$s$-wave quasiparticle resonance in neutron-rich drip-line nuclei

We investigate unbound single-particle states in pair-correlated drip-line nuclei by describing a low-energy elastic scattering of a neutron in the $s$-wave within the framework of the coordinate space Hartree-Fock-Bogolibov (Bogoliubov-de Genne) equation. Numerical study is performed for a neutron drip-line carbon isotope where the neutron $2s_{1/2}$ orbit is located close to zero energy. Analyzing the S-matrix poles of the elastic scattering, we discuss properties of the $s$-wave quasiparticle resonance and, in particular, behaviors characteristic to drip-line nuclei. It is found that the S-matrix has two pairs of poles; one pair appears as either a weakly bound state, a virtual state or a resonance while the other pair gives contribution analogous to a bound single-particle state. The $s$-wave quasiparticle resonance emerges with a large variation depending on the pairing gap and the single-particle energy of the $s$-orbit.