Proton-induced positive and neutral pion production: the stripping model

A theoretical model is put forth of the proton-induced π+ and π0 production process, A(p,π+0)A + 1, with the residual nucleus in a discrete state. Expressions for the asymmetries and the unpolarized cross sections are developed with full proton and pion distortions in a DWBA Stripping model formalism, which emphasizes a careful examination of the rescattering effects of the outgoing pion. For this purpose, in addition to the well-known Kisslinger and Laplacian pion-nucleus optical potentials, a local form is introduced that avoids the unphysical off-shell divergence of the first two potentials. This is accomplished by adding multiplicative off-shell damping form-factors of the modified Gaussian type to the Laplacian potential. Corrections for Pauli-blocking, true-pion absorption, angle transformation, and isovector contribution are also included. A DWBA code is used with standard proton and Coulomb distortions. The usual nonrelativistic form of the pseudoscalar-pseudoscalar pion-nucleon interaction is used in either its static or Galilean-invariant limits. Shell-model wave functions for the captured nucleon in a Woods-Saxon potential are employed. Finally, an extensive comparison is made of this model with most of the existing experimental results in the close-to-threshold region. In particular, the theoretical predictions for the differential cross sections and the asymmetries give a qualitative agreement with most data for the target nuclei 10B, 12C, 16O, 40Ca, 90Zr, and 208Pb. These results, however, are found to be sensitive to both proton and pion distortions and the parameters of the binding potential for the captured nucleon