Baryon Stopping in Heavy-Ion Collisions at E lab = 2–160 GeV/nucleon Yu.B. Ivanov 1, 2, ∗ $^{1}$GSI Helmholtzzentrum f¨ ur Schwerionenforschung GmbH, D-64291 Darmstadt, Germany $^{2}$Kurchatov Institute, Moscow RU-123182, Russia It is argued that the experimentally observed baryon stopping may indicate (within the present experimental uncertainties) a non-monotonous behaviour as a function of the incident energy of colliding nuclei. This can be quantified by a midrapidity reduced curvature of the net-proton rapidity spectrum. The above non-monotonous behaviour reveals itself as a “zig-zag” irregularity in the excitation function of this curvature. The three-fluid dynamic calculations with a hadronic equation of state (EoS) fail to reproduce this irregularity. At the same time, the same calculations with an EoS involving a first-order phase transition into the quark-gluon phase do reproduce this “zig-zag” behaviour, however only qualitatively. I. INTRODUCTION PACS numbers: 24.10.Nz, 25.75.-q Keywords: relativistic heavy-ion collisions, baryon stopping, hydrodynamics, phase transition A degree of stopping of colliding nuclei is one of the basic characteristics of the collision dynamics, which de- termines a part of the incident energy of colliding nuclei deposited into produced fireball and hence into produc- tion of secondary particles. The deposited energy in its turn determines the nature (hadronic or quark-gluonic) of the produced fireball and thereby its subsequent evo- lution. Therefore, a proper reproduction of the baryon stopping is of prime importance for theoretical under- standing of the dynamics of the nuclear collisions. A direct measure of the baryon stopping is the net- baryon rapidity distribution. However, since experimen- tal information on neutrons is unavailable, we have to rely on proton data. Presently there exist extensive experi- mental data on proton (or net-proton) rapidity spectra at AGS [1–4] and SPS [5–9] energies. These data were analyzed within various models [10–18] The most exten- sive analysis has been done in [14, 17]. Since that time new data at SPS energies have appeared [7–9]. There- fore, it is appropriate to repeat this analysis of already extended data set. In the present Letter it is done within the framework of the model of the three-fluid dynamics (3FD) [17]. comparison. The data are plotted as functions of a “di- mensionless” rapidity ( y − y$_{cm}$ ) /y$_{cm}$ , where y$_{cm}$ is the center-of-mass rapidity of colliding nuclei. In particular, this is the reason why the experimental distributions are multiplied y$_{cm}$ . This representation is chosen in order to make different distributions of approximately the same width and the same height. This is convenient for com- parison of shapes of these distributions. To make this comparison more quantitative, the data are fitted by a simple formula where a , y$_{s}$ and w$_{s}$ are parameters of the fit. The form (1) is a sum of two thermal sources shifted by ± y$_{s}$ from the midrapidity. The width w$_{s}$ of the sources can be interpreted as w$_{s}$ = (temperature)/(transverse mass), if we assume that collective velocities in the sources have no spread with respect to the source rapidities ± y$_{s}$ . The parameters of the two sources are identical (up to the sign of y$_{s}$ ) because we consider only collisions of identical nuclei. Results of these fits are demonstrated in Fig. 1. Energy dependence of parameters y$_{s}$ and w$_{s}$ deduced from these fits revels no significant irregularities: they monotonously rise with the energy. The above fit has been done by the least-squares method. Data were fitted in the rapidity range | y − y$_{cm}$ | /y$_{cm}$ < 0 . 7. The choice of this range is dictated by the data. As a rule, the data are available in this rapidity range, sometimes the data range is even more narrow (40 A , 80 A GeV and new data at 158 A GeV [9]). We put the above restriction in order to treat different data in approximately the same rapidity range. Notice that the rapidity range should not be too wide in order to exclude contribution of cold spectators. We met problems with fitting the data at 80 A GeV [8] and the new data at 158 A GeV [9]. These data do not go beyond the side maxima in the rapidity distributions. The fit within such a narrow region results in the source rapidities y$_{s}$ very close (at 80 A GeV) or even exceeding Available data on the proton (at AGS energies) and net-proton (at SPS energies) rapidity distributions from central heavy-ion collisions are presented in Fig. 1. Only the midrapidity region is displayed in Fig. 1, since it is of prime interest in the present consideration. The data at 10 A GeV are repeated in the right panel of Fig. 1 in order to keep the reference spectrum shape for the II. ANALYSIS OF EXPERIMENTAL DATA ∗ e-mail: Y.Ivanov@gsi.de arXiv:1001.0670v3 [nucl-th] 25 May 2010 dN dy = a (exp {− (1 /w$_{s}$ ) cosh( y − y$_{cm}$ − y$_{s}$ ) } + exp {− (1 /w$_{s}$ ) cosh( y − y$_{cm}$ + y$_{s}$ ) } ) (1)