The matrix element for the interaction $W+N\to \pi +N$ is studied, where $W$ is a virtual intermediate boson for the weak interactions (or just the weak current). Weak pion production—production of a pion by high-energy neutrino collisions with nucleons—is governed by this matrix element. The main case of interest is in the energy region where the pion-nucleon 3-3 resonance is dominant. Formulas are derived for solving the problem in this region.

• Received 15 January 1962

DOI:https://doi.org/10.1103/PhysRev.127.653