Extracting the nuclear symmetry potential and energy from neutron-nucleus scattering data

TL;DR

This paper refines the extraction of the nuclear symmetry energy and its density slope from neutron-nucleus scattering data by including second-order isospin asymmetry terms, revealing significant effects of the second-order potential at high nucleon momentum.

Contribution

It introduces a consistent inclusion of second-order isospin asymmetry terms in the optical model potential and symmetry energy decomposition, improving the accuracy of symmetry energy constraints.

Findings

Second-order symmetry potential $U_{sym,2}$ is significant at high momentum.

$U_{sym,2}$ decreases with nucleon momentum, opposite to $U_{sym,1}$.

Data favor a softer density dependence of the symmetry energy with negligible $U_{sym,2}$ contribution.

Abstract

According to the Hugenholtz-Van Hove theorem, the symmetry energy and its density slope can be decomposed uniquely in terms of the single-nucleon potential in asymmetric nuclear matter which, at normal density, can be constrained by the nucleon optical model potential extracted from analyzing the nucleon-nucleus scattering data. To more accurately extract information on the symmetry energy and its density slope at normal density from neutron-nucleus scattering data, going beyond the well-known Lane potential, we include consistently the second order terms in isospin asymmetry in both the optical model potential and the symmetry energy decomposition. We find that the strength of the second-order symmetry potential $U_{sym,2}$ in asymmetric nuclear matter is significant compared to the first-order one U_{sym,1}$, especially at high nucleon momentum. While the $U_{sym,1}$ at normal density decreases with nucleon momentum, the $U_{sym,2}$ is found to have the opposite behavior. Moreover, we discuss effects of the $U_{sym,1}$ and $U_{sym,2}$ on determining the density dependence of the symmetry energy, and we find that the available neutron-nucleus scattering data favor a softer density dependence of the symmetry energy at normal density with a negligible contribution from the $U_{sym,2}$.