Double-Scattering Corrections to Medium- and High-Energy Inelastic Nucleon Scattering

We calculate double-scattering corrections to the differential cross section for the inelastic scattering of nucleons from complex nuclei. The Watson formalism of multiple scattering is employed. Numerical computations are performed for the reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(p,p^{\prime }){}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{*}{}_{}{}^{}$ ($2^{+}$ state, 4.43 MeV) for the incident proton energies $E_o=156,100,\mathrm{and} 90$ MeV. Our $2^{+}$-state eigenvector is taken from a microscopic random-phase-approximation model calculation. The computed double-scattering corrections to $\sigma \left(\theta \right)$ are appreciable and negative at small $\theta$ (at 156 MeV of the order of -10∼ -20%). They are rather sensitive to the details of the final-state nuclear wave function.