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Impacts of momentum dependent interaction, symmetry energy and near-threshold $NN\to NΔ$ cross sections on isospin sensitive flow and pion observables

Based on the ultra-relativistic quantum molecular dynamics (UrQMD) model, the impacts of momentum dependent interaction, symmetry energy and near-threshold $NN\to NΔ$ cross sections on isospin sensitive collective flow and pion observables are investigated. Our results confirm that the elliptic flow of neutrons and charged particles, i.e. $v_2^n$ and $v_2^{ch}$, are sensitive to the strength of momentum dependence interaction and the elliptic flow ratio, i.e., $v_2^n/v_2^{ch}$, is sensitive to the stiffness of symmetry energy. For describing the pion multiplicity near the threshold energy, accurate $NN\to NΔ$ cross sections are crucial. With the updated momentum dependent interaction and $NN\to NΔ$ cross sections in UrQMD model, seven observables, such as directed flow and elliptic flow of neutrons and charged particles, the elliptic flow ratio of neutrons to charged particles, charged pion multiplicity and its ratio $π^-/π^+$, can be well described by the parameter sets with the slope of symmetry energy from 5 MeV to 70 MeV. To describe the constraints of symmetry energy at the densities probed by the collective flow and pion observables, the named characteristic density is investigated and used. Our analysis found that the flow characteristic density is around 1.2$ρ_0$ and pion characteristic density is around 1.5$ρ_0$, and we got the constrains of symmetry energy at characteristic densities are $S(1.2ρ_0)=34\pm 4$ MeV and $S(1.5ρ_0)=36\pm 8$ MeV. These results are consistent with previous analysis by using pion and flow observable with different transport models, and demonstrate a reasonable description of symmetry energy constraint should be presented at the characteristic density of isospin sensitive observables.