  Low-lying nuclear states of Sm isotopes are studied in the framework of a
collective Hamiltonian based on covariant energy density functional theory.
Pairing correlation are treated by both BCS and Bogoliubov methods. It is found
that the pairing correlations deduced from relativistic Hartree-Bogoliubov
(RHB) calculations are generally stronger than those by relativistic mean-field
plus BCS (RMF+BCS) with same pairing force. By simply renormalizing the pairing
strength, the diagonal part of the pairing field is changed in such a way that
the essential effects of the off-diagonal parts of the pairing field neglected
in the RMF+BCS calculations can be recovered, and consequently the low-energy
structure is in a good agreement with the predictions of the RHB model.
