Two-Step Contribution to Intermediate Energy (p,p′) and (p,n) Reactions

We calculate the two-step contribution to (p, p′) and (p, n) reactions at intermediate energy. We describe the motion of the incident nucleon with a plane wave and compare the contribution from two-step processes with that from one-step processes. To describe the two-step processes, we extend the response functions to nondiagonal forms with respect to the momentum transfer q. We performed a numerical calculation for the cross sections of the C, Ca(p, p′) scattering and the spin longitudinal and spin transverse cross sections of the C, Ca(p, n) reactions at 346 MeV and 494 MeV. We found that the two-step contribution is appreciable in comparison with the one-step processes in the higher-energy transfer region for the spin longitudinal and the spin transverse (p, n) reactions. We also found that the two-step processes give larger contributions to the spin transverse (p, n) reaction than to the spin longitudinal reaction. This finding is very encouraging to interpret the discrepancy between the DWIA calculation and the experimental results of the spin longitudinal and the spin transverse cross sections.