New effective interactions, PK1, PK1r and PKDD, in the relativistic mean field (RMF) theory, are proposed with the center-of-mass correction included in a microscopic way. They are able to provide an excellent description not only for the properties of nuclear matter and neutron stars, but also for the nuclei near and far from the β-stability line, including halos and giant halos at the neutron drip line in nuclei and hypernuclei. Based on the solution of the RMF equations, a good spin symmetry is found in anti-nucleon spectra. The magic proton and neutron numbers are searched in the superheavy region by the relativistic continuum Hartree-Bogoliubov (RCHB) theory. Spherical doubly magic superheavy nuclei are systematically investigated and their stabilities against deformation are discussed.
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