Deep inelastic pion-induced nuclear reactions are calculated in the isobar model, which assumes that an interacting resonant pion and nucleon form an unstable particle, the $\Delta$, which can propagate through the nucleus and either decay or be absorbed by interacting with other nucleons in the nucleus. The propagation of the particles is treated classically and the interactions are assumed to be incoherent. The lifetime of the $\Delta$ is taken to be energy dependent as prescribed by measured pion-nucleon scattering and the cross section of the $\Delta$ absorption is determined by measured pion production in two nucleon collisions. The formation of the $\Delta$ by a pion and nucleon and the subsequent absorption of the $\Delta$ provide a two-step mechanism for pion absorption. These calculations indicate that the pion is absorbed mostly on the inside forward edge of the nuclear surface where the nuclear density has almost reached central density. The calculations are compared with measured pion absorption cross sections, proton spectra, and spallation products in pion-induced reactions. All of these data indicate that pion absorption is underestimated in this model by perhaps as much as 35%, particularly for low energy (∼ 100 MeV) pions. Possible explanations for these discrepancies are discussed.

[NUCLEAR REACTIONS Calculated absorption cross section, proton spectra, and spallation products for pion-induced reactions on various nuclei.]

• Received 19 July 1977

DOI:https://doi.org/10.1103/PhysRevC.17.195