Relativistic Effects in 3-Nucleon Forces for Nuclear Matter and Finite Nuclei

In order to simulate the relativistic effects of the Dirac Brueckner Hartree Fock approach for finite nuclei the part of the Urbana 3 nucleon (3N) force is considered, which represents the enhancement of the small components of the Dirac spinors for the nucleons in the nuclear medium. This 3N force is included in a Brueckner Hartree Fock calculation with rearrangement terms using a realistic model for the NN interaction. The strength of the 3N force is adjusted to reproduce the empirical saturation point of nuclear matter and then used in corresponding studies of the closed shell nuclei $^{16}$O and $^{40}$Ca. Special attention is paid to a consistent treatment of the spectrum of particle states in the NN propagator of the Bethe-Goldstone equation.