Directed flow in Au+Au, Xe+CsI, and Ni+Ni collisions and the nuclear equation of state

We present new experimental data on directed flow in collisions of $\mathrm{Au}+\mathrm{Au},$ $\mathrm{Xe}+\mathrm{CsI},$ and $\mathrm{Ni}+\mathrm{Ni}$ at incident energies from $90A$ to $400A\mathrm{MeV}.$ We study the centrality and system dependence of integral and differential directed flow for particles selected according to charge. All the features of the experimental data are compared with isospin quantum molecular dynamics (IQMD) model calculations in an attempt to extract information about the nuclear matter equation of state (EoS). We show that the combination of rapidity and transverse momentum analysis of directed flow allows to disentangle various parametrizations in the model. At $400A\mathrm{MeV},$ a soft EoS with momentum dependent interactions is best suited to explain the experimental data in $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Xe}+\mathrm{CsI},$ but in the case of $\mathrm{Ni}+\mathrm{Ni}$ the model underpredicts flow for any EoS. At $90A\mathrm{MeV}$ incident beam energy, none of the IQMD parametrizations studied here are able to consistently explain the experimental data.