: We present the results of a study performed on the interactions of 10.6A GeV gold nuclei in nuclear emulsions. In a minimum bias sample of 1311 interactions, 5260 helium nuclei and 2622 heavy fragments were observed as Au projectile fragments. The experimental data are analyzed with particular emphasis of target separation interactions in emulsions and study of critical exponents. Multiplicity distributions of the fast-moving projectile fragments are investigated. Charged fragment moments, conditional moments as well as two and three -body asymmetries of the fast moving projectile particles are determined in terms of the total charge remaining bound in the multiply charged projectile fragments. Some differences in the average yields of helium nuclei and heavier fragments are observed, which may be attributed to a target effect. However, two and three-body asymmetries and conditional moments indicate that the breakup mechanism of the projectile seems to be independent of target mass. We looked for evidence of critical point observable in finite nuclei by study the resulting charged fragments distributions. We have obtained the values for the critical exponents γ, β and τ and compare our results with those at lower energy experiment (1.0A GeV data). The values suggest that a phase transition like behavior, is observed .

The midrapidity transverse momentum distributions of the charged pions, kaons, protons, and antiprotons, measured by ALICE Collaboration at ten centrality classes of Pb + Pb collisions at = 5.02 TeV in the Large Hadron Collider (LHC, CERN, Switzerland), are successfully analyzed using combined minimum χ2 fits with a thermodynamically non-consistent, as well as thermodynamically consistent, Tsallis function with transverse flow. The extracted non-extensivity parameter q decreases systematically for all considered particle species with increasing Pb+Pb collision centrality, suggesting an increase in the degree of system thermalization with an increase in collision centrality. The results for q suggest quite a large degree of thermalization of quark–gluon plasma (QGP) created in central Pb + Pb collisions at = 5.02 TeV with the average number of participant nucleons > 160. The obtained significantly different growth rates of transverse flow velocity, , in regions < 71 ± 7 and > 71 ± 7 with the temperature parameter T0 remaining constant within uncertainties in region > 71 ± 7 probably indicates that ≈ 71 ± 7 (corresponding to ≈ 251 ± 20) is a threshold border value for a crossover transition from a dense hadronic state to the QGP phase (or mixed phase of QGP and hadrons) in Pb + Pb collisions at = 5.02 TeV. The threshold border value for transverse flow velocity ≈ 0.46 ± 0.03 (corresponding to ≈ 71 ± 7), estimated by us in Pb + Pb collisions at = 5.02 TeV, agrees well with the corresponding border value ≈ 0.44 ± 0.02, recently obtained in Xe + Xe collisions at = 5.44 TeV, and with almost constant values extracted earlier in the Beam Energy Scan (BES) program of the Relativistic Heavy-Ion Collider (RHIC, Brookhaven, USA) in central Au + Au collisions in the = 7.7 − 39 GeV energy range, where the threshold for QGP production is achieved. The correlations between extracted T0 and parameters are found to be greatly different in regions < 0.46 and > 0.46, which further supports our result obtained for the threshold border value in Pb + Pb collisions at = 5.02 TeV.

It is proposed to use the Hurst method for a rapidity correlation analysis in multiple processes. For simulated processes, it is shown that by this method, one may find the `length' and `power' of correlations.

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