Probing the density dependence of the symmetry potential in intermediate energy heavy ion collisions

Based on the ultrarelativistic quantum molecular dynamics (UrQMD) model, the effects of the density-dependent symmetry potential for baryons and of the Coulomb potential for produced mesons are investigated for neutron-rich heavy ion collisions at intermediate energies. The calculated results of the $\Delta^-/\Delta^{++}$ and $\pi ^{-}/\pi ^{+}$ production ratios show a clear beam-energy dependence on the density-dependent symmetry potential, which is stronger for the $\pi ^{-}/\pi ^{+}$ ratio close to the pion production threshold. The Coulomb potential of the mesons changes the transverse momentum distribution of the $\pi ^{-}/\pi ^{+}$ ratio significantly, though it alters only slightly the $\pi^-$ and $\pi^+$ total yields. The $\pi^-$ yields, especially at midrapidity or at low transverse momenta and the $\pi^-/\pi^+$ ratios at low transverse momenta, are shown to be sensitive probes of the density-dependent symmetry potential in dense nuclear matter. The effect of the density-dependent symmetry potential on the production of both, K$^0$ and K$^+$ mesons, is also investigated.