Inelastic scattering of 40 MeV protons fromMg24. I. Natural parity transitions

Angular distributions for the inelastic scattering of protons from ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ have been measured at a proton energy $E_p=40\mathrm{}$ MeV with a resolution of 16 keV. The results for the natural parity states in the excitation energy range from the ground state up to $E_x\approx 13.5$ MeV are presented. The data have been analyzed using a macroscopic collective model. Coupled-channel calculations assuming the rigid-rotor model have been performed for the ground-state rotational band in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$. Previous conclusions on the smallness of the parameter of the hexadecapole deformation have been confirmed. The angular distribution for the $6^{+}$ member of the ground-state rotational band at 8.120 MeV made it possible to extract the sixth order deformation parameter. Negative values of ${\beta }_6$ are suggested by the data. Collective model distorted-wave Born approximation calculations were performed to determine the deformation parameters ${\beta }_L$ and isoscalar transition rates $B(\mathrm{IS},0_1^{+}\to L)$ for most of the observed states. Nearly half of the strength observed below $E_x=13.5\mathrm{}$ MeV for the transitions of multipolarities $L=2,3, \mathrm{and} 4$ is contained in the high-energy region between $E_x=7.5\mathrm{} \mathrm{and} 13.5$ MeV. Good agreement with the inelastic electron scattering data has been obtained for most of the low-energy transitions which were previously studied via ($e,e^{\prime }$). Evidence is presented in favor of a particular spin value for a number of states for which only multiple spin assignments were previously made.