Proton scattering fromMg24at 0.8 GeV

Angular distributions for the elastic and inelastic scattering of 800 MeV protons from ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ are presented. Results of distorted-wave Born-approximation (DWBA) and coupled-channels (CC) analyses of the data for the $0_1^{+}$, $2_1^{+}$, $4_1^{+}$, and $6_1^{+}$ members of the ground state rotational band, the $2_2^{+}$, $3_2^{+}$, $4_2^{+}$, and $5_2^{+}$ members of the $\gamma$ band and the $0^{+}$ member of the $\beta$ band are discussed, and the effects of ground state deformation and multistep contributions are assessed. The DWBA calculations for the $4_1^{+}$ and $6_1^{+}$ angular distributions fail to even qualitatively reproduce the data, while a CC calculation, using a symmetric rotator model with quadrupole and hexadecapole ground state deformations, provides good fits for the $0_1^{+}$, $2_1^{+}$, and $4_1^{+}$ angular distributions. A CC calculation in which the ground band is coupled to the $\gamma$ band, with an assumed asymmetric vibrational amplitude, gives a fair fit to the data for the $2_2^{+}$ state, but fails to fit the $3_2^{+}$, $4_2^{+}$, and $5_2^{+}$ data. This failure in the calculation may be due to the lack of a direct step to the $4_2^{+}$ state, as well as neglect of the spin-flip process. The result of coupling the ground band with the 6.43 MeV $0_{\beta }^{+}$ state indicates that this axially symmetric deformed vibrational model may be essentially correct, but also seems to indicate that a direct $0_1^{+}-0_{\beta }^{+}$ step needs to be considered, based on the behavior of the forward angle $0_{\beta }^{+}$ data. Additional coupling of a $2_{\beta }^{+}$ state does not dramatically improve the fit to the $0_{\beta }^{+}$ data. The results obtained here from analyses of the 800 MeV data are compared with those obtained through analyses of lower energy data.