Analysis of soliton bag model

Within the mean field approximation the nontopological soliton bag model of Friedberg and Lee is analysed with the solutions expressed in terms of power series expansion. It is shown that the mathematical problem of finding the soliton solutions reduces to that of a set of three coupled algebraic equations concerning the fermion (quark) energy, the normalization constant of fermion's wave function and one of the potential parameters. These equations are obtained as a result of the boundary condition, the normalization condition for fermion's wave function and the mean square charge radius of the proton. The solutions obtained in this manner may agree to the exact solutions for r<=0.8R where R is the bag radius, but some deviations appear for r>=0.8R. We have calculated the bag mass for a low-lying state and examined its stability. Also the magnetic moment of the proton and the axial-vector/vector coupling constant ratio are evaluated. (author)