Chiral Sigma Model with Pion Mean Field in Finite Nuclei

The properties of infinite matter and finite nuclei are studied by using thechiral sigma model in the framework of the relativistic mean field theory. Wereconstruct an extended chiral sigma model in which the omega meson mass isgenerated dynamically by the sigma condensation in the vacuum in the same wayas the nucleon mass. All the parameters of chiral sigma model are essentiallyfixed from the hadron properties in the free space. In nuclear matter, thesaturation property comes out right, but the incompressibility is too large andthe scalar and vector potentials are about a half of the phenomenological ones,respectively. This fact is reflected to the properties of finite nuclei. Wecalculate N = Z even-even mass nuclei between N = 16 and N = 34. The extendedchiral sigma model without the pion mean field leads to the result that themagic number appears at N = 18 instead of N = 20 and the magic number does notappear at N = 28 due to the above mentioned nuclear matter properties. Thelatter problem, however, could be removed by the introduction of the finitepion mean field with the appearance of the magic number at N = 28. We find thatthe energy differences between the spin-orbit partners are reproduced by thefinite pion mean field which is completely a different mechanism from thestandard spin-orbit interaction.Comment: 19 pages, 9 figures. Prog. Theor. Phys. to be publishe