Constraining the symmetry energy of the EoS in relativistic

heavy-ion reactions

A. Krasznahorkay, ATOMKI, Debrecen

2

r r r dv2 2

)(r

r

neutrons

protons

2/122/12pn rrR

Introduction

The neutron-skin thickness

Krasznahorkay et al., NP 731, 224 (2004)Krasznahorkay et al., PRL, 82 (1999) 3216.

4

Constraining the symmetry energy

Furnstahl, Nucl. Phys. A706 (2002) 85

The symmetry energy in nuclear matter

A

ZN

OSEE

...0,, 42

...),(

2

1)( 02

0

0402

2

pa

ES

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

Bethe – Weizsäcker mass formula

asym = 23.7 MeV

Symmetry energy

• The density dependence of symmetry energy is largely unconstrained.

• What is “stiff” or “soft” (curvature) is density dependent

The asymmetry term contributes a greater uncertainty than does the

symmetric matter EOS.Z.

Xia

o et

al.,

PRL

102

(200

9) 0

6250

2

Recent workshops and conferences • Asy-EOS-2010, "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.

• Probing the Equation of State of Neutron-Rich Matter with Heavy-Ion Reactions

• Properties of Asymmetric nuclear matter within Extended BHF Approach

• Determining the Nuclear Symmetry Energy

of Neutron-Rich Matter and its Impacts on Astrophysics

• The Nuclear Symmetry Energy and Neutron Star Crusts

Where Esym shows up Nuclear structure

Nuclear reactions

Supernova collapse

Pygmy Dipole Resonance

Neutron star

Stability against gravitational collapse

Radial density profile Internal structure,

composition and evolution Cooling mechanism

Esym dependent

J.M

. La

ttim

er

an

d M

. Pra

kash

, S

cien

ce 3

04

(2

00

4)

53

6

N-star observations

PULSAR

BINARY OBJECTS

R & M coupled observables

J.M. Lattimer and M. Prakash, Science 304 (2004) 536

“SQM” vs. “normal” matter EOS ?

Quark Stars still theoretical, but evidence continues to accumulate to support themQuark Stars would offer unique opportunities to study exotic matter

Cooling rates of proto-neutron star

Cooling rates for X-ray bursters

NS masses, radii and moments of inertia

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

Constraining Esym

0,K, p, n

Intermediate & relativistic energy HIC

Isospin sensitive observables - n/p differential flow - meson production, π+/π-,K0 /K+

- etc.

Nuclear structure

data

By HIC in the Fermi energy regime

SIS18 EOS- neutron-skin experiment S408

Spoakperson: A. Krasznahorkay (approved by GSI-PAC)

R3B , EXL, ALADIN, … collaborations1. Institute of Nuclear Research (ATOMKI), Debrecen, Hungary2. GSI, Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany3. IFIC (CSIC-Univ. Valencia), Valencia, Spain4. Kernfysisch Versneller Instituut, Groningen, The Netherlands5. Daresbury, Liverpool, United Kingdom

pnSDRSDR rZrNSS 22

2

9

2/122/12pn rrR

2/12

2/12exp

2

)()1(2/122/12

p

p

rN

rZNB

pn rr

Sum rule for the SDR strength Neutron-skin

thickness

SSB /

aa r

JM

a a

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– Spin-Dipole Res. [S r(i)x(i)] t−(i)

– IAS S t−(i)

• The QFC background is not precisely defined

14

The previous sum rule is valid also for the GDR if it excited in (p,n) reaction !!!

(actually the analog of the GDR is excited)

We are proposing the excitation of the well known GDR in (p,n) reaction

Advantages of the proposed GDR method

• Very little quenching, and it is precisely known for the whole nuclear chart

• Normalisation can be more precise– GDR Sr(i)t −(i) => DL =1– IAS St −(i) => DL =0

• In coincidence with γ-decay no QFC background is expected16

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

v

v

voc

v

V(q

=0

) (M

eV

fm3)

Ground-state γ-decay of the GDR

19

Reaction kinematics

IVGDR

Schematic layout of the setup

Geometrical arrangement

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

ALADIN (dipole magnet)

Counting rate for the IVGDR ≈ 250 count/h

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

SIS18 ASY-EOS experiment S394

Spoakpersons of ASY-EOS experiment R. Lemmon and P. Russotto (approved by GSI-PAC)

Zagreb, CroatiaCaen, Orsay, FranceDarmstadt, Frankfurt, GermanyIoannina, GreeceCatania, Milano, Napoli, ItalyKatowice, Krakow, Warsaw, PolandBucharest, RomaniaSantiago de Compostela, SpainLund, Malmo, SwedenDaresbury, Liverpool, United KingdomInstitute of Nuclear Research (ATOMKI), Debrecen, HungaryKolkata, IndiaNSCL-MSU, Rochester, USA

Main observable: n/p differential flow

SIS18 ASY-EOS experiment S394

Au+Au @ 400A MeV (increased statistics)96Zr+96Zr @ 400A MeV 96Ru+96Ru @ 400A MeV (increased isospin

sensitivity)}

Detect: n, p, t, 3He, N/Z of light IMFsDetermine: reaction plane, reaction centralityImprove: statistics and neutron background determination + code clusterization algorithm

IPJ p

hosw

ich

MSU

min

ibal

l

.5 mLund

-SdC

Cal

ifa

GSI

LAN

D

LNS

Chim

era

Towards FAIR

132Sn, 106Sn beams

Conclusion

• New experimental data for the symmetry energy term of the EoS.– Nuclear structure data (Giant resonances) for ρ ≈

ρ0

– Nuclear reaction data (elliptic flow differences) for ρ ≈ 2ρ0

new predictions for neutron rich isotopes and neutron stars.

Thank you for your attention !