Spherical relativistic Hartree theory in a Woods-Saxon basis

Abstract

The Woods-Saxon (WS) basis is suggested to replace the widely used harmonic oscillator basis for solving the relativistic mean-field theory in order to generalize it to study exotic nuclei. As an example, the relativistic Hartree theory is solved for spherical nuclei in a Woods-Saxon basis obtained by solving either the Schr\"odinger equation or the Dirac equation (labeled as SRHSWS and SRHDWS, respectively, and SRHWS for both). In SRHDWS, the negative energy states in the Dirac sea must be properly included. The WS 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., ${}^{72}\mathrm{Ca},$ 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.