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

Searching for single-particle resonances with the Green's function method

“…In the investigations with the continuum Skyrme HFB approach in Refs. [38,39], the authors concluded that the pairing correlation can enhance the resonant energies and widths for all quasiparticle resonances, whether hole-like or particle-like. However, in Ref.…”

“…For example, to describe the continuum exactly in exotic nuclei near the drip line and study the possible effects of the continuum on the properties of the ground state, Zhang et al developed the self-consistent continuum Skyrme Hartree-Fock-Bogoliubov (HFB) theory [35,36], based on which a series of research projects have been conducted. These include establishment of the energies and wave functions for single-particle canonical bound and resonant states with different space sizes [37], study of the possible impacts of meanfield and pairing on the resonances [38,39], and the extension to the odd-A systems by including the blocking effect [40]. To explore the contribution of the continuous spectrum to nuclear collective excitations, Matsuo applied the HFB Green's function [41] to the quasiparticle random-phase approximation [42,43], enabling further study of the collective excitations coupled to the continuum [44][45][46][47], microscopic structures of monopole pair vibrational modes and associated twoneutron transfer amplitudes [48], and neutron capture reactions.…”

Neutrons in the classically forbidden region in neutron-rich nucleus 68Ca *

“…This method can also nicely describe the resonant energy and width in the continuum, especially taking into account the contribution from the resonant width to the energy density functional self-consistently [10][11][12]. Recently, the canonical states in the HFB model, corresponding to singleparticle states in the HF model but including the pairing effects, were obtained via the diagonalization of the density matrix constructed by the Green 's function method [13,14]. These canonical states can be used to investigate the neutron numbers in the CF region in neutron-rich nuclei.…”

“…The density matrix can be constructed from the quasiparticle wave functions obtained by either discretization under the box boundary condition [20,21] ("boxdiscretized method" for short in the following), or expanded on the Woods-Saxon basis [9,22,23]. The density matrix can be also calculated directly from the contour integration of the Green's function on the complex energy plane [13,14]. In this way, the asymptotic wave function can be properly described for the continuum states, and the bad asymptotic behavior under the box boundary condition can be avoided.…”

Continuum Skyrme Hartree-Fock-Bogoliubov theory with Green's function method for neutron-rich Ca, Ni, Zr, Sn isotopes

“…In 2009, the continuum HFB theory in a coupled channel representation was developed to explore the effects of the continuum and pairing correlation in deformed Mg isotopes near the neutron drip line [67]. In 2011, Zhang et al developed the fully selfconsistent continuum Skyrme-HFB theory with Green's function method [68], which was further applied to investigate the giant halos [69] and the effects of pairing correlation on the quasiparticle resonances [70,71]. In 2019, to explore the halo phenomena in the neutron-rich odd-A nuclei, the self-consistent continuum Skyrme-HFB theory was further extended by including the blocking effect [72].…”