Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing 1 Coherent signals of the critical behavior in light...

Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing

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Coherent signals of the critical behavior Coherent signals of the critical behavior in light nuclear systemsin light nuclear systems

Yu-Gang Ma Shanghai Institute of Applied Physics (SINAPSINAP), 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,6 M. Lunardon,3 Y. 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,3 R. 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


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outline

• Motivation

• Experimental set-up: NIMROD and some analysis details

• Coherent evidence of critical behavior • Model comparisons

• Conclusions


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Introduction (I): Phase Transition in Nuclei

Liquid Gas Phase Transition from cool nuclei to the full disassembly of nuclei Isis Data: 8-10GeV/c - , p+AuLabs: MSU-Miniball, TAMU-Nimrod, Indiana U-Isis, GANIL-Indra,GSI-Aladin, Catania-Chimera

Quark-Gluon Phase Transition ： from Hadronic Matter to QGPRHIC Detectors:

STAR, PHENIX, PHOBOS, BRAHMS

Recent results: dAu vs AuAu

ISiS

STAR

Central Collisions130GeV/c Au+Au


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Motivation

Ref: J. Elliott et al., Phys. Rev. Lett. 88 (2002) 042701

J.Natowitz, K. Hagel, Y.G. Ma et al., Phys Rev Lett 89, 212701 (2002); arXiv:nucl-ex/0206010

Limiting Temperatures

Nucleonic MatterTc

Nuclear Matter Tc


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Brief Description of Brief Description of the Experimental the Experimental

Set-up: Set-up:

Texas A&M NIMRODTexas A&M NIMROD


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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


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Reaction systems

• 47MeV/u Ar + Al, Ti and Ni• Complete events of central collisions are ch

osen • 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


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Event Selection: central collisions

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

Ar+Ni

Central collisions

Peripheral collisions

Nearly Complete Event


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A New Method to A New Method to Reconstruct Reconstruct

Quasi-ProjectileQuasi-Projectile


11Vpar (cm/ns)

Vp

er (

cm/n

s)

Bin5-Peripheral Bin4

Bin3 Bin2

Bin1-Central

Velocity contours of protons

Vini


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A new method to reconstruct QP

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.

deutrons tritons

6.4º

18.2º

32.1º

61.2º

120º

Previous methods to reconstruct the Quasi-projectile:

(1) Selected very peripheral collisions;(2) velocity cut: assuming the particles whose v

elocities 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!

3 source fits: red: QP, blue:NN, pink:QT


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QP Source Reconstruction and Determination of E*/A

Mixed QP Vparp

d

t

3He

4He

Li

Velocity contour plots and parallel velocity distribution for Ar+Ni at Bin2 window

RED hatch areas are QP component

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


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Similarity of Quasi-projectiles


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Coherent Experimental EvidCoherent Experimental Evidence for Critical Behaviorence for Critical Behavior

a. The Fisher droplet model analysisb. 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


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Charge Distribution of QP: Fisher Droplet Model

• Zqp

The minimum The minimum effeff ~ 2.31, close to the Critical Exponent of ~ 2.31, close to the Critical Exponent of

liquid gas phase transition universal class (~2.23) preliquid gas phase transition universal class (~2.23) predicted by the Fisher droplet model!dicted by the Fisher droplet model!

1 2 3 4 5 6 7 8 92

3

5.85.96.06.16.26.36.46.5

eff

E*/A (MeV)

lines: Fisher Droplet Power-Law fit: dN/dZ ~Z-eff

Ref: Fisher, Rep. Prog. Phys. 30, 615 (1969).

Fisher Droplet Model predicts that there exists a minimu

m of eff for the charge distributions when the phase transition occurs!


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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


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The Largest Fluctuation: Campi Plots

Ref : Campi, J Phys A19 (1988) L917

Campi plot:

ln(Zmax) vs ln(Sln(Zmax) vs ln(S22)) (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

The GAS Branch

Transition Region

Ch

arg

e o

f th

e la

rges

t fr

agm

ent

2nd Normalized moment

1. LIQUID

3. GAS

2. Critical points


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The Largest Fluctuation of Zmax and Ektot

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:


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Universal flucutuation: Δ-Scaling Analysis of Zmax

Central 25,32,39,45,50MeV/u

Semicentral 25,32,39

Semicentral 45,50 + central 39,45,50

INDRA: Xe+Sn

KNO scaling ~ =1

variable rescaling

normalization rescaling

increasing energy

Δ-scaling law is observed when two or more probability distributions P[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.


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Universal flucutuation: Δ-Scaling Analysis of Zmax


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Fragment Topological Structure: Zipf plot

• Assuming we have M particles in a certain event, we can define Rank n 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 R

ank(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 topolo

gical structure in fragmentation.

Ref: Y.G. Ma., Y.G. Ma., Phys. Rev. Lett.Phys. Rev. Lett. 83, 3617 (1999) 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


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Nuclear Zipf’s Law in Lattice Gas Model

Ref: Y.G. Ma, Eur. Phys. J. A 6, 367 (1999);

129Xe, f=0.38

•Zipf’s law (=1)It’s consistent with

other signaturesZipf-type plot:


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Pb+Pb/Plastic

Zipf-law (~1 ) is satisfied


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Fragment hierarchical Structure: nuclear Zipf plot

Zipf law fit:

Zrank ~ rank-

NIMROD Data: Zipf-law (~1 ) is satisfied around E*/A ~ 5.6 MeV/u

Zipf-plots

our data


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Zmax-Z2ndMax Correlation (scattering plots)

Exc1 Exc2 Exc3

Exc4 Exc5 Exc6

Exc7 Exc8 Exc9

Z2n

dm

ax

Zmax

Transition Region

Ref to: Sugawa and Horiuchi, Prog The Phys 105 (2001) 131


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Zmax-Z2ndMax Correlation (average values)


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caloric curve: apparent Kinetic Energy Spectra in the Source Rest Fra

me; Sorting QP events by ~ 1 MeV/u E*/A window;

apparent kinetic temperature

apparent isotopic temperatureapparent isotopic temperature

apparent caloric curve


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Caloric Curve: initialCaloric Curve: initial1. Sequential Decay Dominated Region

(LIQUID-dominated PHASE): Tini = (M2T2 –M1T1)/(M2-M1) where M1, T1 and M2, T2 is apparent sl

ope 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(Ecm

kin-Vcoul)

T0 = 8.3±0.5MeV at E*/A = 5.6 MeV No obvious plateau was observed at the No obvious plateau was observed at the largest fluctuation point, in comparison largest fluctuation point, in comparison with the heavier system! different physicswith the heavier system! different physics


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Determination of the Critical Exponents: , ,,

Z

dN

/dZ

=2.31


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Determination of the Critical Exponents: , ,,


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Model Model Comparisons:Comparisons:Lattice Gas ModelLattice Gas Model

Classical MDClassical MD

SMMSMM

Sequential Decay (Gemini)Sequential Decay (Gemini)


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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 modelFragment prescription: Congilio-Klein method

Ref: Pan, Das Gupta, PRL80, 1182 (1998)

P-V phase diagram


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Model ComparisonsModel 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!


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Model comparisons: Campi plotdata

GEMINI

LGM

CMD

TRANSITIONTRANSITION

TRANSITION

NO TRANSITION


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Model comparison: Zmax-Z2max correlation

data

GEMINI

LGM

CMD

TRANSITION

TRANSITION

TRANSITION

NO TRANSIT

ION


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SMM calculation (A=36) (Botvina)


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Campi Plots

Zmax-Z2max Correl.TRANSITION

TRANSITION

ma


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CONCLUSIONS(1) The lightest system and the most complete studies in nuclear LGPT experimentall

y (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, =1.150.06; =0.680.04 ==> Liquid-Gas Universal Class!

(6) Overall good agreements with Phase Transition Model calc. were attainedThis body of evidence is coherent and suggests a phase change in an equilibrated syst

em 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).


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AcknowledgementsNIMROD 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,6 M. Lunardon,3 Y. 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,3 R. Wada1, J. Wang1, E. M. Winchester1 and 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, Mexico6 UCL, Louvain-la-Neuve, Belgium

a Shanghai Insititute of Applied Physics, Shanghai


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Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing 1 Coherent signals of the critical behavior in light...

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