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Evolutions of single-particle energies and Z=64 sub-shell along the isotonicchain of N=82 are investigated in the density dependent relativisticHartree-Fock (DDRHF) theory in comparison with other commonly used mean fieldmodels such as Skyrme HF, Gogny HFB and density dependent relativistic Hartreemodel (DDRMF). The pairing is treated in the BCS scheme, except for Gogny HFB.It is pointed out that DDRHF reproduces well characteristic features ofexperimental $Z$-dependence of both spin orbital and pseudo-spin orbitalsplittings around the sub-shell closure Z=64. Non-local exchange terms of theisoscalar $\sigma$ and $\omega$ couplings play dominant roles in theenhancements of the spin-orbit splitting of proton 2d states, which is the keyingredient to give the Z=64 sub-shell closure properly. On the other hand, the$\pi$ and $\rho$ tensor contributions for the spin-orbit splitting cancel eachother and the net effect becomes rather small. The enhancement of the sub-shellgaps towards Z=64 is studied by the DDRHF, for which the local terms of thescalar and vector meson couplings are found to be important.

Non-local mean field effect on nuclei near Z=64 sub-shell