## 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{sub sym}({rho}) and its density slope L({rho}) at normal density {rho}{sub 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 E{sub sym}({rho}{sub 0})=31.3 MeV and L({rho}{sub 0})=52.7 MeV are simultaneously obtained. Moreover, the corresponding neutron-proton effective mass splitting in neutron-rich matter of isospin asymmetry {delta} ismore »