Pion fluctuation around the hedgehog solution in the chiral bag plus skyrmion hybrid model

The Roper excitation is studied in the chiral bag plus skyrmion hybrid model. The lagrangian is expanded around the classical solution in the hedgehog vibrational mode. In the adiabatic approximation we find a self consistent solution for the fluctuating system of quarks and pions up to the first order of the fluctuations. Only half of the excitation energy was found in the phase shift analysis. It is also discussed that the system is stable for all bag radii against the hedgehog vibration. (orig.)