Modifications of the pion-production threshold in the nuclear medium in heavy ion collisions and the nuclear symmetry energy

Abstract

Using the relativistic Vlasov-Uehling-Uhlenbeck (RVUU) equation based on mean fields from the nonlinear relativistic $\text{NL}\ensuremath{\rho}$ and $\text{NL}\ensuremath{\rho}\ensuremath{\delta}$ models, which have same nuclear equation of state and symmetry energy but different symmetry energy slope parameters, we study the effect of medium modification of the pion-production threshold on the total pion yield and the ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio in Au+Au collisions. We find that the in-medium threshold effect enhances both the total pion yield and the ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio, compared to those without this effect. Furthermore, including the medium modification of the pion-production threshold leads to a larger ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio for the $\text{NL}\ensuremath{\rho}\ensuremath{\delta}$ model with a larger symmetry energy parameter than the $\text{NL}\ensuremath{\rho}$ model with a smaller symmetry energy parameter, opposite to that found without the in-medium threshold effect. To reproduce the total pion yield measured by the FOPI Collaboration, we introduce a density-dependent cross section for $\ensuremath{\Delta}$ baryon production from nucleon-nucleon collisions, which suppresses the total pion yield but hardly changes the ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio. Because of the small difference in the stiffness of their symmetry energies, the ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratios obtained from both the $\text{NL}\ensuremath{\rho}$ and $\text{NL}\ensuremath{\rho}\ensuremath{\delta}$ models are consistent with the FOPI data within the experimental errors.