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

Evolutions of single-particle energies and Z=64 sub-shell along the isotonic chain of N=82 are investigated in the density dependent relativistic Hartree-Fock (DDRHF) theory in comparison with other commonly used mean field models such as Skyrme HF, Gogny HFB and density dependent relativistic Hartree model (DDRMF). The pairing is treated in the BCS scheme, except for Gogny HFB. It is pointed out that DDRHF reproduces well characteristic features of experimental $Z$-dependence of both spin orbital and pseudo-spin orbital splittings around the sub-shell closure Z=64. Non-local exchange terms of the isoscalar $\sigma$ and $\omega$ couplings play dominant roles in the enhancements of the spin-orbit splitting of proton 2d states, which is the key ingredient 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 each other and the net effect becomes rather small. The enhancement of the sub-shell gaps towards Z=64 is studied by the DDRHF, for which the local terms of the scalar and vector meson couplings are found to be important.