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

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