Proton excitation ofMg24,Mg26, andγbands

Abstract

Differential cross sections for proton scattering to the first three levels of the ground-state (${0}^{+}$,${2}^{+}$,and ${4}^{+}$) and $\ensuremath{\gamma}$ (${2}_{\ensuremath{\gamma}}^{+},{3}_{\ensuremath{\gamma}}^{+},{4}_{\ensuremath{\gamma}}^{+}$) bands of $^{32}\mathrm{S}$ have been measured at ${E}_{p}=20.37$ MeV. These data, together with similar ones on $^{24,26}\mathrm{Mg}$ available in the literature, have been analyzed by means of coupled channel calculations in which a hexadecapole vibrational term, accounting for direct excitation of the ${4}_{\ensuremath{\gamma}}^{+}$ state, is added to the asymmetric rotor model. Satisfactory fits have been obtained for all the transitions considered except the ${3}_{\ensuremath{\gamma}}^{+}$ cross sections; for $^{24}\mathrm{Mg}$ these remain unfitted even if contributions from a direct spin-flip mechanism are added incoherently. The importance of the "missing" contributions in the excitation of the ${3}_{\ensuremath{\gamma}}^{+}$ levels is estimated for the three nuclei considered.NUCLEAR REACTIONS $^{32}\mathrm{S}(p,{p}^{\ensuremath{'}})$, ${E}_{p}=20.37$ MeV; measured $\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}$ for 6 levels, coupled channel analyses for $^{24,26}\mathrm{Mg}$ and $^{32}\mathrm{S}$; deformed vibrational model; deduced deformation parameters.