Based on transport equations we argue that the chiral dynamics in heavy-ion collisions at high collision energies effectively decouples from the thermal physics of the fireball. With full decoupling at LHC energies the chiral condensate relaxes to its vacuum expectation value on a much shorter time scale than the typical evolution time of the fluid dynamical fields and their fluctuations. In particular, the net-baryon density remains coupled to the bulk evolution at all collision energies. As the mass scales of the hadrons are controlled by the chiral condensate, it is reasonable to employ vacuum masses in the statistical description of the hadron production at the chemical freeze-out for high collision energies. We predict that at lower collision energies the coupling of the chiral condensate to the thermal medium gradually increases with consequences for the related hadronic masses. A new estimate for the location of the freeze-out curve takes these effects into account.
We investigate the baryon number susceptibilities up to fourth order along different freeze-out lines in a holographic QCD model with the critical end point (CEP), and we propose that the peaked baryon number susceptibilities along the freeze-out line can be used as a clean signature to locate the CEP in the QCD phase diagram. On the temperature and baryon chemical potential plane, the ratio of the baryon number susceptibilities (up to fourth order) forms a ridge along the phase boundary, and develops a sword shape mountain standing upright around the CEP in a narrow and oblate region. This fe…
The strong longitudinal expansion of the reaction zone formed in relativistic heavy-ion collisions is found to significantly reduce the spatially averaged pion phase-space density, compared to naive estimates based on thermal distributions. This has important implications for data interpretation and leads to larger values for the extracted pion chemical potential at kinetic freeze-out.
We investigate the form of the viscous correction to the equilibrium distribution function in the context of a Cooper-Frye freeze out prescription for viscous hydrodynamic simulations of relativistic heavy ion collisions. The standard quadratic ansatz used by all groups for the case of shear viscosity is found to be disfavored by experimental data for v4/(v2)^2 at the Relativistic Heavy Ion Collider, and is unlikely to be correct for the hadron resonance gas present at freeze out. Instead, data for v2(pt) along with v4/(v2)^2 favor a momentum dependence between linear and quadratic.
We revisit the problem of the production of light atomic nuclei in ultrarelativistic heavy-ion collisions. While their production systematics is well produced by hadro-chemical freezeout at temperatures near the QCD pseudo-critical temperature, their small binding energies of a few MeV per nucleon suggest that they cannot survive as bound states under these conditions. Here, we adopt the concept of effective chemical potentials in the hadronic evolution from chemical to thermal freezeout (at typically $T_{\rm fo}$$\simeq$100\,MeV), which, despite frequent elastic rescatterings in hadronic matt…
Dissipative relativistic fluid-dynamical descriptions of the extended fireball formed in high-energy heavy-ion collisions are quite successful, yet require a prescription for converting the fluid into particles. We present arguments in favour of using a locally anisotropic momentum distribution for the particles emitted from the fluid, so as to smooth out discontinuities introduced by the usual conversion prescriptions. Building on this ansatz, we investigate the effect of the asymmetry on several observables of heavy ion physics.
The experimental data from the RHIC and LHC experiments of invariant pT spectra in A+A and p + p collisions are analysed with Tsallis distributions in different approaches. The information about the freeze-out surface in terms of freeze-out volume, temperature, chemical potential and radial flow velocity for different particle species are obtained. Further, these parameters are studied as a function of the mass of the secondary particles. A mass-dependent differential freeze-out is observed which does not seem to distinguish between particles and their antiparticles. Further a mass-hierarchy i…
We present lattice QCD results along the freezeout curve of heavy-ion collisions for the ongoing RHIC energy scan as well as the LHC heavy-ion runs planned for this year. The skew and kurtosis of the event distribution of baryon number are positive at all energies studied, We predict three ratios of non-linear susceptibilities along the freezeout curve as functions of the colliding energy, Sqrt[S_{NN}]. They have smooth behaviour except in the vicinity of a critical point; this can have multiple benefits.
We introduce a new prescription for obtaining the chemical freeze-out parameters in the heavy-ion collision experiments using the Hadron Resonance Gas model. The scheme is found to reliably estimate the freeze-out parameters and predict the hadron yield ratios, which themselves were never used in the parametrization procedure.
Two-particle femtoscopy reveals the space-time substructure of the freeze-out configuration from heavy ion collisions. Detailed fingerprints of bulk collectivity are evident in space-momentum correlations, which have been systematically measured as a function of particle type, three-momentum, and collision conditions. A clear scenario, dominated by hydrodynamic-type flow emerges. Reproducing the strength and features of the femtoscopic signals in models involves important physical quantities like the Equation of State, as well as less fundamental technical details. An interesting approximate "…
An expanding fireball model with two freeze-outs, which assumes that the chemical freeze-out occurs earlier at higher temperature and the thermal freeze-out occurs later at lower temperature, is developed and successfully applied to fit simultaneously the hadron ratios, transverse momentum spectra of measured hadrons and rapidity distribution of charged hadrons measured in Au+Au collision at 200 A$\cdot$GeV by STAR, PHENIX and PHOBOS collaborations. The quality of all the fittings is very good and the resulting parameters are in agreement with published values.
Using an analytical parameterization of hadronic freeze-out in relativistic heavy ion collisions, we present a detailed study of the connections between features of the freeze-out configuration and physical observables. We focus especially on anisotropic freeze-out configurations (expected in general for collisions at finite impact parameter), azimuthally-sensitive HBT interferometry, and final-state interactions between non-identical particles. Model calculations are compared with data taken in the first year of running at RHIC; while not perfect, good agreement is found, raising the hope tha…
We study the sensitivity of the higher-order moments of produced particle multiplicity distributions to the chemical freeze-out parameters in relativistic heavy ion collisions using the Hadron Resonance Gas (HRG) model. We compare the obtained sensitivity level to the one extracted from the ratios of particle yields. We find that, for certain final state hadrons, the fluctuation measurements add significant information to the determination of the hadro-chemical freeze-out properties of the deconfined phase of matter obtained at RHIC and the LHC.
We present calculations of the chemical freeze-out temperature (T_ch) based on particle yields from STAR and ALICE measured at collision energies ranging from sqrt{s_{NN}} = 11.5 GeV to 5.02 TeV. Employing the Grand Canonical Ensemble approach using the Thermal-FIST Hadron Resonance Gas model package, we show evidence for a flavour-dependent chemical freeze-out in the crossover region of the QCD phase diagram. At a vanishing baryochemical potential, we calculate light and strange flavour freeze-out temperatures T_L = 150.2 +- 2.6 MeV and T_S = 165.1 +- 2.7 MeV, respectively.
We discuss the production of light nuclei in heavy ion collisions within a multiple freezeout scenario. Thermal parameters extracted from the fits to the observed hadron yields are used to predict the multiplicities of light nuclei. Ratios of strange to non strange nuclei are found to be most sensitive to the details of the chemical freezeout. The well known disagreement between data of $^3_Λ\text{H/}^3\text{He}$ and $\overline{^3_Λ\text{H/}^3\text{He}}$ at $\sqrt{s_{NN}}=200$ GeV and models based on thermal as well as simple coalescence using a single chemical freezeout surface goes away when…
We confront the hypothesis of chemical freeze-out in ultra-relativistic heavy-ion collisions with the hypothesis of large modifications of hadron masses in nuclear medium. We find that the thermal-model predictions for the ratios of particle multiplicities are sensitive to the values of in-medium hadronic masses. In particular, the $π^+/p$ ratio decreases by 35% when the masses of all hadrons (except for pseudo-Goldstone bosons) are scaled down by 30%.
It is demonstrated that there exists a direct correlation between chemical freeze-out point and the softest point of the equation of state where the pressure divided by the energy density, $p(ε)/ε$, has a minimum. A dynamical model is given as an example where the passage of the softest point coincides with the condition for chemical freeze-out, namely an average energy per hadron $\approx$ 1 GeV. The sensitivity of the result to the equation of state used is discussed.
Using the UrQMD/coarse graining approach we explore the kinetic freeze-out stage in central Au + Au collisions at various energies. These studies allow us to obtain detailed information on the thermodynamic properties (e.g. temperature and chemical potential) of the system during the kinetic decoupling stage. We explore five relevant collision energies in detail, ranging from $\sqrt{s_{NN}}=2.4\,\mathrm{GeV}$ (GSI-SIS) to $\sqrt{s_{NN}}=200\,\mathrm{GeV}$ (RHIC). By adopting a standard Hadron Resonance Gas equation of state, we determine the average temperature $\langle T \rangle$ and the aver…
We argue that the chemical freeze-out in heavy ion collisions at high baryon density is not associated to a phase transition or rapid crossover. We employ the linear nucleon-meson model with parameters fixed by the zero-temperature properties of nuclear matter close to the liquid-gas quantum phase transition. For the parameter region of interest this yields a reliable picture of the thermodynamic and chiral properties at non-zero temperature. The chemical freeze-out observed in low-energy experiments occurs when baryon densities fall below a critical value of about 15 percent of nuclear densit…
We fit the single-particle $p_t$ spectra of identified pions, kaons, and (anti)protons from central collisions of gold or lead nuclei at energies between 7.7 and 2760~GeV per nucleon pair. Blast wave model with included resonance production and with an assumption of partial chemical equilibrium is used and the fits are performed with the help of a Gaussian emulator process. A kinetic freeze-out temperature is found about 100~MeV for the lowest collision energies and 80~MeV at the LHC. The average transverse expansion velocity grows with increasing $\sqrt{s_{NN}}$ from 0.45 to 0.65. Due to part…
A QCD phase transition may reflect in a inhomogeneous decoupling surface of hadrons produced in relativistic heavy-ion collisions. We show that due to the non-linear dependence of the particle densities on the temperature and baryon-chemical potential such inhomogeneities should be visible even in the integrated, inclusive abundances. We analyze experimental data from Pb+Pb collisions at CERN-SPS and Au+Au collisions at BNL-RHIC to determine the amplitude of inhomogeneities.
We analyze the hadronic freeze-out in ultra-relativistic heavy ion collisions at RHIC in a transport approach which combines hydrodynamics for the early, dense, deconfined stage of the reaction with a microscopic non-equilibrium model for the later hadronic stage at which the hydrodynamic equilibrium assumptions are not valid. With this ansatz we are able to self-consistently calculate the freeze-out of the system and determine space-time hypersurfaces for individual hadron species. The space-time domains of the freeze-out for several hadron species are found to be actually four-dimensional, a…
The influence of the nuclear Coulomb field on transverse spectra of $π^+$ and $π^-$ measured in $Pb+Pb$ reactions at 158 A GeV has been investigated. Pion trajectories are calculated in the field of an expanding fireball. The observed enhancement of the $π^-/π^+$ ratio at small momenta depends on the temperature and transverse expansion velocity of the source, the rapidity distribution of the net positive charge, and mainly the time of the freeze-out.
We determine the decoupling surfaces for the hydrodynamic description of heavy ion collisions at RHIC and LHC by comparing the local hydrodynamic expansion rate with the microscopic pion-pion scattering rate. The pion $p_T$ spectra for nuclear collisions at RHIC and LHC are computed by applying the Cooper-Frye procedure on the dynamical-decoupling surfaces, and compared with those obtained from the constant-temperature freeze-out surfaces. Comparison with RHIC data shows that the system indeed decouples when the expansion rate becomes comparable with the pion scattering rate. The dynamical dec…
A system size scan program was recently proposed for the STAR experiments at the Relativistic Heavy Ion Collider(RHIC). In this study, we employ a multiphase transport (AMPT) model for considering the bulk properties at the freeze-out stage for $\mathrm{^{10}B+^{10}B}$, $\mathrm{^{12}C+^{12}C}$, $\mathrm{^{16}O+^{16}O}$, $\mathrm{^{20}Ne+^{20}Ne}$, $\mathrm{^{40}Ca+^{40}Ca}$, $\mathrm{^{96}Zr+^{96}Zr}$, and $\mathrm{^{197}Au+^{197}Au}$ collisions at RHIC energies $\sqrt{s_{NN}}$ of 200, 20, and 7.7 GeV. The results for $\mathrm{^{197}Au+^{197}Au}$ collisions are comparable with those of previo…
We discuss systematic uncertainties in the chemical freeze-out parameters from the $χ^2$ analysis of hadron multiplicity ratios in the heavy-ion collision experiments. The systematics due to the choice of specific hadron ratios are found to lie within the experimental uncertainties. The variations obtained by removing the usual constraints on the conserved charges show similar behavior. The net charge to net baryon ratios in such unconstrained systems are commensurate with the expected value obtained from the protons and neutrons of the colliding nuclei up to the center of mass energies $\sim …
We study chemical freeze-out parameters for heavy-ion collisions by performing two different thermal analyses. We analyze results from thermal fits for particle yields, as well as, net-charge fluctuations in order to characterize the chemical freeze-out. The Hadron Resonance Gas (HRG) model is employed for both methods. By separating the light hadrons from the strange hadrons in thermal fits, we study the proposed flavor hierarchy. For the net-charge fluctuations, we calculate the mean-over-variance ratio of the net-kaon fluctuations in the HRG model at the five highest energies of the RHIC Be…
One surprising result in relativistic heavy-ion collisions is that the abundance of various particles measured in experiments is consistent with the picture that they reach chemical equilibrium at a temperature much higher than the temperature they freeze out kinetically. Using a multiphase transport model to study particle production in these collisions, we find that the above result is due to the constancy of the entropy per particle during the evolution of the hadronic matter from the chemical to the kinetic freeze-out. We further use a hadron resonance gas model to illustrate the result fr…
The space-averaged phase-space density and entropy per particle are both fundamental observables which can be extracted from the two-particle correlation functions measured in heavy-ion collisions. Two techniques have been proposed to extract the densities from correlation data: either by using the radius parameters from Gaussian fits to meson correlations or by using source imaging, which may be applied to any like pair correlation. We show that the imaging and Gaussian fits give the same result in the case of meson interferometry. We discuss the concept of an equivalent instantaneous source …
Popular parameterizations of the freeze-out conditions in relativistic heavy-ion collisions are discussed. Similarities and differences between the blast-wave model and the single-freeze-out model, both used recently to interpret the RHIC data, are outlined. A non-boost-invariant extension of the single-freeze-out model is proposed and applied to describe the recent BRAHMS data.
High energy heavy-ion collisions in laboratory produce a form of matter that can test Quantum Chromodynamics (QCD), the theory of strong interactions, at high temperatures. One of the exciting possibilities is the existence of thermodynamically distinct states of QCD, particularly a phase of de-confined quarks and gluons. An important step in establishing this new state of QCD is to demonstrate that the system has attained thermal equilibrium. We present a test of thermal equilibrium by checking that the mean hadron yields produced in the small impact parameter collisions as well as grand cano…
In hydrodynamical modeling of ultrarelativistic heavy-ion collisions, the freeze-out is typically assumed to take place at a surface of constant temperature or energy density. A more physical approach is to assume that freeze-out takes place at a surface of constant Knudsen number. We evaluate the Knudsen number as a ratio of the expansion rate of the system to the pion scattering rate, and apply the constant Knudsen number freeze-out criterion to ideal hydrodynamical description of heavy-ion collisions at RHIC ($\sqrt{s_\mathrm{NN}}=200$ GeV) and the LHC ($\sqrt{s_\mathrm{NN}}=2760$ GeV) ener…
We investigate what conditions allow us to extract the relative distribution of freeze-out space and time points in an arbitrary reference frame using tomography and source imaging. The source function may be extracted from the two-particle correlation function measured in heavy-ion collisions using imaging techniques. This imaged source function is related to the relative distribution of freeze-out space and time points through a generalization of the Radon transform found in tomography. Using tomography, the imaged source function may be converted into the relative freeze-out distribution in…
Global evolution of the matter in relativistic collisions of heavy nuclei and the resulting global freeze-out parameters are analyzed in a wide range of incident energies 2.7 GeV $\le \sqrt{s_{NN}}\le$ 39 GeV. The analysis is performed within the three-fluid model employing three different equations of state (EoS): a purely hadronic EoS, an EoS with the first-order phase transition and that with a smooth crossover transition. Global freeze-out parameters deduced from experimental data within the statistical model are well reproduced within the crossover scenario. The 1st-order-transition scena…
We investigate freeze--out in hydrodynamic models for relativistic heavy--ion collisions. In particular, instantaneous freeze--out across a hypersurface of constant temperature (``isothermal'' freeze--out) is compared with that across a hypersurface at constant time in the center-of-momentum frame (``isochronous'' freeze--out). For one--dimensional (longitudinal) expansion the rapidity distributions are shown to differ significantly in the two scenarios, while the transverse momentum spectra are remarkably similar. We also investigate the rapidity distribution in greater detail and show that t…
Relative hadron abundances from high-energy heavy-ion collisions reveal substantial inhomogeneities of temperature and baryon-chemical potential within the decoupling volume. The freeze-out volume is not perfectly "stirred", i.e. the concentrations of pions, kaons, (anti-) nucleons etc are inhomogeneous. Such inhomogeneities in the late stages of the hydrodynamic expansion might be traces of a first-order phase transition.
We show that the simultaneous measurement of yields and fluctuations in heavy ion collisions is capable of falsifying and constraining the statistical hadronization model. We show how such a measurement can test for chemical non-equilibrium, and distinguish between a high temperature chemically equilibrated freeze-out from a supercooled freeze-out with an over-saturated phase space. We further explain how this measurement can be used to obtain a model-independent estimate of the effect of post-freezeout hadronic interactions.
We introduce a new scenario for heavy ion collisions that could solve the lingering problems associated with the so-called HBT puzzle. We postulate that the system starts expansion as the perfect quark-gluon fluid but close to freeze-out it splits into clusters, due to a sharp rise of bulk viscosity in the vicinity of the hadronization transition. We then argue that the characteristic cluster size is determined by the viscosity coefficient and the expansion rate. Typically it is much smaller and independent of the total system volume. These clusters maintain the pre-existing outward-going flow…
It is shown that the chemical freeze-out parameters obtained at CERN/SPS, BNL/AGS and GSI/SIS energies all correspond to a unique value of 1 GeV per hadron in the local rest frame of the system, independent of the beam energy and of the target and beam particles.
We study the role of temperature and density inhomogeneities on the freeze-out of relativistic heavy ion collisions at CERN SPS. Especially the impact on the particle abundancies is investigated. The quality of the fits to the measured particle ratios in 158 AGeV Pb+Pb collisions significantly improves as compared to a homogeneous model.
We present a determination of chemical freeze-out conditions in heavy ion collisions based on ratios of cumulants of net electric charge fluctuations. These ratios can reliably be calculated in lattice QCD for a wide range of chemical potential values by using a next-to-leading order Taylor series expansion around the limit of vanishing baryon, electric charge and strangeness chemical potentials. From a computation of up to fourth order cumulants and charge correlations we first determine the strangeness and electric charge chemical potentials that characterize freeze-out conditions in a heavy…
We study the mass dependent hierarchy of kinetic freeze-out parameters of hadrons in low energy heavy-ion collisions. For this purpose, the transverse momentum and rapidity spectra of the identified hadrons produced in central Pb+Pb collisions, available at SPS energies ranging from $\rm E_{Lab}=20A-158A $ GeV, are analyzed within a generalized non boost-invariant blast wave model. We consider separate simultaneous fits for light hadrons ($π^{-}$, $K^{\pm}$) and heavy strange hadrons ($Λ$, $\barΛ$, $ϕ$, $Ξ^{\pm}$, $Ω^{\pm}$), for which the transverse momentum spectra as well as rapidity spectr…
The scaling properties of elliptic flow of hadrons produced in ultrarelativistic heavy-ion collisions are investigated at low transverse momenta, $p_T\lsim 2$\,GeV. Utilizing empirical parameterizations of a thermalized fireball with collective-flow fields, Resonance Recombination Model (RRM) is employed to describe hadronization via quark coalescence at the hadronization transition. We reconfirm that RRM converts equilibrium quark distribution functions into equilibrated hadron spectra including the effects of space-momentum correlations on elliptic flow. This provides the basis for a control…
The reduced velocity correlation function for fragments from the reaction Fe + Au at 100 A~MeV bombarding energy is investigated using the dynamical--statistical approach QMD+SMM and compared to experimental data to extract the Freeze--Out volume assuming simultaneous multifragmentation.
Clustering of the four-nucleon system at kinetic freezeout conditions is studied using path-integral Monte Carlo techniques. This method seeks to improve upon previous calculations which relied on approximate semiclassical methods or few-body quantum mechanics. Estimates are given for the decay probabilities of the 4N system into various light nuclei decay channels and the strength of spatial correlations is characterized. Additionally, a simple model is presented to describe the impact of this clustering on nucleon multiplicity distributions. The effects of a possible modification of the inte…
I discuss the effects and quantities that influence the decoupling of particles from the fireball. The crucial role is played by the scattering rate. I show the results for the scattering rate at SPS and RHIC and discuss their implications.
We construct a hadronic equation of state consistent with chemical freezeout and discuss how such an equation of state modifies the radial and elliptic flow in a hydrodynamic + hadronic cascade model of relativistic heavy ion collisions at the SPS. Incorporating chemical freezeout does not change the relation between pressure and energy density. However, it does change the relation between temperature and energy density. Consequently, when the hydrodynamic solution and freezeout are expressed in terms of energy density, chemical freezeout does not modify the hydrodynamic radial and elliptic fl…
We explore the consequences of a freeze-out criterion for heavy-ion collisions, based on pion escape probabilities from the hot and dense but rapidly expanding collision region. The influence of the expansion and the scattering rate on the escape probability is studied. The temperature dependence of this scattering rate favors a low freeze-out temperature of ~100 MeV. In general, our results support freeze-out along finite four-volumes rather than sharp three-dimensional hypersurfaces, with high-pt particles decoupling earlier from smaller volumes. We compare our approach to the proposed unive…
I discuss the quantities and effects important for the freeze-out and outline a formalism for the description of continuous decoupling of particles from the fireball. Then I present a calculation of the scattering rates of pions at various temperatures and argue that it is important to take continuous particle decoupling into account when modelling the collision dynamics.
Freeze-out of particles across 3-dimensional space-time hypersurface with space-like normal is discussed in a simple kinetic model. The final momentum distribution of emitted particles shows a non-exponential transverse momentum spectrum, which is in quantitative agreement with recently measured SPS pion and $h^-$ spectra.
Detailed knowledge of the hadronic spectrum is still an open question, which has phenomenological consequences on the study of heavy-ion collisions. A previous lattice QCD study concluded that additional strange resonances are missing in the currently tabulated lists provided by the Particle Data Group (PDG). That study identified the list labeled PDG2016+ as the ideal spectrum to be used as an input in thermal-model-based analyses. In this work, we determine the effect of additional resonances on the freeze-out parameters of systems created in heavy-ion collisions. These parameters are obtain…
One of the most remarkable results to emerge from heavy-ion collisions over the past two decades is the striking regularity shown by particle yields at all energies. This has led to several very successful proposals describing particle yields over a very wide range of beam energies, reaching from 1 A GeV up to 200 A GeV, using only one or two parameters. A systematic comparison of these proposals is presented here. The conditions of fixed energy per particle, baryon+anti-baryon density, normalized entropy density as well as percolation model are investigated. The results are compared with the …
We present an analysis of hadronic multiplicities measured in Pb-Pb collisions at \sqrt s_{NN} = 2.76 TeV as a function of the collision centrality within the statistical hadronization model. Evidence is found of a dependence of the chemical freeze-out temperature as a function of centrality, with a slow rise from central to peripheral collisions, which we interpret as an effect of post-hadronization inelastic scatterings. Using correction factors calculated by means of a simulation based on the UrQMD model, we are able to obtain a significant improvement in the statitical model fit quality an…
In hydrodynamical modelling of ultrarelativistic heavy-ion collisions the freeze-out is typically assumed to take place on a surface of constant temperature or energy density. In this work we apply a dynamical freeze-out criterion, which compares the hydrodynamical expansion rate with the pion scattering rate, to an event-by-event ideal hydrodynamics at the full RHIC collision energy. We present hadron spectra and elliptic flow calculated using (2+1)-dimensional ideal hydrodynamics, and show the differences between constant temperature and dynamical freeze-out criteria. We find that when the f…
The LHC data on event-by-event harmonic flow coefficients measured in PbPb collisions at center-of-mass energy 2.76 TeV per nucleon pair are analyzed and interpreted within the HYDJET++ model. To compare the model results with the experimental data the unfolding procedure is employed. The essentially dynamical origin of the flow fluctuations in hydro-inspired freeze-out approach has been established. It is shown that the simple modification of the model via introducing the distribution over spatial anisotropy parameters permits HYDJET++ to reproduce both elliptic and triangular flow fluctuatio…
The freeze-out conditions in the light (S+S) and heavy (Pb+Pb) colliding systems of heavy nuclei at 160 AGeV/$c$ are analyzed within the microscopic Quark Gluon String Model (QGSM). We found that even for the most heavy systems particle emission takes place from the whole space-time domain available for the system evolution, but not from the thin ''freeze-out hypersurface", adopted in fluid dynamical models. Pions are continuously emitted from the whole volume of the reaction and reflect the main trends of the system evolution. Nucleons in Pb+Pb collisions initially come from the surface regio…
