Pion mass shift and the kinetic freeze-out process

The kinetic freeze-out process of a pion gas through a finite layer with time-like normal is considered. The pion gas is described by a Boltzmann gas with elastic collisions among the pions. Within this model, the impact of the in-medium pion mass modification on the freeze-out process is studied. A marginal change of the freeze-out variables temperature and flow velocity and an insignificant modification of the frozen-out particle distribution function has been found.     

Abundance of Δ resonances in 58Ni + 58Ni collisions between 1 and 2 AGeV

Charged pion spectra measured in ⁵⁸Ni⁵⁸Ni collisions at 1.06, 1.45 and 1.93 AGeV are interpreted in terms of a thermal model including the decay of Δ resonances. The transverse momentum spectra of pions are well reproduced by adding the pions originating from the Δ -resonance decay to the component of thermal pions, deduced from the high transverse momentum part of the pion spectra. About 10 and 18% of the nucleons are excited to Δ states at freeze-out for beam energies of 1 and 2 AGeV, respectively.     

Identified particle distributions in pp and Au+Au collisions at square root of (sNN)=200 GeV

Transverse mass and rapidity distributions for charged pions, charged kaons, protons, and antiprotons are reported for square root of [sNN]=200 GeV pp and Au+Au collisions at Relativistic Heary Ion Collider (RHIC). Chemical and kinetic equilibrium model fits to our data reveal strong radial flow and long duration from chemical to kinetic freeze-out in central Au+Au collisions. The chemical freeze-out temperature appears to be independent of initial conditions at RHIC energies.     

In-plane elliptic flow of resonance particles in relativistic heavy-ion collisions

We analyze the second Fourier coefficient v(2) of the pion azimuthal distribution in noncentral heavy-ion collisions in a relativistic hydrodynamic model. The exact treatment of the decay kinematics of resonances leads to almost vanishing azimuthal anisotropy of pions near the midrapidity, while the matter elliptic flow is in plane at freeze-out. In addition, we reproduce the rapidity dependence of v(2) for pions measured in noncentral Pb+Pb collisions at 158A GeV. This suggests that resonance particles as well as stable particles constitute the in-plane flow and are important ingredients for the understanding of the observed pion flow.     

The excluded volume hadron gas model and pion production at the SPS

Experimental data for nucleus-nucleus collisions at the CERN SPS suggest that an ideal hadron gas model is unable to account simultaneously (same baryonic chemical potential and temperature at freeze-out) for the strange anti-baryon to baryon ratios and pion abundances. Using a thermodynamically consistent excluded volume model we examine possibilities to account for the observed excess of pions.     

Multiplicity dependence of the pion source in S+A collisions at the CERN SPS

The emission of pions from relativistic heavy-ion collisions of S+S, S+Ag and S+Pb at 200 GeV/nucleon is characterized using two-particle interferometry. The multiplicity dependence of the pion source parameters near midrapidity is studied. The transversal (R _t) and longitudinal (R _l) pion source parameters are independent of the initial nuclei in the interaction and increase with increasing multiplicity. This suggests that the freeze-out process is governed mainly by the particle multiplicity. The multiplicity dependence is weaker than that expected from a simple model of a freeze-out at a constant density.     

Pion entropy and phase-space densities in A+A collisions

We propose a method to estimate the entropy of thermal pions in A+A collisions irrespective of the unknown form of freeze-out (isothermal) hypersurface and transverse flows developed. We analyse the average phase-space densities and entropies of the thermal pions vs, their multiplicities and collision energies. The behaviour of these values apparently indicates the deconflnement and chiral phase transitions in relativistic nucleus-nucleus collisions.     

Pion-proton correlations and asymmetry measurement in Au + Au collisions at √<Emphasis Type="Italic">s</Emphasis><Subscript><Emphasis Type="Italic">NN</Emphasis></Subscript> = 200 GeV data

Correlations between non-identical particles at small relative velocity probe asymmetries in the average space-time emission points at freeze-out. The origin of such asymmetries may be from long-lived resonances, bulk collective effects, or differences in the freeze-out scenario for the different particle species. STAR has extracted pion-proton correlation functions from a dataset of Au+Au collisions at √s _NN = 200 GeV. We present correlation functions in the spherical harmonic decomposition representation, for different centralities and for different combinations of pions and (anti-)protons.     

Probing nuclear expansion dynamics with π−/π+-spectra

We study the dynamics of charged pions in the nuclear medium via the ratio of differential π^? - and π⁺-spectra in a coupled-channel BUU (CBUU) approach. The relative energy shift of the charged pions is found to correlate with the pion freeze-out time in nucleus-nucleus collisions as well as with the impact parameter of the heavy-ion reaction. Furthermore, the long-range Coulomb force provides valuable information on the expansion dynamics of the hot nuclear system. Detailed comparisons with experimental data for Au + Au at 1 AGeV and Ni + Ni at 2.0 AGeV are presented.     

The hadronisation of a quark-gluon plasma

We consider two scenarios for the expansion of a quark-gluon plasma. If the evolution is slow enough, the system can remain in equilibrium throughout its entire history up to the freeze-out of a hadron gas; for a very rapid expansion, it may break up into hadrons before or at the confinement transition, without ever going through an equilibrium hadron phase. We compare hadron production rates in the two approaches and show that for a hadronisation temperatureT?200 MeV and baryonic chemical potential μ _B ?500 MeV, their predictions essentially coincide. Present data on strange particle production lead to values in this range and hence cannot provide a distinction between the two scenarios. Pion, nucleon and non-strange meson production seem to require a considerably lower freeze-out temperature and baryonic chemical potential. In the hadron gas picture, this is in accord with the difference in mean free path of the different hadrons in the medium; it suggests a sequential freeze-out, in which strange hadrons stop interacting earlier than non-strange hadrons. In the quark-gluon plasma break-up, the hadronic final state fails to provide the high entropy per baryon observed in non-strange hadron production. The break-up moreover leads to a decrease of the entropy per baryon; hence it must be conceptually modified before it can be considered as a viable hadronisation mechanism.     

System size dependence of the non-monotonous pion freeze-out volume excitation function

Hanburry-Brown-Twiss (HBT) correlation functions and radii of negatively charged pions from C+C, Si+Si, Cu+Cu, and In+In at lower RHIC/SPS energies are calculated with the UrQMD transport model and the CRAB analyzing program. We find a minimum in the excitation function of the pion freeze-out volume at low transverse momenta and around E _lab ?? 20?C30AGeV which can be related to the change from initial string emission to bulk emission from the created resonance matter. For small systems, we predict a local minimum in the excitation function of the HBT (freeze-out) volume which is explained by the competition of two mechanisms of the particle production, namely resonance decays and string formation/fragmentation.     

Transverse momentum spectra of the produced hadrons at SPS energy and a random walk model

The transverse momentum spectra of the produced hadrons have been compared to a model, which is based on the assumption that a nucleus–nucleus collision is a superposition of isotropically decaying thermal sources at a given freeze-out temperature. The freeze-out temperature in nucleus–nucleus collisions is fixed from the inverse slope of the transverse momentum spectra of hadrons in nucleon–nucleon collision. The successive collisions in thessss nuclear reactions leads to gain in transverse momentum, as the nucleons propagate in the nucleus following a random walk pattern. The average transverse rapidity shift per collision is determined from the nucleon–nucleus collision data. Using this information, we obtain parameter-free result for the transverse momentum distribution of produced hadrons in nucleus–nucleus collisions. It is observed that such a model is able to explain the transverse mass spectra of the produced pions at SPS energies. However, it fails to satisfactorily explain the transverse mass spectra of kaons and protons. This indicates the presence of collective effect which cannot be accounted for, by the initial state collision broadening of transverse momentum of produced hadrons, the basis of random walk model.     

Excitation Functions of Tsallis-Like Parameters in High-Energy Nucleus–Nucleus Collisions

The transverse momentum spectra of charged pions, kaons, and protons produced at mid-rapidity in central nucleus–nucleus (AA) collisions at high energies are analyzed by considering particles to be created from two participant partons, which are assumed to be contributors from the collision system. Each participant (contributor) parton is assumed to contribute to the transverse momentum by a Tsallis-like function. The contributions of the two participant partons are regarded as the two components of transverse momentum of the identified particle. The experimental data measured in high-energy AA collisions by international collaborations are studied. The excitation functions of kinetic freeze-out temperature and transverse flow velocity are extracted. The two parameters increase quickly from ≈3 to ≈10 GeV (exactly from 2.7 to 7.7 GeV) and then slowly at above 10 GeV with the increase of collision energy. In particular, there is a plateau from near 10 GeV to 200 GeV in the excitation function of kinetic freeze-out temperature.     

Rapidity distributions of hadrons in the HydHSD hybrid model

A multistage hybrid model intended for describing heavy-ion interactions in the energy region of the NICA collider under construction in Dubna is proposed. The model combines the initial, fast, interaction stage described by the model of hadron string dynamics (HSD) and the subsequent evolution that the expanding system formed at the first stage experiences at the second stage and which one treats on the basis of ideal hydrodynamics; after the completion of the second stage, the particles involved may still undergo rescattering (third interaction stage). The model admits three freeze-out scenarios: isochronous, isothermal, and isoenergetic. Generally, the HydHSD hybrid model developed in the present study provides fairly good agreement with available experimental data on proton rapidity spectra. It is shown that, within this hybrid model, the two-humped structure of proton rapidity distributions can be obtained either by increasing the freeze-out temperature and energy density or by more lately going over to the hydrodynamic stage. Although the proposed hybrid model reproduces rapidity spectra of protons, it is unable to describe rapidity distributions of pions, systematically underestimating their yield. It is necessary to refine the model by including viscosity effects at the hydrodynamic stage of evolution of the system and by considering in more detail the third interaction stage.     

Measurements of the Mean Free Paths of the Proton and Pions in the Nuclear Matter

The results of measuring the yields of neutral and charged pions in the (, p) reaction on Li, C, and Al nuclei are presented as functions of the proton energy and azimuth angle of pion emission. The experiment was performed in the second resonance region of the photon energy. The measurements are analyzed within the model of single and double quasi-free pion photoproduction. The energy dependences of the mean free path of the proton and neutral and charged pions are obtained based on the dependence of the reaction yield on the atomic number of the target nucleus.     

Collective flow model for the pion transverse momentum spectra from relativistic nuclear collisions at CERN

The transverse momentum spectra for pions observed by WA80 and NA35 collaborations are analysed within a fireball model with collective isentropic expansion and a realistic freeze-out criterion. By varing the initial state of the fireball, an excellent fit to the data is achieved for the whole measured range ofP _T . Slight differences in the data for the spectral slopes from central and pheripheral collisions originate in our model from the difference in the size of the fireball and in the number of participating nucleons in central and peripheral collisions. Using additional information from two-pion correlations, we can extrapolate our model back from the freeze-out point (determined from the spectra) to the initial state; we find that an initial energy density of 1.5–2GGeV/fm³ is sufficient to explain the data from central O+Au collisions at 200A GeV.