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The odd-even staggerings (OES) on nuclear binding energies are studiedsystematically within the covariant density functional (CDF) theories,specifically the relativistic Hartree-Fock-Bogoliubov (RHFB) and therelativistic Hartree-Bogoliubov (RHB) theories. Taking the finite-range Gognyforce D1S as an effective pairing interaction, both CDF models can provideappropriate descriptions on the OESs of nuclear binding energies for C, O, Ca,Ni, Zr, Sn, Ce, Gd and Pb isotopes as well as for N=50 and 82 isotones.However, due to the inconsistence between the non-relativistic pairinginteraction and the relativistic effective Lagrangians, there exist somesystematical discrepancies from the data, i.e., the underestimated OESs inlight C and O isotopes and the overestimated ones in heavy region,respectively. Such discrepancies can be eliminated partially by introducing a$Z$- or $N$-dependent strength factor into the pairing force Gogny D1S. Inaddition, successful descriptions of the occupation numbers of Sn isotopes areachieved with the optimized Gogny pairing force. Furthermore, the analysis ofthe systematics of both pairing effects and nuclear binding energy indicate therequirement of an unified relativistic mechanism in both p-p and p-h channelsto improve the quantitative precision of the theory.

Odd-even staggerings on nuclear binding energy described by the covariant density functional theory