Pion Production in Neutrino-Nucleon Collisions

An evaluation of the scattering amplitude for pion production in neutrino-nucleon collisions is made assuming that the $\frac{3}{2}-\frac{3}{2}$ $\pi$-nucleon resonance dominates the dispersion integrals. No assumption is made concerning nucleon recoil. The vector part of the amplitude is related to the isovector part of the amplitude for electroproduction of pions by use of the Feynman-Gell-Mann conserved vector current theory. An independent calculation is given for the axial vector part of the amplitude.