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A systematic study of the in-medium correction factor ($F$) onnucleon-nucleon elastic cross section is performed within theUltra-relativistic Quantum Molecular Dynamics (UrQMD) model. The effects of thebeam energy dependence of $F$ on the directed, elliptic flow and nuclearstopping in $^{197}$Au+$^{197}$Au collisions with energy ranging from $0.09$ to$0.8A$ GeV are explored. It is found that the directed, elliptic flow andnuclear stopping at relatively low energies are very sensitive to $F$, and thesensitivity gradually weakens with increasing beam energy. The beam energydependent in-medium correction factor $F$ is deduced from the comparison of theexcitation functions of the directed, elliptic flow and nuclear stoppingbetween the calculated results and the FOPI experimental data.

Accessing the in-medium effects on nucleon-nucleon elastic cross section with collective flows and nuclear stopping