Elliptic flow in heavy-ion collisions at intermediate energy: the role of impact parameter, mean field potential, and collision term

Within the ultrarelativistic quantum molecular dynamics (UrQMD) model, by reverse tracing nucleons that are finally emitted at mid-rapidity (|$y_0$| < 0.1) in the entire reaction process, the time evolution of elliptic flow ($v_2$) of these traced nucleons produced in Au+Au collisions at beam energy of 0.4 GeV$/$nucleon with different impact parameters ($b$) is studied. The initial value of $v_2$ is positive and increases with $b$, then it decreases as time passes and tends to saturate at a negative value. It is found that nucleon-nucleon collisions always depress the value of $v_2$ (enhance the out-of-plane emission), while the nuclear mean field potential may slightly raise the value of $v_2$ during the expansion stage in peripheral reactions. The related density mostly probed by $v_2$ of nucleons at mid-rapidity is found to be $\sim$ 60% of the maximum density reached during the collisions.