Impact Parameter Dependence ofπ-/π+Ratio in Probing the Nuclear Symmetry Energy Using Heavy-Ion Collisions

Abstract

The impact parameter dependence ofπ-/π+ratio is examined in heavy-ion collisions at 400 MeV/nucleon within a transport model. It is shown that the sensitivity ofπ-/π+ratio on symmetry energy shows a transition from central to peripheral collisions; that is, the stiffer symmetry energy leads to a largerπ-/π+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 ofπ-/π+ratio, we found this transition of sensitivity ofπ-/π+ratio to symmetry energy is mainly from less energetic pions; that is, the softer symmetry energy gets the less energetic pions to form a smallerπ-/π+ratio in peripheral collisions while these pions generate a largerπ-/π+ratio in central collisions. Undoubtedly, the softer symmetry energy can also lead more energetic pions to form a largerπ-/π+ratio in peripheral collisions. Nevertheless, considering that most of pions are insufficiently energetic at this beam energy, we therefore suggest theπ-/π+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 inπ-/π+ratio from peripheral collisions.