Constraining the symmetry energy of the EoS in relativistic energy - - PowerPoint PPT Presentation

Constraining the symmetry energy of the EoS in relativistic energy of the EoS in relativistic heavy-ion reactions

• A. Krasznahorkay, ATOMKI, Debrecen

) (r ρ

Introduction

The neutronskin thickness

2

( )

r r r dv

2 2

≡ ∫ ρ

r

• 2

/ 1 2 2 / 1 2 p n

r r R > > > > < < < < − − − − > > > > =< =< =< =<

Krasznahorkay et al., NP 731, 224 (2004)

Krasznahorkay et al., PRL, 82 (1999) 3216.

Constraining the symmetry energy Constraining the symmetry energy

Furnstahl, Nucl.

• Phys. A706 (2002)

85

4

The symmetry energy in nuclear matter

B (N,Z) = a A - a A2/3 – a Z (Z - 1)/A1/3 - a (N – Z )2 / A + Δ(A)

Bethe – Weizsäcker mass formula

( ) ( ) ( )

( )

A Z

• O

S E E − = + + + = α α α ρ ρ α ρ ... , ,

4 2

( ) ...

) , ( 2 1 ) (

2 4 2 2

+ − + = ∂ ∂ =

=

ρ ρ ρ α α ρ ρ

α

p a E S

B (N,Z) = aVA - aSA2/3 – aCZ (Z - 1)/A1/3 - asym (N – Z )2 / A + Δ(A)

asym = 23.7 MeV

• The density dependence of

symmetry energy is largely largely largely unconstrained unconstrained unconstrained.

• What is “stiff” or “soft”

“stiff” or “soft” “stiff” or “soft” (curvature) is density

al., PRL 102 (2009) 062502

(curvature) is density dependent

• Z. Xiao et al.,

Recent workshops and conferences

• AsyEOS2010, "International Workshop on Nuclear Symmetry Energy at

Medium Energies", May 21 to May 24, 2010, in the town Noto (SR), Italy.

• International symposium on Nuclear Symmetry Energy, July 26 to July 28,

2010 at RIKEN, Wako, Japan. 2010 at RIKEN, Wako, Japan.

• Probing the Equation of State of "eutronRich Matter with HeavyIon

Reactions

• Properties of Asymmetric nuclear matter within Extended BHF

Approach

• Determining the "uclear Symmetry Energy
• f "eutronRich Matter and its Impacts on Astrophysics
• The Nuclear Symmetry Energy and Neutron Star Crusts

Nuclear structure

Pygmy Dipole Resonance

Nuclear reactions

Supernova collapse

• Stability

Stability Stability against gravitational collapse

Radial density profile

density profile density profile

Internal structure

structure structure,

!"#$

• composition and evolution

Cooling

Cooling Cooling mechanism

• PULSAR

BINARY OBJECTS

R & M coupled

• bservables

“SQM” vs. “normal” matter EOS

Cooling rates of proto-

neutron star

Cooling rates for X-ray

bursters

NS masses, radii and

moments of inertia

!"#$

“SQM” vs. “normal” matter EOS Quark Stars still theoretical, but evidence continues to accumulate to support them Quark Stars would offer unique opportunities to study exotic matter

• +

±

π π π π

p, n Nuclear structure data

Intermediate & relativistic energy HIC

Isospin sensitive observables

• n/p differential flow
• meson production, π+/π-,K0 /K+
• etc.

Lack of data, but …

• ASY-EOS experiment @ GSI
• SAMURAI @ RIKEN

Intermediate & relativistic energy HIC

Isospin sensitive observables

• n/p differential flow
• meson production, π+/π-,K0 /K+
• etc.

%&'()

!"

Spoakperson: A. Krasznahorkay (approved by GSI-PAC) R3B , EXL, ALADIN, … collaborations

1. Institute of Nuclear Research (ATOMKI), Debrecen, Hungary 2. GSI, Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany 3. IFIC (CSIC-Univ. Valencia), Valencia, Spain 3. IFIC (CSIC-Univ. Valencia), Valencia, Spain 4. Kernfysisch Versneller Instituut, Groningen, The Netherlands 5. Daresbury, Liverpool, United Kingdom

2 / 1 2 2 / 1 2 p n

r r R > > > > < < < < − − − − > > > > =< =< =< =<

• Sum rule for the SDR strength

Neutron-skin thickness

      ⊗ ∑

→ →

±

a a

r

a a σ

τ

( )

p n SDR SDR

r Z r

• S

S 〉 〈 − 〉 〈 = −

+ − 2 2

2 9 π

2 / 1 2 2 / 1 2 exp

2 ) ( ) 1 ( 2 / 1 2 2 / 1 2

p p

r

• r

Z

• B

p n

r r

> < > < − − −

= > < − > <

ασ

− − − − + + + +

= = = = S S B /

   

JM

τ

Bohr, Mottelsson Nuclear Structure (1969) Vol. 2

• A. Krasznahorkay et al., Phys. Rev. Lett. 82

(1999) 3216.

Problems with the SDR method

Quenching of the SDR is not known Normalization of the strength is not solved

Σ[r(i)xσ σ σ σ(i)] τ τ τ τ−(i) Σ[r(i)xσ σ σ σ(i)] τ τ τ τ (i) IAS Σ τ τ τ τ−(i)

The QFC background is not precisely defined

14

• ! "#"

! "#"

Advantages of the proposed GDR method

Very little quenching, and it is precisely known for the whole nuclear chart Normalisation can be more precise

Σr(i)τ τ τ τ −(i) => L =1 $% Στ τ τ τ −(i) => L =0

In coincidence with γ-decay no QFC background is expected

16

Neutron energy spectra and differential cross sections from (p,n) reaction (S. Nishihara et a., Phys. Lett. B 160 (1985) 369

Excitation with strong interaction

στ

στ στ στ

τ

τ τ τ

• σ

σ σ σ

&'()*&+

Ground-state γ-decay of the GDR

19

Reaction kinematics

IVGDR

Schematic layout of the setup

Efficiency for neutrons

The liquid hydrogen target

Beam time estimates

E = 600 A.MeV I = 106 particles/s d(target) = 100 mg/cm2 1.5 cm long liquid hydrogen LENA (ToF neutron spectrometer) ε≈ 0.15 CB (γ-spectrometer) ε≈ 0.2 CB (γ-spectrometer) ε≈ 0.2 ALADIN (dipole magnet) Counting rate for the IVGDR ≈ 250 count/h

9 shift / beam Althogether 29 shifts for 116Sn, 124Sn and 208Pb

#$ %&!

Spoakpersons of ASY-EOS experiment

• R. Lemmon and P. Russotto (approved by GSI-PAC)

Zagreb, Croatia Caen, Orsay, France Darmstadt, Frankfurt, Germany Ioannina, Greece Catania, Milano, Napoli, Italy Catania, Milano, Napoli, Italy Katowice, Krakow, Warsaw, Poland Bucharest, Romania Santiago de Compostela, Spain Lund, Malmo, Sweden Daresbury, Liverpool, United Kingdom Institute of Nuclear Research (ATOMKI), Debrecen, Hungary Kolkata, India NSCL-MSU, Rochester, USA

Main observable: n/p differential flow

#$ %&!

%,%@ -))%*&

./0,./0@ -))%*& ./,./ @ 400A MeV

• 1

Detect: Detect: Detect: n, p, t, 3He, N/Z of light IMFs

IPJ phoswich MSU miniball

GSI LAND

light IMFs Determine: Determine: Determine: reaction plane, reaction centrality Improve: Improve: Improve: statistics and neutron background determination + code clusterization algorithm

M

.5 m

Lund-SdC Califa

GS

LNS Chimera

'(#)

132Sn, 106Sn beams

Conclusion

New experimental data for the symmetry energy term of the EoS.

Nuclear structure data (Giant resonances) for ρ ≈ ρ0 ρ0

• Nuclear reaction data (elliptic flow differences)

for ρ ≈ 2ρ0

new predictions for neutron rich isotopes and neutron stars.

Thank you for your attention ! attention !