Weakly bound neutrons and quadrupole response function in the many-body pair correlation of neutron drip line nuclei

A simplified model of the Hartree-Fock Bogoliubov (HFB) equation with surface-type or volume-type pairing is solved in coordinate space with the correct asymptotic boundary conditions. By using the resulting HFB wavefunctions, the low-energy quadrupole (L ≤ 2) response function is studied for the system with weakly bound s and d neutrons. As the binding energy of the neutrons becomes small or approaches zero, the discrete solutions of the HFB equation disappear. Then, without any further correlation (for example, random phase approximation (RPA) correlation), the threshold quadrupole response becomes broader and moves toward very low excitation energies, while the total strength increases very rapidly. The important role of the continuum character of the upper component u_ℓj(r) of the HFB s_1/2 wavefunction in the increasing strength is pointed out. The large and broad quadrupole response with a very low peak energy is expected for neutron drip line nuclei with N ≈ 56 and Z ≈ 28, of which both the neutron 2d _5/2 and 3s_1/2 orbits may be weakly bound in the Hartree-Fock (HF) potential.