Relativistic Model for Electroproduction of Nucleon Resonances. II

A relativistic gauge-invariant model for electron excitation of nucleon resonances introduced previously is developed and extended. A coupled-channel calculation is carried out retaining the $|\pi N〉$ and $\left|\pi N^{*}\mathrm{}\right(1236)\mathrm{}〉$ channels and assuming that one eigenphase shift is resonant. The eigenphase shift is determined from phase-shift analyses of $\pi -N$ scattering, and the mixing angle from the decay widths of the resonance. The model chosen for the resonant amplitude is a product of two factors: a generalized Feynman amplitude for excitation of the resonant channel, and a final-state enhancement factor which is related to an integral over the eigenphase shift. The model is shown to be an approximate solution to the coupled-channel Omnès equations. Further extensions consist of including $N^{*}\mathrm{}\left(1236\right)\mathrm{}$ exchange in the excitation amplitude for the $|\pi N〉$ channel and of investigating the effect of different fits to $G_{\mathrm{En}}$ on the inelastic form factors. The predictions of the theory are compared with all existing data—in particular, with the recent results from SLAC.