Spin-flip probability angular distributions for proton scattering from the $2_1^{+}$ level of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ have been determined between 25° and 165° (in steps of 10°) at 15 incident energies between 14.5 and 35.5 MeV and, to obtain a more detailed energy dependence at backward angles, spin-flip probabilites have also been measured between 115° and 165° at ten additional energies. In order to extend the study of spin-flip probabilities also to other nuclei and to complement previous angular distributions, further backward angle data have been taken at 13 energies for ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ and near 40 MeV for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. The experimental results have been compared with coupled-channel calculations based on the rotational model and, for ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, also with the predictions of microscopic antisymmetrized distorted wave calculations including two-step contributions. The collective analysis proves that spin-flip probabilities are particularly sensitive to the sign of the quadrupole deformation.

NUCLEAR REACTIONS ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$($p$,$p^{\prime }\gamma$), $E_p=14.5-41.1\mathrm{}$ MeV; ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$($p$,$p^{\prime }\gamma$), $E_p=15.5-40.9\mathrm{}$ MeV; ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($p$,$p^{\prime }\gamma$), $E_p=41.1\mathrm{}$ Mev; ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$($p$,$p^{\prime }\gamma$), $E_p=35.3, 40.9$ MeV; measured $\sigma (E_p,{\theta }_{p^{\prime }},{\phi }_{\gamma }=90\mathrm{}°)$ for the $2_1^{+}$ level; microscopic CC analysis; deduced sign of quadrupole deformation parameters; microscopic ADWBA analysis including two-step GR contributions for ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$. ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ enriched target. ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, and ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ natural targets.

• Received 18 May 1981

DOI:https://doi.org/10.1103/PhysRevC.25.107