Excitation of Collective States in Light Nuclei by Inelastic Scattering of 20.3-MeV Polarized Protons

Asymmetries and relative differential cross sections have been measured for elastic and inelastic scattering of 20.3-MeV polarized protons from light elements. The targets included ${\mathrm{C}}^{12}$, ${\mathrm{O}}^{16}$, ${\mathrm{Mg}}^{24}$, ${\mathrm{Mg}}^{25}$, ${\mathrm{Mg}}^{26}$, ${\mathrm{Al}}^{27}$, ${\mathrm{Si}}^{28}$, and ${\mathrm{Ca}}^{40}$. Significant differences have been observed in both the asymmetries and cross sections for transitions with a given angular momentum transfer. The shapes of the asymmetries for ${\mathrm{Al}}^{27}$ and ${\mathrm{Si}}^{28}$ show some disagreement with the weak-coupling model prediction. Coupled-channels and distorted-wave Born-approximation calculations (DWBA) have been performed for the first $2^{+}$ and $4^{+}$ states in ${\mathrm{Mg}}^{24}$ and ${\mathrm{Si}}^{28}$, with several types of deformed spin-orbit potential. In principle, it should be possible with a coupled-channel analysis to distinguish between vibrational and rotational models, and between positive and negative deformations. In fact, there are differences between the predictions of these models. However, none of them gives a good account of the $2^{+}$ and $4^{+}$ asymmetries in ${\mathrm{Mg}}^{24}$ and ${\mathrm{Si}}^{28}$, even when the full Thomas form of the spin-orbit potential is used. Microscopic- and macroscopic-model DWBA predictions of the $3_1^{-}$ and $5_1^{-}$ asymmetries in ${\mathrm{Ca}}^{40}$ yield fair agreement with the experimental data.