NN correlations and relativistic Hartree-Fock in finite nuclei.

Two different approximation schemes for the self-consistent solution of the relativistic Brueckner-Hartree-Fock equation for finite nuclei are discussed using realistic One-Boson-Exchange potentials. In a first scheme, the effects of correlations are deduced from a study of nuclear matter and parameterized in terms of an effective σ, ω and π exchange. Employing this effective interaction rela-tivistic Hartree-Fock equations are solved for finite nuclei 16 O, 40 Ca and 48 Ca. In the second approach the effect of correlations are treated in the Brueckner-Hartree-Fock approximation directly for the finite nuclei, but the modifications of the Dirac spinors in the medium are derived from nuclear matter assuming a local-density approximation. Both approaches yield rather similar results for binding energies and radii in fair agreement with experimental data. The importance of the density dependent correlation effects is demonstrated and different ingredients to the spin-orbit splitting in the shell-model of the nucleus are discussed.