FIG. 5: Dynamical trajectories of the matter in the central box of the colliding nuclei (4fm × 4fm $_{×}$γ cm 4fm), where γ cm is the Lorentz factor associated with the initial nuclear motion in the c.m. frame, for central ( b = 0) collisions of Au+Au at 4 A and 10 A GeV energies and Pb+Pb at 20 A GeV. The trajectories are plotted in terms of baryon density ( n B ) and the energy density minus n B multiplied by the nucleon mass ( ε$_{−}$ m N n B ). Only expansion stages of the evolution are dis- played for two EoS’s. Symbols on the trajectories indicate the time rate of the evolution: time span between marks is 1 fm/c. However, if even the same friction is used in both phases, the calculated (with 2-ph. EoS) reduced cur- vature still reveals a “zig-zag” behaviour but with con- siderably smaller amplitude (see the thin dashed-dotted line in Fig. 2). This happens because the EoS in a gener- alized sense of this term, i.e. viewed as a partition of the total energy between kinetic and potential parts, also af- fects the stopping power. The friction is proportional to the relative velocity of the counter-streaming nuclei [17]. Therefore, it is more efficient when the kinetic-energy part of the total energy is higher, i.e. when the EoS is softer. This effect of the softening was demonstrated in Ref. [18]. It was shown that application of a soft, but still hadronic EoS changes the rapidity distributions, making them closer to the data at low SPS energies. This is pre- cisely what the phase transition does: it makes the EoS essentially softer in the mixed-phase region. The latter naturally results in a non-monotonous evolution of the proton rapidity spectra with the energy rise. Figure 5 demonstrates that the onset of the phase tran- sition in the calculations indeed happens at top-AGS– In conclusion, it is argued that the experimentally ob- served baryon stopping may indicate (within the present experimental uncertainties) a non-monotonous behaviour as a function of the incident energy of colliding nuclei. This reveals itself in a “zig-zag” irregularity in the exci- tation function of a midrapidity reduced curvature of the (net)proton rapidity spectrum. Notice that the energy location of this anomaly coincides with the previously observed anomalies for other hadron-production proper- ties at the low SPS energies [21, 31]. The 3FD calculation with the hadronic EoS fails to reproduce this irregularity. At the same time, the same calculation with the EoS in- volving a first-order phase transition into the quark-gluon phase (within the Gibbs construction) [20] reproduces this “zig-zag” behaviour, however only qualitatively. Pre- liminary simulations with the EoS of Ref. [32], also based on the first-order phase transition but within the Maxwell construction, show the same qualitative trend. It is ar- gued that the non-monotonous behaviour of the baryon stopping is a natural consequence of a phase transition. The question why these calculations do not qualitatively reproduce the “zig-zag” irregularity deserves special dis- cussion elsewhere. It is very probable that either the Gibbs and Maxwell constructions are inappropriate for the fast dynamics of the heavy-ion collisions [33, 34] or the phase transition is not of the first order. Fruitful discussions with B. Friman, M. Gazdzicki, J. low-SPS energies, where the “zig-zag” irregularity takes place. Similarly to that it has been done in Ref. [30], the figure displays dynamical trajectories of the matter in the central box placed around the origin r = (0 , 0 , 0) in the frame of equal velocities of colliding nuclei: | x | ≤ 2 fm, | y | ≤ 2 fm and | z | ≤ γ$_{cm}$ 2 fm, where γ$_{cm}$ is Lorentz factor associated with the initial nuclear motion in the c.m. frame. Initially, the colliding nuclei are placed sym- metrically with respect to the origin r = (0 , 0 , 0), z is the direction of the beam. The ε - n$_{B}$ representation is chosen because these densities are dynamical quantities and, therefore, are suitable to compare calculations with different EoS’s. Subtraction of the m$_{N}$ n$_{B}$ term is taken for the sake of suitable representation of the plot. Only expansion stages of the evolution are displayed, where the matter in the box is already thermally equilibrated. The size of the box was chosen to be large enough that the amount of matter in it can be representative to con- clude on the onset of the phase transition and to be small enough to consider the matter in it as a homo- geneous medium. Nevertheless, the matter in the box still amounts to a minor part of the total matter of col- liding nuclei. Therefore, only the minor part of the total matter undergoes the phase transition at 10 A GeV en- ergy. As seen, the trajectories for two different EoS’s are very similar at AGS energies and start to differ at SPS energies because of the effect of the phase transition. 5 IV. CONCLUSIONS 0 0.5 1 1.5 2 n$_{B}$[fm$^{-3}$] 1 2 3 4 m N n B [ GeV/fm 3 ] 2-ph. EoS  4A GeV 10A GeV 20A GeV (T=0)-m$_{N}$n$_{B}$ inaccessible region mixed  phase hadr. EoS 4A GeV 10A GeV 20A GeV