Toward a bridge between relativistic and nonrelativistic density functional theories for nuclei

The nonrelativistic reduction of the self-consistent covariant density functional theory is realized for the first time with the similarity renormalization group method. The reduced nonrelativistic Hamiltonian and densities are calculated by solving the corresponding flow equations with a novel expansion in terms of the inverse of the Dirac effective mass. The efficiency and accuracy of this newly proposed framework have been demonstrated for several typical spherical nuclei. It is found that the exact solutions of the total energies, traces of vector and scalar densities, and the root-mean-square radii are reproduced quite well for all nuclei. This allows one to directly compare and bridge the relativistic and nonrelativistic nuclear energy density functional theories in the future.