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Effect of Delta potential on the pion-/pion+ ratio in heavy-ion collisions at intermediate energies

Based on the isospin-dependent Boltzmann-Uehling-Uhlenbeck(IBUU) transport model, effects of $Δ$ resonance potential on the free n/p and $π^-/π^+$ ratios in the central collision of $^{197}Au+^{197}Au$ at beam energies of 200 and 400 MeV/A are studied. It is found that the effect of $Δ$ potential on the ratio of pre-equilibrium free $n/p$ is invisible. The effect of $Δ$ isovector potential on the kinetic energy integrating ratio of $π^-/π^+$ may be observable only at lower incident beam energies and with stiffer symmetry energy. The strength of the $Δ$ isoscalar potential affects the height of the $π^-/π^+$ ratio around the Coulomb peak but does not affect the kinetic energy integrating ratio of $π^-/π^+$. In heavy-ion collisions at intermediate energies, relating to the question of non-conservation of energy on $Δ$ or $π$ productions, one can replace the $Δ$ potential by nucleon isoscalar potential especially a soft symmetry energy is employed.