Inelastic Scattering of 40-MeV Polarized Protons

The left-right asymmetry and differential cross section for the inelastic scattering of 40-MeV polarized protons were measured over a large angular region for each of the following $2^{+}$ excitations: 1.78 MeV in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, 1.41 and 2.97 MeV in ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, 1.45 MeV in ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, and 1.33 MeV in ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$. Some asymmetry and cross-section data were also obtained for $3^{-}$ states: 6.9 MeV in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, 4.8 and 6.4 MeV in ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, 4.5 MeV in ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, and 4.08 MeV in ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$. The inelastic scattering was analyzed in the distorted-wave approximation, using the collective-model extension of the optical-model potential determined by fitting elastic polarization and cross-section measurements for each target. The inelastic asymmetry and cross-section data are best reproduced with a collective-model interaction obtained by deforming the complete optical potential, including its imaginary and spin-orbit parts.