Excitation of giant resonances in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ with 250 MeV protons

Differential cross section measurements have been made for 250 MeV proton inelastic scattering from ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. Hadronic deformation lengths for the states at 1.78 ($2^{+}$), 4.62 ($4^{+}$), 6.8 ($3^{\mathrm{-}}$ and $4^{+}$), 9.70 ($5^{\mathrm{-}}$), and 10.2 MeV ($3^{\mathrm{-}}$) have been extracted using a first-order vibration model distorted-wave Born approximation description. Deformation lengths for the $2^{+}$ and $4^{+}$ states are found to be independent of proton energy from 40 to 500 MeV. Cross sections for the excitation of the giant resonance region are found to be highly fragmented between 16 to 25 MeV. This region of excitation is found to contain an energy weighted sum rule depletion of 70% for the isovector giant dipole resonance, 26% for the isoscalar giant quadrupole resonance, and 5% for the isoscalar hexadecapole resonance. No structure was observed in the inelastic continuum region of 25 to 45 MeV of excitation energy.