Continuum Skyrme-Hartree-Fock-Bogoliubov theory with Green's function method for odd- A nuclei

Abstract

To study the exotic odd nuclear systems, the self-consistent continuum Skyrme-Hartree-Fock-Bogoliubov theory formulated with Green's function technique is extended to include blocking effects with the equal filling approximation. Detailed formula are presented. To perform the integrals of the Green's function properly, the contour paths C − b and C + b introduced for the blocking effects should include the blocked quasi-particle state but can not intrude into the continuum area. By comparing with the box-discretized calculations, the great advantages of the Green's function method in describing the extended density distributions, resonant states, and the couplings with the continuum in exotic nuclei are shown. Finally, taking the neutron-rich odd nucleus 159 Sn as an example, the halo structure is investigated by blocking the quasi-particle state 1p 1/2 . It is found that it is mainly the weakly bound states near the Fermi surface that contribute a lot for the extended density distributions at large coordinate space.

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

“…For these details, it can be referred to Ref. [72]. To do the contour integration, an energy step of ∆E = 0.01 MeV on the contour path is adopted.…”

“…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]. In recent years, considering the great successes of the covariant density functional theory (CDFT) in the studies of nuclear structure [73][74][75][76][77][78][79][80][81], Green's function method has also been combined with the CDFT.…”

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

“…When introducing the Green's function method [? ] to mean-field density functionals, the densities and singleparticle spectrum can be determined directly by the Green's functions [35,36,40,66]. Following the definition of the single-particle Green's function,…”

“…Many exotic phenomena such as halos [1], deformed halos [2], and giant halos [3][4][5] are explained by the occupations of valence neutrons in the continuum. For example, giant halos predicted in neutron-rich Zr and Ca isotopes are caused by valence neutrons scattered to the continuum and occupying p orbitals [3,4], and the possible deformed halos in 40,42 Mg and 22 C are mainly caused by the occupations of single-particle states around the Fermi surface [6][7][8]. Numerous studies have shown that, in weakly bound exotic nuclei with very small gaps, between the Fermi surface and the continuum threshold, the valence nucleons can be scattered to the continuum effortlessly by pairing correlations.…”

“…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.…”