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

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.