Low-energy dipole excitations in $^{20}$O with antisymmetrized molecular dynamics

Abstract: Low-energy dipole (LED) excitations in $^{20}$O were investigated by variation after $K$-projection of deformation($\beta$)-constraint antisymmetrized molecular dynamics combined with the generator coordinate method. We obtained two LED states, namely, the $1_1^-$ state with one-proton excitation on the relatively weak deformation and the $1_2^-$ state with a parity asymmetric structure of the normal deformation. The former is characterized by a toroidal dipole (TD) mode with vortical nuclear current, whereas the latter is associated with a low-energy $E1$ mode caused by surface neutron oscillation along the prolate deformation. The TD (vortical) and $E1$ modes separately appear as the $K^\pi=1^-$ and $K^\pi=0^-$ components of the deformed states, respectively, but couple with each other in the $1_1^-$ and $1_2^-$ states of $^{20}$O because of $K$-mixing, and shape fluctuation. As a result of the mixing, TD and $E1$ transition strengths are fragmented into the $1_1^-$ and $1_2^-$ states. We also obtained the $K^\pi=0^+$, $K^\pi=0^-$, and $K^\pi=1^-$ bands with cluster structures in the energy region higher than the LED states.