Experimental Investigations of The Equation of State
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Experimental Investigations of The Equation of State of Low Density Nuclear Matter. J. B. Natowitz Department of Chemistry and Cyclotron Institute

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J b natowitz

Experimental Investigations of The Equation of State

of Low Density Nuclear Matter

J. B. Natowitz

Department of Chemistry and Cyclotron Institute

, Texas A&M University, College Station


J b natowitz

HAPPY 75th BIRTHDAY, YURI

AND

MANY MANY MORE !


Exploring the nuclear matter phase diagram with collisional heating

Exploring The Nuclear Matter Phase Diagram With Collisional Heating

AMD Calculation

  • Dynamic Evolution

  • Excitation Energy ?

  • Temperatures ?

  • Degree of expansion

  • Composition ?

  • Chemical and Thermal Equilibrium ?

  • Equation of State ?

  • Liquid-gas phase transition?

T

I

M

E

  • 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.


J b natowitz

Light Charged Particle Emission - High Total Multiplicity Collisions

NIMROD

4 Pi Charged Particles

4 Pi Neutrons


Event selection

Event Selection

Most Violent Collision Events

@ 30% Top Highest Multiplicity

MCP

Neutron + Charged Particle multiplicity distribution for 64Zn+124Sn. Bin4 corresponds to the most violent collision events

Mn


Source analysis of emission energy angle

Source Analysis of Emission ( Energy, Angle)

Angular Distribution

1

2

3

PLF

NN

TLF

4

5

6

7

8

9

10

11

12

Elab, MeV 

Source Fitting – 4He from 40Ar + 124Sn


Reaction tomography particles

Reaction Tomography-Particles

From Fitting

Velocity Plot Protons 40Ar+124Sn

PLF

Experiment

Sum of Sources

Evaporation-like

NN

V perpendicular

NN

Coalescence

V parallel

TLF

Evaporation-like


Critical temperature of symmetric nuclear matter

Critical Temperature of Symmetric Nuclear Matter

Phys.Rev. C65 (2002) 034618

Phys.Rev.Lett. 89 (2002) 212701

TC =16.6  0.86 MeV

employing Skyrme interactions with the  = 1/6 density dependence,

this value of Tcleads 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.


J b natowitz

Derived Average Freeze-Out Densities Coalescence ModelNon-Dissipative Analyses Expanding Fermi Gas

47A MeV

J.B. Natowitz et al.,

Phys.Rev. C 66 031601 (2002)

K. Hagel et al.

Phys. ReV. C 62 034607 (2000)


J b natowitz

STARS

Giant Nuclei

And Sites of Nucleosynthesis

Large Changes in

Temperature, Density,

Proton/Neutron content

SUPERNOVA

NEUTRON STAR

R ~ 10 km


C j horowitz a schwenk nucl th 0507033

C.J. Horowitz, A. Schwenk nucl-th/0507033


J b natowitz

ASTROPHYSICAL EQUATIONS OF STATE

AT LOW DENSITY

DOMINATED BY ALPHA CLUSTERING

Density


Cluster formation and the equation of state of low density nuclear matter

Cluster Formation and The Equation of State of Low-Density Nuclear Matter

symmetric nuclear matter, T=2, 4, 8 MeV

C.J. Horowitz, A. Schwenk nucl-th/0507033


J b natowitz

  • . nucl-th/0507064

    • The Virial Equation of State of Low-Density Neutron MatterC.J. Horowitz and A. Schwenk

SYMMETRY ENERGY(T,)

Clustered Gas

VEOS

SF

T/2

Skyrme,

Fermi gas etc.

T/2

SE


J b natowitz

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


J b natowitz

NN SOURCE EMISSION- Experimental Data and Calculated Yields from AMD and Chimera QMD Codes

COALESCENCE

Average Freeze-out Density 64Zn + 124Sn ~ 0.06 fm-3

“Gas” density ~ ANN/(Atot-ANN) * 0.06 fm-3

~ 0.01 fm-3


Isoscaling analyses and symmetry energy

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

Fsym

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


Isoscaling analyses and symmetry energy1

Isoscaling Analyses and Symmetry Energy

T

α═ (4F/T)[(Z/A)21 – (Z/A)22]

Temperature

THHe = 14.3/ [ln (1.59R)]

R = [ Yd ] [ Y4He ]

LOW DENSITY

CHEMICAL EQUILIBRIUM

MODEL(Albergo)

[ Yt ] [ Y3He ]

Density

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 + 2d + 3t + 33He + 4


Clusterization in low density nuclear matter

Clusterization in Low Density Nuclear Matter


C j horowitz a schwenk nucl th 05070331

C.J. Horowitz, A. Schwenk nucl-th/0507033

Private Communication

O’Connor, Schwenk, Horowitz

Manuscript in Preparation August 2007


J b natowitz

Proton Rich

Neutron Rich


J b natowitz

Reaction System List

Thesis – L. Qin TAMU

  • 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 tomography temperatures

Reaction Tomography-Temperatures

DOUBLE ISOTOPE RATIO THHe

CHEMICAL EQUILIBRIUM TEMPERATURES

THHe = 14.3/ [ln (1.59R)]

(albergo)

R = [ Yd ] [ Y4He ]

[ Yt ] [ Y3He ]

Vperp cm/ns

Significant Temperature Evolution With Velocity

Relatively Small Changes with Projectile Size

Vpar cm/ns


Reaction tomography densities

Reaction Tomography-Densities

“Gas” Density

TLF REMOVED

L. Qin – PhD Thesis, In Progress

Fm-3

CHEMICAL EQUILIBRIUM DENSITIES (Albergo)

FROM ISOTOPE RATIOS


J b natowitz

4He

DERIVED VALUES OF Fsym

as a

FUNCTION of VELOCITY

47 MeV/u Projectiles on 112Sn, 124Sn

64Zn

10B

V perpendicular

20Ne

40Ar

NN

V parallel


J b natowitz

Derived Average Freeze-Out Densities Coalescence ModelNon-Dissipative Analyses Expanding Fermi Gas

J.B. Natowitz et al.,

Phys.Rev. C66 (2002) 031601

K. Hagel et al.

PHYSICAL REVIEW C 62 034607 (2000)


J b natowitz

P. Danielewicz

Esym(nuclides) = Esym(NM)

(1 + 2.7/A 1/3)


J b natowitz

IN MEDIUM BINDING ENERGIES and MOTT TRANSITION

M. Beyer, G. Roepke et al.,

Phys.Lett. B488, 247-253 (2000)

Few Body Syst.Suppl. 14 (2003) 361-366

Eur.Phys.J. A22 (2004) 261-269


Alpha mass fractions

Alpha Mass Fractions


J b natowitz

M. Beyer et al.

nucl-th/0310055

Light Clusters in Nuclear Matter of Finite Temperature

Note: Same at low density

Rho LE ~.005 fm-3


J b natowitz

Correlations Bose Condensates

Superfluidity Efimov States


J b natowitz

The NIMROD Collaboration

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


Major contributors

Major Contributors

  • TAMU, PADOVA, LEGNARO, KRAKOW, LOUVAIN la NEUVE, CATANIA, LANZHOU

  • 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. NatowitzL. Qin, S. Pesente, G. Prete, V. Rizzi, P. Sahu, S. ShlomoJ. Wang, G. Viesti

  • S. Shlomo, A. Ono, G. Roepke

  • A. Schwenk, E. O’Connor

AND THE NIMROD COLLABORATION


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