Perturbative Hartree-Fock-Bogoliubov model for many-body pairing correlations

We develop a perturbative model to treat the off-diagonal components in the Hartree-Fock-Bogoliubov (HFB) transformation matrix, which are neglected in the Bardeen-Cooper-Schrieffer (BCS) approximation. Applying the perturbative model to a weakly bound nucleus ⁸⁴Ni, it is shown that the perturbative approach reproduces well the solutions of the HFB method both for the quasiparticle energies and the radial dependence of quasiparticle wave functions. We find that the nonresonant part of the continuum single-particle state can acquire an appreciable occupation probability when there exists a weakly bound state close to the Fermi surface. This result originates from the strong coupling between the continuum particle state and the weakly bound state, and it is absent in the BCS approximation. The limitations of the BCS approximation are pointed out in comparison with the HFB and the present perturbative model.