(p,p’π+) reaction at energies below 1 GeV

The features of the (N,N’π) reaction are examined at intermediate energies, i.e., for 300–800 MeV incident nucleon energies, when the continuum nucleon and pion are observed in coincidence. In comparison with the (N,π) reaction, which has been studied in considerable detail both theoretically and experimentally, there are some advantages in analyzing the (N,N’π) reaction. Both reactions can deliver large momentum transfer to the nucleus; however, the (N,N’π) reaction can also occur for relatively small momentum transfer (e.g., q≊200 MeV/c). Thus this reaction can be studied in regions where nuclear single-particle wave functions and transition densities are large and well known. In this paper we consider one particular reaction: the exclusive (p,p’ ${\pi }^{+}$) reaction. For this process we focus on the amplitudes which are dominated by a Δ(1232) resonance in intermediate states. A nonrelativistic formalism for the reaction amplitudes is derived and examined in detail. The theoretical cross sections are shown to be quite sensitive to the pion self-energy, and relatively insensitive to the isobar self-energy in the medium. Furthermore, the calculations suggest that certain amplitudes may dominate the cross sections in different kinematic regions. The differences between relativistic and nonrelativistic approximations for the pion self-energy are examined. Because of the exploratory nature of this investigation, simple forms are used for the bound-state wave functions and transition densities, and the continuum particles are approximated by plane waves; the effects of distorted waves are estimated.