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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]. 

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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 

<img src='content_image/329216.jpg'>

In Table I are shown the contributions to the single-particle energies and spin-orbit splittings 

