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

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…

Recent highlights from INDRA studies Zmax = Order parameter of the phase transition Distribtuion and Fluctuations Xe+Sn E/A=25-50 MeV Central Indra@ GANIL ln(σ2) ln(<Zmax>) Δ-scaling Δ=1 Δ=1/2 Zmax distributions vs Ebeam D. Gruyer et al., PRL 110, 172701 (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

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)

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, PRC74 047304 (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

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

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.

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

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

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

Probing small effects with SIB Indra-Vamos experiment @ 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

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…

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

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

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.

Neck emissions Vs. PLF/TLF fission 124Sn+64Ni @ 35 MeV/u Chimera @ 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)

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.

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

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)

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…

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

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

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) Lassa@MSU Source functions T. Minniti, B. Barker, G. Verde et al., in preparation

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

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

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 2015-2018 @ GANIL and LNS-Catania

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)

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, …)