Differential cross sections are reported for elastic scattering and for exciting the $2_1^{+}$ (1.81 MeV), $2_2^{+}$ (2.94 MeV), $4_1^{+}$ (4.32 MeV), and the $4_2^{+}$ (4.90 MeV) states of ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$ from ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$ (200 MeV)${+}^{208}$Pb scattering. In addition, we have measured complete particle-γ angular correlations for the $2_1^{+}$→$0_1^{+}$, $2_2^{+}$→$2_1^{+}$, and $4_2^{+}$→$2_1^{+}$ γ decays. Coupled-channels analysis was performed to extract E2 and E4 matrix elements. For the ground-state rotational band we find M(E2;$0_1^{+}$⇆$2_1^{+}$)=-16.79±0.13 e ${\mathrm{fm}}^2$, M(E4;$0_1^{+}$⇆$4_2^{+}$)=+95±10 e ${\mathrm{fm}}^4$, and ${\mathit{Q}}_2$($2_1^{+}$)=-20.9±1.9 ${\mathrm{fm}}^2$, where we have identified the $4_2^{+}$ (4.90 MeV) state as a member of the ground-state band rather than the $4_1^{+}$ (4.32 MeV) state. The $2_2^{+}$ (2.94 MeV) state is not well accounted for by the asymmetric-rotor model.

• Received 3 December 1990

DOI:https://doi.org/10.1103/PhysRevC.43.2546