Abstract
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 ${3}^{\ensuremath{-}}$ 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.
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