  The quark sigma model describes the quarks interacting via exchange the pions
and sigma meson fields. A new version of mesonic potential is suggested in the
frame of some aspects of the quantum chromodynamics (QCD). The field equations
have been solved in the mean-field approximation for the hedgehog baryon state.
The obtained results are compared with previous works and other models. We
conclude that the suggested mesonic potential successfully calculates nucleon
properties.
