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Here, we develop an original approach to investigate the grand canonical partition function of the multicomponent mixtures of Boltzmann particles with hard-core interaction in finite and even small systems of the volumes above 20 fm3. The derived expressions of the induced surface tension equation of state (EoS) are analyzed in detail. It is shown that the metastable states, which can emerge in the finite systems with realistic interaction, appear at very high pressures at which the hadron resonance gas, most probably, is not applicable at all. It is shown how and under what conditions the obtained results for finite systems can be generalized to include into a formalism the equation for curvature tension. The applicability range of the obtained equations of induced surface and curvature tensions for finite systems is discussed and their close relations to the equations of the morphological thermodynamics are established. The hadron resonance gas model on the basis of the obtained advanced EoS is worked out. Also, this model is applied to analyze the chemical freeze-out of hadrons and light nuclei with the number of (anti-) baryons not exceeding 4. Their multiplicities were measured by the ALICE Collaboration in the central lead–lead collisions at the center-of-mass energy s NN = 2. 7 6 TeV. [ABSTRACT FROM AUTHOR]

From the analysis of light (anti)nuclei multiplicities that were measured recently by the ALICE collaboration in Pb+Pb collisions at the center-of-mass collision energy s N N = 2. 7 6 TeV, there arose a highly nontrivial question about the excluded volume of composite particles. Surprisingly, the hadron resonance gas model (HRGM) is able to perfectly describe the light (anti) nuclei multiplicities under various assumptions. Thus, one can consider the (anti)nuclei with a vanishing hard-core radius (as the point-like particles) or with the hard-core radius of proton, but the fit quality is the same for these assumptions. It is clear, however, that such assumptions are unphysical. Hence we obtain a formula for the classical excluded volume of loosely bound light nuclei consisting of A baryons. To implement a new formula into the HRGM, we have to modify the induced surface tension concept to treat the hadrons and (anti)nuclei on the same footing. We perform a thorough analysis of hadronic and (anti)nuclei multiplicities measured by the ALICE collaboration. The HRGM with the induced surface tension allows us to verify different assumptions on the values of hard-core radii and different scenarios of chemical freeze-out of (anti)nuclei. It is shown that the unprecedentedly high quality of fit χ tot 2 / dof ≃ 0. 7 2 4 is achieved, if the chemical freeze-out temperature of hadrons is about T h = 1 5 0 MeV, while the one for all (anti)nuclei is T A = 1 7 4 − 1 7 5. 2 MeV. [ABSTRACT FROM AUTHOR]

Here we develop a new strategy to analyze the chemical freeze-out of light (anti)nuclei produced in high energy collisions of heavy atomic nuclei within an advanced version of the hadron resonance gas model. It is based on two different, but complementary approaches to model the hard-core repulsion between the light nuclei and hadrons. The first approach is based on an approximate treatment of the equivalent hard-core radius of a roomy nuclear cluster and pions, while the second approach is rigorously derived here using a self-consistent treatment of classical excluded volumes of light (anti)nuclei and hadrons. By construction, in a hadronic medium dominated by pions, both approaches should give the same results. Employing this strategy to the analysis of hadronic and light (anti)nuclei multiplicities measured by ALICE at s NN = 2.76 TeV and by STAR at s NN = 200 GeV, we got rid of the existing ambiguity in the description of light (anti)nuclei data and determined the chemical freeze-out parameters of nuclei with high accuracy and confidence. At ALICE energy the nuclei are frozen prior to the hadrons at the temperature T = 175. 1 - 3.9 + 2.3 MeV, while at STAR energy there is a single freeze-out of hadrons and nuclei at the temperature T = 167.2 ± 3.9 MeV. We argue that the found chemical freeze-out volumes of nuclei can be considered as the volumes of quark-gluon bags that produce the nuclei at the moment of hadronization. [ABSTRACT FROM AUTHOR]

Using the model of hexagonal clusters we express the surface, curvature and Gauss curvature coefficients of the nuclear binding energy in terms of its bulk coefficient. Using the derived values of these coefficients and a single fitting parameter we are able to reasonably well describe the experimental binding energies of symmetric nuclei with more than 100 nucleons. To improve the description of lighter nuclei we introduce the same correction for all the coefficients. In this way we determine the apparent values of the surface, curvature and Gauss curvature coefficients which may be used for infinite nuclear matter equation of state. This simple model allows us to fix the temperature dependence of all these coefficients, if the temperature dependence for the bulk term is known. The found estimates for critical temperature are well consistent both with experimental and with theoretical findings. [ABSTRACT FROM AUTHOR]

Using the most advanced formulation of the hadron resonance gas model we analyze the two sets of irregularities found at chemical freeze-out of central nuclear-nuclear collisions at the center of mass energies 3.8-4.9 GeV and 7.6-9.2 GeV. In addition to previously reported irregularities at the collision energies 4.9 and 9.2 GeV we found sharp peaks of baryonic charge density. Also we analyze the collision energy dependence of the modified Wroblewski factor and the strangeness suppression factor. Based on the thermostatic properties of the mixed phase of a 1st order phase transition and the ones of the Hagedorn mass spectrum we explain, respectively, the reason of observed chemical equilibration of strangeness at the collision energy 4.9 GeV and above 8.7 GeV. It is argued that the both sets of irregularities possibly evidence for two phase transitions, namely, the 1st order transition at lower energy range and the 2nd order transition at higher one. In combination with a recent analysis of the light nuclei number fluctuations we conclude that the center of mass collision energy range 8.8-9.2 GeV may be in the nearest vicinity of the QCD tricritical endpoint. The properties of the phase existing between two phase transitions are revealed and discussed. [ABSTRACT FROM AUTHOR]

Here we present two explicit counterexamples to the widely spread beliefs about an exclusive role of bimodality as the first-order phase transition signal. On the basis of an exactly solvable statistical model generalizing the statistical multifragmentation model of nuclei, we demonstrate that the bimodal distributions can naturally appear both in infinite and in finite systems without a phase transition. In the first counterexample a bimodal distribution appears in an infinite system at the supercritical temperatures due to the negative values of the surface tension coefficient. In the second counterexample we explicitly demonstrate that a bimodal fragment distribution appears in a finite volume analog of a gaseous phase. In contrast to the statistical multifragmentation model, the developed statistical model corresponds to the compressible nuclear liquid with the tricritical endpoint located at one third of the normal nuclear density. The suggested parameterization of the liquid phase equation of state is consistent with the L. Van Hove axioms of statistical mechanics and it does not lead to an appearance of the nonmonotonic isotherms in the macroscopic mixed phase region which are typical for the classical models of the Van der Waals type. Peculiarly, such a way to account for the nuclear liquid compressibility automatically leads to an appearance of an additional state that in many respects resembles the physical antinuclear matter. [ABSTRACT FROM AUTHOR]

Two approaches to treat the chemical freeze-out of strange particles in the hadron resonance gas model are analyzed. The first one employs their non-equillibration via the usual factor and such a model describes the hadron multiplicities measured in nucleus-nucleus collisions at AGS, SPS and RHIC energies with . Surprisingly, at low energies we find not the strangeness suppression, but its enhancement. Also we suggest an alternative approach to treat the strange particle freeze-out separately, but with the full chemical equilibration. This approach is based on the conservation laws which allow us to connect the freeze-outs of strange and non-strange hadrons. Within the suggested approach the same set of hadron multiplicities can be described better than within the conventional approach with . [ABSTRACT FROM AUTHOR]

Here we present a generalization of the multicomponent Van der Waals equation of state in the grand canonical ensemble. For the one-component case the third and fourth virial coefficients are calculated analytically. It is shown that the adjustment of a single model parameter allows us to reproduce the third and fourth virial coefficients of the gas of hard spheres with small deviations from their exact values. A thorough comparison of the compressibility factor and speed of sound of this model with the one- and two-component Carnahan-Starling equation of state is made. We show that the model with the induced surface tension can reproduce the results of the Carnahan-Starling equation of state up to the packing fractions 0.2-0.22 at which the Van der Waals equation of state is inapplicable. Using this approach we develop an entirely new hadron resonance gas model and apply it to a description of the hadron yield ratios measured at AGS, SPS, RHIC and ALICE energies of nuclear collisions. We confirm that the strangeness enhancement factor has a peak at low AGS energies and that there is a jump of chemical freeze-out temperature between the two highest AGS energies. Also we argue that the chemical equilibrium of strangeness, i.e.γs≃1, observed above the center of mass collision energy 8.7 GeV, may be related to a hadronization of quark gluon bags which have a Hagedorn mass spectrum, and, hence, it may be a new signal for the onset of deconfinement. [ABSTRACT FROM AUTHOR]