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