Differential cross sections of elastic and inelastic scattering with excitation of states of the rotational band of the ground state of \(^{24}\)Mg were measured at an \(\alpha \)-particle energy of 50.5 MeV and \(^{3}\)He 60 MeV. The angular distributions were analyzed using an optical model and a coupled channel method. A number of potentials with significantly different geometries are obtained, which describe well the elastic scattering at the measured angular range. The collective model was used in the calculations via the coupled channel method. In addition to the ground state, three low-lying states of \(^{24}\)Mg, 2\(^{+}\) (1.368 MeV), 4\(^{+}\) (4.122 MeV), and 4.238 MeV (2\(^{+}\)), were included in the coupling scheme. The values of quadrupole (\(\beta _{2}\)) and hexadecapole (\(\beta _{4}\)) deformation parameters were extracted. According to the analysis of scattering of \(\alpha \)-particles, they are 0.52 and 0.05. For \(^{3}\)He, they are 0.75 and 0.07, respectively. The extracted parameters correspond to the previously obtained values from the scattering of protons, deuterons and \(\alpha \)-particles.

弹性和非弹性散射的微分截面与基态的转动带的状态的激励\（^ {24} \）的Mg物在一个测量\（\阿尔法\） -粒子50.5兆电子伏和的能量\（^ {3} \）他为60 MeV。使用光学模型和耦合通道方法分析角度分布。获得了许多具有明显不同的几何形状的电势，这些电势很好地描述了在测得的角度范围内的弹性散射。通过耦合通道法将集体模型用于计算。除了基态之外，还包括\（^ {24} \） Mg，2 \（^ {+} \）（1.368 MeV），4 \（^ {+} \）（4.122 MeV）的三个低洼状态和4.238 MeV（2\（^ {+} \））已包含在耦合方案中。提取四极（\（\ beta _ {2} \））和十六极（\（\ beta _ {4} \））变形参数的值。根据\（\ alpha \）-粒子的散射分析，它们分别为0.52和0.05。对于\（^ {3} \） He，它们分别是0.75和0.07。提取的参数对应于先前从质子，氘核和\（\ alpha \）粒子的散射获得的值。