Effects of mean-field and pairing correlations on the Bogoliubov quasiparticle resonance

Abstract

The quasiparticle resonances are investigated by examining three kinds of quasiparticle spectra, i.e., the density of quasiparticle states, the occupation number density, and the pair number density in the continuum Skyrme Hartree-Fock-Bogoliubov theory with the Greens function method.Taking the weakly bound nucleus $^{66}$Ca as an example, the quasiparticle resonant energies and widths extracted from these three kinds of quasiparticle spectra are compared.For the narrow resonances, the extracted resonant energy and the width are consistent with each other. However, it is difficult to use the density of quasiparticle states to identify the broad resonances due to the background of nonresonant continuum.By switching off the pairing potential and/or the Hartree-Fock (HF) potential respectively in the calculation of these quasiparticle spectra, the roles of HF mean-field and pairing correlations in the quasiparticle resonances are demonstrated clearly. It turns out that all the quasiparticle resonances corresponding to the deeply bound, weakly bound and positive-energy single-particle resonant states, are mainly contributed by the HF potential.The pairing potential helps to slightly increase the resonant energy and the width. However, the pairing potential is important to make the nucleons occupy the low-lying nonresonant continuum states near the threshold and take part in the pairing correlations here, especially for the partial waves with small angular momentum $\ell$.