Single-nucleon potential decomposition of the nuclear symmetry energy

Abstract

The nuclear symmetry energy ${E}_{\mathrm{sym}}(\ensuremath{\rho})$ and its density slope $L(\ensuremath{\rho})$ can be decomposed analytically in terms of the single-nucleon potential in isospin asymmetric nuclear matter. Using three popular nuclear effective interaction models which have been extensively used in nuclear structure and reaction studies, namely, the isospin and momentum-dependent MDI interaction model, the Skyrme-Hartree-Fock approach, and the Gogny-Hartree-Fock approach, we analyze the contribution of different terms in the single-nucleon potential to ${E}_{\mathrm{sym}}(\ensuremath{\rho})$ and $L(\ensuremath{\rho})$. Our results show that the observed different density behaviors of ${E}_{\mathrm{sym}}(\ensuremath{\rho})$ for different interactions are essentially due to the variation of the symmetry potential ${U}_{\mathrm{sym},1}(\ensuremath{\rho},k)$. Furthermore, we find that the contribution of the second-order symmetry potential ${U}_{\mathrm{sym},2}(\ensuremath{\rho},k)$ to $L(\ensuremath{\rho})$ generally cannot be neglected. Moreover, our results demonstrate that the magnitude of ${U}_{\mathrm{sym},2}(\ensuremath{\rho},k)$ is generally comparable with that of ${U}_{\mathrm{sym},1}(\ensuremath{\rho},k)$, indicating that the second-order symmetry potential ${U}_{\mathrm{sym},2}(\ensuremath{\rho},k)$ may have significant corrections to the widely used Lane approximation for the single-nucleon potential in extremely neutron rich or proton rich nuclear matter.