Examination of the stability of a rod-shaped structure in $^{24}$Mg

Abstract: The stable existence of a six-$\alpha$ linear structure in highly excited states of $^{24}$Mg is studied based on a systematic Cranked Hartree-Fock calculation with various Skyrme-type interactions. Its stability is examined by allowing the transition of the cluster structure to the shell-model like structure. Especially, the six-$\alpha$ linear state is exposed to two major instabilities: the bending motion, which is the main path for the transition to low-lying states, and the spin-orbit interaction, which is the driving force to break the $\alpha$ clusters and enhance the independent motion of the nucleons. The linear structure with large angular momentum is obtained as a meta-stable stationary state.