Ground states and excitation spectra of baryons in a non-relativistic model with the anharmonic potential

Abstract

In this work the mass spectra for some of the baryon resonances of the particle data group with three and four star status are obtained, and a unified description of the ground states and excitation spectra of baryons are provided in the framework of a non-relativistic potential model. For this goal we have analytically solved the radial Schrödinger equation for three identical interacting particles with the anharmonic potential by using the Ansatz method and then we have calculated the baryon resonances spectrum by using the Gürsey Radicati mass formula (GR) and with generalized Gürsey Radicati mass formula (GGR). The results of our model show that the calculated masses of baryon resonances by using the generalized Gürsey Radicati mass formula are found to be in good agreement with the tabulations of the Particle Data Group. The overall good description of the spectrum which we obtain shows that our model can also be used to give a fair description of the energies of the excited multiples up to 3 GeV mass and negative-parity resonance. Moreover, we have shown that our model reproduces the position of the Roper resonance of the nucleon.