Untangling the interplay of the Equation-of-State and the Collision Term towards the generation of Directed and Elliptic Flow at intermediate energies

Abstract

The mechanism for generating directed and elliptic flow in heavy-ion collisions is investigated and quantified for the SIS18 and SIS100 energy regimes. The observed negative elliptic flow $v_2$, at midrapidity has been explained either via (in-plane) shadowing or via (out-of-plane) squeeze-out. To settle this question, we employ the Ultra-relativistic Quantum Molecular Dynamics model (UrQMD) to calculate Au+Au collisions at E${}_{\mathrm{lab}}=0.6A$ GeV, E${}_{\mathrm{lab}}=1.23A$ GeV and $\sqrt{s_{\mathrm{NN}}}=3.0$ GeV using a hard Skyrme type Equation-of-State to calculate the time evolution and generation of directed flow and elliptic flow. We quantitatively distinguish the impact of collisions and of the potential on $v_1$ and $v_2$ during the evolution of the system. These calculations reveal that in this energy regime the generation of $v_1$ and $v_2$ follows from a highly intricate interplay of different processes and is created late, after the system has reached its highest density and has created a matter bridge between projectile and target remnant, which later breaks. Initially, we find a strong out-of-plane pressure. Then follows a strong stopping and the built up of an in-plane pressure. The $v_2$, created by both processes, compensate to a large extend. The finally observed $v_2$ is caused by the potential, reflects the freeze-out geometry and can neither be associated to squeeze-out nor to shadowing. The results are highly relevant for experiments at GSI, RHIC-FXT and the upcoming FAIR facility, but also for experiments at FRIB, and strengthens understanding on the Equation-of-State at large baryon densities.

Comments: 19 pages, 18 figures