Structural connection of highly deformed shape isomeric states in 28Si, 24Mg, and 20Ne by alpha-alpha coincidence studies in 12C(16O, alpha )24Mg*--> alpha +20Ne*

Abstract

Alpha-alpha coincidence measurements have been made in the reaction $^{12}\mathrm{C}$${(}^{16}$O,\ensuremath{\alpha}${)}^{24}$${\mathrm{Mg}}^{\mathrm{*}}$\ensuremath{\rightarrow}\ensuremath{\alpha}${+}^{20}$${\mathrm{Ne}}^{\mathrm{*}}$ at the bombarding energy of E${(}^{16}$O)=63 MeV corresponding to the resonance in the $^{12}\mathrm{C}$${+}^{16}$O system at ${\mathit{E}}_{\mathrm{c}.\mathrm{m}.}$=26.9 MeV leading to the compound nuclear state at 43.7 MeV in $^{28}\mathrm{Si}$. The coincidence alphas are detected, one at 0\ifmmode^\circ\else\textdegree\fi{} to the beam and the other at 20\ifmmode^\circ\else\textdegree\fi{} to 80\ifmmode^\circ\else\textdegree\fi{} in steps of 10\ifmmode^\circ\else\textdegree\fi{}. The spins of the states in $^{24}\mathrm{Mg}$ at 20.2 and 21.4 MeV are fed strongly at this resonance are inferred to be J\ensuremath{\ge}8 from the branching of these states to the states in the ground state band of $^{20}\mathrm{Ne}$. From the result it is deduced that these states of $^{24}\mathrm{Mg}$ do not correspond to the near Coulomb barrier resonances in the $^{12}\mathrm{C}$${+}^{12}$C system. In addition, the coincidence measurements also lead to the result that the states of $^{24}\mathrm{Mg}$ in the 20--22 MeV region fed at the resonance preferentially decay to the eight-particle--four-hole states of $^{20}\mathrm{Ne}$ near 7.2 MeV. These results establish the structural connection of highly deformed shape isomeric states in the region of \ensuremath{\epsilon}=1.17 to 1.35 and \ensuremath{\gamma}=50\ifmmode^\circ\else\textdegree\fi{} to 60\ifmmode^\circ\else\textdegree\fi{} in $^{28}\mathrm{Si}$, $^{24}\mathrm{Mg}$, and $^{20}\mathrm{Ne}$ expected from the Nilsson-Strutinsky calculations of Leander and Larsson.