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 Eₒₘ₌ () and its density slope L () at normal density 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 Eₒₘ₌ (₀) =31. 3 MeV and L (₀) =52. 7 MeV are simultaneously obtained. Moreover, the corresponding neutron-proton effective mass splitting in neutron-rich matter of isospin asymmetry is estimated to be (m₍^*-m₏^*) /m=0. 32.