Equation of state of nuclear matter from collective flows and stopping in intermediate energy heavy-ion collisions

Abstract

The equation of state of nuclear matter, momentum dependence of the effective interaction and in-medium modification of elastic nucleon-nucleon cross-sections are studied by comparing theoretical predictions for stopping, directed and elliptic flows of protons and light clusters in intermediate energy heavy-ion collisions of beam energy between 150 and 800 MeV/nucleon to experimental data gathered by the FOPI Collaboration. A multivariate analysis that takes into account systematic uncertainties induced on model predictions by the coalescence afterburner leads to the following constraint for the equation of state at 68 percent confidence level: compressibility modulus of isospin symmetric matter $K_0=230^{+9}_{-11}$ MeV and slope of the symmetry energy $L=63^{+10}_{-13}$ MeV. The momentum dependence of the isoscalar potential is found to be similar to that of the empirical optical potential, with an effective isoscalar mass $m^*=0.695^{+0.014}_{-0.018}$. The isovector potential displays a momentum dependence corresponding to a positive neutron-proton effective mass difference $\Delta m^*_{np}=(0.17^{+0.10}_{-0.09})\delta$, close to the world average for this quantity. A suppression of elastic nucleon-nucleon cross-sections in symmetric nuclear matter at saturation by about 60$\%$ relative to vacuum values is deduced, in qualitative agreement with microscopical results. A strong dependence of the suppression factor on isospin asymmetry is evidenced, experimental data for isospin symmetric systems proving crucial for this last conclusion.