Green's function method for the single-particle resonances in a deformed Dirac equation

Abstract

Single-particle resonances are crucial for exotic nuclei near and beyond the drip lines. Since the majority of nuclei are deformed, the interplay between deformation and orbital structure near threshold becomes very important and can lead to improved descriptions of exotic nuclei. In this work, the Green's function (GF) method that can treat the single-particle bound and resonant states on the same footing is applied to solve the coupled-channel Dirac equation with a quadrupole-deformed Woods-Saxon potential for the first time. Detailed formalism for the partial-wave expansion of Green's function is presented. Numerical checks are carried out by comparing with our previous implementation of spherical GF method and the results from the deformed analytical continuation of the coupling constant (ACCC) and scattering phase shift (SPS) methods. Finally, Nilsson levels for bound and resonant orbitals in a halo candidate nucleus 37 Mg from the deformed GF method are calculated over a wide range of deformations and show some decisive hints of p-wave halo formation in this nucleus, namely, crossing between the configurations 1/2[321] and 5/2[312] at deformation parameter β > 0.5 may enhance the probability to occupy the 1/2[321] orbital coming from 2p 3/2 .

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

“…For example, in the Sn chain, S 2n drops from 13.25 MeV at 132 Sn to 4.94 MeV at 134 Sn with the neutron number exceeding the magic number N = 82. In the Ca, Ni, and Zr chains, the two-neutron separation energies quickly reach zero at large mass range, resulting in relative short neutron drip lines, which are 67 Ca, 89 Ni, and 123 Zr, respectively. On the contrary, in the Sn chain, S 2n keeps less than 1.0 MeV in a wide mass region after the gap of N = 82 and finally becomes negative until A = 178, determining 177 Sn as the neutron drip line nucleus.…”

“…By combining the Green's function method with the RCHB theory, the pairing correlation and continuum are well described in the giant halos of the Zr isotopes [88]. By extending the GF-RMF model to the coupled channel representation, the halo candidate nucleus 37 Mg reported experimentally is analyzed and confirmed to be a p-wave one-neutron halo according to the Nilsson levels [89]. All those works have proved the great successes of Green's function method in the descriptions of the continuum.…”

Angular momentum projection in the deformed relativistic Hartree-Bogoliubov theory in continuum

“…It has been shown in Refs. [142,155] that there is a cross between the 5/2 − and 1/2 − orbitals when β ≈ 0.5 around the neutron Fermi energy. Because of the near degeneracy of (1/2 − , 5/2 − ), it is reasonable to regard 40 Mg as a " 36 Mg+4n" system instead of " 38 Mg+2n" from the point of view of the structure of SPLs.…”

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

“…[66], we introduced the Green's function approach to the relativistic-mean-field (RMF) model and studied singleparticle resonances for the first time. Later, this approach was further extended to studies of single-particle resonances of protons [67], hyperons [68], and those in deformed nuclei with a quadrupole-deformed Woods-Saxon potential [69]. In addition, the pseudospin symmetries hidden in resonant states were also investigated by applying the Green's function method [70].…”

“…With this method, one can describe narrow resonances very well, but the accuracy is poor for wide ones. Therefore, in our recent studies [69,72], we proposed an effective and direct way to identify the resonant states by exploring for the extremum of the DOS. The exact energies and widths for the resonant states in all types can be obtained, whether for wide or narrow resonant states.…”