Model for Electron Excitation of the Nucleon. II

The model of oscillations of the meson field in the nucleon introduced in a previous paper is developed and extended. The model provides a dynamical framework for investigating the electromagnetic properties of the nucleon and gives an excitation spectrum similar to that observed for the nucleon. In this paper we discuss an improved variational solution for the ground-state meson field and the construction of a conserved current. We investigate the problems presented by a fixed-source theory and the linearization of the ${\phi }^4$ theory in constructing this current. Once we have a model for the current, we can calculate all the electromagnetic properties of the nucleon on a consistent basis. We calculate the allowed transverse and Coulomb electron scattering form factors for all the levels of the nucleon up through 2850 MeV, and we compare with existing data wherever possible. We also compare with what is known from phenomenological analysis of photoproduction. Using the magnitude of the ground-state field obtained from a fit to the experimental inelastic form factors, we can compute the anomalous magnetic moment of the nucleon and the pion-nucleon coupling constant. We also use our parameters to investigate the elastic form factors. We show that our model is the appropriate limit of the coupled equations of motion for the meson field and the spin and isospin of the nucleon source. The model is only very crude, but it does indicate some of the interesting things that can be learned from electron excitation of the nucleon.