Relativistic Mean Field Theory of Surface Pion Condensation in Finite Nuclei

We study the possible occurrence of surface pion condensation in finite nuclei in the relativistic mean field (RMF) theory. We are led to this conjecture due to the essential role of pions in few-body systems and the recent (p,n) experiments performed at RCNP for spin-isospin excitations of medium and heavy nuclei. We calculate explicitly various N=Z closed shell nuclei with finite pion mean field in the RMF framework and demonstrate the actual occurrence of surface pion condensation. The pion is conjectured by Yukawa as the mediator of nucleon-nucleon interaction [1]. The pion is identified then as the Nambu-Goldstone mode when the underlying symmetry, the chiral symmetry, is spontaneously broken [2]. The pion plays the central role in hadron physics, particularly for the low energy phenomena, and now the chiral perturbation approach with the pion as the essential degree of freedom is the powerful tool for the study of hadron properties and collisions. On the other hand, since the establishment of the shell model, we usually solve nuclear many-body problems in the model space, where single particle states have good parities. Because the parity of a nucleon changes when it absorbs or emits a pion, we must include the higher configurations like 2p-2h (2 particle–2 hole), . . ., to incorporate the effect of the pion in the parity-conserved space. To avoid such complications we renormalize the central and the spin-orbit interactions in nuclei to incorporate the effect of the strong correlations caused by the pion. It means that we make a model space in which the parity is conserved and then define the effective interaction acting between nucleons in the model space. One of the main purpose of the present study is to expand the model space for the pion to play its important role explicitly and see the effect on nuclear structure. As for the importance of the pion, we remind ourselves of the findings of few-body systems, where they are solved rigorously without the restriction of model space with a realistic nucleon-nucleon interaction. The calculations are performed in the non-relativistic framework and hence the pion is hidden mainly in the tensor force, which is much larger than the central force in the one pion exchange interaction even up to the Compton length. There are many extensive calculations us