  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.
