Relativistic chiral mean-field model with parity and charge projection for finite nuclei

Abstract

We study the role of pions on the ground states of finite nuclei with explicit treatment of pions by variation after charge and parity projection based on the relativistic chiral mean-field (CPPCMF) model. This CPPCMF model has been applied to $^{4}\mathrm{He}$ and demonstrated to provide good ground-state properties within a spherical pion field ansazt. We further apply this model to heavier nuclei up to $^{56}\mathrm{Ni}$ in this article. We find that pions play dominant role also for properties of $^{12}\mathrm{C}$. However, this pionic effect is significantly suppressed in $^{16}\mathrm{O}$ due to the Pauli blocking effect. We find that pionic correlations reflect largely the particle configurations in the shell structure. As for the heavier nuclei, the pionic energy systematics as a function of nuclear mass number are clearly separated into two groups, the LS and $\mathit{jj}$ closed-shell nuclei. The large amount of pionic contributions are obtained for $\mathit{jj}$ closed-shell nuclei as compared with those for LS closed-shell nuclei. This fact may indicate that the pion plays an important role on the formation of the $\mathit{jj}$ magic numbers. The pionic contributions are reduced approximately as ${A}^{\ensuremath{-}2/3}$ with the nuclear mass number. We discuss the reason of this reduction of the pionic energy with the nuclear mass and propose to improve our present ansatz of dealing with pions for heavier nuclei.