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

The stable existence of rod-shaped structures in highly excited states of $^{24}\mathrm{Mg}$ 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 clusterlike structure to the shell-model-like structure. Especially, the rod-shaped 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 $\ensuremath{\alpha}$ clusters and enhance the independent motion of the nucleons. The rod-shaped structure with large angular momentum is obtained as a metastable stationary state.