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

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