  The nonrelativistic reduction of the self-consistent covariant density
functional theory is realized for the first time with the similarity
renormalization group (SRG) 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.
