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Based on the ultra-relativistic quantum molecular dynamics (UrQMD) model, theimpacts of momentum dependent interaction, symmetry energy and near-threshold$NN\to N\Delta$ cross sections on isospin sensitive collective flow and pionobservables are investigated. Our results confirm that the elliptic flow ofneutrons and charged particles, i.e. $v_2^n$ and $v_2^{ch}$, are sensitive tothe 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. Fordescribing the pion multiplicity near the threshold energy, accurate $NN\toN\Delta$ cross sections are crucial. With the updated momentum dependentinteraction and $NN\to N\Delta$ cross sections in UrQMD model, sevenobservables, such as directed flow and elliptic flow of neutrons and chargedparticles, the elliptic flow ratio of neutrons to charged particles, chargedpion multiplicity and its ratio $\pi^-/\pi^+$, can be well described by theparameter sets with the slope of symmetry energy from 5 MeV to 70 MeV. Todescribe the constraints of symmetry energy at the densities probed by thecollective flow and pion observables, the named characteristic density isinvestigated and used. Our analysis found that the flow characteristic densityis around 1.2$\rho_0$ and pion characteristic density is around 1.5$\rho_0$,and we got the constrains of symmetry energy at characteristic densities are$S(1.2\rho_0)=34\pm 4$ MeV and $S(1.5\rho_0)=36\pm 8$ MeV. These results areconsistent with previous analysis by using pion and flow observable withdifferent transport models, and demonstrate a reasonable description ofsymmetry energy constraint should be presented at the characteristic density ofisospin sensitive observables.

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