Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing 1 Coherent signals of the critical behavior in light...
-
Upload
shanna-maxwell -
Category
Documents
-
view
214 -
download
1
Transcript of 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
1
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
2
outline
• Motivation
• Experimental set-up: NIMROD and some analysis details
• Coherent evidence of critical behavior • Model comparisons
• Conclusions
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
3
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
4
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
5
Brief Description of Brief Description of the Experimental the Experimental
Set-up: Set-up:
Texas A&M NIMRODTexas A&M NIMROD
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
7
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
8
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
9
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
10
A New Method to A New Method to Reconstruct Reconstruct
Quasi-ProjectileQuasi-Projectile
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
11Vpar (cm/ns)
Vp
er (
cm/n
s)
Bin5-Peripheral Bin4
Bin3 Bin2
Bin1-Central
Velocity contours of protons
Vini
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
12
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
13
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
14
Similarity of Quasi-projectiles
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
15
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
16
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!
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
17
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
18
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
19
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:
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
20
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.
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
21
Universal flucutuation: Δ-Scaling Analysis of Zmax
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
22
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
23
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:
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
24
Pb+Pb/Plastic
Zipf-law (~1 ) is satisfied
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
25
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
26
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
27
Zmax-Z2ndMax Correlation (average values)
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
28
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
29
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
30
Determination of the Critical Exponents: , ,,
Z
dN
/dZ
=2.31
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
31
Determination of the Critical Exponents: , ,,
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
32
Model Model Comparisons:Comparisons:Lattice Gas ModelLattice Gas Model
Classical MDClassical MD
SMMSMM
Sequential Decay (Gemini)Sequential Decay (Gemini)
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
33
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
34
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!
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
35
Model comparisons: Campi plotdata
GEMINI
LGM
CMD
TRANSITIONTRANSITION
TRANSITION
NO TRANSITION
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
36
Model comparison: Zmax-Z2max correlation
data
GEMINI
LGM
CMD
TRANSITION
TRANSITION
TRANSITION
NO TRANSIT
ION
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
37
SMM calculation (A=36) (Botvina)
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
38
Campi Plots
Zmax-Z2max Correl.TRANSITION
TRANSITION
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
39
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).
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
40
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
Y. G. Ma, CCAST Workshop, Aug 19-21, Beijing
41