Symmetry energy, its density slope, and neutron-proton effective mass splitting 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({ρ})$ and its density slope $L({ρ})$ at normal density ${{ρ}}₀$ are completely determined by the nucleon global optical potentials. The latter can be extracted directly from nucleon-nucleus scatterings, ($p,n$) charge-exchange reactions, and single-particle energy levels of bound states. Averaging all phenomenological isovector nucleon potentials constrained by world data available in the literature since 1969, the best estimates of Esym(ρ₀)=31.3 MeV and L(ρ₀)=52.7 MeV are simultaneously obtained. Moreover, the corresponding neutron-proton effective mass splitting in neutron-rich matter of isospin asymmetry δ is estimated to be (mₙ*-mₚ*)/m=0.32δ.