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