Relativistic chiral mean field model for finite nuclei

We study the role of pion for the structure of finite nuclei. We take the chiral sigma model, where the pions are the Nambu–Goldstone bosons of the chiral symmetry breaking. We then take the finite pion mean field in the relativistic mean field approximation. We study first the nuclei in the range of A=36A=36 to A=64A=64 with equal number of neutrons and protons. We find that the magic number gap at N=Z=28N=Z=28 appears due to the finite pion mean field effect. The pion provides a large spin–orbit splitting effect due to a mechanism totally different from the ordinary spin–orbit term of the relativistic origin. On the other hand, we are not able to shift the magic number appearing at A=36A=36 instead of A=40A=40, which is now a motivation to work out the parity and charge projection. The standard projection technique provides an integro-differential equation for the Dirac equation. As an example, we work out 4He in the relativistic chiral mean field model. We find good properties for the ground state energy and the size and the pion energy contribution. The form factor also comes out to be quite satisfactory. We discuss further the renormalization procedure of the linear chiral model by treating both the nucleon loop and the boson loop in the Coleman–Weinberg renormalization scheme with the hope to calculate the negative energy contribution from the nucleon vacuum. We are able to obtain a stable chiral model Lagrangian with the nucleon vacuum polarization effect due to strong cancellation between the nucleon loop and the boson loop.