In this talk, the density dependent relativistic Hartree-Fock (DDRHF) theory will be introduced as well as the extensions. For the applications of the DDRHF theory, I would like to concentrate on the following three topics:

1. Neutron star properties within the DDRHF theory:

With the equations of state provided by the DDRHF theory for hadronic matter, the properties of the static and beta-equilibrium neutron stars without hyperons are studied and compared to the predictions of the relativistic mean-field models and recent observational data. The influences of Fock terms on properties of asymmetric nuclear matter at high densities are discussed in detail.

2. Non-local mean field effects in 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 HF and density dependent relativistic Hartree model (DDRMF). 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 subshell closure Z=64.

3. Cerium Halo strutures within the density dependent relativistic Hartree-Fock-Bogoliubov (DDRHFB) theory:

Relativistic Hartree-Fock-Bogoliubov theory with density dependent meson-nucleon couplings is used to study halo phenomena close to the neutron drip line. Cerium isotopes are investigated as representative cases. Giant halos, as well as the ordinary ones, are found in these nuclei. The Fock terms, especially the rho-tensor couplings, play a crucial role in the stability of the halo structures, from which is well demonstrated the necessity of Fock terms.