  The properties of infinite matter and finite nuclei are studied by using the
chiral sigma model in the framework of the relativistic mean field theory. We
reconstruct an extended chiral sigma model in which the omega meson mass is
generated dynamically by the sigma condensation in the vacuum in the same way
as the nucleon mass. All the parameters of chiral sigma model are essentially
fixed from the hadron properties in the free space. In nuclear matter, the
saturation property comes out right, but the incompressibility is too large and
the scalar and vector potentials are about a half of the phenomenological ones,
respectively. This fact is reflected to the properties of finite nuclei. We
calculate N = Z even-even mass nuclei between N = 16 and N = 34. The extended
chiral sigma model without the pion mean field leads to the result that the
magic number appears at N = 18 instead of N = 20 and the magic number does not
appear at N = 28 due to the above mentioned nuclear matter properties. The
latter problem, however, could be removed by the introduction of the finite
pion mean field with the appearance of the magic number at N = 28. We find that
the energy differences between the spin-orbit partners are reproduced by the
finite pion mean field which is completely a different mechanism from the
standard spin-orbit interaction.
