  Taking into account more accurately the isospin dependence of nucleon-nucleon
interactions in the in-medium many-body force term of the Gogny effective
interaction, new expressions for the single nucleon potential and the symmetry
energy are derived. Effects of both the spin(isospin) and the density
dependence of nuclear effective interactions on the symmetry potential and the
symmetry energy are examined. It is shown that they both play a crucial role in
determining the symmetry potential and the symmetry energy at supra-saturation
densities. The improved single nucleon potential will be useful for simulating
more accurately nuclear reactions induced by rare isotope beams within
transport models.
