical coordinates for taking into account the angular momenta of the levels. The only parameters used in the calculation are the constituent masses of quarks. By making a comparison between the two solutions the energies and the corresponding angular momenta (and parity) of almost all baryon levels are described. The agreement with the experimental data is quite impressive. The solution in Cartesian coordinates also produces some very important figures for the sizes of baryons and for the harmonic oscillator constant which is clearly related to confinement.