IFIN-HH Bucharest, ROMANIA
The Tübingen QMD transport model has been expanded by including contributions due to the in-medium pion potential , in addition to the conservation of total energy at an event by event level . The included S-wave part mimics the density and isospin asymmetry dependence of a potential capable of explaining the existence and spectrum of pionic atoms . The P wave potential was extracted from a non-relativistic, so called, "three-level" model [4,5] for pion-nucleon scattering. The strength of the latter leads to the reduction, by a factor of about 2, of the S wave repulsion for the $\pi^-$ meson at saturation and for a value of the isospin asymmetry parameter equal to 0.2 (Au nuclei) and momenta of the pion close to the average that is expected in heavy-ion reactions above pion-production threshold by 100-200 MeV/nucleon. The impact of the pion potential on observables relevant for constraining the high density dependence of the symmetry energy is discussed. An almost negligible impact on the charged pion multiplicity ratio is demonstrated. For its momentum dependent version, the impact of the pion potential is comparable in magnitude to the sensitivity to the symmetry-energy stiffness in the region of the Coulomb peak (low momentum). It is proven that the inclusion of the pion potential allows an important improvement of the description of the experimental FOPI data  for the charged pion ratio of average momenta, however a perfect agreement will most likely require a stronger attractive P wave pion potential than is suggested by "three-level" type models.