## Nuclear Equation of State

#0842

Nuclear Equation of State with Deconfinement Phase Transition and 3D Relativistic Dissipative Hydrodynamics. Development of the Approach and Confrontation of Results to Experimental Data on Heavy-ion Collisions

**Tech Area / Field**

- PHY-PFA/Particles, Fields and Accelerator Physics/Physics

**Status****3** Approved without Funding

**Registration date****29.12.1996**

**Leading Institute**

VNIIEF, Russia, N. Novgorod reg., Sarov

**Supporting institutes**

- Joint Institute of Nuclear Research, Russia, Moscow reg., Dubna\nKurchatov Research Center, Russia, Moscow

**Collaborators**

- Los-Alamos National Laboratory, USA, NM, Los-Alamos\nUniversity of Bergen, Norway, Bergen\nUniversität Frankfurt am Main / Institut für Theoretische Physik, Germany, Frankfurt am Main

**Project summary**

Relativistic heavy-ion collisions provide us with a unique tool for studying properties of highly exited nuclear matter at laboratory conditions. On the one hand, the general strategy of getting higher and higher incident energies is caused by a hope that signals of produced quark-gluon plasma will be more distinct and unambiguous at higher energies. On the other hand, it was found that presence of a phase-transition point in an equation of state may significantly affect evolution of the system and result in new observable signals. In particular, a so-called "softest-point" effect recently put forward results in experimental consequences that can be observed at moderate incident energies of the order of 10 GeV/nucleon. This fact gives rise to a new strategy of searching for signals of the deconfinement phase transition.

Specific signals and the energy, at which these "softest-point" signals might be observed, depend on the equation of state and dynamics of nuclear interaction. Thus, this approach implies that we exactly know both the equation of state of QCD matter and the dynamic model, which relates the equation of state to observables. Two-phase models, used in the first estimates, predict the phase transition of the first kind for the *SU(3) *system, whereas gauge QCD theories point to a phase transition of the crossover type. A statistical model of mixed phase, developed in Dubna, properly reproduces main results of the lattice QCD calculations. Various versions of the hydrodynamic model, used till now, predict different values of energy, at which the "softest-point" effect should occur. However, no one of these versions takes simultaneously into consideration all basic hydrodynamic effects that affect the system evolution. To this end, it is quite natural to join together the experience of the RFNC-VNIIEF in developing three-dimensional hydrodynamic codes and that of JINR and IGNP in investigating the mixed phase and various dynamical effects accompanying the fireball formation and its decay.

In the proposed project, three codes of the relativistic 3D hydrodynamics will be de-signed with due regard for dissipative processes for various equations of state. Based on these hydrodynamic codes and the developed statistical model of the mixed phase, we assume to extensively study properties of hot and dense nuclear matter produced in relativistic heavy-ion collisions, as well as signals of the deconfinement phase transition. Special attention will be paid to an analysis of experimental consequences of the "softest-point" effect of the equation of state as revealed in both collective properties of nuclear interaction and specific processes, associated with the production of photons and dileptons. First made within relativistic dis-sipative hydrodynamics of the mixed QCD phase, such an analysis of experimental data will allow us to restrict essentially the form of equation of state for excited nuclear matter.

As a reference point to check correctness of the techniques used and the role of dissipation in fireball evolution, we assume to take calculation results for 3D relativistic hydrodynamics but without dissipation. Such calculations are doing now in JINR-Los Alamos-Bergen collaboration where D. Strottmah (Los Alamos), L.P. Chernai (Bergen) and the group of the project manager V.D. Toneev (Dubna) are involved. It is planned to continue actively this collaboration as to some special project points (in particular, developing a freezing procedure for the mixed phase) and the whole problem as well by a critical discussion of physics results obtained.

*Some Previous Publications of the Project Participants:*

1. V.S. Barashenkov, V.D. Toneev. High Energy Interaction of Particles and Atomic Nuclei with Nuclei, Atomizdat, Moscow, 1972, pp.1-648 (in Russian).

2. V.D. Toneev, H. Schulz, K.K. Gudima, G.Ropke, On the way of investigating the hot arid compressed nuclear matter, Particles & Nuclei 17

**(1986) 1093.**

3. N.S. Amelin, E.F. Staubo, L.P. Csernai, V.D. Toneev, K.K. Gudima, D. Strottman, Trans-verse flow and collectivity in ultra-relativistic heavy ion collisions, Phys. Rev. Letters 67

**(1991) 1523.**

4. N.S. Amelin, L.V. Bravina, L.P. Csernai, V.D. Toneev, K.K. Gudima, S.Yu. Sivoklokov, Strangeness production in proton and heavy-ion collisions at 200

*A GeV.*Phys. Rev. C47 (1993) 2299.

5. E.P. Kadantseva, A.A. Shanenko, V.I. Yukalov, Quark-hadron matter at low tempera-tures, Phys. Lett. В 255 (1991) 427.

6. A.A. Shanenko, E.P. Yukalova, V.I. Yukalov, Deconfmement in heterophase mixture of quark-gluon plasma and hadrons, Yad. Fiz. 56 (1993) 151.

7. A.A. Shanenko, E.P. Yukalova, V.I. Yukalov, Statistical model of quark-hadron matter, Nuovo Cim. A106

**(1993) 1269.**

8. A.A. Shanenko, E.P. Yukalova, V.I. Yukalov, Mixed phase of nuclear matter, Dokl. of Rus. Acad. Sci. 342

**(1995) 759.**

9. A.A. Shanenko, V.D. Toneev, Towards a new strategy of searching for QCD phase tran-sition in heavy ion collisions, JINR Rapid Communication 5(73)-95 (1995) 21.

10. E.G. Nikonov, A.A. Shanenko, V.D. Toneev, Mixed phase thermodynamics near the point of QCD phase transition. In: Proceedings of the Xllth workshop on "soft" physics "Hadrons-96" (Novy Svet, Crimea June 9-16) ed. by G. Bugrij, L.Jenkovszky, E.Martynov, Kiev, 1996, p.292.

11. N.S. Amelin, K.K. Gudima, V.D. Toneev, Model of quark-gluon strings and ultrarela-tivistic collisions of heavy ions, Yad. Fiz. 51 (1990) 512.

12. V.D. Toneev, N.S. Amelin, K.K. Gudima, S.Yu. Sivoklokov, Dynamics of relativistic heavy-ion collisions, Nucl. Phys. A519 (1990) 463c.

13. N.S. Amelin, L.V. Bravina, L.P. Csernai, V.D. Toneev, K.K. Gudima, S.Yu. Sivoklokov, Strangeness production in proton and heavy-ion collisions at 200

*A GeV,*Phys. Rev. C47 (1993) 2299.

14. K.K. Gudima, A.I. Titov, V.D. Toneev, Hadronic sources of dileptons from heavy ion collisions at intermediate and relativistic energies, Phys. Lett. В 287 (1992) 302.

15. V.M. Galitsky, Yu.B. Ivanov, V.A. Hangulyan, Kinetic coefficients of nuclear matter, Yad. Fiz. 30 (1979) 778.

16. Yu. B. Ivanov, Relativistic mean-field kinetic approach to hadron plasma and three-fluid dynamics, Nucl. Phys. A474 (1987) 669.

17. V. N. Russkikh, Yu. В. Ivanov, Yu. E. Pokrovsky, P. A. Henning, Analysis of intermediate-energy heavy-ion collisions within relativistic mean-field two-fluid model, Nucl. Phys. A572 (1994) 749.

18. Yu. B. Ivanov, V. N. Russkikh, Nucl. Phys. A580

**(1994) 614.**

19. S. Ayik, Yu. B. Ivanov, V. N. Russkikh, W. Norenberg, Nucl. Phys. A578 (1994) 640.

20. V. N. Russkikh, Yu. B. Ivanov, Nucl. Phys. A591 (1995) 699.

21. A.A. Stadnik, V.P. Statsenko, Yu.V. Yanilkin, V.A. Zhmailo, Direct numerical simulation of turbulent mixing in shear flows.In: The 5rd International Workshop on the Physics of Compressible Turbulent Mixing, Stony Brook (USA), (1995).

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