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(rho) and its density slope L(rho) at normal density rho(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-sym(rho(0)) = 31.3MeV and L(rho(0)) = 52.7MeV are simultaneously obtained. Moreover, the corresponding neutron-proton effective mass splitting in neutron-rich matter of isospin asymmetry delta is estimated to be (m*(n) -m*(p))/m = 0.32 delta.