Relativistic chiral mean field approximation with projection and the role of tensor correlations in5He and11Li

Abstract

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 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=36 to A=64 with equal number of neutrons and protons. We find that the magic number gap at N = 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=36 instead of A=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 He 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 then switch to the non-relativistic method to describe the large tensor correlations in terms of the tensor optimized shell model (TOSM). We describe 4He and 9Li in TOSM where the tensor force is treated fully by taking enough configuration space. We show important consequenses of the tensor correlations caused by the tensor interaction due to the Pauli blocking effect on the phase shifts of neutron scattering from 4He and the halo structure of 11Li.