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

Abstract

Angular distributions for the inelastic scattering of protons from $^{24}\mathrm{Mg}$ have been measured at a proton energy ${E}_{p}=40$ 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 ${E}_{x}\ensuremath{\approx}13.5$ 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 ${\ensuremath{\beta}}_{6}$ are suggested by the data. Collective model distorted-wave Born approximation calculations were performed to determine the deformation parameters ${\ensuremath{\beta}}_{L}$ and isoscalar transition rates $B(\mathrm{IS},{0}_{1}^{+}\ensuremath{\rightarrow}L)$ for most of the observed states. Nearly half of the strength observed below ${E}_{x}=13.5$ MeV for the transitions of multipolarities $L=2,3, \mathrm{and} 4$ is contained in the high-energy region between ${E}_{x}=7.5 \mathrm{and} 13.5$ MeV. Good agreement with the inelastic electron scattering data has been obtained for most of the low-energy transitions which were previously studied via ($e,{e}^{\ensuremath{'}}$). Evidence is presented in favor of a particular spin value for a number of states for which only multiple spin assignments were previously made.NUCLEAR REACTIONS $^{24}\mathrm{Mg}(p,{p}^{\ensuremath{'}})$, $E=40$ MeV; measured $\ensuremath{\sigma}({E}_{{p}^{\ensuremath{'}}};\ensuremath{\theta})$; deduced ${\ensuremath{\beta}}_{L}'\mathrm{s}$, optical parameters. Enriched target.