Equilibration and baryon densities attainable in relativistic heavy-ion collisions

TL;DR

This paper investigates how kinetic and chemical equilibration, as well as baryon densities, evolve in central Au+Au collisions across a range of energies using a three-fluid dynamics model, highlighting energy-dependent equilibration times and densities.

Contribution

It introduces a method to compare baryon densities across energies using an invariant 4-volume, providing a new way to analyze high-density matter in heavy-ion collisions.

Findings

Kinetic equilibration occurs faster at higher energies.

Highest baryon densities increase with collision energy.

A 4-volume measure helps compare densities independent of model specifics.

Abstract

Kinetic equilibration of the matter and baryon densities attained in central region of colliding Au+Au nuclei in the energy range of $\sqrt{s_{NN}}=$ 3.3--39 GeV are examined within the model of the three-fluid dynamics. It is found that the kinetic equilibration is faster at higher collision energies: the equilibration time (in the c.m. frame of colliding nuclei) rises from $\sim$5 fm/c at $\sqrt{s_{NN}}=$ 3.3 GeV to $\sim$1 fm/c at 39 GeV. The chemical equilibration, and thus thermalization, takes longer. We argue that the presented time evolution of the net-baryon and energy densities in the central region is a necessary prerequisite of proper reproduction of bulk observables in midrapidity. We suggest that for informative comparison of predictions of different models it is useful to calculate an invariant 4-volume ($V_4$), where the proper density the equilibrated matter exceeds certain value. The advantage of this 4-volume is that it does not depend on specific choice of the 3-volume in different studies and takes into account the lifetime of the high-density region, which also matters. The 4-volume $V_4=$ 100 fm$^4$/c is chosen to compare the baryon densities attainable at different different energies. It is found that the highest proper baryon density increases with the collision energy rise, from $n_B/n_0\approx$ 4 at 3.3 GeV to $n_B/n_0\approx$ 30 at 39 GeV. These highest densities are achieved in the central region of colliding system.