Kinetic equilibration of the matter and baryon densities attained in the central region of colliding Au+Au nuclei in the energy range of root s(NN) = 3.3-39 GeV are examined within the model of three-fluid dynamics. It is found that the kinetic equilibration is faster at higher collision energies: the equilibration time (in the center-of-mass frame of colliding nuclei) rises from approximate to 5 fm/c at root s(NN) = 3.3 GeV to approximate to 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 four-volume (V-4), where the proper density of the equilibrated matter exceeds a certain value. The advantage of this four-volume is that it does not depend on specific choice of the three-volume in different studies and takes into account the lifetime of the high-density region, which also matters. The four-volume V-4 = 100 fm(4)/c is chosen to compare the baryon densities attainable at different energies. It is found that the highest proper baryon density increases with the collision energy rise, from n(B)/n(0) approximate to 4 at 3.3 GeV to n(B)/n(0) approximate to 30 at 39 GeV. These highest densities are achieved in the central region of the colliding system.
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