Dispersion Theory Treatment of Pion Production in Electron-Nucleon Collisions

Abstract

The production of mesons in electron-nucleon collisions is treated by using the method of dispersion relations. The result is analogous to that obtained by Chew, Low, Goldberger, and Nambu for photo-production using the same method. Apart from the appearance of longitudinal and scalar components of the virtual photon polarization, the important difference is that charge and magnetic moments have to be multiplied by the appropriate nucleon electromagnetic form factors. Two formulas are given for the scattering amplitude: one is a static approximation which is valid if the electron invariant momentum transfer $\lambda$ is less than 500 Mev; the other takes account of the recoil effects, and may be trusted within 30% even up to $\lambda \sim 1$ Bev. It is suggested that the measurement of the energy and angular distribution of the electron can offer an alternative method for the determination of the nucleon form factors.