  We test the compatibility of chiral symmetry, dynamic mass generation of the
nucleon due to spontaneous breaking of chiral symmetry, and the description of
finite nuclear systems by employing an NJL model understood as a chiral
invariant effective theory for nucleons. We apply the model to nuclear matter
as well as to finite nuclei. In the latter case, the model is adjusted to
nuclear ground-state observables. We treat the case of a pure chiral theory and
the physically more realistic case where a portion of the nucleon mass (160
MeV) explicitly breaks chiral symmetry. The best version of this current model
is found to deliver reasonably good results simultaneously for both finite
nuclei and the nucleon mass, which supports our motivation of probing a link
between low-momentum QCD and the nuclear many-body problem. However, the
observables calculated for finite nuclei are not as good as those coming from
existing relativistic mean field models without explicit chiral symmetry.
