Probing spin and pseudospin symmetries in deformed nuclei by the Green's function method

Abstract

(Pseudo)spin symmetries play vital roles in nuclear physics and have been studied extensively in spherical nuclei. In this work, possible spin and pseudospin symmetries in deformed nuclei are examined by solving a coupled-channel Dirac equation with quadruple deformation. The Green's function method is taken which provides a novel way to exactly determine the single-particle levels and properly describe the spacial density distributions. Taking axially-deformed nucleus ${}^{154}$Dy as an example, the spin doublets with a combination of Nilsson levels $\Lambda \pm 1/2[\mathcal{N},n_z,\Lambda ]$ and pseudospin doublets with a combination of $\tilde{\Lambda }\pm 1/2[\widetilde{\mathcal{N},n_z,\Lambda }]$ are determined. Different behaviors are displayed for the spin and pseudospin doublets. For the spin partners, those with smaller angular momentum $l$ and the third component $\Lambda$ owns better symmetry such as the $1p$ doublet while good pseudospin symmetry appears in partners locating close to the continuum threshold. By examining the single-particle Nilsson levels $\Omega [\mathcal{N},n_z,\Lambda ]$ and the energy splittings between the partners, the conservation and breaking of SS and PSS are examined at different deformations. In the prolate side, the Nilsson levels for the spin and pseudospin doublets are almost parallel and the energy splittings are stable against varying deformations. By examining the density distributions, great similarities have been observed in the upper components for the spin doublets while great similarities in the lower component for the pseudospin doublets. Besides, these similarities maintain well at different deformations.

10 pages, 8 figures, 1table

References in corpus (15)

• Hidden pseudospin and spin symmetries and their origins in atomic nuclei
• Pseudospin symmetry in single particle resonant states
• Perturbative interpretation of relativistic symmetries in nuclei
• Pseudospin symmetry in supersymmetric quantum mechanics: Schrödinger equations
• Spin symmetry in Dirac negative energy spectrum in density-dependent relativistic Hartree-Fock theory
• Green's function method for single-particle resonant states in relativistic mean field theory
• Isospin dependence of pseudospin symmetry in nuclear resonant states
• Persistent contribution of unbound quasiparticles to the pair correlation in continuum Skyrme-Hartree-Fock-Bogoliubov approach
• Continuum Hartree-Fock-Bogoliubov theory for weakly bound deformed nuclei using coordinate-space Green's function method
• Continuum quasiparticle random phase approximation for astrophysical direct neutron capture reaction of neutron-rich nuclei
• Green's function method for the spin and pseudospin symmetries in the single-particle resonant states
• Continuum Skyrme-Hartree-Fock-Bogoliubov theory with Green's function method for odd-$A$ nuclei
• Searching for single-particle resonances with the Green's function method
• Study of single-particle resonant states with Green's function method
• Conservation and breaking of pseudospin symmetry

Cited by in corpus (1)

• Ground-state properties and structure evolutions of odd-$A$ transuranium Bk isotopes from deformed relativistic Hartree-Bogoliubov theory in continuum