III. RESULTS AND DISCUSSION 5 Taking p orbits with n = 0 , 1 , 2 , 3 as examples, the Dirac wave functions of spin partners are shown in Fig. 2. The dominant components F ( r ) for the spin doublets are almost identical, whereas the small components G ( r ) show dramatic deviations from each other due to the node relation given in Eq. (2). The features of the spin partners for both the energies and wave functions are similar to those in RMF [15]. In the following, the origin and mechanisms of the spin symmetry will be investigated in comparison with those in RMF. The spin-orbit splittings Δ E$_{ls}$ = E$_{n}$$_{˜}$ l$_{˜}$ l +1 / 2 − E$_{n}$$_{˜}$ l$_{˜}$ l − 1 / 2 in the negative energy spectrum of $^{16}$O versus the average binding energies E$_{av}$ = ( E$_{n}$$_{˜}$ l$_{˜}$ l +1 / 2 + E$_{n}$$_{˜}$ l$_{˜}$ l − 1 / $_{2}$) / 2 are given in Fig. 3. In In Fig. 1, all the bound single neutron states in the Dirac sea for $^{16}$O are given. The dash- dot line represents the corresponding Hartree potential V D which is not strong enough for the 0 s and 0 p orbits, the importance and contribution of the Fock terms is thus illustrated. For each pair of the spin doublets, the left levels are those with j = ˜ l − 1 / 2 and the right ones with j = ˜ l + 1 / 2. It can be clearly seen that the spin symmetry is well conserved in the Dirac sea. FIG. 1: (color online) Single neutron spectrum in the Dirac sea for $^{16}$O calculated by DDRHF with PKO1. The dash-dot line represents the Hartree potential V $^{D}$. For each pair of the spin doublets, the left levels are those with j = ˜ l − 1 / 2 and the right ones with j = ˜ l + 1 / 2. Solving the DDRHF equations Eq. (5) with the parameter set PKO1 [21] in coordinate space self-consistently as in RMF [27], the neutron and proton single-particle energies can be obtained. We take the nucleus $^{16}$O as an example to examine the negative energy spectrum and its spin symmetry. GLYPH<s48> GLYPH<s49> GLYPH<s50> GLYPH<s51> GLYPH<s52> GLYPH<s53> GLYPH<s45>GLYPH<s49>GLYPH<s48>GLYPH<s48>GLYPH<s48> GLYPH<s45>GLYPH<s56>GLYPH<s48>GLYPH<s48> GLYPH<s45>GLYPH<s54>GLYPH<s48>GLYPH<s48> GLYPH<s45>GLYPH<s52>GLYPH<s48>GLYPH<s48> GLYPH<s45>GLYPH<s50>GLYPH<s48>GLYPH<s48> GLYPH<s48> GLYPH<s49>GLYPH<s54> GLYPH<s79>GLYPH<s32>GLYPH<s110>GLYPH<s101>GLYPH<s117>GLYPH<s116>GLYPH<s114>GLYPH<s111>GLYPH<s110> GLYPH<s86> GLYPH<s68> GLYPH<s32> GLYPH<s40> GLYPH<s77> GLYPH<s101> GLYPH<s86> GLYPH<s41> GLYPH<s114>GLYPH<s32>GLYPH<s40>GLYPH<s102>GLYPH<s109>GLYPH<s41> GLYPH<s112> GLYPH<s100> GLYPH<s102> GLYPH<s103> GLYPH<s104> GLYPH<s105> GLYPH<s106> GLYPH<s107> GLYPH<s108> GLYPH<s115>