We consider some extensions of the relation which has been obtained by Nambu and Lurié between an elastic process and the accompanying soft pion emission process under the assumption of approximate ${\gamma }_5$ invariance. In particular, a generalized formula is found which enables one to describe the electropion production $e+N\to N+e+\pi$ and the neutrino-pion production $\nu +N\to N+e+\pi$ at the threshold of $N\pi$ system in terms of the vector (Hofstadter) and the axial-vector form factors. Explicit forms of the cross sections are given.

• Received 25 May 1962

DOI:https://doi.org/10.1103/PhysRev.128.862