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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.
γ
s
≃
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.
The multiplicities of light (anti)nuclei were measured recently by the ALICE collaboration in Pb+Pb collisions at the center-of-mass collision energy sNN=2.76TeV. Surprisingly, the hadron resonance ...gas model is able to perfectly describe their multiplicities under various assumptions. For instance, 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. In this paper we assume the hard-core radius of nuclei consisting of A baryons or antibaryons to follow the simple law R(A)=Rb(A)13, where Rb is the hard-core radius of nucleon. To implement such a relation into the hadron resonance gas model we employ the induced surface tension concept and analyze the hadronic and (anti)nuclei multiplicities measured by the ALICE collaboration. The hadron resonance gas model with the induced surface tension allows us to verify different scenarios of chemical freeze-out of (anti)nuclei. It is shown that the most successful description of hadrons can be achieved at the chemical freeze-out temperature Th = 150 MeV, while the one for all (anti)nuclei is TA = 168.5 MeV. Possible explanations of this high temperature of (anti)nuclei chemical freeze-out are discussed.
We develop a novel formulation of the hadron resonance gas model which, besides a hard-core repulsion, explicitly accounts for the surface tension induced by the interaction between the particles. ...Such an equation of state allows us to go beyond the Van der Waals approximation for any number of different hard-core radii. A comparison with the Carnahan–Starling equation of state shows that the new model is valid for packing fractions 0.2–0.22, while the usual Van der Waals model is inapplicable at packing fractions above 0.1–0.11. Moreover, it is shown that the equation of state with induced surface tension is softer than the one of hard spheres and remains causal at higher particle densities. The great advantage of our model is that there are only two equations to be solved and neither their number nor their form depend on the values of the hard-core radii used for different hadronic resonances. Such an advantage leads to a significant mathematical simplification compared to other versions of truly multi-component hadron resonance gas models. Using this equation of state we obtain a high-quality fit of the ALICE hadron multiplicities measured at the center-of-mass energy 2.76 TeV per nucleon and we find that the dependence of χ2/ndf on the temperature has a single global minimum in the traditional hadron resonance gas model with the multi-component hard-core repulsion. Also we find two local minima of χ2/ndf in the model in which the proper volume of each hadron is proportional to its mass. However, it is shown that in the latter model a second local minimum located at higher temperatures always appears far above the limit of its applicability.
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.
The chemical freeze-out irregularities found with the most advanced hadron resonance gas model and possible signals of two QCD phase transitions are discussed. We have found that the center-of-mass ...collision energy range of tricritical endpoint of QCD phase diagram is 9; 9.2 GeV which is consistent both with the QCD inspired exactly solvable model and experimental findings.
We present a summary of the recent results obtained with the novel hadron resonance gas model with the multicomponent hard-core repulsion which is extended to describe the mixtures of hadrons and ...light (anti-, hyper-)nuclei. A very accurate description is obtained for the hadronic and the light nuclei data measured by STAR at the collision energy sNN=200GeV and by ALICE at sNN=2.76TeV. The most striking result discussed here is that for the most probable chemical freeze-out scenario for the STAR energy the found parameters allow us to reproduce the values of the experimental ratios S3 and S¯3 without fitting.
Results of a study of 1,2-epoxycyclopentane carboxylation to cyclopentene carbonate (CPC) in the presence of various catalyst systems have been described. It has been found that the reaction occurs ...most efficiently in the presence of cobalt (nickel) chloride (bromide) hydrate and a quaternary ammonium salt (TEAB, TBAB). It has been recommended that CPC should be synthesized under a CO
2
pressure of no less than 3.5 MPa at a temperature of 140–150°С without any solvent or in the medium of a solvent, such as target CPC, DMF, or
N
-MP, at a 1,2-epoxycyclopentane weight fraction in the feed mixture of no less than 25%. These conditions provide the formation of CPC with a selectivity of 97–99% and almost complete epoxide conversion within 2–4 h. It has been shown that the developed catalyst system can be recycled.
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