Microscopic models and effective equation of state in nuclear collisions in the vicinity ofElab=30AGeV at the GSI Facility for Antiproton and Ion Research (FAIR) and beyond

Abstract

Two microscopic models, ultrarelativistic quantum molecular dynamics and quark-gluon string model, were employed to study the formation of locally equilibrated hot and dense nuclear matter in heavy-ion collisions at energies from $11.6A$ to $160A$ GeV. Analysis was performed for the fixed central cubic cell of volume $V=125$ fm${}^{3}$ and for the expanding cell that followed the growth of the central area with uniformly distributed energy. To decide whether the equilibrium was reached, results of the microscopic calculations were compared to that of the statistical thermal model. Both dynamical models indicate that the state of kinetic, thermal and chemical equilibrium is nearly approached at any bombarding energy after a certain relaxation period. The higher the energy, the shorter the relaxation time. Equation of state has a simple linear dependence $P=a(\sqrt{s})\ensuremath{\varepsilon}$, where $a\ensuremath{\equiv}{c}_{s}^{2}$ is the sound velocity squared. It varies from $0.12\ifmmode\pm\else\textpm\fi{}0.01$ at ${E}_{\mathrm{lab}}=11.6A$ GeV to $0.145\ifmmode\pm\else\textpm\fi{}0.005$ at ${E}_{\mathrm{lab}}=160A$ GeV. Change of the slope in $a(\sqrt{s})$ behavior occurs at ${E}_{\mathrm{lab}}=40A$ GeV and can be assigned to the transition from baryon-rich to meson-dominated matter. The phase diagrams in the $T\text{\ensuremath{-}}{\ensuremath{\mu}}_{\mathrm{B}}$ plane show the presence of kinks along the lines of constant entropy per baryon. These kinks are linked to the inelastic (i.e., chemical) freeze-out in the system.