Single-nucleon potential decomposition of the nuclear symmetry energy

TL;DR

This paper analytically decomposes the nuclear symmetry energy and its slope into contributions from single-nucleon potentials using three effective interaction models, highlighting the importance of second-order symmetry potentials.

Contribution

It introduces a detailed decomposition of symmetry energy components and emphasizes the significance of second-order symmetry potentials in nuclear matter models.

Findings

Different density behaviors of $E_{sym}( ho)$ are due to variations in the symmetry potential $U_{sym,1}( ho,k)$.

The second-order symmetry potential $U_{sym,2}( ho,k)$ significantly influences the slope $L( ho)$.

$U_{sym,2}( ho,k)$ is comparable in magnitude to $U_{sym,1}( ho,k)$, affecting the Lane approximation.

Abstract

The nuclear symmetry energy $E_{sym}(\rho)$ and its density slope $L(\rho)$ 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 the $E_{sym}(\rho)$ and $L(\rho)$. Our results show that the observed different density behaviors of $E_{sym}(\rho)$ for different interactions are essentially due to the variation of the symmetry potential $U_{sym,1}(\rho,k)$. Furthermore, we find that the contribution of the second-order symmetry potential $U_{sym,2}(\rho,k)$ to the $L(\rho)$ generally cannot be neglected. Moreover, our results demonstrate that the magnitude of the $U_{sym,2}(\rho,k)$ is generally comparable with that of $U_{sym,1}(\rho,k)$, indicating the second-order symmetry potential $U_{sym,2}(\rho,k)$ may have significant corrections to the widely used Lane approximation to the single-nucleon potential in extremely neutron(proton)-rich nuclear matter.