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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 !
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