Nuclear symmetry energy and its density slope at normal density extracted from global nucleon optical potentials

TL;DR

This paper demonstrates that the nuclear symmetry energy and its density slope at normal density can be directly derived from global nucleon optical potentials obtained from scattering experiments and bound state data, providing precise estimates.

Contribution

It introduces a method to determine symmetry energy and its slope from nucleon optical potentials using the Hugenholtz-Van Hove theorem, offering updated estimates based on world data.

Findings

Symmetry energy at normal density estimated as 31.3 MeV.

Density slope at normal density estimated as 52.7 MeV.

Uncertainties in estimates are discussed.

Abstract

Based on the Hugenholtz-Van Hove theorem, it is shown that both the symmetry energy E$_{sym}(\rho)$ and its density slope $L(\rho)$ at normal density $\rho_0$ are completely determined by the global nucleon optical potentials that can be extracted directly from nucleon-nucleus scatterings, (p,n) charge exchange reactions and single-particle energy levels of bound states. Adopting a value of $m^*/m=0.7$ for the nucleon effective k-mass in symmetric nuclear matter at $\rho_0$ and averaging all phenomenological isovector nucleon potentials constrained by world data available in the literature since 1969, the best estimates of $E_{sym}(\rho_0)=31.3$ MeV and $L(\rho_0)=52.7$ MeV are simultaneously obtained. Uncertainties involved in the estimates are discussed.