Relativistic Model for Electroproduction of Nucleon Resonances

Abstract

We have made a simple model to obtain some estimates of the inelastic form factors for electron excitation of the nucleon resonances. The model is covariant and gauge invariant, and satisfies all the general requirements of the theory. It relies heavily on the lead of previous theoretical work on the form factor for the ${\frac{3}{2}}^{+}$, $\frac{3}{2}$ (1238-MeV) level. The basic idea is to take from experiment the knowledge of which nucleon states are resonant. We then look at single-pion electroproduction and project out the relevant multipoles from a covariant, gauge-invariant set of graphs which are thought to play an important role as an excitation mechanism. The multipoles are then multiplied by a final-state enhancement factor which provides a resonance mechanism. We give some theoretical justification for this procedure. If just the electron is detected, one measures the virtual-photon width for formation of the resonance, and our result contains the possibility that the resonance can decay into other channels than just $\ensuremath{\pi}+N$. We calculate only the inelastic form factors. The individual contributions of the resonance levels are normalized to photoabsorption, where such data exist. We keep $\ensuremath{\pi}$, $\ensuremath{\omega}$, and $N$ exchange as an excitation mechanism, and treat the over-all contribution of the $\ensuremath{\omega}$ exchange as a single parameter, with which we are able to fit all the existing inelastic-electron-scattering data. We actually find two equally acceptable fits with quite different properties. The $\ensuremath{\omega}$-nucleon coupling constant we get from this analysis is in reasonable agreement with other determinations of this quantity. Form factors for all the nucleon levels up through 2650 MeV are presented out to momentum transfers of interest in the SLAC experiments.