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

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