Probing the density dependence of the symmetry energy with central heavy ion collisions

An improved isospin dependent Boltzmann Langevin model, in which the inelastic channels and momentum dependent interactions are incorporated, is used to investigate the high-density behavior of nuclear symmetry energy. By taking several forms of nuclear symmetry energy, we calculate the time evolutions of neutron over proton ratio, π multiplicity and π^-/π⁺ ratio, and the kinetic energy and transverse momentum spectra of π^-/π⁺ ratio in the heavy ion collisions at 400A MeV It is found that the neutron over proton ratio and π^-/π⁺ ratio are very sensitive to the nuclear symmetry energy, and the π^- is more sensitive to the nuclear symmetry energy than the π⁺. A supersoft symmetry energy results in a larger π^-/π⁺ ratio. (authors)