Chiral sigma model with pion mean field in finite nuclei

The properties of infinite matter and finite nuclei are studied using the chiral sigma model in the framework of relativistic mean field theory. We reconstruct an extended chiral sigma model in which the omega meson mass is generated dynamically by sigma condensation in the vacuum in the same manner as the nucleon mass., All the parameters of the chiral sigma model are essentially fixed by the hadron properties in free space. In nuclear matter, the saturation property is described correctly, but the incompressibility is too large, and the scalar and vector potentials are about half as large as their phenomenological values. This fact is reflected in the properties of finite nuclei. We carry out calculations for 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 through the introduction of a 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 a completely different mechanism from the standard spin-orbit interaction.