Nonlinear model of chiral bag (CBM) in approximation of mean meson field

The cloudy bag model (CBM) which contains the completely nonlinear interaction of quarks with the classical mean field is investigated for the nucleon. The equations for the bag size R, quark momentum p, mean pion field φ are obtainted from the boundary conditions which provide the quark confinement and the bag stability. The expression for the total bag-nucleon energy is obtained and investigated. By means of proper averaging of all expressions it is possible to make all investigations in the spherical bag approach. It is shown that in the nonlinear CBM under investigation the equations for R, p, φ posess a consistent solution which corresponds to the absolute minimum of the energy E and consequently a stable equilibrium state of the bag-nucleon exists