Exploring the symmetry energy with isospin
effects in heavy-ion collisions
Abdou Chbihi
GANIL
For the INDRA collaboration••••

Introduction to the nuclear EOS
Analysis of the experiment 40,48Ca+40,48Ca @ E/A=35 MeVExtraction of the symmetry energy term of EOS
Conclusions
ARIS, Tokyo, June
2014

A. Chbihi

1Time evolution of central collisions at intermediate
energies
M. Colonna, A. Ono and J. Rizzo PRC82, 054613 (2010) 	

Pre-equilibrium,
stopping, compression	Flow, expansion	

Fragmentation	

Secondarydecays	

Explore the EOS under laboratory controlled conditionsHIC is Femtonovae which mimic Supernovae
ECT* 2014 : Simulating the Supernova
Neutrinosphere with Heavy Ion Collisions

ARIS, Tokyo, June
2014

A. Chbihi2

Accessing the symmetry energy
AMD simulations: 48Ca+48Ca and 40Ca+40Ca, E/A=35 MeV and b > 6 fm	

Primary fragment distributions	A.  Ono  et  al.,    Phys.  Rev.  C70,  041604(R)  (2004)	

From isotopic distribution…	

-lnY(N,Z)

From isoscaling…	

Aprimary
Aprimary− lnY (N, Z ) = ξ (Z )N + η (Z ) + ζ (Z )(N − Z )N+Z2

ζ (Z ) ∝1 / σ ∝ Csym (Z ) / T
ARIS, Tokyo, June
2014

A. Chbihi

Y2 ( N,Z )Y1 ( N,Z )isocaling parameter= C exp(α N + β Z)

α = Δµ n / T, β = Δµ p / Tα
4Δ = Csym (Z) / T

Δ = ( <AZ1> )2 − ( <AZ2 > )23

Effects of secondary decaysAMDprimary

GEMINI : secondary
Isotopic distζ (Z)α4Δ•After decay : Cannot
distinguish between the twointeractions (soft/stiff)•Secondary decays need to betaken into account forcomparison to experimental
data

isoscaling • Statistical model•Zprimary
ARIS, Tokyo, June
2014

ZPLF
A. Chbihi

Or/and : experimentallyprovide the primary
distributions
4

Q2	 Symmetry energy experiments
VAMOS PLF (E503)	

Dipole	• 40Q1	

Ca + 40Ca @ E/A = 35 MeVHigh Isotopic Resolution	

40•
Ca + 48Ca @ E/A = 35 MeV
isospin diffusion
INDRA	

detection	

• 48Ca + 40Ca @ E/A = 35 MeV
isospin diffusion• 48Ca + 48Ca @ E/A = 35 MeV
For Bρ (Tm)= 2.2 , 2.12 , 1.957 , 1.80 , 1.656 , 1.523 ,beam	

1.401 , 1.289 , 1.186 , 1.091 , 1.004 , 0.923 , 0.849,0.782 , 0.719 , 0.661

INDRA in coincidence LCP /IMF 	

event characterization 	

(b, excitation energy)	

ARIS, Tokyo, June
2014

A. Chbihi

5Isotopic distributions of PLF• Broad APLF distributions (more than 13 isotopes)• Sensitive to the n-richness of the system• N/Z up to 1.58 (11% N/Z 48Ca) very exotic
ARIS, Tokyo, June
2014

A. Chbihi

6

Reconstruction of primary fragments
ZPLF = 20
proton0-51

V>0ARIS, Tokyo, June
2014

010

∑

2i=1M LCP10A

pr− M n = APLF + ∑ Ai

1A. Chbihi-1-0.50i=10.5b)

50-55

Corrected for the reaction planno constraint
3M LCP v >010CMIVZ pr = Z PLF +ZvCMi >0, v >vrelrelY(arb.unit)

For-5v//(cm/ns)

vperp(cm/ns)

a)

5-10

cm//

10

10-1010Y(arb.unit)

vperp(cm/ns)

10

3

102
10
1

1-5v//(cm/ns

7-1-0.50

Reconstruction of primary fragments
M LCP

Apr − M n = APLF + ∑ Ai

••••

•

i=1Up to 20 isotopes
Average value and σincreases with Zpr
Small differences forlight Zpr
Strong dependence on
the n-richness of thesystem for heavy
fragments
small dependence on
the n-richness of thetarget

A −M

prn
Can be used as an observable
Evaluation of the effect of neutron emission on the width : AMD+GEMINI
It will be used as correction to the data.
ARIS, Tokyo, June
2014

A. Chbihi

8Symmetry energy term vs the excitation energy
comparison with AMD-N(Gemini), b>6 fm

Csym/T

From width of isotopic dist

σ=Zprimary1(exp− calc)2∑N i

Temperature obtained from slope of p-spectra 4-6 MeV
Values of Csym around 30 MeV
Consistent with the values of saturation density
The method is validated and should be applied to moredissipative collisions
ARIS, Tokyo, June
2014

A. Chbihi

9Surface to volume contribution
Csym / T ≈ 1− CCvs (2Z)−1/3

Fit with

Surface effect is important
No big difference between the two interactions
ARIS, Tokyo, June
2014

A. Chbihi

10Summary and Conclusions• Exploration of Esym(ρ) with HI-Collisions (48,40Ca+48,40Ca)• Observables : isotopic distribution & isoscaling• Accessing the symmetry energy– Take into account the secondary effects– Primary experimental isotopic distributions• Zprimay distributions were reconstructed experimentally• Aprimary – neutrons distributions reconstructed exp. but need to take into account theeffect of neutron emission on the Apr – neutrons distributions• Staggering effects are washed with this reconstruction•••

Both methods (isoscaling and isotopic distributions) can be used toextract the symmetry energy term if applied for primary quantities
Esym was extracted for peripheral collisions, the values obtained
are consistent with the value at normal density :work is in progress for central collisions
ARIS, Tokyo, June
2014

A. Chbihi

11A. Chbihi, G. Verde, E. Bonnet, J.D. Frankland, M. Boisjoli, P. Marini, J. Moisan, B. Sorgunlu, F. Rejmund, M.
Rejmund, J.P. Wieleczko,	Sarmishtha Bhattacharya, P. Napolitani	

GANIL, CEA, IN2P3‑CNRS, FRANCE	INFN, Catania, ITALY	

B. Borderie, E. Galichet, N. Le Neindre, M.F. Rivet	

IPN Orsay, IN2P3‑CNRS, FRANCE	

R. Dayras, L. Nalpas, C. Volant	

DAPNIA/SPhN, CEA Saclay, FRANCE	

D. Guinet, P. Lautesse	

Institut de Physique Nucléaire, IN2P3‑CNRS et Université, Caen Cedex, FRANCE	

R. Bougault, O. Lopez, B. Tamain, E. Vient	LPC. IN2P3‑CNRS. ENSICAEN et Université, Caen Cedex, FRANCE	

A. Ono	Department of Physics, Tohoku University, Sendai, JAPAN	R. Roy	

Université de Laval, Quebec, CANADA	W. Trautmann, J. Lukasik	

GSI, D-64291 Darmstadt, GERMANY	

E. Rosato, M. Vigilante	

Dipartimento di Scienze Fisiche, Un. Federico II, Napoli, ITALY	

M. Bruno, M. D’Agostino, E. Geraci, G. Vannini	

INFN and Dipartimento di Fisica, Bologna ITALY	

L. Bardelli, G. Casini, A. Olmi, S. Piantelli, G. Poggi	

INFN and Dipartimento di Fisica, Firenze,ITALY	

F. Gramegna, G. Montagnoli	

INFN, Laboratori Nazionali di Legnaro, ITALY	U. Abbondanno	

INFN, Trieste, ITALY	M. Parlog,
G. Tabacaru	

ARIS, Tokyo, June
A. Chbihi
122014 National Institute for Physics and Nuclear Engineering, Bucarest‑Maguerele, ROMANIA