-200 -400 -600 -800 -1000 -3 -2 -1 0 1 2 3 E$_{av}$ (MeV) $^{16}$O neutron  p  d  f  g  h  i  j  k  l Δ E D,E ls  (MeV) Hartree Fock FIG. 6: (color online) Hartree and Fock contributions to spin-orbit splitting in the negative energy spectrum of $^{16}$O versus the average energy of the spin doublets. The vertical dashed line shows the continuum limit. In order to get a deeper understanding of the cancellation and competition between the Hartree and Fock terms, we first separate the different meson contributions to single-particle energies. It is found that in both Hartree and Fock contributions, the isoscalar mesons, σ and ω , play dominant roles in the spin-orbit splitting, while the contributions from the ρ -, π -mesons, and the rearrangement terms are negligible. Then, to make the mathematical structure simple and clear, one could replace the finite range Yukawa propagators with a pure delta function δ ( $^{r}$1 − r $_{2}$) for these two heavy isoscalar mesons, but keeping their Dirac scalar and vector couplings. In this simple picture, it is found that the direct term of the σ -meson makes the spin-orbit splitting positive, whereas that of the ω -meson makes the splitting negative. Since the attractive σ field is slightly stronger than the repulsive ω field in realistic nuclei, the net Hartree contribution to the splitting is positive, as shown in the upper part of Fig. 6. Meanwhile, it is also found analytically that the effect of the σ exchange term is roughly one half as the effect of its direct term, but with an opposite sign. The effect of the ω exchange term almost vanishes due to the cancellation between the time and space components. Therefore, the net Fock contribution to the splitting is negative and comparable to the Hartree contribution, as shown in the lower part of Fig. 6. All the above discussions for the case of $^{16}$O are also valid for heavier nuclei, e.g., $^{208}$Pb. It is known that the presence of strong annihilation channels and various many-body effects could cause significant deviations from the G-parity values of the meson-antinucleon couplings [28] and a global fits to antiprotonic X-rays and radiochemical data indicates the 10