  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.
