Spherical Relativistic Hartree theory in a Woods-Saxon basis

Abstract

The Woods-Saxon basis has been suggested to replace the widely used harmonic oscillator basis for solving the relativistic mean field (RMF) theory in order to generalize it to study exotic nuclei. As examples, relativistic Hartree theory is solved for spherical nuclei in a Woods-Saxon basis obtained by solving either the Schrödinger equation or the Dirac equation (labelled as SRHSWS and SRHDWS, respectively and SRHWS for both). In SRHDWS, the negative levels in the Dirac Sea must be properly included. The basis in SRHDWS could be smaller than that in SRHSWS which will simplify the deformed problem. The results from SRHWS are compared in detail with those from solving the spherical relativistic Hartree theory in the harmonic oscillator basis (SRHHO) and those in the coordinate space (SRHR). All of these approaches give identical nuclear properties such as total binding energies and root mean square radii for stable nuclei. For exotic nuclei, e.g., ${}^{72}$Ca, SRHWS satisfactorily reproduces the neutron density distribution from SRHR, while SRHHO fails. It is shown that the Woods-Saxon basis can be extended to more complicated situations for exotic nuclei where both deformation and pairing have to be taken into account.

arXiv comment12 pages, 9 figures

References in corpus (10)

• Mean-field description of ground-state properties of drip-line nuclei: Pairing and continuum effects
• A Giant Halo at the Neutron Drip Line
• Relativistic Hartree-Bogoliubov theory with finite range pairing forces in coordinate space: Neutron halo in light nuclei
• Deformation of Nuclei Close to the Two-Neutron Drip Line in Mg Region
• 3D Solution of Hartree-Fock-Bogoliubov Equations for Drip-Line Nuclei
• New Discrete Basis for Nuclear Structure Studies
• Solution of relativistic Hartree-Bogoliubov equations in configurational representation: spherical neutron halo nuclei
• An HFB scheme in natural orbitals
• Particles in classically forbidden area, neutron skin and halo, and pure neutron matter in Ca isotopes
• B-Spline Finite Elements and their Efficiency in Solving Relativistic Mean Field Equations

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