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Coherent signals of the critical behavior in light nuclear systems

Coherent signals of the critical behavior in light nuclear systems. Yu-Gang Ma Shanghai Institute of Applied Physics ( SINAP ), CAS For NIMROD Collaboration: R. Alfarro, 5 J. Cibor, 4 M. Cinausero, 2 Y. El Masri 6 , D. Fabris, 3 E. Fioretto, 2

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Coherent signals of the critical behavior in light nuclear systems

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  1. Coherent signals of the critical behavior in light nuclear systems Yu-Gang Ma Shanghai Institute of Applied Physics (SINAP), CAS For NIMROD Collaboration: R. Alfarro,5 J. Cibor,4 M. Cinausero,2 Y. El Masri 6, D. Fabris,3 E. Fioretto,2 K. Hagel1, A. Keksis1, T. Keutgen,6M. Lunardon,3Y. G. Ma1,a, Z. Majka,4A.Makeev1,E. Martin1, A.Martinez-Davalos,5 A.Menchaca-Rocha,5 M. Murray1, J.B.Natowitz1, G. Nebbia3, L. Qin1, G. Prete,2 V. Rizzi,3 A.Ruangma1, D. V. Shetty1, P. Smith1, G. Souliotis1, P.Staszel,4 M. Veselsky1, G. Viesti,3R. Wada1, J. Wang1, E.Winchester1, S. J. Yennello1 1 Texas A&M University, College Station, Texas 2 INFN Laboratori Nazionali di Legnaro, Legnaro, Italy 3 INFN Dipartimento di Fisica, Padova, Italy 4 Jagellonian University, Krakow, Poland 5 UNAM, Mexico City, Mexico 6 UCL, Louvain-la-Neuve, Belgium a Shanghai Insititute of Applied Physics, Shanghai

  2. outline • Motivation • Experimental set-up: NIMROD and some analysis details • Coherent evidence of critical behavior • Model comparisons • Conclusions

  3. Introduction (I): Phase Transition in Nuclei ISiS Quark-Gluon Phase Transition： from Hadronic Matter to QGP RHIC Detectors: STAR, PHENIX, PHOBOS, BRAHMS Recent results: dAu vs AuAu Liquid Gas Phase Transition from cool nuclei to the full disassembly of nuclei Isis Data: 8-10GeV/c  - , p+Au Labs: MSU-Miniball, TAMU-Nimrod, Indiana U-Isis, GANIL-Indra, GSI-Aladin, Catania-Chimera Central Collisions 130GeV/c Au+Au STAR

  4. Motivation Ref: J. Elliott et al., Phys. Rev. Lett. 88 (2002) 042701 Nuclear Matter Tc Nucleonic MatterTc Limiting Temperatures J.Natowitz, K. Hagel, Y.G. Ma et al., Phys Rev Lett 89, 212701 (2002); arXiv:nucl-ex/0206010

  5. Brief Description of the Experimental Set-up: Texas A&M NIMROD

  6. Experimental Set-up: 4-NIMROD Array NIMROD = Neutron Ion Multidetector for Reaction Oriented Dynamics The NIMROD multidetector -- a new 4  array of detectors build at Texas A&M to study reactions mechanisms in heavy ion reactions.  The charged particle detectors are composed of silicon telescopes and CsI(Tl) scintillators covering angles between 3º and 170º. These charged particle detectors are placed in a cavity inside the revamped TAMU neutron ball. 166 CsI; 2 Si-Si-CsI telescopes + 3 Si-CsI telescopes in each forward ring (Ring2-9 ); CsI Si

  7. Reaction systems • 47MeV/u Ar + Al, Ti and Ni • Complete events of central collisions are chosen • Quasi-projectile (QP) was reconstructed on the base of event-by-event by our new method: Monte Carlo sampling based on three source fits for LCP and rapidity cut for IMF

  8. Event Selection: central collisions Ar+Ni Mn: total neutron numbers; Mcp: total charge numbers What is central collisions? Bin1+Bin2 are selected by Mcp and Mn Bin1+Bin2 : ~20% all events; Nearly Complete events: Zqp>=12, 4% of all evts Central collisions Peripheral collisions Nearly Complete Event

  9. A New Method to Reconstruct Quasi-Projectile

  10. Velocity contours of protons Bin5-Peripheral Bin4 Bin2 Bin3 Vper (cm/ns) Vini Bin1-Central Vpar (cm/ns)

  11. A new method to reconstruct QP deutrons tritons • Previous methods to reconstruct the Quasi-projectile: • Selected very peripheral collisions; • velocity cut: assuming the particles whose velocities V>Vcm(QP) as the QP particles, and then double the backward hemisphere to obtain E* and T • DRAWBACK: (1) low E*/A! • (2) fluctuation was washed out! 6.4º 18.2º Our new method to reconstruct QP: • First, 3 source fits to LCPs • Second, employ the parameters of fits to control the EVENT-BY-EVENT assignment of individual LCP to one of the source (QP, or NN, or QT) using Monte Carlo sampling techniques. The probability of QP’s LCP is • We associate IMFs (Z>3) with the QP source if they have rapidity >0.65Yproj. 32.1º 61.2º 120º 3 source fits: red: QP, blue:NN, pink:QT

  12. QP Source Reconstruction and Determination of E*/A Mixed QP Vpar Energy Balance: E* = (ECP+En) + Q where ECP,En=kinetic energy of CP and neutron in the source frame; En was obtained assuming a Maxwell-Boltzmann thermal distribution, consistent with volume emission, i.e., En = 3/2MnT = 3/2MnSqrt(E*/a), where a=A/8 is used, Mn was obtained as the difference between the nucleon number (A0) of the QP and the sum of nucleons bound on the detected CP (Mn=A0-ACP), Q is the mass excess of the QP system p d t 3He 4He Li Velocity contour plots and parallel velocity distribution for Ar+Ni at Bin2 window RED hatch areas are QP component • 

  13. Similarity of Quasi-projectiles

  14. Coherent Experimental Evidence for Critical Behavior • The Fisher droplet model analysis • The largest fluctuations c. Fragment hierarchical distribution: nuclear Zipf law d. caloric curve: determination of critical temperature e. critical exponent analysis: universal class of LGPT

  15. Zqp The minimum eff ~ 2.31, close to the Critical Exponent of liquid gas phase transition universal class (~2.23) predicted by the Fisher droplet model! Charge Distribution of QP: Fisher Droplet Model Fisher Droplet Model predicts that there exists a minimum of eff for the charge distributionswhen the phase transition occurs! lines:Fisher Droplet Power-Law fit: dN/dZ ~Z-eff Ref: Fisher, Rep. Prog. Phys. 30, 615 (1969).

  16. Charge Distribution without Zmax of QP Exponential-law fit: dN/dZ’ ~ exp(-effZ’), where Z’ ~ Z but Zmax excluded on the event-by-event basis

  17. The Largest Fluctuation: Campi Plots • Campi plot: • ln(Zmax) vs ln(S2) • (event-by-event) can explore the critical behavior, where Zmax is the charge number of the heaviest fragment and S2 is normalized second moment • Features: • The LIQUID Branch is dominated by the large Zmax • The GAS Branch is dominated by the small Zmax • Critical point occurs as the nearly equal Liquid and Gas branch. The LIQUID Branch Charge of the largest fragment Transition Region 1. LIQUID 2. Critical points The GAS Branch 3. GAS Ref : Campi, J Phys A19 (1988) L917 2nd Normalized moment

  18. Zmax (order paramter) Fluctuation: Normalized Variance of Zmax/ZQP: NVZ =  2/<Zmax> There exists the maximum fluctuation of NVZ around phase transition point by CMD and Percolation model, see: Dorso et al., Phys Rev C 60 (1999) 034606 Total Kinetic Energy Fluctuation: Normalized Variance of Ek/A: NVE = 2(Ek/A)/<Ek/A> The maximum fluctuation of NVE exists in the same E*/A point! A possible relation of Cv to kinetic energy fluctuation was proposed: The Largest Fluctuation of Zmax and Ektot

  19. Universal flucutuation: Δ-Scaling Analysis of Zmax Δ-scaling law is observed when two or more probability distributionsP[m] of the stochastic observable m collapse onto a single scaling curve Φ(z) if a new scaling observable is defined: z =(m-m*)/<m>Δ This curve is: <m>ΔP[m] = Φ(z)= Φ[(m-m*)/<m>Δ] where Δ is a scaling parameter, m* is the most probable value of the variable m, and <m> is the mean of m. Central 25,32,39,45,50MeV/u Semicentral 25,32,39 INDRA: Xe+Sn KNO scaling ~ =1 variable rescaling normalization rescaling increasing energy Semicentral 45,50 + central 39,45,50

  20. Universal flucutuation: Δ-Scaling Analysis of Zmax

  21. Fragment Topological Structure: Zipf plot • Assuming we have M particles in a certain event, we can define Rankn from 1 to M for all particles from Zmax to Zmin. • Rank (n) = 1 if the heaviest fragment • = 2 if 2nd heaviest fragment, • = 3 if 3rd heaviest fragment • and so on • Accumulating all events, we can get the Rank(n) sorted mean atomic number <Zn> for the each corresponding Rank(n), and plot <Zn> vs n. • We called such plot as Zipf-type plot • Nuclear Zipf-type plot reflects the topological structure in fragmentation. • Ref: Y.G. Ma., Phys. Rev. Lett. 83, 3617 (1999) • Original concept was introduced in Language Analysis by G. Zipf . • Later on the similar behaviors were found in the various fields, e.g., the distributions of cities, populations, Market structure, and earthquake strength, and DNA sequence length etc. – Related to Self-organized Criticality

  22. Nuclear Zipf’s Law in Lattice Gas Model It’s consistent with other signatures Zipf-type plot: • Zipf’s law (=1) 129Xe, f=0.38 Ref: Y.G. Ma, Eur. Phys. J. A 6, 367 (1999);

  23. Pb+Pb/Plastic Zipf-law (~1 ) is satisfied

  24. Fragment hierarchical Structure: nuclear Zipf plot Zipf-plots our data Zipf law fit: Zrank ~ rank- NIMROD Data: Zipf-law (~1 ) is satisfied around E*/A ~ 5.6 MeV/u

  25. Zmax-Z2ndMax Correlation (scattering plots) Exc1 Exc2 Exc3 Transition Region Exc6 Exc4 Exc5 Z2ndmax Exc7 Exc8 Exc9 Ref to: Sugawa and Horiuchi, Prog The Phys 105 (2001) 131 Zmax

  26. Zmax-Z2ndMax Correlation (average values)

  27. caloric curve: apparent Kinetic Energy Spectra in the Source Rest Frame; Sorting QP events by ~ 1 MeV/u E*/A window; apparent kinetic temperature apparent isotopic temperature apparent caloric curve

  28. 1. Sequential Decay Dominated Region (LIQUID-dominated PHASE): Tini = (M2T2 –M1T1)/(M2-M1) where M1, T1 and M2, T2 is apparent slope temperature and multiplicity in a given neighboring E*/A window. Ref: K. Hagel et al., Nucl. Phys. A 486 (1988) 429; R. Wada et al., Phys. Rev. C 39 (1989) 497 2. Vapor Phase (Quantum Statistical Model correction): feed-correction for isotopic temperature Tiso Ref: Z. Majka et al., Phys. Rev. C 55 (1997) 2991 3. Assuming vapor phase as an ideal gas of clusters: Tkin = 2/3Ethkin = 2/3(Ecmkin-Vcoul) T0 = 8.3±0.5MeV at E*/A = 5.6 MeV Caloric Curve: initial No obvious plateau was observed at the largest fluctuation point, in comparison with the heavier system! different physics

  29. Determination of the Critical Exponents: ,  ,,  =2.31 dN/dZ Z

  30. Determination of the Critical Exponents: ,  ,, 

  31. Model Comparisons: Lattice Gas Model Classical MD SMM Sequential Decay (Gemini)

  32. Model comparison Lattice gas model (LGM) GEMINI: sequential decay model the hot compound nuclei de-excite via binary decay Ref: R. Charity et al., ,NPA483,371(1988) ------------------------------------------------ Classical Molecular Dynamics model Fragment prescription: Congilio-Klein method P-V phase diagram Ref: Pan, Das Gupta, PRL80, 1182 (1998)

  33. Model Comparisons Model Calculation (A=36, Z=16) • Statistical Evaporation Model: GEMINI (Pink dotted lines) NO PHASE TRANSITION Ref: R. Charity et al., ,NPA • Lattice Gas Model (LGM) (Black lines) • Classical Molecular Dynamics Model (CMD) (LGM+Coulomb) (Red dashed lines) Both with PHASE TRANSITION! Ref: Das Gupta and Pan, PRL Observables vs T scaled by T0: T0(Exp)=8.3 ±0.5MeV (Black Points) T0(GEMINI) = 8.3 MeV T0(LGM) = 5.0MeV T(PhaseTran) T0(CMD) = 4.5MeV T(PhaseTran) Evaporation model fails to fit the Data; Phase Transition Models give a correct trends as Datal!

  34. Model comparisons: Campi plot data  LGM TRANSITION TRANSITION TRANSITION NO TRANSITION CMD GEMINI

  35. Model comparison: Zmax-Z2max correlation LGM data TRANSITION TRANSITION  GEMINI CMD TRANSITION NO TRANSITION

  36. SMM calculation (A=36) (Botvina)

  37. Zmax-Z2max Correl. TRANSITION TRANSITION Campi Plots

  38. CONCLUSIONS (1) The lightest system and the most complete studies in nuclear LGPT experimentally (2) The Maximum Fluctuation Shows around E*/A~5.6MeV/u via: near equal Liquid branch and Gas branch coexists in Campi Plots fluctuation of order parameter (Zmax) fluctuation of total kinetical energy (3) Fragment hierarchical Structures: Zipf’s law , fragment hierarchy, is satisfied around E*/A|crit rather than the equal-size fragment distribution which is predicted by spinodal instablity (1st phase transition) (4) Caloric Curve has no plateau, in comparison with heavier system : E*/A|crit ~ 5.6 ±0.5MeV, T|crit ~ 8.3 ±0.5MeV (5) Fisher Droplet Model and Critical Exponent Analysis: τeff =2.31 0.03 for distribution of Z – close to Critical Exponent of LGPT =0.33 0.01, =1.150.06; =0.680.04 ==> Liquid-Gas Universal Class! (6) Overall good agreements with Phase Transition Model calc. were attained This body of evidence is coherent and suggests a phase change in an equilibrated system at, or extremely close to, the critical point for such light nuclei rather than 1st order phase transition For details, see Y.G. Ma et al., Phys. Rev. C71, 054606 (2005); PRC69, 031604 ( R ) (2004).

  39. NIMROD Collaboration: R. Alfarro,5 J. Cibor,4 M. Cinausero,2 Y. El Masri 6, D. Fabris,3 E. Fioretto,2K. Hagel1, A. Keksis1, T. Keutgen,6M. Lunardon,3Y. G. Ma1,a, Z. Majka,4A.Makeev1,E. Martin1, A.Martinez-Davalos,5 A.Menchaca-Rocha,5 M. Murray1, J.B.Natowitz1, G. Nebbia3, L. Qin1, G. Prete,2 V. Rizzi,3 A.Ruangma1, D. V. Shetty1, P. Smith1, G. Souliotis1, P.Staszel,4 M. Veselsky1, G. Viesti,3R. Wada1, J. Wang1, E. M. Winchester1and S. J. Yennello1 1 Texas A&M University, College Station, Texas 2 INFN Laboratori Nazionali di Legnaro, Legnaro, Italy 3 INFN Dipartimento di Fisica, Padova, Italy 4 Jagellonian University, Krakow, Poland 5 UNAM, Mexico City, Mexico 6 UCL, Louvain-la-Neuve, Belgium a Shanghai Insititute of Applied Physics, Shanghai Acknowledgements

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