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On ring and bubble formation mechanisms in the heavy ion collisions.

On ring and bubble formation mechanisms in the heavy ion collisions. K.V. Cherevko 1,2 , J. Su 1 , L.A. Bulavin 2 , V.M. Sysoev 2 , F. S. Zhang 1 1 Beijing Normal University 2 Taras Shevchenko National University of Kiev. p. n. 16 O. 16 O. 11 C. n. 12 C. 12 C. 15 O. n. 15 O. 16 O.

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On ring and bubble formation mechanisms in the heavy ion collisions.

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  1. On ring and bubble formation mechanisms in the heavy ion collisions. K.V. Cherevko1,2, J. Su1, L.A. Bulavin2, V.M. Sysoev2, F. S. Zhang1 1Beijing Normal University 2Taras Shevchenko National University of Kiev

  2. p n 16O 16O 11C n 12C 12C 15O n 15O 16O 16O • Nuclear equation of state. IWND 2012, Dec. 16-19, Shenzhen, China • Equation of state describes fundamental properties of the matter. Accelerator (600 MeV - 4 mA proton) • Reactor • Subcritical and Critical modes • 65 to 100 MWth • The equation of state of nuclear matter is an important ingredient in: • Study of properties of nuclei at and far from stability • Study of structures and evolution of compact astrophysical objects, such as neutron stars and core-collapse supernovae • Applied nuclear physics p p European prototype ADS 1H: E = 110 MeV Target: PMMA 11C, 10C • Equation of state Spallation Source 12C: E = 212 AMeV Target: PMMA 15O, 11C, 13N ... Fast eutron Source 15O, 11C, 13N ... Lead-Bismuth coolant

  3. Nuclear equation of state. Current state of art. IWND 2012, Dec. 16-19, Shenzhen, China The knowledge of the nuclear equation of state is one of the fundamental goals in nuclear physics which has not yet been achieved. (M. Baldo, et al, J. Phys. G: Nucl. Part. Phys. 34 (2007) R243) • The possibility of extracting information • on the nuclear EOS, in particular at high baryon density, is restricted to two fields of research: • Observations of astrophysical compact objects • Studies of hot nuclear systems, created in high energy proton induced reactions or in intermediate and relativistic energy heavy-ion collisions (HIC) The energy per nucleon in SNM E0(n) (left panel), the symmetry energy Es (n) (middle panel) and the energy per nucleon in NSM (β-equilibrated and charge neutral) for different models(right panel).(T. Kl.ahn, et. al., Phys. Rev. C 74 (2006) 035802)

  4. Heavy ion collisions. IWND 2012, Dec. 16-19, Shenzhen, China • Why heavy ion collisions? • Direct excess to supernova core or neutron star impossible • High temperature & density can be achieved in intermediate energy heavy ion collision. • Coupled with the possibility of neutron rich beams, very asymmetric nuclear matter (N/Z > 1) can be probed. • The largely unconstrained density dependence of the asymmetry term in the EOS is sensitive to many observables in heavy ion collisions • The main questions: • What are nuclei made of? • What are the properties of the matter that form the nuclei? Heavy ion collisions physics = material science/ physics of simple liquids (P-V-T studies)

  5. spallation fragmentation fission • Heavy ion collisions. IWND 2012, Dec. 16-19, Shenzhen, China proton ( ~1 GeV) on 238U fusion Spallation, fission and multifragmentation in a field of multiplicity of heavy fragments versus mass of the fragment. The scheme is coarse and the boundaries are not sharp. The location of deep spallation is tentative. (J. Hűfner, Phys. Rep. 125 (1985) 129) Heavy fragments can he formed by: - Spallation (fragments whose mass is close to the target mass AT and only one heavy fragment is observed (m = 1)) - Fission (two heavy fragments with masses in the interval around A ~AT/2) - Multifragmentation (the process which leads to fragments with A < 50 several (more than two) fragments are produced) (B. Jonson, Cern Courier, December, 2011; P. Van Duppen, La Rabida, September 2012)

  6. Heavy ion collisions. Intermidiate energies IWND 2012, Dec. 16-19, Shenzhen, China Why intermidiate energies : In intermediate heavy ion collisions, the composite system of the projectile and target nuclei is compressed and excited at an early stage of the reaction. This hot-dense nuclear system expands and can break into fragments by a multifragmentation process. • Why multifragmentation: • Multifragmentation is a phase transition? • Allows to have a deep insight into the properties of nuclear matter and for developing the proper EOS. Investigation of the nuclear matter in the vicinity of critical point. • Origin of the idea: - Fisher’s formulae for the droplet mass distribution seems to describe well the multifragmentation data. (A.D. Panagiotou et al Phys. Rev. Lett. 52 (1984) 496; M.E. Fisher, Physics 3 (1967) 255.) • At the time of intermediate mass fragments formation (IMFs) with 3 ≤ Z ≤ 20, their characteristic properties, such as excitation energy and isotopic distributions, are governed by the characteristics of the break-up source,such as the temperature, density and N/Z ratio. Therefore IMFs may provide a unique probe to study the reaction mechanism and hot nuclear matter properties. (M R D Rodrigues, et al, J. Phys.: Conf. Ser. 312 (2011) 082009)

  7. Heavy ion reactions and the nuclear equation of state. IWND 2012, Dec. 16-19, Shenzhen, China Difficulties when extracting information on the EOS: The colliding system is over a large time span of the reaction out of global and even local equilibrium (C. Fuchs, et al, Eur. Phys. J. A 30 (2006) 5) Transport models that include the possibility for the occurrence of dynamical bifuracations are needed for the adequate description of the initial stage. The HIC experiments are inclusive and will remain so in the foreseeable future. Only the degree of inclusiveness may change if more sophisticated counter arrays are introduced (J. Hűfner, Phys. Rep. 125 (1985) 129) Although much progress has been made over the past couple of decades, we are still far from having models that are formally well founded, practically applicable, and sufficiently realistic to be quantitatively useful. The description of nuclear fragmentation dynamics requires that proper account be taken of the basic quantal nature of the system. (A. Ono, et al., Eur. Phys. J. A 30 (2006) 109) A schematic picture of a fragmentation reaction in which a given initial channel may develop into many different fragmentation channels during the dynamical evolution. (A. Ono, et al, Eur. Phys. J. A 30 (2006) 109)

  8. Existing multifragmentation phenomenon models pros and cons. IWND 2012, Dec. 16-19, Shenzhen, China • Unfortunately the underlying mechanism of nuclear multifragmentation remains unclear. • Phenomena involved • Spinodal decomposition (e.g. F.-S. Zhang, Z. Phys. A 356 (1996) 163). • Phase transitions in small systems (e.g. F. Gulminelli, et al, Phys. Rev. C 72 (2005) 064618 ) • Problems with the existing models? • The widely used suggestions concerning the thermalization of the whole system is unproven. There are evidences of only a small part of the system being heated. (J. Hufner, Phys.Rep., 125, 129, (1985); X. Campi et. al., Phys. Rev. C, 67, 044610, (2003)) • Equilibrium at low freeze-out density and the statement concerning the spherical fragments are not confirmed by microscopic approaches (X. Campi et. al., Phys. Rev. C, 67, 044610, (2003); T. Furuta, et. al., Phys. Rev. C 79 (2009), 014608). • Kinetic energies of the fragments in experiments are lower then the temperature of the gas fragments (X. Campi et. al., Phys. Rev. C, 67, 044610, (2003)). • Phase transition is a quality which is difficult to prepare. • Most statistical multifragmentation codes have been developed to describe specific sets of data and nearly all of them have different assumptions. They are not equivalent. Not always able to describe the other experiments. (M.B. Tsang,etal,Eur. Phys. J. A 30 (2006) 129) There should be a simple description of a complicated process like fragmentation that works because the process is extremely complicated

  9. Nuclear matter and ordinary liquids. Equation of State IWND 2012, Dec. 16-19, Shenzhen, China Thermodynamic description of the nuclear matter is very similar to that for the liquid-gas systems. The physical reason for that is the qualitative Van der Waals and nucleon-nucleon interactions similarity (E.g. Brueckner K.A., The Many Body Problem, Paris, 1959; Karnaukhov V.A. Nuclear Multifragmentation and Phase Transitions In Hot Nuclei // Phys. Elem. Part. Atom. Nucl., 37, N.2, 2006; S. Shlomo, V.M. Kolomietz. Hot Nuclei // Rep. Prog. Phys, 68, 2005 ). In both cases an attraction between the particles is replaced by repulsion at a small interaction range. Despite the tremendous difference in the energy and space scales their equations of state are very similar. J.D. Van der Waals suggested his famous equation in 1873. A hundred years later his finding was fruitfully used to describe the properties of the nuclear matter unknown to the nineteenth century scientists. Nuclearmatter E.g. Equation of state relating the pressure and the volume (normalized to critical values) in nuclear matter and in the Van der Waals gas. The curves represent isotherms. The red line is the spinodal line VanderWaalsgas Nuclear matter could be described by the modified laws of the ordinary liquid physics. “Macroscopic” analysis may give an insight into the mechanisms involved in heavy ion collision (e. g. thermodynamic approach to proton induced multifragmentationCherevko K.V, et al, PRC 84(2011) 044603)

  10. Nuclear matter and ordinary liquids. Hydrodynamics. IWND 2012, Dec. 16-19, Shenzhen, China • Hydrodynamic behavior of the nuclear systems in heavy ion collisions suggested at 70th -80th (e.g. J. Siemens et. al. PRL 42, 880 (1979); H. Stocker et. al. Z. Phys. A 294, 125 (1980)) Typical mean free path of nucleons (for an average nucleon-nucleon cross-section ) Hydrodynamic behavior important for the initial development of the shock (H.G. Baumgardt et al Z. Phys. A 273 (1975) 359) Total and elastic cross sections for pp collisions as a function of laboratory beam momentum (Particle Data Group. J. Phys. G 33 (2006) 1). Relativistic shrinking The mean free pass is small compared to the target nucleus – possible to use hydrodynamics.

  11. Bubble and ring formation in the head-on heavy ion collisions. IWND 2012, Dec. 16-19, Shenzhen, China Possible geometries (from the BUU calculations) (C.-Y. Wong, Phys Rev. Lett. 55 (1985) 1973; W. Bauer, et al, Phys. Rev. Lett, 69, (1992), 1888; H.M. Xu, et al, Phys. Rev. C., 48 (1993), 933) Torroid Bubble “Compact” Energy range: E=60÷75 MeV/A Stiff EOS, K=375 MeV Soft EOS, K=200 MeV • Experimental evidence of the exotic shapes:exists(e.g. 86Kr+93Nb reactions at 60-75 MeV/nucleon showed the signatures of the torroidalstractures; N.T.B. Stone et al, Phys. Rev. Lett. 78, (1997), 2084) • Comprehensive physical model: up to now there is no model describing in details the underlying physical mechanisms of the exotic shapes formation in the head-on ion collisions.

  12. Bubble and ring formation in the head-on heavy ion collisions. IWND 2012, Dec. 16-19, Shenzhen, China Possible explanations • “Shock” waves in the system. • Possibility of realization in real systems: The existence of shock waves in nuclear matter is confirmed by the NFD model (E.g. Frankfurt group, e.g. H. Stocker and W. Greiner, Phys. Rep. 137 (1986) 277) • Questions: • What is the origin of the shock waves (only from compression, thermal pressure) • What are the timescales of the process? • How do one get different topology from the same mechanism? • 2) The exotic structures caused by the nonuniform energy distribution within the system. • Possibility of realization in real systems: The nonuniform energy distribution within the colliding system is suggested in literature (e.g. W.A. Friedman, Phys. Rev. C, 42 (1990) 667) • Questions: • What is the actual mechanism of the exotic structures formation? • 3) Free energy minimization. • Questions: • According to thermodynamics it should be all the other way round for the K values. • Influence of the EOS. Some factor not taken into account? • Is the difference in the topology observed at the stage of the collision when the thermodynamic effects are of greater importance than the dynamic one? • 4) Surface effects. • Possibility of realization in real systems: Energy at the breakdown ~1-2 MeV/ A is similar to the energy of capons (e.g. Khodel V. A., Nucl. Phys. 19 (1974) 792) • Questions: • Is the process connected with the introduced angular momentum L? • Influence of the EOS. Some factor not taken into account? • The structure of the “doughnuts”. Do the positions of minima and maxima of the density correspond to the one suggested by the capillary waves?

  13. Bubble and ring formation in the head-on heavy ion collisions. IWND 2012, Dec. 16-19, Shenzhen, China Keypoints that may help to find the answer: • The inner surface starts from zero and continues to increase, while the outer surface remains relatively unchanged. The final stage is the simultaneous breakup. A kind of a “shockwave”? • Fragments of almost equal masses. Does it mean some periodic structure on the surface? Possible signature of the capillary waves being responsible for the process? • Directions of the fragments emission: for “doughnut shape” preliminary in the direction perpendicular to the beam; for bubble in all directions isotropicaly. • Low kinetic energies of the fragments. • Energy range where the phenomena is observed (E=60÷75 MeV/A). • Why to study this question: • Different shapes observed in the experiment may yield valuable information about the nuclear incompressibility that is the key parameter of the nuclear equation of state. • Information regarding the surface tension and nuclear matter viscosity. • Links between the Boltzman- like transport theory and the hydrodynamic approach.

  14. Hydrodynamic model. IWND 2012, Dec. 16-19, Shenzhen, China • Symmetrical system → the model of a nuclei impact on a solid wall. Modification: no viscose forces in the contact plane between the wall • and the nuclei (slip boundary condition).Different mechanisms are • involved in respect to the EOS stiffness? Initial stage of the process: • The matter is assumed to be inviscid. • The governing parameters are the impact velocity, nuclei size and compressibility. V V R V βc Ue

  15. Bubble and ring formation in the head-on heavy ion collisions. First stage. IWND 2012, Dec. 16-19, Shenzhen, China Compressed matter • Governing parameters: • Compressibility • Velocity • Nuclei size Shock front R V βc 0 < t ≤tjet • The edge velocity remains higher than the shock speed. Nuclei remains “spherical”. (Huyghens principle: the expanding liquid edge emit a wavelet moving at ) • Asthecontactedgepropagatessideways, aradialflowdevelops. Nosubstantialvariationsofpressurealongz- axis. Pressureincreasestowardthecontactline. • Whentheedgevelocitydecreasestotheshockvelocityvaluejettingoccurs. t=0 Ue t >tjet t=0 Pressure distribution .

  16. Governing equations. IWND 2012, Dec. 16-19, Shenzhen, China Dependence of the shock velocity on the matter velocity Difference from the NFD approach (by Frankfurt group) – lower energies and weak shock waves. Continuity equations with the momentum and energy conservation Rankine-Hugoniot jump conditions Adjustable parameter NM equation of state Equation of State for the linear dependence C=C(U)

  17. Preliminary results IWND 2012, Dec. 16-19, Shenzhen, China Model parameters: System 93Nb+93Nb; • Impact velocity: • Incompressibility coefficient • Sound velocity has linear dependence on the particle velocity (k=1 on the figure) • Maximum value of the shock velocity (anomaly on the graph) Particle radial velocity / time k – adjusting parameter Adjusting method: From fitting the jetting time with the results of the NFD calculations for the Kr-Kr collisions at Elab=400 MeV/nucleon (H. Stocker and W. Greiner Phys. Rep. 137 (1986) 277.) βc t >tjet t=0 Ue Adopted value: k=0.77 (“stiff” EOS) Jetting time : Sensitive to k value

  18. Governing parameters: • Compressibility • Velocity • Nuclei size Preliminary results IWND 2012, Dec. 16-19, Shenzhen, China Calculated values: Jetting time • Size change at jetting • Critical angle • Pressure release time • Maximum density • at the contact line Results for the maximum density and pressure release time are in good correspondence with the BUU calculations. βc t >tjet In difference with the Boltzman-like transport theories the suggested approach gives the clear physical picture of the phenomena t=0 Ue

  19. Bubble and ring formation in the head-on heavy ion collisions. Intermediate stage. IWND 2012, Dec. 16-19, Shenzhen, China “Stiff” EOS, K=400, t=21 fm/c “Soft” EOS, K=200, t=23.8 fm/c 2R=11.8 fm 2R=11.8 fm L=3.8 fm L=0.87 fm ΔD= 0.82 R ΔD= 1.01 R • “Doughnut” shape • Shock waves don’t influence much the behavior of the system after the side jet being formed. • Inertia forces are in charge for the first stage of the process. Surface and viscose forces are responsible for the formation of the rim and therefore for the “doughnut” shape. • Bubble shape • Compressible liquid. • Shock waves and capillary waves are responsible for the system geometry. • Bubble formation through the formation of the cylindrical cavity that collapses with the bubble entrapment. • Different mechanisms are involved in respect to the EOS stiffness. • Governing parameters: • Compressibility, Velocity, Size, Surface tension

  20. Bubble and ring formation in the head-on heavy ion collisions. Intermediate/final stage. IWND 2012, Dec. 16-19, Shenzhen, China “Stiff” EOS, K=400, t~60 fm/c “Soft” EOS, K=200, t~70 fm/c • Governing parameters: • Surface tension, • Viscosity Deceleration of the surface leads to indtability. Cavity collapse Surface forces Rim being formed on the edge of the expanding sheet Rarefaction due to the reflected shockwaves Future “bubble” Energy dissipation • Dependenceofthevelocityofthefirstsoundoncompressibility - mainreasonforthedifferentphysicsintheexoticshapesformation. The scenario of the system evolution is defined during the initial stage of the impact.

  21. Conclusions IWND 2012, Dec. 16-19, Shenzhen, China • Suggested approach allows for a simple “macroscopic”physical picture of the exotic structure formation in the head-on heavy ion collisions • The qualitative picture obtained within the developed model is in a good correspondence with the one observed within the BUU calculations • The straightforward link between the EOS of state and the exotic shapes of different topology is explained from the hydrodynamic point of view. • Preliminary quantitative estimations show that the suggested model gives the same results for the maximum density and pressure release time as the BUU calculations by the order of magnitude. • Combination of the introduced “macroscopic” approach together with the Boltzman-like transport theory calculations can reveal the physical nature of the bubble and ring formation in the multifragmentation phenomena and give the possibility to extract the data on the EOS from the head-on heavy ion collisions.

  22. Thank you for your attention!

  23. IWND 2012, Dec. 16-19, Shenzhen, China

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