Linear chain structure of four-$\alpha$ clusters in ${}^{16}$O

We investigate the linear-chain configurations of four-$\alpha$ clusters in ${}^{16}$O using a Skyrme cranked Hartree-Fock method and discuss the relationship between the stability of such states and angular momentum. We show the existence of a region of angular momentum (13-18 $\mathrm{\hslash }$) where the linear chain configuration is stabilized. For the first time we demonstrate that stable exotic states with a large moment of inertia (${\mathrm{\hslash }}^2\mathrm{/}2\mathrm{\Theta }$ $\sim$ 0.06-0.08 MeV) can exist.