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.

Quadrupole deformation(β,γ)of lightΛhypernuclei in a constrained relativistic mean field model: Shape evolution and shape polarization effect of theLü1, Zhao2, Zhou3 2011Phys. Rev. CSelf Cite

“…22 C is suggested to be a halo nucleus according to the mea-sured large enhancement of the reaction cross section for it compared to those for neighboring carbon isotopes [84]. We certainly can not reproduce the halo structure for 22 C because in the present work a Harmonic Oscillator basis is used which is not able to give the large spatial density distributions in halo nuclei [85][86][87][88].…”

Relativistic Hartree-Fock-Bogoliubov theory with density dependent meson-nucleon couplings

“…In this work we solve the radial RHFB equations (26) by using the Dirac Woods-Saxon (DWS) basis introduced by Zhou et al [52]. This basis has been constructed for the investigation of weakly-bound nuclei.…”

Description of carbon isotopes within relativistic Hartree-Fock-Bogoliubov theory

“…Due to the numerical difficulties originating from both RHF mean field and finite-range pairing interactions, the integrodifferential RHFB equation (5) is solved by expanding the quasi-particle spinors on the Dirac Woods-Saxon (DWS) basis [39], which can provide appropriate asymptotic behaviors for the continuum states in the weakly bound nuclei. For the calculations of Carbon isotopes, the DWS basis parameters are taken as follows: the spherical box-size is fixed to 30 fm and consistently the numbers of basis states with positive and negative energies are chosen as 48 and 12, respectively.…”