j. b. natowitz department of chemistry and cyclotron institute, texas a&m university, college...
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J. B. Natowitz Department of Chemistry and Cyclotron Institute , Texas A&M University, College Station
Experimental Investigations of The Equation of State of Low Density Nuclear Matter
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Exploring The Nuclear Matter Phase Diagram With Collisional Heating
• Collisions of normal density nuclei create initially compressed and excited systems, which expand and cool.
• During this process, the properties of the expanding system is manifested in the matter flow, in the energy spectra, and in the yield patterns and nature of produced species which emerge from the collision zone.
THERMAL SHOCK COMPRESSION
FREEZEOUT
SEPARATION
SECONDARY EMISSION
EXPANSIONPRE-EQUILIBRIUM EMISSIONEQUILIBRIUM EMISSION ?
AMD Calculation
TI
ME
• Dynamic Evolution
• Excitation Energy ?
• Temperatures ?
• Degree of expansion
• Composition ?
• Chemical and Thermal Equilibrium ?
• Equation of State ?
• Liquid-gas phase transition?
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Light Charged Particle Emission - High Total Multiplicity Collisions
NIMROD4 Pi Charged Particles4 Pi Neutrons
THERMAL SHOCK COMPRESSION
FREEZEOUT
SEPARATION
SECONDARY EMISSION
EXPANSIONPRE-EQUILIBRIUM EMISSIONEQUILIBRIUM EMISSION ?
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Event Selection
Neutron + Charged Particle multiplicity distribution for 64Zn+124Sn. Bin4 corresponds to the most violent
collision events
Most Violent Collision Events
@ 30% Top Highest Multiplicity
Mn
MCP
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Source Analysis of Emission ( Energy, Angle)
Source Fitting – 4He from 40Ar + 124Sn
PLF
1 2 3
10
4
7
5 6
98
1211
Angular Distribution
NN TLF
Elab, MeV
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Reaction Tomography-Particles
TLF
NN
Experiment
From Fitting
Velocity Plot Protons 40Ar+124Sn PLF
V parallel
V p
erpe
ndic
ular
Evaporation-like
Evaporation-like
Coalescence
NN
Sum of Sources
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12
14
16
18
20
22
0 50 100 150 200 250
A
Tcri
t, M
eV
TC =16.6 0.86 MeV
Critical Temperature of Symmetric Nuclear Matter
Phys.Rev.Lett. 89 (2002) 212701Phys.Rev. C65 (2002) 034618
employing Skyrme interactions with the = 1/6 density dependence,
this value of Tc leads to K = 232 22 MeV.
Using Gogny interactions with = 1/3 leads to K = 233 37 MeV.
These results for K lead to m* value = 0.674 A value of K = 231 5 MeV, was derived by D. H. Youngblood, H. L. Clark, and Y.-W. Lui, Phys. Rev. Lett. 82, 691 (1999) by comparison of data for the GMR breathing mode energy of five different nuclei.
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K. Hagel et al. Phys. ReV. C 62 034607 (2000)
J.B. Natowitz et al., Phys.Rev. C 66 031601 (2002)
Derived Average Freeze-Out Densities
Coalescence Model Non-Dissipative
Analyses Expanding Fermi Gas 47A MeV
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R ~ 10 km
SUPERNOVA
NEUTRON STAR
STARS Giant NucleiAnd Sites of Nucleosynthesis
Large Changes in Temperature, Density, Proton/Neutron content
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C.J. Horowitz, A. Schwenk nucl-th/0507033
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Alpha Particle Mass Fraction vs Density
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.0001 0.001 0.01 0.1Density, fm-3
X a
lph
a
Shen-Toki T = 4 Yp = 0.45
Shen-Toki T = 5
Shen-Toki T = 8
Lattimer SKM* T = 5.03 Yp = 0.5
Lattimer T = 8.05 SKM*
ASTROPHYSICAL EQUATIONS OF STATE AT LOW DENSITY DOMINATED BY ALPHA CLUSTERING
Density
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Cluster Formation and The Equation of State of Low-Density Nuclear Mattersymmetric nuclear matter, T=2, 4, 8 MeV C.J. Horowitz, A. Schwenk nucl-th/0507033
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. nucl-th/0507064 The Virial Equation of State of Low-Density Neutron Matter C.J. Horowitz and A. Schwenk
Clustered Gas VEOS
SF
SE
T/2
T/2
Skyrme, Fermi gas etc.
SYMMETRY ENERGY(T,)
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Many Nucear and Astrophysical Phenomena Strongly Affected by the Symmetry Energy
At Normal Density aa ~ 23 MeV for Finite Nuclei ~30 MeV for Symmetric Nuclear Matter
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V perpendicu
lar
S c h e m a t ic V e lo c i t y P lo t -I n t e r m e d ia t e E n e r g y H e a v y I o n C o l l is io n A s y m m e t r i c E n t r a n c e C h a n n e lE a r l y E m is s io n N N -L i k e
E a r l y E m is s io nP r o je c t i l e -L ik e
V p
erp
en
dic
ula
r
Schematic Veloc ity P lot-Intermediate Energy Heavy Ion Collis ion A symmetric Entranc e Channel
Early Emiss ion N N -L ike
E arlyE miss ionP rojec tile-L ike
EARLY EMISSION TOTAL MASS in Z=1,2 Charged
Particles 47A MeV Projectiles on 124Sn
0
5
10
15
20
25
30
35
0 20 40 60 80
A projectile
Acp
(Z=
1-,2
) 124 EXPT ACPCentral NN + PLFChimera ACP R=3 300fm/cAMD ACP 2300 fm/c
NN SOURCE EMISSION- Experimental Data and Calculated Yields from AMD and Chimera QMD Codes
Average Freeze-out Density 64Zn + 124Sn ~ 0.06 fm-3
“Gas” density ~ ANN/(Atot-ANN) * 0.06 fm-3
~ 0.01 fm-3
COALESCENCE
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Isoscaling Analyses and Symmetry Energy
A Comparison of the Yields of Emitted Species for Two Different Sources of Similar Excitation Energy and Temperature but Differing in Their Neutron to Proton Ratios
M.B. Tsang, W.A. Friedman, C.K. Gelbke, W.G. Lynch, G. Verde and H.S. Xu, Phys.Rev. C64 (2001) 041603
Fsym
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T
α ═ (4F/T)[(Z/A)21 – (Z/A)2
2]
n = 0.62 x 1036 T3/2 exp[- 20.6/T] Y(4He)/ Y(3He) cm-3
p = 0.62 x 1036 T3/2 exp[ -19.8/T] Y(4He)/ Y(3H) cm-3
nuc tot = p + n + 2d + 3t + 33He + 4
Density
LOW DENSITY CHEMICAL EQUILIBRIUM MODEL(Albergo)
43
/surf
YdYHeYtYHeV R
Temperature
THHe = 14.3/ [ln (1.59R)]R = [ YR = [ Yd d ] [ Y] [ Y44He He ]]
[ Y[ Yt t ] [ Y] [ Y33He He ]]
Isoscaling Analyses and Symmetry Energy
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Clusterization in Low Density Nuclear Matter
0
5
10
15
20
25
30
35
0.001 0.01 0.1 1
Rho , nuc/fm3
Esym
, MeV
Expt
Gogny
1̂.05
HS calc
Density corr
Poly. (HS calc)
Poly. (Densitycorr)
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C.J. Horowitz, A. Schwenk nucl-th/0507033
Private Communication O’Connor, Schwenk, Horowitz Manuscript in Preparation August 2007
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Neutron Rich
Proton Rich
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• p + 112Sn and 124Sn • d + 112Sn and 124Sn • 3He + 112Sn and 124Sn • 4He + 112Sn and 124Sn • 10B + 112Sn and 124Sn • 20Ne + 112Sn and 124Sn • 40Ar + 112Sn and 124Sn • 64Zn+ 112Sn and 124Sn
Projectile Energy - 47A Mev
Reaction System ListThesis – L. Qin TAMU
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||V
||V
Vpar cm/ns
Vp
e rp c
m/ n
s
Significant Temperature Evolution With Velocity Relatively Small Changes with Projectile Size
DOUBLE ISOTOPE RATIO THHe
CHEMICAL EQUILIBRIUM TEMPERATURES
THHe = 14.3/ [ln (1.59R)](albergo)
R = [ YR = [ Yd d ] [ Y] [ Y44He He ]] [ Y[ Yt t ] [ Y] [ Y33He He ]]
Reaction Tomography-Temperatures
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“Gas” DensityTLF REMOVED
L. Qin – PhD Thesis, In Progress
CHEMICAL EQUILIBRIUM DENSITIES (Albergo) FROM ISOTOPE RATIOS
Fm-3
Reaction Tomography-Densities
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1 4 7 10 13 16 19 22 25 28 31 34 37 40 43
S1
S4
S7
S10
S13
S16
S19
25-30
20-25
15-20
10-15
5-10
0-5
1 5 9 13 17 21 25 29 33 37 41 45
S1
S4
S7
S10
S13
S16
S19
25-30
20-25
15-20
10-15
5-10
0-5
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43
S1
S4
S7
S10
S13
S16
S19
25-30
20-25
15-20
10-15
5-10
0-5
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43
S1
S4
S7
S10
S13
S16
S19
25-30
20-25
15-20
10-15
5-10
0-5
-6.2
5
-4.7
5
-3.2
5
-1.7
5
-0.2
5
1.2
5
2.7
5
4.2
5
5.7
5
7.2
5
8.7
5
10
.25
11
.75
13
.25
14
.75
10.25
8.75
7.25
5.75
4.25
2.75
1.25
4He Fsym
25-30
20-25
15-20
10-15
5-10
0-5
64Zn
40Ar20Ne
10B
4He DERIVED VALUES OF Fsym
as a FUNCTION of VELOCITY
47 MeV/u Projectiles on 112Sn, 124Sn
V parallel
NN
V p
erp
end
icu
lar
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F sym Roepke Calculation 4 April 08
0
5
10
15
20
25
30
35
40
0.0001 0.001 0.01 0.1 1 10
density, fm-3
F s
ym,
MeV Roepke T = 4 Fsym
Roepke T = 6
Roepke T = 10
Gogny D1S T = 0
31.6(rho/rho0)^0.69
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F sym Roepke Calculation 4 April 08
0
5
10
15
20
25
30
35
40
0.0001 0.001 0.01 0.1 1 10
density, fm-3
F s
ym,
MeV Roepke T = 4 Fsym
Roepke T = 6
Roepke T = 10
Qin NN
Gogny D1S T = 0
31.6(rho/rho0)^0.69
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K. Hagel et al. PHYSICAL REVIEW C 62 034607 (2000)
J.B. Natowitz et al., Phys.Rev. C66 (2002) 031601
Derived Average Freeze-Out Densities
Coalescence Model Non-Dissipative
Analyses Expanding Fermi Gas
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F sym Roepke Calculation 4 April 08
0
5
10
15
20
25
30
35
40
0.0001 0.001 0.01 0.1 1 10
density, fm-3
F s
ym,
MeV
Roepke T = 4 Fsym
Roepke T = 6
Roepke T = 10
Qin NN
Gogny D1S T = 0
31.6(rho/rho0)^0.69
He-Zn + Sn TLF at Liquid Densities
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F sym Roepke Calculation 4 April 08
0
5
10
15
20
25
30
35
40
45
0.0001 0.001 0.01 0.1 1 10
density, fm-3
F s
ym,
MeV
Roepke T = 4 Fsym
Roepke T = 6
Roepke T = 10
Qin NN
Gogny D1S T = 0
31.6(rho/rho0)^0.69
He-Zn + Sn TLF at Liquid Densities
Liquid scaled to NMDanielewiczEsym(nuclides) = Esym(NM)
(1 + 2.7/A 1/3)
P. Danielewicz
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Few Body Syst.Suppl. 14 (2003) 361-366 Eur.Phys.J. A22 (2004) 261-269
M. Beyer, G. Roepke et al., Phys.Lett. B488, 247-253 (2000)
IN MEDIUM BINDING ENERGIES and MOTT TRANSITION
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Alpha Mass Fractions
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0001 0.001 0.01 0.1
Shen-Toki T = 4 Yp = 0.45Shen-Toki T = 5 Shen-Toki T = 8Roepke T = 4 Yp = 0.42Roepke T = 5 Roepke T = 8 Series6Series8Series9
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Multiplicities with Free Cluster Bindiing Energies (Albergo model-like)T= 10 MeV, A = 250
0.01
0.1
1
10
100
1000
0 0.05 0.1 0.15
Density nucleons/fm3
Mu
ltip
lici
ty
Nucleons
d
t + 3He
4He
Beyer Model Multiplicities( In Medium Binding Energies)
T= 10 MeV A = 250
0.01
0.1
1
10
100
1000
0 0.05 0.1 0.15
Density, nucleons/fm3
Mu
ltip
licit
y
Nucleons
d
T + 3He
4He
Note: Same at low densityRho LE ~.005 fm-3
M. Beyer et al. nucl-th/0310055
Light Clusters in Nuclear Matter of Finite
Temperature
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Calculated Density vs Roepke DensityFree Binding Energies
0
0.005
0.01
0.015
0.02
0 0.005 0.01 0.015
Density fm-3
Calc
. Den
sity
fm
-3 T = 4T = 5T = 8T = 4T = 5T = 8Series4
Calculated.Temperature vs Roepke Density Free Binding Energies
0
2
4
6
8
10
12
0.0001 0.001 0.01 0.1
Roepke Density fm-3
Cal
c. T
M
eV
Series1
Series2
Series3
T = 4
T = 5
T = 8
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Correlations Bose Condensates Superfluidity Efimov States
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E. Bell1, M. Cinausero2, Y. El Masri 6,D. Fabris3, K. Hagel1, J. Iglio1, A. Keksis1, T. Keutgen6, M. Lunardon3, Z. Majka4, A. Martinez-Davalos,5 A. Menchaca-Rocha5, S. Kowalski1,T. Materna1, S. Moretto3, J. B. Natowitz1, G. Nebbia3, L. Qin1, G. Prete,2 R. Murthy1, S. Pesente3, V. Rizzi,3 D. V. Shetty1, S. Soisson1, B. Stein1, G. Souliotis1, P. M. Veselsky1,A. Wieloch1, G. Viesti3, R. Wada1, J. Wang1, S. Wuenshel1, and S. J. Yennello1
1Texas A&M University, College Station, Texas 2INFN Laboratori Nazionali di Legnaro, Legnaro, Italy 3INFN Dipartimento di Fisica, Padova, Italy 4Jagellonian University, Krakow, Poland 5UNAM, Mexico City, Mexico 6UCL, Louvain-la-Neuve, Belgium
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Major Contributors
• M. Barbui, A. Bonasera, C. Bottosso, M. Cinausero, Z. Chen, D. Fabris, Y. El Masri, K. Hagel, T. Keutgen, S. Kowalski, M. Lunardon, Z. Majka, S. Moretto, G. Nebbia, J. Natowitz L. Qin, S. Pesente, G. Prete, V. Rizzi, P. Sahu, S. ShlomoJ. Wang, G. Viesti
• S. Shlomo, A. Ono, G. Roepke
• A. Schwenk, E. O’ConnorAND THE NIMROD COLLABORATION
•TAMU, PADOVA, LEGNARO, KRAKOW, LOUVAIN la NEUVE, CATANIA, LANZHOU