Isobaric Nucleon Model for Pion Production in Nucleon-Nucleon Collisions

A detailed quantitative model for pion production via excitation of one or both nucleons to an isobaric state with subsequent decay via pion emission is presented. The model is applied to the 0.8- to 3.0-Bev incident nucleon energy range and its predictions are compared to various experiments in this energy range performed at the Brookhaven Cosmotron. The isobaric state with isotopic spin and angular momentum=$\frac{3}{2}$ observed in the pion-nucleon scattering was assumed to be predominantly responsible for pion production in this energy range. The relative probability for isobar formation and subsequent decay with a variable total energy or mass in the isobar rest system were phenomenologically related to the ${\pi }^{+}-p$ interaction cross section. The energy or momentum spectra of pions, and nucleons, the variation of the ratio of double to single production, the angular correlation, and the $Q$ value distribution for pion-nucleon pairs have been calculated at various energies from 0.8- to 3.0-Bev and generally agree with the experimental results.