Within the RMF framework, it has been pointed out that the strong centrifugal bar- rier and weak spin-orbit potential lead to the pseudo-spin symmetry in the single nucleon spectrum [10] and the spin symmetry in the single anti-nucleon spectrum [15]. 0 1 2 3 4 5 6 7 -0.002 -0.001 0.000 0.001 0.002 0.003 0 1 2 3 4 5 6 7 -0.0004 0.0000 0.0004 0.0008 0 1 2 3 4 5 6 7 0.00 0.05 0.10 0.15 0.20 V$_{CB}$ 0p$_{1/2}$ V$_{SOP}$ 0p$_{1/2}$ V$_{CB}$ 0p$_{3/2}$ V$_{SOP}$ 0p$_{3/2}$ $^{16}$O neutron r (fm) 0 1 2 3 4 5 6 7 0.00 0.05 0.10 0.15 0.20 0.25 0.30 $^{16}$O neutron r (fm) V$_{CB}$ 3p$_{1/2}$ V$_{SOP}$ 3p$_{1/2}$ V$_{CB}$ 3p$_{3/2}$ V$_{SOP}$ 3p$_{3/2}$ FIG. 5: (color online) Centrifugal barriers V$_{CB}$ and spin-orbit potentials V$_{SOP}$ multiplied by the factor ∓ F $^{2}$/ ( V$_{+}$ − E ) for the spin doublets ( ν 0 p$_{1}$$_{/}$$_{2}$, ν 0 p$_{3}$$_{/}$$_{2}$ ) (left panel) and ( ν 3 p$_{1}$$_{/}$$_{2}$, ν 3 p$_{3}$$_{/}$$_{2}$ ) (right panel) in the negative energy spectrum of $^{16}$O. The insets show the Hartree contributions of the spin-orbit potentials. In Fig. 5 are shown the centrifugal barriers V$_{CB}$ and the spin-orbital potentials V$_{SOP}$ multiplied by the factor ∓ F $^{2}$/ ( V$_{+}$ − E ) for the spin doublets 0 p and 3 p , and their integrals over r are respectively proportional to their contributions to the single-particle energy. It is clearly shown that the contribution of the centrifugal barriers V$_{CB}$ is much larger than that of the spin-orbital potentials V$_{SOP}$ . Therefore, it can be concluded that similar reasons as in RMF lead to the spin symmetry in the negative energy spectrum in DDRHF, and the spin-orbit splitting is due to the different spin-orbit potentials V$_{SOP}$ of the spin doublets. In the insets of Fig. 5 are given the Hartree contributions to the spin-orbit potentials. It is found that the contributions from the Fock terms to V$_{SOP}$ are one order of magnitude larger than those from the Hartree terms. Therefore, the Fock terms must play important roles in the spin-orbit splitting of the spin doublets. From Eq. (7), the contributions to the single-particle energies E from different channels can be estimated quantitatively. For example, the CB contribution can be calculated by In Table I are shown the contributions to the single-particle energies and spin-orbit splittings 8 1 ∫ ∞ 0 F $^{2}$dr ∫ ∞ 0 V$_{CB}$ V$_{+}$ − E F $^{2}$dr. (10)