Low-energy dipole excitations in O20 with antisymmetrized molecular dynamics

Low-energy dipole (LED) excitations in $^{20}\mathrm{O}$ were investigated by variation after $K$ projection of $\mathrm{deformation}\phantom{\rule{0.28em}{0ex}}(\ensuremath{\beta}$)-constraint antisymmetrized molecular dynamics combined with the generator coordinate method. A low-energy $E1$ mode, which is caused surface neutron oscillation along prolate deformation was obtained as ${1}_{2}^{\ensuremath{-}}$ state. Moreover, a toroidal (TD) mode vortical nuclear current ${1}_{1}^{\ensuremath{-}}$ state one-proton excitation on relatively weak deformation. The LED peculiar to neutron-rich systems that does not appear stable oxygen isotopes, whereas TD (vortical) also $^{16}\mathrm{O}$ and $^{18}\mathrm{O}$. modes separately ${K}^{\ensuremath{\pi}}={1}^{\ensuremath{-}}$ ${K}^{\ensuremath{\pi}}={0}^{\ensuremath{-}}$ components deformed states, respectively, but couple each other because mixing, shape fluctuation. As result transition strengths are fragmented into states. excited bands ${K}^{\ensuremath{\pi}}={0}^{+}, {K}^{\ensuremath{\pi}}={0}^{\ensuremath{-}}$, cluster structures energy region higher than