14-40 MeV proton scattering from low-lying states ofSi28

Differential cross sections for proton scattering from the six lowest states of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ have been measured at 30 incident energies in the range 14-40 MeV. Differential spin-flip probabilities for proton scattering from ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ $2^{+}$(1.78 MeV) state have been determined at ten incident energies in the range 16-22 MeV. Elastic data have been analyzed by means of the optical model. Compound nucleus contributions present at low energies in experimental data have been evaluated by means of the Hauser-Feshbach statistical model. Coupled-channels calculations and a macroscopic model have been used to analyze transitions to natural parity states. An anomalous behavior of the deduced deformation parameters has been obtained at low energies. The experimental data related to the $2^{+}$ level and to the $3^{+}$ unnatural parity state have been compared with the prediction of a microscopic antisymmetrized distorted wave calculation in which a direct reaction mechanism is supplemented by a two-step resonance contribution corresponding to the virtual excitation of giant resonance states of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. These contributions, essential to fully explain the data, have made the evaluation of the $E1$, $E2\mathrm{}$, and $E3\mathrm{}$ giant resonance strengths in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ possible.