Inelastic Scattering of 42-MeV Alpha Particles byMg24

Angular distributions for elastic and inelastic scattering of 42-MeV $\alpha$ particles by ${\mathrm{Mg}}^{24}$ have been measured in the range $\theta \left(\mathrm{lab}\right)={10}^{\circ }-{60}^{\circ }$. Eight inelastic $\alpha$ groups were identified with the following —$Q$ values: 1.37, 4.16 (doublet), 5.22, 6.005, 6.44, 7.35, 7.62, and 8.37 MeV. Two theoretical models, the distorted-wave Born-approximation version of the extended optical model and the smoothed Fraunhofer inelastic diffraction model, have comparable degrees of success in fitting the observed angular distributions. Further, extracted values of the deformation distances ${\delta }_{\lambda }\equiv {\beta }_{\lambda }{R}_0$, which parametrize the nuclear matrix elements, show good agreement between the two methods of analysis for low $Q$ values and angular momentum transfer; as these quantities increase, however, the smoothed Fraunhofer model tends to underestimate ${\delta }_{\lambda }$ by as much as 30%. The present results on the nature and strength of the transitions to the positive-parity levels at 1.37, 4.16 (doublet), 5.22, 6.005, 6.44, and 7.35 MeV are in agreement with the broad features of the rotational-vibrational collective-model predictions for these levels, but not with its literal interpretation in terms of macroscopic quadrupole surface excitations of the nuclear intrinsic states. The present results indicate the presence of the two $3^{-}$ levels, strongly collective in nature, at 7.62 and 8.37 MeV. Comparisons are made with other experiments of similar nature on the ${\mathrm{Mg}}^{24}$ nucleus.