Particle correlation probes of nuclear dynamics and symmetry

Particle correlation probes of nuclear dynamics and symmetry energy Projectile Target Unbound states Pre-equilibrium, stopping, compression Expansion Equation of State G. Verde, INFN Catania Zimanyi School ‘ 13, Budapest, Dec 2 -6 2013 Fragmentation Spectroscopy tools

Outline • Introduction to symmetry energy in HIC and present status • Correlation measurements as probes for spectroscopy and dynamics spectroscopy Nuclear equation of state Symmetry energy Spectroscopic properties of unbound states (spins, branching ratios, …)

Equation of state at intermediate energies Projectile Target Secondary decays Flow, expansion ρ/ρ0 Temperature Pre-equilibrium, stopping, compression Asymmetric nuclear matter time (fm/c) Fragmentation QMD time (fm/c)

Symmetry energy in finite nuclei Bethe-Weiszacker 16 O

Eo. S of asymmetric nuclear matter Asymmetry term B. A. Li et al. , Phys. Rep. 464, 113 (2008) Stiff Soft Esym(Me. V) Many approaches… large uncertainties…. Microscopic many-body, phenomenological, variational, … Especially at high densities (three-body forces) ZH Li, U. Lombardo, PRC 74 047304 (2006) Brown, Phys. Rev. Lett. 85, 5296 (2001) Fuchs and Wolter, EPJA 30, 5 (2006)

Parameterizations of density dependence Ur. QMD by Q. Li High γ, L Low γ, L Microscopic transport models: - input Asy. Eo. S parameterizations - compare predictions to observables measured in Heavy-Ion collisions strength curvature slope

What do you need? • Produce density gradients in the lab HIC • Enhance effects induced by symmetry energy – Increase isospin asymmetry [high δ=(N-Z)/N+Z)] and compare to symmetric systems [δ=0, N=Z] – Ex. : 40 Ca+40 Ca Vs. 48 Ca+48 Ca – New facilities for exotic beams… 56 Ca? High δ… better isolating Esym effects

Producing density gradients in the lab Intermediate energies: E/A<80 Me. V High energies: E/A>200 Me. V SMF - Baran, Colonna, Di Toro, Greco Ganil, Eurisol, Frib, Lns, Nscl, Spiral 2, Tamu, … f if St y- As Asy-Soft CSR, GSI/Fair, NSCL/FRIB, Riken, …

Constraints on density dependence of symmetry energy Measurements of Esym(ρ), L and S 0 from different experimental approaches Pygmy Dipole Resonance Heavy-ion collision 0. 4 < γ < 1 Neutron Stars Astrophysical studies (X-ray data )

Constraints on density dependence of symmetry energy Measurements of Esym(ρ), L and S 0 from different experimental approaches Heavy-ion collision dynamics 0. 4 < γ < 1

Experimental probes • Intermediate energies nuclear matter E/A=20 -100 Me. V: Low density – Neutron/proton pre-equilibrium emissions and correlation functions – Isospin diffusion between quasi-projectile and quasi-target (time-scales important) – Isotopic composition of fragments and clustering – Elliptic and direct flow measurements for neutron and protons • Sub-relativistic energies E/A=200 -1500 Me. V – Neutron/proton ratios – Meson production: K+/K 0 and π+/π– Neutron/proton elliptic flow

Intermediate energies: time-scales involved Projectile Target Secondary decays Pre-equilibrium, stopping, compression Flow, expansion Fragmentation • We only measure the asymptotic state of observables • Sources evolve over very short time-scales (10 -23 s-10 -16 s) deuteron-alpha correlation function 6 Li deuteron + alpha Typical long-lived resonance decay in our systems (τ ≈ 3× 10 -20 s ) …beyond any timing resolution for known detectors 2. 186 Me. V Femtoscopy and resonance decays

Building correlations Deuteron-Alpha correlations Final-state interactions Y 12 (q) + Coincidence pairs + Uncorrelated pairs 1+R(q) q (Me. V/c) Nuclear FSI: correlation at q=42 and 84 Me. V/c 6 Li deuteron-alpha q (Me. V/c) Coulomb FSI: anti-correlation at small q values High angular resolution required: Low q and resonances

• • Farcos: Femtoscope Array for Correlations and Femtoscopy Based on (62 x 64 mm 3) clusters 1 square (0. 3 x 62 mm 3) DSSSD 32+32 strips 1 square (1. 5 x 62 mm 3) DSSSD 32+32 strips 4 60 x 32 mm 3 Cs. I(Tl) crystals 4 Cs. I(Tl) crystals (3 rd stage) DSSSD 1500 μm (2 nd stage) DSSSD 300 μm (1 st stage) Assembly cluster 132 channels by each cluster Fully reconfigurable (more Si layers, neutron detection) • Coupling to 4 pi Chimera array • Coupling to Magnex spectrometer INFN, Catania & Milano

Charge Identification Techniques. Charge (isotopic) DESi-ECs. I ESi-RT for ions stopping in Cs. I(Tl) for ions stopping in Silicon Si Mass Cs. I(Tl) Superconducting Cyclotron Reference Signal ESi-To. F for ions stopping in Silicon Digitalization + ASIC integration of “Fazia-like” ideas + interest for GET chips and logics Isotopic (LCP) Fast-Slow for ions stopping in Cs. I(Tl)

First experiment April 2013: 4 -tel prototype+Chimera May 2013 DE-E (300 -1500 µm) T 2 Farcos E/A=35 Me. V FAST-SLOW T 4 Farcos

Proton-proton correlations Extensively used Nuclear Coulomb • Final State interactions (FSI) Nuclear peak at 20 Me. V/c Coulomb anti-correlation at small q • Anti-symmetrization of wave function (Fermions)

Time-scales involved Projectile Target Secondary decays Pre-equilibrium, stopping, compression Flow, expansion Strong contributions from pre-equilibrium emissions: most sensitive probes of the Eo. S of nuclear matter ~ 10 -22 s Expanding and evaporating long-lived… as long as ~10 -16 s Fragmentation Long-lived resonance decays… half-life around ~10 -20 s-10 -16 s

Imaging p-p correlations G. Verde et al. , PRC 65, 069604 (2002) P. Danielewicz, D. A. Brown 14 N+197 Au E/A=75 Me. V Fast pre-equilibrium emitting sources Slow evapor. emission Slow Source size q e • Short range profiles dominated by early sources (< 100 fm/c)

Information content Sizes and long-lived emissions 1 -f (%) Long-lived contributions (%) Space-time image profiles of emitting sources compare to models

Sizes from multiple-particle correlations Deuteron-Alpha Ed>40 Me. V Eα>45 Me. V fast Proton-Proton Ep>30 Me. V r 0=2. 2 fm 20<Ed<40 Me. V 25<Eα<45 Me. V 1+R(q) G. Verde et al. , Physics Letters B 653, 12 (2007) Xe+Au E/A=50 Me. V bred<0. 3 r 0=5. 6 fm fast 15 <Ep<30 Me. V 1+R(q) Different particles emitted at different stages: r =9. 4 r =6 fm unlike particle correlations chronology! fm medium “which 0<Eparticle was emitted first? ” 0 <E <15 Me. V <20 Me. V 0 0 p 0<Eα<25 Me. V …see talk by K. Poniatowska (Tuesday, Dec 3) slow q (Me. V/c) r 0=9 fm 1+R(q) d Deformations induced by position -momentum correlations r 0=14 fm slow q (Me. V/c)

Symmetry energy and neutron/proton -equilibrium space-time probes IBUU simulations 52 Ca+48 Ca E/A=80 Me. V Correlation functions Central collisions neutron-neutron 7 Asy-soft 5 3 Asy-stiff 1+R(q) 1 1. 5 1. 0 0. 5 proton-proton 0. 0 4 3 Lie-Wen Chen et al. , PRL (2003), PRC(2005) Proton/neutron emission times sensitive to density dependence of the symmetry energy proton-neutron 2 1 q (Me. V/c) pre

“Lednicky’s recipe”: p-n correlations 1+R+(q) p first -100 fm/c n first +100 fm/c R. Lednicky et al. , Phys. Lett. B 373, 30 (1996) Proton faster 1+R−(q) Neutron faster Ratio +/p-n q (Me. V/c) R+/R- ratios tell who is emitted first Chronology Esym(ρ)

Isolating pre-equilibrium emissions Secondary evaporation Early emissions BUU simulations Early 112 Sn+124 Sn 0. 4 E/A=50 Me. V bred=0 - d. N/dt Late PT/m > 0. 2 PT/m > 0. 3 time (fm/c) B. Barker, G. Verde et al.

Imaging pre-equilibrium PT/m > 0. 2 Xe+Au E/A=50 Me. V Lassa@MSU MCP=36 (~bred<0. 3) Sensitivity to symmetry energy under study No PT gate pp correlations Source functions T. Minniti, B. Barker, G. Verde et al. , in preparation

Size of source vs. PT T. Minniti, G. Verde et al. , WPCF 2013

Strength of early dynamical emission Isolating of early sources (before 100 fm/c up to microscopic models) use femtoscopy to probe Eo. S

Effects of clustering in low density Eo. S Central Pre-equilibrium emission Flow Multifragmentation ρ ≈ 0. 01∙ρ0 Clustering (~alphas) at small densities affects Esym NIMROD @ TAMU Esym(ρ) not vanishing at very low ρ 64 Zn+92 Mo, 197 Au 40 Ar, 64 Zn+112, 124 Sn Esym(Me. V) E/A=35 Me. V Density ρ(fm-3) J. B. Natowitz et al, PRL 104 (2010) 202501 R. Wada et al. , PRC 85, 064618 (2012) Perspectives and challenge: access to Symmetry Energy at very low densities C. J. Horowitz et al. , NPA 776, 55 (2006), G. Wanatabe et al. , PRL 103, 121101 (2009)

Clusters and resonance decays in heavyion collisions @ intermediate energies Not only Eo. S… Expansion 10 C* Several unbound species in just one single experiment! HIC and correlations as a spectroscopic tool • Cluster states in stable and exotic nuclei • BEC, Hoyle, …

Spectroscopy Dynamics E/A=50 Me. V 8 B 8 Be p-7 Li p-7 Be 10 B p-p-16 O correlation function 18 Ne p+p+16 O 1+R Xe+Au 12 C α+α+α 9 B p+α+α α-6 Li

Sequential decay modes and branching ratios • Peripheral projectile fragmentation 12 C+24 Mg E/A=53, 95 Me. V (Indra@GANIL) Decay of 12 C and 10 C quasi projectiles (QP*) α+α+α 10 C* ct dire dir e ct 12 C* α+α+α α+α+p+p 2α+2 p α + 8 Be α+α α+6 Be α+2 p p+9 B α+ α+p 2 p+8 Be α+α

3 - correlation function - 12 C* states Reaction: 12 C+24 Mg E/A=53 Me. V ---> 12 C* quasi-projectiles F. Grenier, A. Chbihi, G. Verde et al. , Nucl. Phys. A 811 (2008) 233 Event mixing Modified event mixing 12 C+24 Mg 12 C 8 Be+ 2

2α-2 p correlations : states in 10 C* Ek(Me. V) F. Grenier et al. , Nucl. Phys. A 811 (2008) 233 10 C 6 Be+α (2 p+α) α 10 C 8 Be+p+p (α+α)+p p 10 C 9 B+p (p+α α) p

Clusters in dilute nuclear matter Central Pre-equilibrium emission Multifragmentation Flow ρ ≈ 0. 01∙ρ0 Clustering (~alphas) at small densities affects Esym C. J. Horowitz et al. , NPA 776, 55 (2006), G. Wanatabe et al. , PRL 103, 121101 (2009) Predictions with no clustering Esym(ρ) not vanishing at very low ρ NIMROD @ TAMU 64 Zn+92 Mo, 197 Au 40 Ar, 64 Zn+112, 124 Sn Esym(Me. V) E/A=35 Me. V Density ρ(fm-3) Perspectives and challenge: access to Symmetry Energy at very low densities+ cluster properties and resonance decay in dilute medium J. B. Natowitz et al, PRL 104 (2010) 202501 R. Wada et al. , PRC 85, 064618 (2012)

Summary and Perspectives • Particle-particle correlation studies – Interplays HIC dynamics spectroscopy • Heavy-ion collisions and probes of Eo. S and symmetry energy • Imaging tools to access properties of early dynamical sources (probes of Eo. S) • Future experiment: np, pp and nn correlations and chronology • Spectroscopy tools from resonance decays: spectroscopy vs femtoscopy; vacuum vs in-medium effects; clustering effects on low density Eo. S