Impact parameter dependence of pion ratio in probing the nuclear   symmetry energy using heavy-ion collisions
  The impact parameter dependence of \rpi ratio is examined in heavy-ion collisions at 400MeV/nucleon within a transport model. It is shown that the sensitivity of \rpi ratio on symmetry energy shows a transition from central to peripheral collisions, i.e., the stiffer symmetry energy leads to a larger \rpi ratio in peripheral collisions while the softer symmetry energy always leads this ratio to be larger in central collisions. After checking the kinematic energy distribution of \rpi ratio, we found this transition of sensitivity of \rpi ratio to symmetry energy is mainly from less energetic pions, i.e., the softer symmetry energy gets the less energetic pions to form a smaller \rpi ratio in peripheral collisions while these pions generate a larger \rpi ratio in central collisions. Undoubtedly, the softer symmetry energy can also lead more energetic pions to form a larger \rpi ratio in peripheral collisions. Nevertheless, considering that most of pions are insufficient energetic at this beam energy, we therefore suggest the \rpi ratio as a probe of the high-density symmetry energy effective only in central at most to midcentral collisions, thereby avoiding the possible information of low-density symmetry energy carried in \rpi ratio from peripheral collisions. 
Gao-Feng Wei, Guo-Qiang He, Xin-Wei Cao, and Yi-Xin Lu
nucl-th