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Heavy-ion-collision measurements in combination with transport modelsimulations serve as important tools for extracting the nuclearincompressibility. However, uncertainties in transport models (or modeldependence) partly affect the reliability of the extracted result. In thepresent work, by using the recently measured data of rapidity-dependent flows,we constrain the incompressibility of nuclear matter and analyse the impact ofmodel uncertainties on the obtained value. The method is based on the newlyupdated version of the ultrarelativistic quantum molecular dynamics (UrQMD)model in which the Skyrme potential energy-density functional is introduced.Three different Skyrme interactions which give different incompressibilitiesvarying from $K_0$=201 to 271 MeV are adopted. The incompressibility is deducedfrom the comparison of the UrQMD model simulations and the FOPI data forrapidity-dependent elliptic flow in Au+Au collisions at beam energies0.4\emph{A} - 1.0\emph{A} GeV. The elliptic flow $v_2$ as a function ofrapidity $y_0$ can be well described by a quadratic fit $v_2=v_{20} +v_{22}\cdot y_0^2 $. It is found that the quantity $v_{2n}$ defined by$v_{2n}=|v_{20}|+|v_{22}|$ is quite sensitive to the incompressibility $K_0$and the in-medium nucleon-nucleon cross section, but not sensitive to the slopeparameter $L$ of the nuclear symmetry energy. With the FU3FP4 parametrizationof the in-medium nucleon-nucleon cross section, an averaged $K_0 = 220 \pm40$~MeV is extracted from the $v_{2n}$ of free protons and deuterons. However,remaining systematic uncertainties, partly related to the choice of in-mediumnucleon-nucleon cross sections, are of the same magnitude ($\pm 40$~MeV).Overall, the rapidity dependent elliptic flow supports a soft symmetric-matterequation-of-state.

physics letters b

Determination of the nuclear incompressibility from the  rapidity-dependent elliptic flow in heavy-ion collisions at beam energies  0.4\emph{A} - 1.0\emph{A} GeV