Cloudy bag model: Convergent perturbation expansion for the nucleon

A previously published bound on the probability of finding $n$ pions in the dressed nucleon in Chew-Low theory is improved. The proof is then extended to the recently derived cloudy-bag-model Hamiltonian. Together with a bound on the average number of pions (0.9±1.0), our result strongly suggests a rapid convergence of the perturbation expansion in the cloudy bag model.