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Radial Flow in Experimental Heavy Ion Collisions: Observations, Characterization, and Implications

This article discusses the experimental facts, observations, and characterization of radial flow in heavy ion collisions, as well as its implications on collision dynamics and underlying reaction mechanisms. It also explores various approaches to observe and characterize radial flow, as well as the challenges associated with model assumptions.

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Radial Flow in Experimental Heavy Ion Collisions: Observations, Characterization, and Implications

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  1. WCI3 Radial Flow F. Rami C.O.Dorso

  2. The Radial Flow: Experimental facts S.G. Jeong et al (FOPI), PRL 72 (1994) 3468 Flow energy identified as an extra KE in the fragments • Generally defined (in experimental papers) • as an azimuthally symmetric collective • expansion of the emitting source  ‘Consensual’ definition - expanding source not necessarily spherical - same over a broad range of energies (MSU/GANIL  SPS and RHIC) • Predicted by Hydrodynamical model • Bondorf et.al. NPA296(1978)320, Siemmens & • Rasmussen PRL 42(1979) 880 (Stoecker & Greiner, Phys. Rep. 137 (1986) 227) • Observed for the first time in central • Au+Au collisions at 150AMeV (FOPI@GSI) Large fraction of the initial KE (~30%) is converted into the collective expansion  Implications on collision dynamics and underlying reaction mechanisms

  3. Extensive studies over the last 12 years • Since the first experimental observation of the radial flow, there have been • extensive experimental studies over a very broad energy range going from a • few tens of MeV/nucleon (MSU, GANIL) up to ultra-relativistic energies • (AGS, SPS and RHIC) • Data around (and above) the Fermi energy (E/A < few 100 MeV) Accelerators SARA (Grenoble) NSCL (MSU) GANIL (Caen) BEVALAC (Berkeley) SIS-GSI (Darmstadt) R.T. de Souza et al, Phys. Lett. B 300 (1993) 29 S.G. Jeong et al, PRL 72 (1994) 3468 W.C. Hsi et al, PRL 73 (1994) 3367 D. Heuer et al, Phys. Rev. C 50 (1994) 1943 M.A. Lisa et al, PRL 75 (1995) 2662 G. Poggi et al, Nucl. Phys. A 586 (1995) 755 J.C. Steckmeyer et al, PRL 76 (1996) 4895 S.C. Jeong et al, Nucl. Phys. A 604 (1996) 208 M. D'Agostino et al, Phys. Lett. B 371 (1996) 175 R. Pak et al, Phys. Rev. C 54 (1996) 1681 N. Marie et al, Phys. Lett. B 391 (1997) 15 W. Reisdorf et al, Nucl. Phys. A 612 (1997) 493 T. Lefort et al, PRC 62 (2000) 031604 B. Borderie et al, Nucl. Phys. A 734 (2004) 495 A. Lefèvre et al, Nucl. Phys. A 735 (2004) 219 Detectors (large acceptance) AMPHORA @ SARA 4-array @ MSU MINIBALL @ MSU, SIS MUR+TONNEAU @ GANIL INDRA @ GANIL, SIS EOS @ BEVALAC, AGS FOPI @ SIS This list is not exhaustive

  4. How to observe the Radial Flow? Prerequisite  Isolate the emission source • At high energies (E/A > 100 MeV) : one can produce a single 'fused' nuclear system (the fireball) in highly central collisions • At lower energies : one can produce nuclear sources via binary dissipative processes ( quasi-projectiles and quasi-targets) The initial mass and excitation energy of the source depend on the collision impact parameter • Several centrality selection criteria are used in heavy-ion experiments: -Total particle multiplicity • -Total detected charge • -Ratio of transverse to longitudinal kinetic energies (ERAT) • -Flow angle • -Principle Component Analysis (PCA) • The choice of the appropriate selection criterion (or combination of criteria) depends on the experimental setup (and the bombarding energy) • Centrality should be selected in a similar way in model calculations (Monte Carlo codes + detection filter)

  5. How to observe the Radial Flow? • Two main features clearly observed in the data: • KE spectra that do not show the characteristic • Boltzmann-like shape expected for a pure thermal emission • Pronounced particle mass dependence of the mean KE The radial expansion of the source adds KE to the particle distributions  superposition of two effects: Thermal (random) + Collective <E> = 3/2 T + 1/2 mv2 • Heavy particles more sensitive to radial flow • Experimentally, ‘Signals’ of collective expansion should appear as an extra KE in the fragments

  6. How to characterize the Radial Flow? Usual Approach: Use statistical models that include a radial flow component • At high energies:Use the Blast wave formalism (Siemens & Rasmussen) •  Fit the data for different species (simultaneously  mass dependence) • Results  T and flow • Generally done at mid-rapidity (cm=900) to avoid possible contamination • of spectator matter and directed flow • At low energies:Use statistical model simulations that include the radial expansion (WIX, SIMON, …) •  Compare to the data with different assumptions on the radial flow • Results  Eflow and sharing of the total available energy among • thermal and collective components Problem  To which extent the extracted values depend on model asssumptions? Not always clear, in particular at low energies close to the threshold where the signal is very small (difficult to extract accurately!)

  7. Kinetic energy spectra of light particles M Lisa et al (EOS), PRL 75 (1995) 26662 • Measured light charged isotopes (Z=1,2) • in central Au+Au from 0.25 to 1.15AGeV • at cm=900 • analyzed using the Blast wave formalism Results • A purely thermal model (flow=0) cannot reproduce simultaneously all data • Fit  flow= 0.32  0.05 at E=1 AGeV  Large collective flow (45 to 60% of total KE) • Source shape: spherical • FOPI  Similar results in the 100-250AMeV • energy range • (Poggi el al, Nucl. Phys. A 586 (1995) 755 )

  8. Kinetic energy spectra of heavy fragments S.G.Jeong et al (FOPI), PRL 72 (1994) 3468 Au on Au @ 150 AMeV, central Advantage of measuring heavy fragments  more sensitive to flow (less affected by thermal fluctuations)  provide ‘cleaner’ characterization of the radial flow  Check the mass dependence (next slide) Centrality via Erat Exp. Data (int 25°-45°), symbols FREESCO w/coulomb (no flow) qmd

  9. The mass dependence W.Reisdorf et al (FOPI), NPA612(97)493 • A quasi-linear dependence is clearly • observed for heavy fragments •  common flow velocity to all • detected fragments Au+Au • The energy taken up by the • radial flow was estimated • to be ~60% of the available • kinetic energy at E=250AMeV • (blast model) Z = 2  A assumed • Event topology isotropic within 20% (C.Roy et al (FOPI), Z. Phys. A358 (1997) 73)

  10. Radial flow energy in Au+Au @ 100 AMeV W.C.Hsi et al (Miniball @ GSI), PRL 73 (1994) 3367 • Measured KE spectra of IMFs • in central Au+Au collisions at • E/A = 100 MeV • Extracted values of the expansion • energy independently for each • fragment ( 3 rel. Max. dist.) • Typical values -> 1/3 to 1/2 of • the available c.m. energy • (consistent with FOPI data) • Mean radial collective energy not linear with A, suggesting that • not all fragments participate • equally in the collective expansion

  11. Radial flow energy in 40Ar+45Sc @ 35-115 AMeV R.Pak et al (MSU), Phys. Rev. C 54 (1996) 1681 • Measured transverse KE as a function of angle and impact parameter • for 40Ar+45Sc at beam energies from 35 to 115 AMeV • Agreement with predictions • of BUU and WIX calculations  The radial flow accounts for ~half of the emitted particle's energy for the heavier fragments (Z4) at the highest beam energy WIX assuming 50% available energy goes into collective motion

  12. Radial flow energy in 64Zn+natTi @ 35-79 AMeV J.C.Steckmeyer et al (GANIL), PRL 76 (1996) 4895 • Measured 64Zr + natTi reaction at • E = 35 to 79 AMeV • Source = fast quasiprojectile •  Observed even in the most • central events (b  2fm) • Comparisons with WIX and EUGENE •  estimate of the radial flow energy • at E = 79 AMeV • between 1.8 and 2.7 AMeV • Shape : found to be isotropic • Similar studies of quasiprojectile sources • in 36Ar+27Al from 55 to 95 AMeV (GANIL) • Jeong et al, Nucl. Phys. A 604 (1996) 208  Eflow grows with excitation energy  At E*/A=10 MeV: Eflow = 1.0–2.2AMeV

  13. Radial flow energy in Central Au+Au @ 35 AMeV Comparison of data to SMM calculations D’Agostino et al, Phys. Lett. B 371 (1996) 175 Mean c.m. KEper nucleon at 90o Cont. lines SMM predictions at ρ0/3 – no flow Dashed lines SMM predictions at ρ0/6 – Eflow = 0.8 AMeV Charge distribution of the six heaviest fragments

  14. Comparison of dynamic observables to SMM through PCA analysis Au + Au central collisions @ 35 AMeV Nucl. Phys. A633 (1998) 547 Mean cm kinetic energy per nucleon Points : experiment Cont. line : SMM prediction Dashed line : SMM predictions + 1.1 MeV radial flow Mean cm kinetic energy (full points) of the heaviest fragments (b) and all but the heaviest (c) compared to SMM predictions + 1.1 MeV radial flow (open points)

  15. Radial flow from INDRA @ GANIL N.Marie et al, Phys. Lett. B 391 (1997) 15 • Measured KE of IMFs in central • Xe+Sn collisions at 50 AMeV • Comparison with SIMON calculations with and without collective motion • Main conclusion: The results indicate a fast disintegration process of the system with a radial collective motion of about 2 AMeV Mass dependence clearly observed

  16. Radial flow from INDRA @ GANIL J.Frankland et al, Nucl. Phys. A 689 (2001) 940 • Data for 129Xe + natSn @ 32AMeV • and 155Gd + natU @ 36AMeV •  Radial flow energy estimated from • stochastic mean field simulations • (BNV+BOB) B.Borderie et al, Nucl. Phys. A 734 (2004) 495 • Data for several reactions at incident energies between 32 and 52 AMeV • Radial flow energy deduced from comparisons with SMM

  17. Radial flow from INDRA @ GSI A.Lefèvre et al, Nucl. Phys. A 734 (2004) 219 • Central collisions of 129Xe + natSn @ 50AMeV • and 197Au + 197Au @ 60, 80 and 100 AMeV •  Comparisons to MMC-NS calculations • (Microcanonical Multifragmentation Model • with Non-spherical Sources) •  Data can be reproduced if an expanding • prolate source aligned along the beam • direction is assumed (flow not included • in energy balance) Eflow

  18. Excitation function of the Radial Flow • Data for  reactions • No significant system-size dependence if expresed in terms of Eflow per nucleon • Discrepancy between • EOS and FOPI/IMF • Importance of including IMFs in the extraction of radial flow energy (IMF contribution to the total emitted charge is found to be significant up to Ebeam~ 600 AMeV) Onset of expansion at Ebeam 30 AMeV • Broad systematics • Better understanding of the origin of flow and disentangle  contributions - Thermal pressure (dominant at low energy) - Influence of Coulomb repulsion - Compressional effects • Need for detailed comparisons with theoretical models

  19. What is the radial flow The existence of a collective degree of freedom related to the presence Of a isotropic radial velocity distribution not generated by coulomb interaction It’s influence on: I Fragment formation Caloric Curve of fragmenting system Dynamical properties of IMF spectra In other words it’s competition with the thermal part of the energy and Coulombian part.

  20. Theoretical models Theoretical models Dynamical Models N-body approaches CMD QMD AMD 1-body approaches BUU, BNV, LV , etc. BOB Hydrodynamics Blast

  21. Theoretical models Theoretical models Statistical models Microcanonical Canonical Grand-canonical Sequential evaporation EES (with expansion and contraction) GEMINI SIMON HIPSE

  22. Classical Molecular Dynamics Bonsera et.al, Campi et.al. Dorso et.al. Interaction potentials: Lennard Jones, Illinois, QCNM Flow : Intrinsic to the development of the dynamics Results: Pedagogical? Non-equilibrium Fragments Local Equilibrium? Challenge : evolve into more realistic/nuclear

  23. CMD (LJ) 1 X.Campi.et.al. Interaction potential Fragment definition : Given a pair of particles they belong to the Same cluster if: This fragment definition si shown to be Equivalent to Coniglio-Klein (Ising Model)

  24. CMD (LJ) 1 Asymptotic fragment kinetic energies related to initial density Non-equilibrium effect.

  25. CMD (LJ) 2 CMD Dorso A.Chernomoretz, F.gulminelli, M.ison & C.O.DorsoPRC 69 (2004),034610 Caloric curve Confined system ECFM indicates fragments are formed Very early in the evolution. The system Reaches “local equilibrium” allowing to Define an effective local temperature ECRA fragments: Evolution of Fragment Mass Distributions Upon removal Of container

  26. CMD (LJ) 2 What is freeze out?

  27. CMD (LJ) 2 Influence of flux on the CC of an Expanding system

  28. Quantum Molecular Dynamics System described in terms of unsymmetrized gaussian wave packets Equations of motion Interaction potential

  29. Quantum Molecular Dynamics Sources of flow At variance with CMD High transparency At 50A MeV (Xe+Sn) High Transparency, no signals of equilibration, The observed apparent flosw is not real but reflects initial fermi motions Coulomb barrier,etc. At 200A MeV Smaller mean free path, Small fragments show strong radial flow due to Strong forces in the central region of the reaction. Phys.let. B 506 (2001) 261

  30. Brownian One Body model P. Chomaz, M.Colonna, A. Guarnera, J.Randrup PRL 73(1994)3512 Allows for the analysis of fragmentation in terms of spinodal decomposition The starting point is the boltzmann kinetic equation augmented to include higher order correlations , with In order to accelerate the calculation process, the following approximation Is used: , with

  31. Brownian One Body model • In NPA 689(2001)940 the analysis of HIC is performed according to : • BNV simulation which provides initial configuration to be fed in BOB • BNV calculation is stopped at maximum compression and BOB evolution is turned on. At 80 fm/c the system enters the spinodal region • At ~250fm/c fragments are well separated and excited • Finally fragments relax via statistical decay

  32. Statistical Models Statistical models come in many flavors Microcanonical (Randrup, Gross, Raduta, Das Gupta, etc.) Canonical (Bondorf, Gross etc. ) Grand canonical (Randrup, etc.) In what follows we pick (arbitrarily) one of the realizations (WIX)

  33. WIX J.Randrup Comp. Phys. Com 77(1993) 153 The explosive transformation of a given source in assumed to happen in a Statistical (microcanonical) manner. The density of states is accordingly: The collective expansion is taken into account by considering that the velocity Of the explosion products can be decomposed in thermal + collective components vn=Un+Vn. Vn is characterized by a Maxwell-Boltzmann distribution while Un is assumed homogeneous The total kinetic energy can be separated in two parts

  34. WIX Mass dependence of the Energy spectra Kinetic energy spectra of final Fragments as a function of the flow energy No flow Flow

  35. Microcanonical Lattice Gas with Flow Protons and neutrons in a lattice. Proton-neutron bond=-5.33 MeV. Coulomb is taken into account. Configurations are sampled with MMC, the weight given by: Configurations are accepted according to (Ray prescription) Momenta is assigned to particles according to Ekin. Flow is included by adding pf(i) = c[ri-rcm] Finally, fragments are recognized by MSTE prescription

  36. Microcanonical Lattice Gas with Flow Lattice gas fragment mass distributions are impervious to Flow

  37. Equilibrium under Flow? F.Gulminelli & P.Chomaz PRE 66 (2002) 46108 In the frame of information theory Given the observables E (average energy) and p(r) (average local radial Momentum), the probability of a microstate n is given by  and (r) are Lagrange multipliers. Imposing p(r)=mr(self similar) And the E reads: There are divergences due to r2 terms

  38. Equilibrium under Flow? Divergences are cured by introducing a confining pressure which “fixes” the Freeze out volume Collective motion is less effective than random motion in producing fragmets

  39. Expanding Emitting Source W.Friedman PRL60(1988)2125, PRC 42(1990) 667 In this model the dynamics is given in (t) -> A(t) and R(t) In the frame of a system with varying (t) induced by emission diven by emission rates according to Weisskopf detailed balance • Energies: • Collective kinetic energy of the residue • Collective compressional energy of the residue • Thermal excitation of the residue • Kinetic energy of the emitted fragment • Separation energy of the emitted fragment Changes in the thermal energy of the residue: particle emission -> taken at constant density density variation -> isotropic expansion Changes in density driven by thermal pressure and collecitve compressional energy

  40. 91Zr at Tmax=15,20,25 MeV T falls exponentially until ~ 5 MeV At 5MeV the mass of the instantaneous Residue declines sharply

  41. Conclusions and outlook The presence of radial flow is well established both Experimentally And Theoretically The dynamical origin of Radial flow is not on firm basis, competition Between compression and thermal effects. Dynamical models should be improved to fully understand the mechanism Through which initial collective motion (colliding nuclei) is transformed into random thermal motion and back into collective (at least partially in The from of radial motion) When are fragments formed? Early fragment formation, or Freeze out Formation, or spinodal decomposition? Further exploration on the effect of flow on CC

  42. Thanks to X. Campi V. Viola F. Gulminelli M. Bruno J. Randrup R. De Souza M. Rivet V. Kamaukhov D. Lacroix

  43. SLAFNAP6 Iguazú, Argentina. October 3 to 7, 2005

  44. NUCLEAR STRUCTURE Nuclear Structure : Experiments and Models Radioactive Beams Applications to Lepto-Nuclear- and Astroparticle-Physics Superheavy Systems New Facilities NUCLEAR REACTIONS Near-Barrier Phenomena Radioactive Beams Weakly Bound Systems Nuclear Astrophysics New Facilities NUCLEAR PHYSICS APPLICATIONS Medicine and Biology Environmental Science Materials Science Energy Production Art and Archeology SUBNUCLEAR PHYSICS Exotic Hadrons Quark-Gluon Plasma Aspects of Non-Perturbative QCD NUCLEAR THERMODYNAMICS AND DYNAMICS Nuclear Fragmentation Phase Transformations in Nuclear Systems Isospin Dynamics

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