Isovector Equation-of-State
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Isovector Equation-of-State in Heavy Ion Collisions and Neutron Stars. Collaborators: Theo Gaitanos, LMU Munich -> U. Giessen M. Colonna, M. Di Toro, V. Greco, LNS, Catania V. Baran, R. Ionescu, NIPNE Bucharest C. Fuchs, A, Faessler, U. Tübingen

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Isovector Equation-of-State in Heavy Ion Collisions and Neutron Stars

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Isovector equation of state in heavy ion collisions and neutron stars

Isovector Equation-of-State

in Heavy Ion Collisions and Neutron Stars

Collaborators:

Theo Gaitanos, LMU Munich -> U. Giessen

M. Colonna, M. Di Toro, V. Greco, LNS, Catania

V. Baran, R. Ionescu, NIPNE Bucharest

C. Fuchs, A, Faessler, U. Tübingen

T. Mikailova, JINR Dubna, Russia

  • Outline:

  • - Motivation: phase diagram of hadronic matter

  • - the isovector EoS und its uncertainity, Lorentz structure

  • - transport calculations of heavy ion collisions

  • - low densities: fragmentation, isospin fractionation

  • - high densities: flow, particle production

  • - constraints from neutron star observables

Int. School in Nuclear Physics, “Radioactive Beams, Nuclear Dynamics and Astrophysics“, Erice, Sicily, Sept. 16-24, 2006


Isovector equation of state in heavy ion collisions and neutron stars

Quark-hadron coexistence

Schematic Phase Diagram of Strongly Interacting Matter

SIS

Liquid-gas coexistence


Isovector equation of state in heavy ion collisions and neutron stars

Quark-hadron coexistence

Schematic Phase Diagram of Strongly Interacting Matter

SIS

Liquid-gas coexistence

1

neutron stars

0

Z/N


Isovector equation of state in heavy ion collisions and neutron stars

Neutron stars

Heavy Ion Collisions

(T>0, non-equilibrium!

Exotic Nuclei

Stable nuclei


Isovector equation of state in heavy ion collisions and neutron stars

Symmetry Energy

Expansion around r0

Asy-superstiff

Asy-stiff

Esym(rB) (MeV)

Pressure & compressibility

Asy-soft

1

0

2

3

rB/r0

V. Baran, et al.,Phys.Rep.410(2005)335-466


Isovector equation of state in heavy ion collisions and neutron stars

Symmetry energy

iso-stiff

stiff

soft

iso-soft

The nuclear EoS-Uncertainties

the nuclear EoS

Esymm[MeV]

C. Fuchs, H.H. Wolter, WCI white book, EPJA in press, nucl-th/0511070


Isovector equation of state in heavy ion collisions and neutron stars

Uncertainities in optical potentials

Isoscalar Potential

Isovector (Lane) Potential


Isovector equation of state in heavy ion collisions and neutron stars

microscopic

phenomenological

s

d

w

r

deJong, Lenske, PRC 58 (98) 890

Density Functional Approach

NN Scatt

Nuclei


Isovector equation of state in heavy ion collisions and neutron stars

swrd-couplings

DD-F

NLrd

NLr

RMF theory with scalar-isovector (d) field


Isovector equation of state in heavy ion collisions and neutron stars

NL(r,rd)

DDH(r,rd)

Finite nuclei: Effects of dMeson

Binding Energies

Neutron-Proton Radii

 Effects of d meson small in nuclei, except for extreme isospin.

 Investigate heavy ion collisions


Isovector equation of state in heavy ion collisions and neutron stars

Relativistic Transport eq. (RBUU)

mean field

drift

“Lorentz Force”→ Vector Fields

pure relativistic term

Transport Description of Heavy Ion Collisions: BUU


Isovector equation of state in heavy ion collisions and neutron stars

  • Demonstrative Examples: Observables for Isovector EoS:

  • Deep Inelastic Collisions

  • - dissipation in very asymmetric systems

  • Low Density in HIC: Fragmentation processes

  • - isospin content of Fragments: Isospin Destillation

  • Isospin Migration

  • - Isospin Transport through Neck

  • - Isoscaling

  • High Density in HIC: relativistic collisions

  • - difference of neutron and proton flows

  • - isospin transparency

  • - kaon production

  • Neutron stars: Consistency with NS observables

  • (see talks by F. Weber, D. Blaschke and T. Klaehn)


Isovector equation of state in heavy ion collisions and neutron stars

  • Demonstrative Examples: Observables for Isovector EoS:

  • Deep Inelastic Collisions

  • - dissipation in very asymmetric systems

  • Low Density in HIC: Fragmentation processes

  • - isospin content of Fragments: Isospin Destillation

  • Isospin Migration

  • - Isospin Transport through Neck

  • - Isoscaling

  • High Density in HIC: relativistic collisions

  • - difference of neutron and proton flows

  • - isospin transparency

  • - kaon production

  • Neutron stars: Consistency with NS observables

  • (see talks by F. Weber, D. Blaschke and T. Klaehn)


Isovector equation of state in heavy ion collisions and neutron stars

loss of energy, friction

exchange of mass

impact parameter b

Dissipation

Deep Inelastic Collisions with Transport Theory

Deflection function

Wilczynski - Plot


Isovector equation of state in heavy ion collisions and neutron stars

Dissipative Reaction sensitive to Isovector EoS for very asymmetric systems:

132Sn + 64Ni, 10 A MeV

isostiff

isosoft

Density distribution after 500 fm/c

Distribution of deformation of residual nuclei

More dissipation with iso-stiff EoS:

->Less repulsive at sub-normal densities


Isovector equation of state in heavy ion collisions and neutron stars

  • Demonstrative Examples: Observables for Isovector EoS:

  • Deep Inelastic Collisions

  • - dissipation in very asymmetric systems

  • Low Density in HIC: Fragmentation processes

  • - isospin content of Fragments: Isospin Destillation

  • Isospin Migration

  • - Isospin Transport through Neck

  • - Isoscaling

  • High Density in HIC: relativistic collisions

  • - difference of neutron and proton flows

  • - isospin transparency

  • - kaon production

  • Neutron stars: Consistency with NS observables

  • (see talks by F. Weber, D. Blaschke and T. Klaehn)


Isovector equation of state in heavy ion collisions and neutron stars

Chemical potential: isosoft, isostiff

neutrons

asy-soft

protons

bulk

neck

Isospin migration

Isospin fractionation

asy-stiff

asy-stiff

asy-soft

V.Baran et al.,

NPA703(2002)603

NPA730(2004)329

Isospin dynamics at Fermi energies

Au+Au, 50 AMeV

Central collision, b=2 fm

Peripheral collision, b=6 fm


Isovector equation of state in heavy ion collisions and neutron stars

asysoft eos superasystiff eos

experimental data

(B. Tsang et al.

PRL 92 (2004) )

ASYSOFT EOS – FASTER EQUILIBRATION

  • Asysoft: more efficient for concentration gradients + larger fast neutron emission

  • Asystiff: more efficient for density gradients + larger n-enrichement of the neck IMFs

  • Momentum Dependence: faster dynamics and smaller isodiffusion

Baran, Colonna, Di Toro, Zielinska-Pfabe, Wolter, nucl-th/05

Isospin Transport through Neck:

Rami imbalance ratio:


Isovector equation of state in heavy ion collisions and neutron stars

Effect of momentum dependence onIsospin transport

Chen, Ko, B.A.Li, PRL94 (2005)


Isovector equation of state in heavy ion collisions and neutron stars

  • Demonstrative Examples: Observables for Isovector EoS:

  • Deep Inelastic Collisions

  • - dissipation in very asymmetric systems

  • Low Density in HIC: Fragmentation processes

  • - isospin content of Fragments: Isospin Destillation

  • Isospin Migration

  • - Isospin Transport through Neck

  • - Isoscaling

  • High Density in HIC: relativistic collisions

  • - difference of neutron and proton flows

  • - isospin transparency

  • - kaon production

  • Neutron stars: Consistency with NS observables

  • (see talks by F. Weber, D. Blaschke and T. Klaehn)


Isovector equation of state in heavy ion collisions and neutron stars

Observables

  • Some results of Transport Calc.

  • Symmetric Nuclear Matter

  • Asymmetric NM

V1: Sideward flow

V2: Elliptic flow

T.Gaitanos, Chr. Fuchs, Nucl. Phys. 744 (2004)


Isovector equation of state in heavy ion collisions and neutron stars

V1: Sideward flow

V2: Elliptic flow

Results from Flow Analysis

(P. Danielewicz, R.Lacey, W. Lynch, Science)


Isovector equation of state in heavy ion collisions and neutron stars

  • Difference at high pt first stage

r+d

r

n

p

r+d

r

Dynamical isovector effects: differential directed and elliptic flow

132Sn + 132Sn @ 1.5 AGeV b=6fm

differential directed flow

differential elliptic flow

r+d

r

Dynamical boosting of the

vector contribution

T. Gaitanos, M. Di Toro, et al., PLB562(2003)


Isovector equation of state in heavy ion collisions and neutron stars

Kaon Production:

A good way to determine the symmetric EOS (C. Fuchs et al., PRL 86(01)1974)

Main production mechanism:

NNBYK

pNYK

  • Also useful for Isovector EoS?

  • charge dependent thresholds

  • in-medium effective masses

  • Mean field effects


Isovector equation of state in heavy ion collisions and neutron stars

Density & asymmetry of the K-source

aAu≈0.2

[email protected] (HIC)

N/ZAu≈1.5

Inf. NM

NL→ DDF→NLρ→NLρδ :

more neutron escape and more n→p transformation

(less asymmetry in the source)

Larger isospin effects in NM: - no neutron escape

- Δ’s in chemical equilibrium→less n-p “transformation”

Strangeness ratio :Infinite Nuclear Matter vs. HIC

G. Ferini, et al., NPA762(2005) 147 and nucl-th/0607005


Isovector equation of state in heavy ion collisions and neutron stars

Kaon production as a probe for the isovector EoS

T. Gaitanos, G. Ferini, M. Di Toro, M. Colonna, H.H. Wolter, nucl-th/06


Isovector equation of state in heavy ion collisions and neutron stars

  • Demonstrative Examples: Observables for Isovector EoS:

  • Deep Inelastic Collisions

  • - dissipation in very asymmetric systems

  • Low Density in HIC: Fragmentation processes

  • - isospin content of Fragments: Isospin Destillation

  • Isospin Migration

  • - Isospin Transport through Neck

  • - Isoscaling

  • High Density in HIC: relativistic collisions

  • - difference of neutron and proton flows

  • - isospin transparency

  • - kaon production

  • Neutron stars: Consistency with NS observables

  • (see talks by F. Weber, D. Blaschke and T. Klaehn)


Isovector equation of state in heavy ion collisions and neutron stars

Heaviest observed neutron star

Flow constraint (Danielewicz, et al.)

Maximum masses for boundaries of flow constraint

Typical neutron stars

Consistency of Heavy Ion Resuts with Neutron Star Data

T.Klähn, D. Blaschke, S.Typel, E.v.Dalen, A.Faessler, C.Fuchs, T.Gaitanos, H. Grigorian, A.Ho, E.Kolomeitsev, M.Miller, G.Röpke, J.Trümper, D.Voskresensky, F.Weber, H.H.Wolter,

Phys.Rev.C, to appear, nucl-th/0602038

Maximum masses

and direct URCA cooling limit

(see D.Blaschke,T. Klaehn)

Lower boundary (LB) leads to too small NS masses!

Flow constraint can be sharpened.


Isovector equation of state in heavy ion collisions and neutron stars

Summary and Conclusions:

  • While the Eos of symmetric NM is fairly well determined, the isovector EoS is still rather uncertain (but important for exotic nuclei, neutron stars and supernovae)

  • Can be investigated in HIC both at low densities (Fermi energy regime, fragmentation) and high densities (relativistic collisions, flow, particle production)

  • Data to compare with are still relatively scarce; it appears that the Iso-EoS is rather stiff.

  • Effects scale with the asymmetry – thus reactions with RB are very important

  • Additional information can be obtained by cross comparison with neutron star observations


Isovector equation of state in heavy ion collisions and neutron stars

stiff Esym

Soft Esym

Au+Au central: Pi and K yield ratios vs. beam energy

Kaons:

~15% difference between

DDF and NLρδ

132Sn+124Sn

No sensitive to

the K-potential

(iso-dep.?)

Pions: less sensitivity ~10%, but larger yields


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