Origin of elliptic flow and its dependence on the equation of state in heavy ion reactions at intermediate energies

Recently it has been discovered that the elliptic flow, $v_2$, of composite charged particles emitted at midrapidity in heavy-ion collisions at intermediate energies shows the strongest sensitivity to the nuclear equation of state (EoS), which has been observed up to now within a microscopic model. This dependence on the nuclear EoS is predicted by quantum molecular dynamics (QMD) calculations [A. Le Fèvre et al.. Nucl. Phys. A 945, 112 (2016)], which show as well that the absorption or rescattering of in-plane emitted particles by the spectator matter is not the main reason for the EoS dependence of the elliptic flow at midrapidity but different density gradients (and therefore different forces) in the direction of the impact parameter ($x$ direction) as compared to the direction perpendicular to the reaction plan ($y$ direction), caused by the presence of the spectator matter. The stronger density gradient in the $y$ direction accelerates the particles more and creates therefore a negative $v_2$. When using a soft momentum-dependent EoS, the QMD calculations reproduce the experimental results.