Surface vibrations of the nucleon

We examine the dynamics of bag vibrations in a model of the nucleon similar to that of Brown, Durso, and Johnson (BDJ). The model consists of a spherical bag with a variable radius and three quarks confined in it. In addition there is a pion cloud which tends to squeeze the bag. An ad hoc inertial mass is assumed for the bag motion. The Roper resonance is interpreted as due to the breathing mode. Unlike the BDJ calculation, we treat the bag-quark coupling in a nonadiabatic manner, although we still use an adiabatic approximation for the pion effect. We find that the nonadiabatic correction for the bag-quark coupling is quite substantial; it is more so when the potential for the bag due to the pion effect becomes more singular. Nevertheless we essentially concur with BDJ; the low-lying levels of the nucleon can be fitted in the correct parity order. The pion plays an important role in doing so.