Evidence for nuclear matter with the highest baryon density in heavy-ion collisions between 3A and 10A GeV

We present a systematic comparison of the phase-space density of protons at the center-of-mass deduced from the available experimental data from 1A to 158A GeV. Nuclear matter with the highest baryon density can be obtained at a beam energy between 3A and 10A GeV, which is also supported by the beam-energy dependence of the transverse flow velocity at the center-of-mass. A search for Quantum Chromodynamical phase transitions in the high baryon-density region at a relatively low temperature should be performed at the Heavy-Ion Synchrotron (SIS) and at the Alternate Gradient Synchrotron (AGS).