Some implications of a small bag radius

We consider the possibility that the bag radius of the nucleon is of the order of the proton Compton wavelength. We explore this possibility for the cloudy-bag-model Hamiltonian when the interaction between the intrinsic isobar source and the pion field is turned off. Because of the large pion-nucleon coupling for a small bag radius, we apply the strong-coupling approximation to this model. Unlike other models of the nucleon with a small bag radius, our approach emphasizes the quantum-mechanical behavior of the infinitely many degrees of freedom of the pion field in the dressed nucleon wave function. Considerable attention is given to the approximate analytic solution of the strong-coupling part of the cloudy-bag-model Hamiltonian, which is a collective Hamiltonian involving nine coupled quantum-mechanical oscillators. An important feature of the model is the existence of collective excitations of the dressed nucleon which are rotational and vibrational excitations in spin and isospin space. The lowest-lying collective state is a spin and isospin rotational excitation which is identified with the $\Delta$, while the $N^{*}$ is a vibrational excitation. The approximate analytic expressions for the low-lying baryon wave functions facilitate the actual calculation of some static properties of the baryons such as masses, magnetic moments, charge radii, etc. We find for a bag radius $R=0.32\mathrm{}$ fm that the average number of pions in the dressed nucleon state is roughly 6. Furthermore, the overall agreement between the model and experiment is roughly 30%; however, the charge radius of the proton is too small. Some speculative ideas for improving the model are discussed.