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Low Density Nucleonic Matter in Fermi Energy Collisions. J.B. Natowitz. Few Body Syst.Suppl. 14 (2003) 361-366 Eur.Phys.J. A22 (2004) 261-269. Perfect Liquid?. Perfect Gas ?. Correlations – Cluster Formation Bose Condensates Efimov States Superfluidity. - PowerPoint PPT Presentation
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J.B. Natowitz
Correlations – Cluster Formation Bose Condensates Efimov States Superfluidity
PerfectLiquid?
PerfectGas ?
Few Body Syst.Suppl. 14 (2003) 361-366 Eur.Phys.J. A22 (2004) 261-269
The Symmetry Energy Problem
Constraining the density dependence of the symmetry energy is a complex problem-
The Nuclei Always Solve the Problem Exactly For Us There is always a model dependence
Requires close synergy between theorists and experimentalists
While low density situation would appear to be easier to constrain- cluster formation changes the
medium (leads to additional complexity opportunity)
Lattimer SKM* Alpha Mass Fraction (T)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.E-06 1.E-04 1.E-02 1.E+00
Density nucl/fm3
Alp
ha
Mas
s F
ract
ion
2.16
3.14
4.17
5.03
6.07
7.33
8.05
8.84
9.71
10.67
11.72
12.88
14.14
15.54
17.07
18.75
20.6
Relativistic Equation of State of Nuclear Matter for Supernova and Neutron StarH.Shen, H.Toki, K. Oyamatsu and K. Sumiyoshi Nucl.Phys. A637 (1998) 435-450
Cluster Formation and The Virial Equation of State of Low-Density Nuclear Matter C.J. Horowitz and A. Schwenk Nucl. Phys. A776 (2006) 55-79
Cluster Formation and The Equation of State of Low-Density Nuclear Matter
Data- Kowalski et al., Phys. Rev. C, 75 014601 (2007)
Calculation -Private Communication – O’Connor, Schwenk, Horowitz 2008
C. J. Horowitz and A. Schwenk nucl-th/0507033
Calculation -Private Communication – O’Connor, Schwenk, Horowitz 2008
What is the composition, EOS and neutrino response of nuclear matter near the neutrinosphere?
Light Charged Particle Emission Studies
• 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
NIMROD4 Pi Charged Particles4 Pi Neutrons
Thesis – L. Qin TAMU- 2008
Reaction System List
Velocity PlotsLight Charged Particles
TLF
NN
Experiment
From Fitting
Velocity Plot Protons 40Ar+124Sn
PLF
V parallel
V p
erpe
ndic
ular NN
Sum of Source Fits
Sampling the GAS-early emission faster particles
Sampling the Liquid – late emission
Evaporation-like
Fsym ═ αT / {(4)[(Z/A)21 – (Z/A)2
2]}
lABLIQUID
GAS
Reaction Tomography
ISOSCALING ANALYSIS
TRANSPORT CALCULATIONSFor Us - Antisymmetrized Molecular Dynamics - ONO Constrained Molecular Dynamics - Bonasera
NUCLEAR MATTER CALCULATIONSBeth-Uhlenbeck Cluster Mean Field Approach- Roepke
Tsang et al.
There is always a model dependence
“The Quantum Nature of a Nuclear Phase Transition. A. Bonasera ,Z. Chen , R. Wada , K. Hagel , J. B. Natowitz, P. Sahu ,
L. Qin , S. Kowalski , Th. Keutgen, T. Materna ,T. Nakagawa, “ Physical Review Letters, 101. 122702 (2008)
L.Qin et al. In Progress
Data - Surface, T Corrected
LIQUID
K. Hagel et al. Phys. ReV. C 62 034607 (2000)
J.B. Natowitz et al., Phys.Rev. C 66 031601 (2002)
Average Density Determination Coalescence Model Non-Dissipative
Analyses Expanding Fermi Gas Model 47A MeV
LIQUID REGION
Clusterization in Very 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)
PRC 75, 014601 (2007)
ρn = 0.0062 x 1036 T3/2 exp[- 20.6/T] Y(4He)/ Y(3He) fm-3
ρ p = 0.0062 x 1036 T3/2 exp[ -19.8/T] Y(4He)/ Y(3H) fm-3
ρ nucl tot = ρ p + ρ n + 2 ρ d + 3 ρ t + 3 ρ 3He + 4 ρ α
Density
LOW DENSITY CHEMICAL EQUILIBRIUM MODEL(Albergo)
Temperature THHe = 14.3/ [ln (1.59R)]
[ Y[ Yd d ] [ Y] [ Y44He He ] ] [ Y[ Yt t ] [ Y] [ Y33He He ]]
LCP Isoscaling Analyses and Symmetry Energy
R R ==
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
K, fm-1
Bin
din
g E
ner
gy,
MeV
Medium Modifications - Gerd Roepke et al. Work in Progress
Free B.E.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.0001 0.001 0.01 0.1
Yp = 0.5 Horo
Roepke T = 5
Lattimer Skm* T = 5
Shen-Toki T = 5
Virial with A=3, T = 5
Liquid upper Limit
AlphaMassFraction
Density nuc/fm3
Virial (no A=3) T = 5A=3 Included
No Medium Effects
Medium Effects
No Additional Momentum of cluster relative to the medium
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
Temperature CorrectionsSurface Corrections
GAS
LIQUID
L.Qin et al. In Preparation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.0001 0.001 0.01 0.1
Yp = 0.5 Horo
Roepke T = 5
Lattimer Skm* T = 5
Shen-Toki T = 5
T = 5 Xa EXPT
Virial with A=3, T = 5
Liquid upper Limit
Poly. (T = 5 Xa EXPT)
Virial Orig T=5
Density nuc/fm3
AlphaMassFraction
K, fm-1
Bin
din
g E
ner
gy,
MeV
Why Mott Point Not Seen? Effect of Momentum Relative to the Medium ?
Free B.E.
Isoscaling Evolution IMFs were measured by a Si quadrant telescope, backed by four CsI
detectors (3cm) at 20°. The Si telescope consisted of four 5cm x 5cm area detectors, having thicknesses
129µm+300µm+1000µm+1000µm (021705 run)
61µm+300µm+1000µm+1000µm (040805 run &060605 run)
Fig. 1 CsI detectors Fig. 3 Demon detectors (right)Fig. 2 Demon detectors (left)
Z. Chen, R. Wada, M. Huang et al ---in ProgressSee Talk of Z. Chen
(1) 021705 40 AMeV 64Zn beam on 58Ni, 64Ni, 112Sn, 124Sn, 197Au targets
(2) 040805 40 AMeV 64Zn beam on 112Sn target
40 AMeV 70Zn beam on 58Ni, 64Ni, 112Sn, 124Sn, 197Au, 232Th targets
(3) 060605 40 AMeV 64Ni beam on 58Ni, 64Ni, 112Sn, 124Sn, 197Au, 232Th targets
Reaction systems studied
Isotope resolution
Z=4
Z=6
Z=8
Z=10
Fig. 4 Isotopes for Z=3 to 12 have been clearly identified in all Si-Si combinations
Fig. 5 Linearized Z distribution
Isoscaling Evolution from AMD.Y(64Ni+124Sn)/ Y(64Zn+112Sn)
Time=2000 fm/cTime=300 fm/c
Fragment –Particle Correlations to Explore Effects of Secondary Decay
S. Hudan et al.
40 MeV/u 64Zn + 112SnSecondary Neutron Multiplicities 6 cm/ns Telescope 0
Preliminary Data
9Li
7Be
10B
12B
13B
12C
15O
16O17O
18O
19O20O
17F
18F
21F
19Ne
20Ne
21Ne
22Ne 23Na
24Na
25Na
24Mg
27Al
27Si
28Si
30Si
31P
32S
20F19F
26Al 28Al8Li
7Li6Li8B12Be
11Be10Be
9Be
11B
11C13C
16C
14C
15C
13N
14N
15N
17N
16N
18N
24Ne20Na
21Na
22Na23Ne
22F26Na
23Mg22Mg
25Mg
26Mg27Mg
28Mg 29Al
29Si
0
1
2
3
4
5
6
7
8
9
10
Z,A
Mul
tiplic
ity
6 cm/ns
Z. Chen, R. Wada, M. Rodrigues et al. Work in Progress
• M. Barbui, A. Bonasera. C. Bottosso, M. Cinausero, Z. Chen, Y. El Masri, D. Fabris, K. Hagel, S. Kimura, T. Keutgen, S. Kowalski, M. Lunardon, Z. Majka, S. Moretto, G. Nebbia, J.
Natowitz, A. Ono, L. Qin, S. Pesente, G. Prete, V. Rizzi, M. Rodrigues, G. Roepke, P. Sahu, S. Shlomo, R. Wada, J. Wang, G. Viesti
Texas A&M, Padova, Legnaro, Krakow, Katowice,Louvain la Neuve, Lanzhou
Texas A&M University, College Station, Texas INFN Laboratori Nazionali di Legnaro, Legnaro, Italy INFN Dipartimento di Fisica, Padova, Italy Jagellonian University, Krakow, Poland UCL, Louvain-la-Neuve, Belgium
Figure 2. The alpha-particle clusterstructure of the Hoyle-state in 12C, aspredicted using Fermionic MolecularDynamics (M. Chernykh, et al., Phys.Rev. Lett. 98, 032501 (2007)).
We Hope To Be Able To Welcome Y’ALL to
NN2012 In San Antonio, Texas
Torch-of-Friendship
River-Walk-
Dining
Shrine of Texas Liberty
Henry B. Gonzalez Convention Center
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
Fig. 9 Isotopic yield ratios for 64Ni+124Sn/64Zn+112Sn are shown for α parameter (upper) and β(lower).
Fig. 10 Similar plot as Fig.9, but for (64Ni+197Au )/ (64Ni+112Sn)
summary
Exp. AMD
300fm/c
AMD
2000fm/c
LP, NN,
Y(64Ni+124Sn)/ Y(64Zn+112Sn)
α = 0.31+/- 0.10
β = -0.40+/- 0.18
α = 0.35+/- 0.04
β = -0.43+/- 0.07
α = 0.26+/- 0.02
β = -0.30+/- 0.04
LP, NN+PLF,
Y(64Ni+124Sn)/ Y(64Zn+112Sn)
α = 0.34+/- 0.10
β =- 0.39+/- 0.18
LP, with coulomb
Y(60Ca+60Ca)/ Y(40Ca+40Ca)
α = 3.08+/- 0.21
β = -4.09+/- 0.31
α = 2.17+/- 0.07
β = -2.34+/- 0.10
LP, without coulomb
Y(60Ca+60Ca)/ Y(40Ca+40Ca)
α =1.36 +/- 0.13
β = -2.84+/-0.12
α = 1.70+/- 0.04
β = -2.37+/-0.08
LP, Lijun’s exp.
Y(40Ar+124Sn)/ Y(40Ar+112Sn)
α = 0.41+/- 0.10
β = -0.49+/-0.11
IMF,
Y(64Ni+124Sn)/ Y(64Zn+112Sn)
α = 0.28+/- 0.01
β = -0.30+/-0.01
α = 0.42+/- 0.10
β = -0.56+/-0.13
α = 0.29+/- 0.10
β = -0.36+/-0.13
IMF, with coulomb
Y(60Ca+60Ca)/ Y(40Ca+40Ca)
α = 3.39+/-3.64
β = -5.07+/-4.40
α =1.88 +/- 0.42
β = -2.33+/-0.21
IMF, without coulomb
Y(60Ca+60Ca)/ Y(40Ca+40Ca)
α = 3.19+/- 0.51
β = -4.40+/-0.59
α = 1.66+/-0.22
β = -1.79+/-0.31
IMF, Lijun’s exp.
Y(40Ar+124Sn)/ Y(40Ar+112Sn)
α = 0.31+/- 0.25
β = -0.43+/-0.34
Experimental setup
IMFs were measured by a Si quadrant telescope, backed by four CsI detectors (3cm) at 20°. The Si telescope consisted of four 5cm x 5cm area detectors, having thicknesses
129µm+300µm+1000µm+1000µm (021705 run)
61µm+300µm+1000µm+1000µm (040805 run &060605 run)
Fig. 1 CsI detectors Fig. 3 Demon detectors (right)Fig. 2 Demon detectors (left)
See Talk of Z. Chen
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