The quark gluon plasma (QGP) produced in high-energy nuclear collisions is known to behave like a perfect fluid. In hydrodynamic simulations at RHIC and the LHC energies, space-time evolution of the QGP is usually described in expanding coordinates. On the other hand, in SPS and RHIC-BES energies, Cartesian coordinates are used for effective description of hydrodynamic expansion. However, the difference of the coordinates makes it difficult to describe the reactions in broad range of collision energy in a unified manner.
In this study, we propose to use the Milne coordinates even at lower collision energies by introducing a dynamic initialization model  towards unified description of the reactions at various collision energies. We first generate the initially produced particles by using an event generator, JAM . Instead of putting initial conditions at fixed (proper-)time, fluids are gradually created during the colliding nuclei overlap with each other: We put energy, momentum, and baryon number of the particles into fluids through source terms in hydrodynamic equations at which these are produced. By solving hydrodynamic equations in one-dimensionally expanding coordinates, we describe space-time evolution of thermodynamic variables at RHIC-BES energies. By employing the first-order phase transition model as an equation of state, we describe the trajectories of the system in the energy density-baryon density plane and show the maximum baryon density gradually decreases with increasing collision energy.
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