Surface pion condensation of finite nucleus in the relativistic mean field theory

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We have made theoretical research on the role of pion for the structure of nucleus in the relativistic and non-relativistic framework. In the relativistic approach, we have also studied the role of the Dirac Sea on the nuclear structure. We list the outcome of the present research :1.We showed the occurrence of pion condensation in the relativistic mean field framework numerically. As a result, we see the appearance of the spin-orbit effect due to the pion. In addition, the pion condensates around the nuclear surface.2.We developed the parity and charge projection by preparing the intrinsic state with the total spin conserved. We then took variation by using the parity and charge projected wave function for He4. We showed the importance of the projection for the nuclear ground state. We found the importance of the pion (tensor interaction) for the structure of He4.3.We calculated the phase shifts of the neutron He4 scattering in order to show the importance of the tensor force quantitatively. We showed the mixture of the p-state in the structure of He4 is essential for the quantitative reproduction of the phase shifts of s,p and d wave phase shifts. This is a decisive result to demonstrate the role of the tensor force for the creation of the spin-orbit splitting.4.We formulated and calculated the parity and charge projection method in the framework of the relativistic mean field model. In order to extract the full strength of the pionic correlations, we showed the importance of the projection.We were able to show that the pion is playing the important role for the nuclear structure. On top, we are convinced that the results of our present study indicate the unification of the hadron physics and nuclear physics through the important role of the chiral symmetry.