Isospin-Dependence of $\pi^-/\pi^+$ Ratio and Density-Dependence of   Nuclear Symmetry Energy
  The $\pi^-/\pi^+$ ratio is examined as a function of isospin asymmetry and beam energy for central collisions induced by neutron-rich nuclei within an isospin-dependent hadronic transport model. The $\pi^-/\pi^+$ ratio is found to increase with the isospin asymmetry, but decrease with the beam energy of the reaction. For neutron-rich systems, such as, $^{124}Sn+^{124}Sn$ and $^{132}Sn+^{124}Sn$, the sensitivity of $\pi^-/\pi^+$ ratio to nuclear symmetry energy is almost beam energy independent. 
Bao-An Li