A new parametrization PC-PK1 for the nuclear covariant energy density functional with nonlinear point-coupling interaction is proposed by fitting to observables of 60 selected spherical nuclei, including the binding energies, charge radii, and empirical pairing gaps. The success of PC-PK1 is illustrated in the description of infinite nuclear matter and finite nuclei including the ground-state and low-lying excited states. In particular, PC-PK1 provides a good description for the isospin dependence of binding energy along either the isotopic or the isotonic chain, which makes it reliable for application in exotic nuclei. The predictive power of PC-PK1 is also illustrated for the nuclear low-lying excitation states in a five-dimensional collective Hamiltonian in which the parameters are determined by constrained calculations for triaxial shapes.

By taking into account the surface diffuseness correction for unstable nuclei, the accuracy of the macroscopic–microscopic mass formula is further improved. The rms deviation with respect to essentially all the available mass data falls to 298 keV, crossing the 0.3 MeV accuracy threshold for the first time within the mean-field framework. Considering the surface effect of the symmetry potential which plays an important role in the evolution of the “neutron skin” toward the “neutron halo” of nuclei approaching the neutron drip line, we obtain an optimal value of the symmetry energy coefficient J=30.16 MeV. With an accuracy of 258 keV for all the available neutron separation energies and of 237 keV for the α-decay Q-values of super-heavy nuclei, the proposed mass formula is particularly important not only for the reliable description of the r process of nucleosynthesis but also for the study of the synthesis of super-heavy nuclei

New parameter sets for the Lagrangian density in the relativistic mean field (RMF) theory, PK1 with nonlinear $\sigma$- and $\omega$-meson self-coupling, PK1R with nonlinear $\sigma$-, $\omega$-, and $\rho$-meson self-coupling, and PKDD with the density-dependent meson-nucleon coupling are proposed. They are able to provide an excellent description not only for the properties of nuclear matter but also for the nuclei in and far from the valley of $\beta$ stability. For the first time in the parametrization of the RMF Lagrangian density, the center-of-mass correction is treated by a microscopic way, which is essential to unify the description of nuclei from light to heavy regions with one effective interaction.

Relativistic Hartree-Bogoliubov theory in coordinate space is used to describe the chain of lithium isotopes reaching from ${}^6$Li to ${}^{11}$Li. Pairing correlations are taken into account by a density dependent force of zero range. In contrast to earlier investigations within a relativistic mean field theory and a density dependent Hartree-Fock theory, where the halo in ${}^{11}$Li could only be reproduced by an artificial shift of the ${1p}_{1/2}$ level close to the continuum limit, the halo is now reproduced in a self-consistent way, without further modifications, using the scattering of Cooper pairs to the ${2s}_{1/2}$ level in the continuum. Excellent agreement with recent experimental data is observed.