Single particle states in the Fermi sea and Dirac sea in spherical nuclei

Abstract

The Dirac equation sits in the center of nuclear covariant density functional theories. In this review, we will introduce briefly the numerical methods of solving the Dirac equation for spherical nuclei and discuss several relevant topics. We introduce the shooting method which is used in solving the radial Dirac equation in the coordinate space and the Woods-Saxon basis expansion approach including the Schr\odinger-Woods-Saxon basis and the Dirac-Woods-Saxon basis. For the Dirac-Woods-Saxon basis, the completeness of the basis requires that not only the positive energy states in the Fermi sea but also the negative energy states in the Dirac sea should be included in the basis. The pseudospin symmetry of those negative energy states, or equivalently, the spin symmetry in the anti-nucleon spectra are discussed.