Cluster correlation and nuclear vorticity in low-lying $1^-$ states of $^{24}$Mg

We investigated cluster correlation and nuclear voricity in low-lying $1^-$ states of $^{24}$Mg within antisymmetrized molecular dynamics framework. We found that the toroidal and compressional dipole modes separately appear as the $K=1$ and $K=0$ states. The $1^-$ ($K=1$) state is the toroidal dipole state with the strong nuclear vorticity but no prominent cluster structure, and the $1^-$ ($K=0$) state is the compressional dipole state having enhanced cluster structure but has the weaker vorticity.