Investigation of ²³N in a three-body model

The neutron-drip-line nucleus $^{23}$N is investigated in a three-body model consisting of a $^{21}$N core and two valence neutrons. By solving the Faddeev equations with the realistic neutron-neutron potentials and the neutron-core potentials, we calculate the ground state properties of $^{23}$N and also find that there is a new excited state with two-neutron separation energy at about 0.18 MeV. The properties, such as the two-neutron separation energies, are obtained with a good agreement with experiments. By calculating the root-mean-square matter radii, the average distances between the valence neutrons, and the average distances between the core and the center-of-mass of the neutron pair, we show that the excited state of $^{23}$N has a clear halo structure. The correlation density distributions of the three-body system are also calculated to analyze its geometric configuration. At last, we find that the excited state of $^{23}$N has a very small binding energy, a large radius and distribution, and a triangular shape similar with the ground state. These roperties of the excited state indicate that it can be an Efimov state.