Charge and parity projected relativistic mean field model with pion for finite nuclei

Abstract

We construct a new relativistic mean field model by explicitly introducing a \ensuremath{\pi}-meson mean field with charge number and parity projection. We call this model the charge and parity projected relativistic mean field (CPPRMF) model. We take the chiral \ensuremath{\sigma} model Lagrangian for the construction of finite nuclei. We apply this framework first for the $^{4}\mathrm{He}$ nucleus as a pilot case and study the role of the \ensuremath{\pi}-meson field on the structure of nuclei. We demonstrate that it is essential to solve the mean field equation with the variation introduced after the projection in order to take the pionic correlations into account explicitly. We study the ground-state properties of $^{4}\mathrm{He}$ by varying several parameters, such as the \ensuremath{\sigma}-meson mass and the \ensuremath{\omega}-meson coupling constant. We are able to construct a good ground state for $^{4}\mathrm{He}$. A depression appears in the central region of the density distribution, and the second maximum and the position of the dip in the form factor of $^{4}\mathrm{He}$ are naturally obtained in the CPPRMF model.