Extension of the Isobaric Nucleon Model for Pion Production in Pion-Nucleon, Nucleon-Nucleon, and Antinucleon-Nucleon Interactions

The isobaric nucleon model of pion production in nucleon-nucleon and pion-nucleon collisions has been extended to include the effect of the higher resonances in the isotopic spin $T=\frac{1}{2}$ state of the pion-nucleon system, in addition to the effect of the well-known low-energy $T=\frac{3}{2}$ resonance which has been previously investigated. The higher $T=\frac{1}{2}$ resonances are centered at incident pion energies of 600 and 880 Mev, and thus correspond to isobar masses $m_{\mathrm{I}}=1.51\mathrm{} \mathrm{and} 1.68$ Bev, respectively, as compared to $m_{\mathrm{I}}=1.23\mathrm{}$ Bev for the $T=\frac{3}{2}$ resonance. For the inelastic pion-nucleon interactions, calculations of the various pion and recoil nucleon energy spectra have been carried out for incident pion energies $T_{\pi ,\mathrm{inc}}=1.0, 1.4, \mathrm{and} 2.0$ Bev. We have considered both single and double pion production by the incident pion, corresponding to two-pion and three-pion final states, respectively. General equations for the center-of-mass energy spectra of the final-state pions and nucleons have been obtained for all single and double pion production reactions from both ${\pi }^{-}-p$ and ${\pi }^{+}-p$ collisions. The results of the present extended isobar model at $T_{\pi ,\mathrm{inc}}=1.0\mathrm{}$ Bev are in reasonable agreement with the combined data from three experiments on ${\pi }^{-}-p$ interactions in the region of 1.0 Bev incident energy. The $Q$ value distributions for pion-nucleon and pion-pion pairs have been calculated for single pion production at $T_{\pi ,\mathrm{inc}}=1.0\mathrm{}$ Bev. The present extension of the isobar model can also be used to treat up to four-pion final states in $\pi -N$ interactions, and up to eight-pion final states in $N-N$ interactions.