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

Abstract EN

The impact parameter dependence of π-/π+ ratio is examined in heavy-ion collisions at 400 MeV/nucleon within a transport model.

It is shown that the sensitivity of π-/π+ ratio on symmetry energy shows a transition from central to peripheral collisions; that is, the stiffer symmetry energy leads to a larger π-/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 of π-/π+ ratio, we found this transition of sensitivity of π-/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 smaller π-/π+ ratio in peripheral collisions while these pions generate a larger π-/π+ ratio in central collisions.

Undoubtedly, the softer symmetry energy can also lead more energetic pions to form a larger π-/π+ ratio in peripheral collisions.

Nevertheless, considering that most of pions are insufficiently energetic at this beam energy, we therefore suggest the π-/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 in π-/π+ ratio from peripheral collisions.