I. INTRODUCTION In the past years, the unstable nuclear beams have extended our knowledge of nuclear physics from the stable nuclei to the unstable nuclei far from the stability line — so-called “exotic nuclei”. Extensive research in this area shows a lot of entirely unexpected features and novel aspects of nuclear structure such as the halo phenomenon [1–3], the disappearance of traditional magic numbers and the occurrence of new ones [4]. The exotic nuclei play important roles in nuclear astrophysics, since their properties are crucial to stellar nucle- osynthesis. To understand the physics in exotic nuclei, it becomes very important to find a reliable theory and improve the reliability for predicting the properties of more exotic nuclei close to proton and neutron drip lines. Nuclear energy density functional (EDF) theory [5] has played an important role in a self-consistent description of nuclei. With a few parameters, EDF theory is able to give a satisfactory description for the ground state properties of spherical and deformed nuclei all over the nuclide chart. Detailed discussion on the EDF theory can be seen in Ref. [6] for nonrelativistic representations and in Refs. [7, 8] for relativistic ones. There exist a number of attractive features in the covariant EDF theory, especially in its practical applications of self-consistent relativistic mean-field (RMF) framework [7, 8]. The most obvious one is the natural inclusion of the nucleon spin degree of freedom and the resulting nuclear spin-orbit potential that emerges automatically with the empirical strength in a covariant way. The relativistic effects are responsible for the empirical existence of approximate pseudospin symmetry in the nuclear single-particle spectra [9]. Moreover, a covariant treatment of nuclear matter provides a distinction between scalar and four-vector nucleon self energies, leading to a natural saturation mechanism. The most widely used RMF framework is based on the finite-range meson-exchange repre- sentation (RMF-FR), in which the nucleus is described as a system of Dirac nucleons which interact with each other via the exchange of mesons. The isoscalar-scalar σ meson, the isoscalar-vector ω meson, and the isovector-vector ρ meson build the minimal set of meson fields that, together with the electromagnetic field, is necessary for a description of bulk and single-particle nuclear properties. Moreover, a quantitative treatment of nuclear mat- ter and finite nuclei needs a medium dependence of effective mean-field interactions, which can be introduced by including nonlinear meson self-interaction terms in the Lagrangian 2