J. B. NatowitzCCAST Workshop, Beijing August 2005

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, J. B. Natowitz1, G. Nebbia3, L. Qin1, G. Prete,2 R. Murthy1, V. Rizzi,3 D. V. Shetty1, S. Soisson1, B. Stein1, G. Souliotis1, P. M. Veselsky1,A. Wieloch1, G. Viesti,3 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

Reactions

26, 35, 47A MeV 26, 35, 47A MeV 6464Zn + Zn + 5858Ni Ni 26, 35, 47A MeV 26, 35, 47A MeV 6464Zn +Zn + 9292MoMo26, 35, 47A MeV 26, 35, 47A MeV 6464Zn +Zn + 197197AuAu

40A MeV 40A MeV 4040Ar + Ar + 112112SnSn35, 47A MeV 35, 47A MeV 6464Zn +Zn + 9292Mo Mo 47A MeV 47A MeV 6464Zn + Zn + 9292Mo Mo 55A MeV 55A MeV 2727Al + Al + 124124SnSn

R. Wada et al. Phys. Rev. C 69, 044610(2004)

J. Wang et al. Phys. Rev. C 71, 054608 (2005)

J. Wang et al. ArXiVnucl-ex/0408002, 2005

Reaction Dynamics and Multifragmentation in Fermi Energy Heavy Ion Reactions - 15,26,35.,47A MeV 64Zn + 58Ni, 92Mo and 197Au

15 26 35 47 15 26 35 47

64Zn + 92Mo 64Zn + 197Au

R.Wada, et al., Phys. Rev. C 69, 044610(2004)

THERMAL SHOCK COMPRESSION

FREEZEOUT

SEPARATION

SECONDARY EMISSION

EXPANSIONPRE-EQUILIBRIUM EMISSIONEQUILIBRIUM EMISSION ?

Evolution ?Equilibration ?Equation of State ?

NIMROD DETECTOR4π Charged Particle Telescopes

and 4π Neutron Calorimeter

NIMROD DATA

Source Fits (and Velocity Plots) are Used to Test for Origin of Ejectiles

4He -CsI Detectors

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

Phase 1

Phase 2

“Central Collision”

26, 35, 47A MeV 26, 35, 47A MeV 6464Zn + Zn + 5858Ni Ni 26, 35, 47A MeV 26, 35, 47A MeV 6464Zn +Zn + 9292MoMo26, 35, 47A MeV 26, 35, 47A MeV 6464Zn +Zn + 197197AuAu

CoalescenceCoalescence ModelModel

==

AA-1-1

––

11

11

__________

A.Z. Mekjian, Phys. Rev. C 17, 1051 (1978); Phys. Rev. Lett. 38 640 (1977); Phys. Lett B 89,177 ( 1980)

11

Double Isotope Temperatures

TTHHeHHe = = 14.314.3

1.59 [ Y1.59 [ Yd d ] [ Y] [ Y44He He ] ] [ Y[ Yt t ] [ Y] [ Y33He He ]]

lnln

Binding Energy DifferencesBinding Energy Differences

Mass and Spin FactorsMass and Spin Factors

THHe

0

5

10

15

0 2 4 6 8 10

vsurf, cm/ns

TH

He,

MeV

47Zn

35Zn

40Ar

55Al

Thermal Coalescence Model Radii

0

2.5

5

7.5

10

12.5

0 2 4 6 8 10

Vsurf, cm/ns

R,

fm

R(Mek)47Zn

R(Mek)35Zn

R(Mek) 40Ar

R(Mek) 55Al

t/3He

0

1

2

3

4

5

6

7

8

0 2 4 6 8 10

Vsurf, cm/ns

Y(t

)/Y

(3H

e)

47Zn

35Zn

40Ar

55Al

Early EmissionEquilibration ?Evaporation or Disassembly

Velocity Dependence of Y(t)/Y(3He), Radius and Temperature

Relationship of Average Emission Time with Surface Velocity (AMD Calculation)

47A MeV 64Zn + 92Mo

t/3He Ratio 5/30/03

0

1

2

3

4

5

50 100 150 200

time, fm/c

t/3

He

Ra

tio

47Zn t/3He

47A MeV 64Zn + 92M0

THHe 5/30/03

0

5

10

15

50 100 150 200

time, fm/c

TH

He

, Me

V

47Zn T

47A MeV 64Zn + 92Mo RMek(t) 5/30/03

05

1015202530

50 100 150 200

time, fm/c

RM

ek,

fm47Zn R

Conversion From Velocity to Time

Evidence for Equilibration(A Ghoshal Experiment)

J. Wang et al. Phys. Rev. C 71, 054608 (2005)

J. Wang et al. nucl-ex/0408002, 2005

26, 35, 47A MeV 26, 35, 47A MeV 6464Zn + Zn + 5858Ni Ni 26, 35, 47A MeV 26, 35, 47A MeV 6464Zn +Zn + 9292MoMo26, 35, 47A MeV 26, 35, 47A MeV 6464Zn +Zn + 197197AuAu

Further Evidence for Equilibration(Thermal and

Chemical)

Evolution of Emission Rates

Proton and Z=1 Mass Fractions vs Vsurf

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8 10

Vsurf, cm/ns

Mas

s fr

acti

on 35 Au prot

35Mo prot

35Au Z=1

35Mo Z=1

Alpha Mass fractions vs Vsurf

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10

Vsurf, cm/ns

Alp

ha

mas

s fr

acti

on

Alpha massfract 35 Au47A MeV

26A MeV

35A Mo

Proton and Z=1 Mass Fractions vs Vsurf

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8 10

Vsurf, cm/ns

Mas

s fr

acti

on

35 Au prot

35Mo prot

35Au Z=1

35Mo Z=1

35 Au alpha

35 Mo alpha

Very Similar Results for Au, Mo Targets

Nucleons Earliest, Then A=2,3 Clusters, Then Alphas

Why Evolve to Such Large Alpha Fractions Late?

Alpha Clustering in Low Density Nuclear Material (Surface, Gas)

Relativistic Equation of State of Nuclear Matter for Supernova and Neutron Star H.Shen, H.Toki, K.Oyamatsu, K.Sumiyoshi Nucl.Phys. A637 (1998) 435-450

Yp = 0.5

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.00001 0.0001 0.001 0.01 0.1

nb fm-3

XA

T=2

T=3

T=4

T=5

T=6

T=7

T=8

T=9

T=10

T=12

T=14

T=16

T=18

Shen 10%lim

Sil Calc RhogasavgV0COAL RADDETDerivedDensities

nucl-th/0507033 Cluster Formation and The Virial Equation of State of Low-Density Nuclear Matter C.J. Horowitz, A. Schwenk

nucl-th/0507064 The Virial Equation of State of Low-Density Neutron Matter

Authors: C.J. Horowitz, A. Schwenk

Alpha Fractions vs DensityCompared to Yp=.447 (SHEN et al.)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.00001 0.0001 0.001 0.01 0.1

nb fm-3

XA

T=2 0.45

T=4

T=6.3

T=8

T=12

T=15

T=10

LOW

High

AVGDDENS

Virial T=4

Virial T=8

DENSITY DETERMINED FROM ALPHA MASS FRACTION and TEMPERATURE

Tapas Sil, B. K. Agrawal, J. N. De, S. K. Samaddar , Phys.Rev. C63 (2001) 054604

Thomas- Fermi Calculations

Alpha Fractions vs DensityCompared to Yp=.447 (SHEN et al.)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.00001 0.0001 0.001 0.01 0.1

nb fm-3

XA

T=2 0.45

T=4

T=6.3

T=8

T=12

T=15

T=10

LOW

High

AVGDDENS

Virial T=4

Virial T=8

T. Sil186ReT= 5-7 MeV

J.B. Elliott, L.G. Moretto, L. Phair, G.J. Wozniak Phys.Rev. C67 (2003) 024609

Constructing the phase diagram of finite neutral nuclear matter

nucl-ex/0206010 J.B. Natowitz, K. Hagel, Y. Ma, M. Murray, L. Qin, S. Shlomo, R. Wada, J. Wang

Isoscaling Analyses and Symmetry Energy

M.B. Tsang, W.A. Friedman, C.K. Gelbke, W.G. Lynch, G. Verde and H.S. Xu, Phys.Rev. C64 (2001) 041603

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

sym4

Isoscaling of LCP Yields From Intermediate Velocity Source

Relative Yields Z = 1 35A MeV Au/Mo

Vsurf = 0.25 to 7.75 cm/ns(displacement factor x1.3)

1

10

100

0 1 2 3

Neutron Number

Rel

ativ

e Y

(2)/

Y(1

)

Relative Yields Z=2 35A MeV Au/Mo

Vsurf =m 0.25 to 7.75 cm/ns ( displacement factor x 1.3)

1

10

100

0 1 2 3

Neutron Number

Rel

ativ

e y(

2)/Y

(1)

Isoscaling Parameter Alpha(Vsurf)

00.20.40.60.8

11.21.41.6

0 2 4 6 8 10

Vsurf cm/ns

Alph

a Global Fit Z=1,2

Fit Z=1

0.25

7.75

Global Isoscaling Parameters (Vsurf)Z=1,2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 2 4 6 8 10

Vsurf cm/ns

be

ta

alp

ha

alpha

beta

beta/alpha

Global beta/alpha vs T35 Au/Mo

-3

-2

-1

0

1

2

0 5 10 15 20

T, MeV

B/A

Au/Mo 35 B/A

EST SYM E ONLY

Isoscaling of LCP Yields From Intermediate Velocity Source

= (4/T)[(Z/A)2Mo – (Z/A)2

Au]

= (4/T)[(N/A)2Mo – (N/A)2

Au]

If Only Symmetry Energy Determines Relative Yields

= [(Z/A)2

Mo – (Z/A)2Au]

[(1- Z/A)2Mo – (1- Z/A)2

Au]

Derived Symmetry Energy Coefficient

Gamma Determination 1 August 05 from Seweryn Fits Z=1 and Z/A eject global

0

5

10

15

20

25

30

3.5 4.5 5.5

Vsurf

Gam

ma,

MeV

delsq glob ejectang

Vsurf dep del

SYMMETRY ENERGY

0.1

1

10

100

1E-05 0.0001 0.001 0.01 0.1 1

nb fm-3

GA

MM

A, M

eV

Horo. T=4

Horo. T=6

Horo T=8

Gamma 35 Au/MoT= 5.19-15.5Horo T=14

FINIS

T=4 SYMMETRY ENERGY FROM INTERPOLATIONVirial Calculation

0.1

1

10

100

0.00001 0.0001 0.001 0.01 0.1 1

nb fm-3

GA

MM

A, M

eV

T=4

T=6

Horo graph T=8

Gogny

PLO)T GOGNY !!!!

Alpha Fractions vs DensityCompared to Yp=.447 (SHEN et al.)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.00001 0.0001 0.001 0.01 0.1

nb fm-3

XA

T=2 0.45

T=4

T=6.3

T=8

T=12

T=15

T=10

LOW

High

AVGDDENS

Virial T=4

Virial T=8

T=4 MeV

T = 8 MeV

Z/A of Gas vs time

0

0.2

0.4

0.6

0.8

1

0 100 200 300

time, fm/c

Z/A

ga

s

2.50 Calc 35 Au

expt

nucl-ex/0408002 Title: Tracing the Evolution of Temperature in Near Fermi Energy Heavy Ion Collisions

Authors: J. Wang, R. Wada, T. Keutgen, K. Hagel, Y. G. Ma, M. Murray, L. Qin, A. Botvina, S. Kowalski, T. Materna, J. B. Natowitz, R. Alfarro, J. Cibor, M. Cinausero, Y. El Masri, D. Fabris, E. Fioretto, A. Keksis, M. Lunardon, A. Makeev, N. Marie, E. Martin, Z. Majka, A. Martinez-Davalos, A. Menchaca

-Rocha, G. Nebbia, G. Prete, V. Rizzi, A. Ruangma, D. V. Shetty, G. Souliotis, P. Staszel, M. Veselsky, G. Viesti, E. M. Winchester, S. J. Yennello, W. Zipper,

A. Ono

A "Little Big Bang" Scenario of MultifragmentationX. Campi, H. Krivine, E. Plagnol, N. Sator

Journal-ref: Phys.Rev. C67 (2003) 044610

Title: Reaction Dynamics and Multifragmentation in Fermi Energy Heavy Ion ReactionsAuthors: R. Wada, T. Keutgen, K. Hagel, Y. G. Ma, J. Wang, M. Murray, L. Qin, P. Smith, J. B. Natowitz, R. Alfarro, J. Cibor, M. Cinausero, Y. El Masri, D. Fabris, E. Fioretto, A. Keksis, M. Lunardon, A. Makeev, N. Marie, E. Martin, A. Martinez-Davalos, A. Menchaca-Rocha, G. Nebbia, G. Prete, V. Rizzi, A. Ruangma, D. V. Shetty, G. Souliotis, P. Staszel, M. Veselsky, G. Viesti, E. M. Winchester, S. J. Yennello, Z. Majka, A. OnoPhys.Rev. C69 (2004) 044610