1. Reaction dynamics – Intermediate energies
G. Verde, CNRS-IPN Orsay (France) & INFN Catania (Italy)
Projectile
Target
Pre-equilibrium, stopping, compression
Flow, expansion
Fragmentation
Secondary decays
Dynamical evolution of quickly evolving systems
Unique terrestrial means to explore the nuclear EoS
nuclear interaction, astrophysics, symmetry energy, clusters
Low density: E/A<100 MeV– high density (2-3ρ0): E/A>150 MeV
Symmetry energy
 Isospin diffusion/drift, Femtoscopy

2. The nuclear EoS – some history
Nuclear interaction ≈ van der Waals
P vs ρ
T vs ρ
T=TC
P=PC
Symmetric nuclear matter
Pressure
Compressibility
Borderie, Rivet, Prog.Part.Nucl.Phys. 61 (2008)
Spinodal instability region (K<0)
Liquid-gas coexistence region at ρ<ρ0 and T<15 MeV – Multifragmentation extensively addressed over the last 20 years…

3. Recent highlights from INDRA studies
Zmax = Order parameter of the phase transition
Distribtuion and Fluctuations
Xe+Sn E/A=25-50 MeV Central GANIL
ln(σ2)
ln(<Zmax>)
Δ-scaling
Δ=1
Δ=1/2
Zmax distributions vs Ebeam
D. Gruyer et al., PRL 110, (2013)
P(Zmax) = η fGauss(Zmax) + (1-η) fGumbel(Zmax)
Analogy with Out-of equilibrium cluster aggregation models
E/A~ 32 MeV  Transition towards “rapid fragmentation” over shorter time-scales  interplay of stopping and radial flow

4. Asymmetric nuclear matter
P vs ρ
T vs ρ
T=TC
P=PC
Asymmetric nuclear matter δ
Borderie, Rivet, Prog.Part.Nucl.Phys. 61 (2008)
Mueller & Serot, PRC52, 2072 (1995)
H. Xu et al., PRL75, 716 (2000)

5. Highlights from symmetry energy
Asymmetry term
Brown, Phys. Rev. Lett. 85, 5296 (2001)
Many approaches… large uncertainties….
Microscopic many-body, phenomenological, variational, …
Especially at high densities (three-body forces)
ZH Li, U. Lombardo, PRC (2006)
Fuchs and Wolter, EPJA 30, 5 (2006)
B.A. Li et al., Phys. Rep. 464, 113 (2008)
Esym(MeV)
Stiff
Soft
Enhance small Esym effects:
RIB facilities (SPES, Spiral2, Eurisol): increase δ
SIB: higher statistics
Detectors with high resolution

6. Nuclear densities away from saturation in the LAB
Projectile
Target
Pre-equilibrium, stopping, compression
Flow, expansion
Fragmentation
Secondary decays
time (fm/c)
ρ/ρ0
Temperature
EoS under laboratory controlled conditions
Transport models: obseravbles ↔︎ EoS, Interaction
QMD
Dynamical mechanisms of cluster formation: instabilities, fluctuation, time-scales
Clustering: formation at early and late stages
Bound States/Fragments & free protons/neutrons  Density dependence of Symmetry Energy in EoS
Unbound States  HIC as a laboratory to produce resonances  multi-particle and fragment correlations  interplays dynamics/spectroscopy in nuclear medium
Au+Au
Au+Au

7. Enhance small Symmetry Energy effects: two experimental directions
N/Z  Radioactive and Stable Ion Beam facilities:
increase N/Z of beams larger δ  larger Esym effects
Examples with existing stable beams:
40Ca+40Ca vs. 48Ca+48Ca + search for isotopic effects on dynamical oberavbles:
fragment production
elliptic flow
two-particle correlations, etc.

8. Enhance small Symmetry Energy effects: two experimental directions
High isotopic resolution
4pi coverage and high granularity
High Energy and Angular resolution: correlations
Low identification thresholds
Reaction mechanism studies at low beam energies
Detailed pulse-shape analysis of signals with digitalization electronics (discrete and ASIC intergrated)
Enormous dynamic range (from 1 mV up to ~10 V signals)
Neutron detection

9. 4π and high (angle, isotopic) resolution arrays
LNS
Analog pulse shape : Si and CsI(Tl)
GANIL, GSI
MSU 4pi + HiRA Si-Strip array
LNL, LNS, GANIL
Digital pulse shape : Si and CsI(Tl)
Correlations

10. Coupling to segmented arrays for correlations
CHIMERA-PS & FARCOS 1m 1°
30°
TARGET
176°
Beam
1192 Si-CsI(Tl) Telescopes CT
(GET electronics)
MSU 4pi + HiRA Si-Strip array
Correlations
…also Indra and Fazia + Correlators

11. Probing small effects with SIB
Indra-Vamos GANIL (France)
40,48Ca+40,48Ca E/A=35 MeV
Vamos  high quality isotopic distributions for heavy-fragments!
VAMOS (PLF residue)
INDRA (LCP coincidences)
Coincidence with LCP in Indra:
Determine E*, T and Densities of PLF
Boson Volumes << Fermion Volumes: Signals of boson condensation and fermion quenching?
P. Marini, H. Zheng, M. Boisjoli, G. Verde, A. Chbihi et al., to be submitted soon

12. Fazia telescopes and capabilities
IPN Orsay: Front-End Electronics
Digitalization of signals (Si and CsI(Tl)) + wide dynamic range
Low identification thresholds  Low energy HIC…
Geometric flexibility  Stand alone mode or Coupling to 4π, Spectrometers, Si-Strip correlators…

13. FAZIA performances/perspectives+
Physics: low and intermediate E/A
Symmetry energy, dynamics
Femtoscopy and correlations
CN decay
DIC/Fission
Interplays dynamics/structure
Next experiment w demonstrator
LNS-Catania December 2014

14. Highlights of Esym observables (SIB@EU)
Flow
Multifragmentation
Pre-equilibrium emission
b=central
b=mid-peripheral
Isospin diffusion & drift
Neck fragments
PLF
TLF
b=peripheral
Isospin diffusion & drift
PLF
TLF

15. Isospin drift & diffusion
Isospin equilibration
Long τint
Isospin translucency
Short τint
ρ ~1/8ρ0
ρ~ρ0
ρ ~ρ0
n drift
Isospin drift
TLF
PLF
Neck
ρ/ρ0 1
PLF
PLF
PLF
Isospin diffusion
TLF
PLF
Neck
N/Z
Proj
Targ
n/p diffusion
Targ
Proj
TLF
TLF
TLF
This shows a mid-peripheral collision between two heavy ions. Let us assume for the moment that they have the same N/Z. For example 112Sn+112Sn. At this stage we have the formation of a neck region where the density is low while the density in the PLF and the TLF regions is about at saturation. Then this means that in going from TLF to PLF there is a gradient of density. Because of this gradient for neutrons it is convenient to move towards the low density region in the neck and one expect therefore that the neck region is more neutron rich as compared to the PLF and the TLF regions that remain almost symmetric. This is called isospin drift and it occurs even in the case of collisions with nuclei having the same N/Z asymmetry.
Now let’s consider a different case. These two nuclei have different N/Z asymmetries. For example the PLF is more neutron rich than the TLF. The collision proceeds… and the two partners exchange nucleons. The exchange proceeds towards a direction that tends to distribute the N/Z uniformly throughout the dinuclear system. The PLF becomes less neutron rich and the TLF becomes more neutron rich. If the collision time is very long, then the process proceeds until a complete N/Z equilibration is attained. Then we say that isospin diffusion has lead to complete N/Z equilibration. On the other hand, if the interaction time is short, then the isospin diffusion process is interrupted before the attainment of complete equilibration. This condition is commonly indicated as isospin translucency, or partial transparency. The result is that the PLF and TLF keep memeory of their initial isospin asymmetries.
P. Danielewicz and M. Colonna tried to describe this with an equation that provide a quantitative description of the relative neutron-proton currents through the neck. This equation has two terms that correspond to the phenomena that I have just described. A term that is proportional to the gradient in density, that is the isospin drift term. And a term that is proportional to the gradient in isospin asymmetry, that is the isospin diffusion term. The drift coefficient depends on the first derivative of the symmetry energy while the diffusion term depends on the strength of the symmetry energy. Therefore Studying these phenomena one can access information about the density dependence of the symmetry energy at sub-saturation density.
Esym vs ρ
Asy-Stiff
Asy-Soft
Low ρ<ρ0
Colonna et al.; Danielewicz et al.

16. Neck emissions Vs. PLF/TLF fission
35 MeV/u LNS
Three-fragment correlations
PLF fission – long time-scales
t>100 fm/c
TLF fission – long time-scales
Vrel (IMF-PLF) / VViola
Vrel (IMF-TLF) / VViola
Neck emission
Fast time-scales
t<100 fm/c
E. De Filippo et al., Phys. Rev. C (2012)

17. Neck and symmetry energy/Chimera
N/Z content of neck fragment (dynamical fast emission)
Statistical
Dynamical - Neck
SMF Simulations Vs Experimental data
N/Z content of statistical emission by PLF and TLF
E. De Filippo et al., Phys. Rev. C (2012)
Data consistent with γ ≈ 0.8
SMF: Stochastic Mean Field calculations by M. Colonna et al.

18. Highlights: pre-equilibrium emissions
Multifragmentation
Pre-equilibrium emission
b=central
b=mid-peripheral
Isospin diffusion & drift
Neck fragments
PLF
TLF
b=peripheral
Isospin diffusion & drift
PLF
TLF

19. Symmetry energy and femtoscopy
Correlation functions
neutron-neutron
proton-proton
0.0
0.5
1.0
1.5 1 2 3 4 5 7
q (MeV/c)
1+R(q)
proton-neutron
Pre-equilibrium emission
b=central
Neutron/proton emission times vs. Esym
tt, t3He, 3He3He…
Asy-stiff
Asy-soft
Lie-Wen Chen et al., PRL (2003); PRC(2005)

20. Preliminary studies on two-proton femtoscopy
Can we actually isolate the proton (and neutron) early dynamical source?
Answer: Yes
What next?
Look for isotopic effects: lots of statistics required…

21. Proton emissions in transport models
Find “measurable” quantity to isolate the early dynamical stage?
 reduce contaminations by long-lived emissions
 improve comparisons to transport models
Transverse Momentum
Time (fm/c)
early
late
Time (fm/c)
Proton Emission rate
Central
B. Barker, NSCL PhD Thesis - Paper in preparation

22. Isolating early emissions
Sn+Sn E/A=50 MeV bred=0-0.4
112Sn+124Sn E/A=50 MeV bred=0-0.4
time (fm/c)
dN/dt
PT/m > 0.2
PT/m > 0.3
Early
B. Barker et al.
Late

23. Imaging sources at high PT
pp correlations
No PT gate
PT/m > 0.2
Xe+Au E/A=50 MeV MCP>36 (~bred<0.3)
Source functions
T. Minniti, B. Barker, G. Verde et al., in preparation

24. Strength of early dynamical emission
Isolating of early sources
(<100 fm/c according to BUU)
T. Minniti, B. Barker, G. Verde et al., in preparation

25. Size of source at high PT
T. Minniti, B. Barker, G. Verde et al., WPCF 2013

26. N/Z effects on p-p correlations: status
MSU: HiRA + 4pi
40Ca+40Ca Vs. 48Ca+48Ca
E/A = 80 MeV
Correlations + 4pi array
Size effect or N/Z effect?
Role of space-time ambiguities?
New experiments planned on
@ GANIL and LNS-Catania

27. Status on symmetry energy
Eur. Phys. Journal A 50
Feb 2014
Edited by:
B.A. Li, A. Ramos,
G. Verde, I. Vidana
40 contributions from:
Heavy-Ion collisions, Hadron Physics, Astrophysical studies, Theory, Experiments, New facilities, etc.
Status on symmetry energy
Heavy-ion collision dynamics
0.4 < γ < 1
Need for future investigations
Better constraints:
 Reduce error bars (SIB and RIB expt.)
 Improve comparison to transport theories
New perspectives from Correlations and Femtoscopy
High densities (GSI energies) need special attention (…not discussed today)
Esym(ρ)

28. Collaborative efforts and opportunities
Technology
High quality pulse-shape analysis  electronics for digitalization of signal shape in silicon detectors (signal integrity, ASIC integration, versatility… we do experiments in different laboratories…)
Data analysis
Femtoscopy, Flow, interplays with dyanmics and nuclear strcture, search for alpha-boson-condensates
Work on existing 4pi data (Indra, Chimera, Fazia, …)