The toroidal states in $^{ 28}$Si with spin extending to extremely high are investigated with the cranking covariant density functional theory on a 3D lattice. Thirteen toroidal states with spin $I$ ranging from 0 to 56$\hbar$ are obtained, and their stabilities against particle emissions are studied by analyzing the density distributions and potentials. The excitation energies of the toroidal states at $I=28$, 36, 44$\hbar$ reasonably reproduce the observed three resonances extracted from the 7-$\alpha$ de-excitation of $^{ 28}$Si. The $\alpha$ clustering of these toroidal states is supported by the $\alpha$-localization function.
Categories: nucl-th nucl-ex