High baryon and energy densities achievable in heavy-ion collisions at $\sqrt{s_{NN}}=39$ GeV

Baryon and energy densities, which are reached in central Au+Au collisions at collision energy of $\sqrt{s_{NN}}=$ 39 GeV, are estimated within the model of three-fluid dynamics. It is shown that the initial thermalized mean proper baryon and energy densities in a sizable central region approximately are $n_B/n_0\approx 10$ and $\varepsilon \approx 40$ GeV/${\mathrm{fm}}^3$, respectively. The study indicates that the deconfinement transition at the stage of interpenetration of colliding nuclei makes the system quite opaque. The final fragmentation regions in these collisions are formed not only by primordial fragmentation fireballs, i.e., the baryon-rich matter passed through the interaction region (containing approximately 30% of the total baryon charge), but also by the baryon-rich regions of the central fireball pushed out to peripheral rapidities by the subsequent almost one-dimensional expansion of the central fireball along the beam direction.

Figure 1

QGP fraction (left column), the proper baryon density in units of the normal nuclear density, $n_0=0.151/{\mathrm{fm}}^3$, see Eq. (1) (middle column), and proper energy density, see Eq. (3) (right column), in the reaction plain $\left(x{\eta }_s\right)$ at various time instants (in the c.m. frame) in the central $(b=2$ fm) Au+Au collision at $\sqrt{s_{NN}}=39$ GeV. ${\eta }_s$ is the space-time rapidity along the beam direction. Calculations are done with the first-order-transition EOS. The bold contours in panels of the right column display the borders between the frozen-out and still hydrodynamically evolving matter.

Figure 2

Proper energy density of the baryon-free (f) fluid in the reaction plain $\left(xz\right)$ at various time instants in the central $(b=2$ fm) Au+Au collision at $\sqrt{s_{NN}}=39$ GeV. Calculations are done with the first-order-transition EOS. The bold contours display the borders between the frozen-out and still hydrodynamically evolving matter.

Figure 3

Proper baryon density in units of the normal nuclear density (dashed lines, right scale axis) and the longitudinal rapidity $\left(y_z\right)$ of the matter (solid lines, left scale axis) along the beam axis $\left(x=y=0\right)$ at various time instants in the central $(b=2$ fm) Au+Au collision simulated within the first-order-transition scenario.

Figure 4

Time evolution of the mean proper baryon (left scale) and energy (right scale) densities in central Au+Au collisions at $\sqrt{s_{NN}}=39$ GeV in simulations with different EOSs.