Vortex Excitations in $\alpha$ Cluster Condensed Nuclei

We point out an intriguing possibility that there exist topological soliton-like excitations in nuclei with $\alpha$ cluster condensation. The excitations are vortices in superfluid, a property possessed by such Bose condensed nuclei. We show that the vortex-like states possess quantum numbers $J^{P}=n^{(-1)^n}$ and energies $\sim$ several MeV, measured from the ground state energies of the $n \alpha$ condensed states. We point out actual candidates, for instance, $2^{+}(3 {MeV})$ for $^{8}$Be, $3^{-}(9.6 {MeV})$ for $^{12}$C, etc, although the topological nature as a vortex is obscure in such light nuclei.