Static-bag-source meson field theory: Strong-coupling approximation

In this paper we discuss quantum-mechanical strong-coupling calculations on a static-source meson field theory in which only the nucleon isospin degrees of freedom are coupled linearly to an isovector-scalar meson field. The nucleon source function is of the chiral bag type, namely a shell source. We perform numerical calculations in the strong-coupling approximation, namely for $g\ensuremath{\gg}{(8{\ensuremath{\pi}}^{2}\ensuremath{\mu}R)}^{\frac{1}{4}}$, where $g$ is a dimensionless bare coupling constant, $\ensuremath{\mu}$ is the meson mass, and $R$ is the bag size. We demonstrate that the corrections to our lowest-order approximation to the dressed nucleon wave function decrease as the coupling strength increases according to the above inequality. We find that there exist reasonable values of the parameters, say $g\ensuremath{\sim}4$ and $R\ensuremath{\sim}0.3$ fm, for which the lowest-order approximation to the dressed nucleon state of this model is good. We also find collective excitations of the dressed nucleon which are rotational and vibrational excitations in isospin space. The lowest-lying collective excitation is a rotational state which is identified as the $\ensuremath{\Delta}$ in this model. Furthermore, we generalize the model field theory by introducing a feature of the cloudy-bag-model Hamiltonian, namely, an intrinsic isobar source coupled to the meson field. We find that the strong-coupling approximation is realized for significantly smaller values of the bare coupling constant or larger values of the bag size when compared to the previous model. We also find a total bare-$\ensuremath{\Delta}$ component on the dressed nucleon state of 36%. Finally, we numerically solve the meson-nucleon scattering problem in the first model by employing the reaction theory of Feshbach.