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The nonrelativistic reduction of the self-consistent covariant densityfunctional theory is realized for the first time with the similarityrenormalization group (SRG) method. The reduced nonrelativistic Hamiltonian anddensities are calculated by solving the corresponding flow equations with anovel expansion in terms of the inverse of the Dirac effective mass. Theefficiency and accuracy of this newly proposed framework have been demonstratedfor several typical spherical nuclei. It is found that the exact solutions ofthe total energies, traces of vector and scalar densities, and theroot-mean-square radii are reproduced quite well for all nuclei. This allowsone to directly compare and bridge the relativistic and nonrelativistic nuclearenergy density functional theories in the future.

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