Excitation of Quadrupole and Octupole Levels ofC12,O16, andCa40by 156-MeV Protons

The inelastic cross sections and polarizations for the excitation of some observed $2^{+}$ and $3^{-}$ levels of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ by 156-MeV protons were calculated in the distorted-wave, impulse approximation using the particle-hole transition densities of Gillet and collaborators. The results were compared with available experimental data and good qualitative agreement was obtained; in particular the particle-hole densities provided the necessary enhancements of the cross sections. Fits were also attempted using the theory of collective excitations. These provide reasonable fits to the cross-section data, but not to the polarization.