Pion Production in Pion-Nucleon Collisions

The single production of pions occurring in pion-nucleon collisions at incident pion energies below ∼1.5 Bev has been considered in terms of the inelastic excitation of the nucleon to the isobaric state with isotopic spin and $\mathrm{angular}\mathrm{momentum}=\frac{3}{2}$, previously identified with the resonant state in the low-energy pion-nucleon scattering. An associated separate recoil pion accompanies the isobar, and conserves energy and momentum. The isobar subsequently decays into a nucleon and a pion. Expressions have been obtained for the branching ratios between the different reactions, ${\pi }^{-}+p\to {\pi }^{-}+{\pi }^{+}+n$, and ${\pi }^{-}+{\pi }^0+p$, and for the separate energy spectra of the ${\pi }^{+}$, ${\pi }^0$, and ${\pi }^{-}$ mesons. The momentum distributions of the pions and recoil nucleons have been calculated at incident pion energies of 0.93 Bev and 1.37 Bev, and are generally in reasonable agreement with the experimental data available at these energies.