The National Superconducting Cyclotron Laboratory Michigan State University Betty Tsang 5th ANL/MSU/JINA/I NT FRIB Workshop on Bulk Nuclear Properties Nov 19-22, 2008 MSU S(  Constraints on the Density dependence of Symmetry Energy in Heavy Ion Reactions

Extracting Density dependence of Symmetry Energy in Heavy Ion Reactions F1 F3 Outline: What does HIC have to offer? What are the pitfalls (in theory)? What constraints do we have now? (Are the constraints believable or reliable?) What research directions are we going towards FRIB?

Extracting Density dependence of Symmetry Energy in Heavy Ion Reactions F1 F3 HIC provides a range of density determined from incident energy and impact parameter Micha Kilburn

Bulk nuclear matter properties from Heavy Ion Central Collisions Highest density reached by central collisions depends on incident beam energy. Types of particles formed depend on emission times and density. Pions, n, pfragments E/A=1600 MeV 200 MeV 50 MeV

Experiment: measure collective flow (emission patterns) of particles emitted in Au+Au collisions from (E/A~1-8 GeV). Transport model (BUU) relates the measurements to pressure and density. pressure contours density contours Danielewicz, Lacey, Lynch, Science 298,1592 (2002)

E/A( ,  ) = E/A( ,0) +  2  S(  ) ;  = (  n -  p )/ (  n +  p ) = (N-Z)/A Equation of State of Nuclear Matter Danielewicz, Lacey, Lynch, Science 298,1592 (2002) Pressure (MeV/fm 3 )

Danielewicz, Lacey, Lynch, Science 298,1592 (2002) Pressure (MeV/fm 3 ) Newer calculation and experiment are consistent with the constraints. E/A( ,  ) = E/A( ,0) +  2  S(  ) ;  = (  n -  p )/ (  n +  p ) = (N-Z)/A Equation of State of Nuclear Matter ?? Transport model includes constraints in momentum dependence of the mean field and NN cross-sections

Experimental Techniques to probe the symmetry energy with heavy ion collisions at E/A<100 MeV Vary the N/Z compositions of projectile and targets 124 Sn+ 124 Sn, 124 Sn+ 112 Sn, 112 Sn+ 124 Sn, 112 Sn+ 112 Sn Measure N/Z compositions of emitted particles  n & p  isotopes   + &  - at higher incident energy Neutron Number N Proton Number Z Isospin degree of freedom Hubble ST Crab Pulsar

Around incident energy: E/A<100 MeV: Reaction mechanism depends on impact parameters Heavy Ion collision: 124 Sn+ 124 Sn, E/A=50 MeV Neck fragments b=7 fm multifragmentation b=0 fm  i =0.5  i =2.0 E sym =12.7(  /  o ) 2/3 + 19(  /  o ) ii subnormal density n & p are emitted throughout Charged fragments (Z=3-20) are formed at subnormal density

II. Statistical models: Describe longer time scale decays from single source. nuclear mass, level densities, decay rates Uncertainties Source parameters: A o, Z o, E o, V o, J Information obtained is for finite nuclei, not for infinite nuclear matter I. Transport models: Describe dynamical evolution of the collision process Self consistent mean field n-n collisions, Pauli exclusion Uncertainties Semi-classical Approximations needed to make computation feasible. Classes of models used to interpret experimental results Theory must predict how reaction evolves from initial contact to final observables Symmetry energy included in the form of fragment masses – finite nuclei & valid for  o only. EOS extrapolated using statistical model is questionable. Symmetry energy included in the nuclear EOS for infinite nuclear matter at various density from the beginning of collision.

x AB, y AB experimental or theoretical observable for AB y AB = a x AB +b R i (x AB )= R i (y AB ) Rami et al., PRL, 84, 1120 (2000) Experimental Observable : Isospin Diffusion -- Isospin Transport Ratio No isospin diffusion between symmetric systems Isospin diffusion occurs only in asymmetric systems A+B Non-isospin diffusion effects  same for A in A+B & A+A ;same for B in B+A & B+B Non-isospin transport effects are “cancelled”?? R i = 1 R i = -1

Experimental Observable : Isospin Diffusion  Probe the symmetry energy at subsaturation densities in peripheral collisions, e.g. 124 Sn Sn  Isospin “diffuse” through low-density neck region Projectile Target 124 Sn 112 Sn x(calc)=  soft stiff  Symmetry energy drives system towards equilibrium. stiff EOS  small diffusion; |R i |>>0 soft EOS  fast equilibrium; R i  0

Constraints from Isospin Diffusion Data of calculation! M.B. Tsang et. al., PRL 92, (2004) L.W. Chen, … B.A. Li, PRL 94, (2005)  pBUU: S=12.7(  /  o ) 2/ (  /  o ) stiffness IBUU04 : S~31.6(  /  o )  stiffness Observable in HIC is sensitive to  dependence of S and should provide constraints to symmetry energy    

Experimental Observables: n/p yield ratios F 1 =2u 2 /(1+u) F 2 =u F 3 =  u F1F1 F2F2 F3F3 u = stiff soft U asy (MeV)  =0.3 n and p potentials have opposite sign. n & p energy spectra depend on the symmetry energy  softer density dependence emits more neutrons. More n’s are emitted from the n- rich system and softer iso-EOS. ImQMD Y(n)/Y(p) S=12.7(  /  o ) 2/ (  /  o ) ii

n/p Double Ratios (central collisions) 124 Sn+ 124 Sn;Y(n)/Y(p) 112 Sn+ 112 Sn;Y(n)/Y(p) Double Ratio minimize systematic errors Data : Famiano et al. PRL 97 (2006) Will repeat experiment for better accuracy

n/p Double Ratios (central collisions) Effect is much larger than IBUU04 predictions  inconsistent with conclusions from isospin diffusion data. 124 Sn+ 124 Sn;Y(n)/Y(p) 112 Sn+ 112 Sn;Y(n)/Y(p) Double Ratio minimize systematic errors Double Ratio Center of mass Energy Famiano et al. RPL 97 (2006)

Nuclear Collisions simulations with Transport Models – Nuclear EOS included from beginning of collisions BUU models: Semiclassical solution of one- body distribution function. Pros Derivable, approximations better understood. Cons Mean field  no fluctuations BUU does not predict cluster formation QMD: Molecular dynamics with Pauli blocking. Pros Predicts cluster production Cons Cluster properties (masses, level densities) approximate Need sequential decay codes to de-excite the hot fragments Code used: ImQMD At high incident energies, cluster production is weak  the two models yield the same results. Clusters are important in low energy collisions.

Cluster effects Zhang et al. PLB 664 (2008)145 Cluster effects are important for low energy nucleons but cannot explain the large discrepancy between data and IBUU04 calculations

Analysis of n/p ratios with ImQMD model E sym =12.5(  /  o ) 2/ (  /  o ) ii  i  Data need better measurements but the trends and magnitudes still give meaningful  2 analysis at 2  level

Analysis of isospin diffusion data with ImQMD model ii S=12.5(  /  o ) 2/ (  /  o ) x(data)=  x(QMD)=  Equilibrium R i =0 No diffusion R i =1; R i =-1  i  Impact parameter is not well determined in the experiment b~5.8 – 7.2 fm

Analysis of rapidity dependence of Ri with ImQMD model ii S=12.5(  /  o ) 2/ (  /  o ) x(data) =f( 7 Li/ 7 Be) x(QMD)=  Equilibrium R i =0 No diffusion R i =1; R i =-1  i  New analysis on rapidity dependence of isospin diffusion ratios – not possible with BUU type of simulations due to lack of fragments. b~5.8 – 7.2 fm

How to connect different representations of the symmetry energy Consistent constraints from the  2 analysis of three observables S=12.5(  /  o ) 2/ (  /  o )  i  i   i   i  IBUU04 : S~31.6(  /  o )    approximation For the first time, we have a transport model that describes np ratios and two isospin diffusion measurements ii

Expansion around  0 :  slope L & curvature K sym L  Symmetry pressure P sym S=12.5(  /  o ) 2/ (  /  o )  i IQMD  i  ImQMD S~31.6(  /  o )  IBUU04   IBUU04

IQMD IBUU04 S=12.5(  /  o ) 2/ (  /  o )  i  i  ImQMD S~31.6(  /  o )    IBUU04  R np =  0.04 fm

S=12.5(  /  o ) 2/3 + C s,p (  /  o )  i No constraints on S o ImQMD Vary C s,p and  i 2   2 analysis

E sym =12.5(  /  o ) 2/3 + C s,p (  /  o )  i Constraints from masses and Pygmy Dipole Resonances

E sym =12.5(  /  o ) 2/3 + C s,p (  /  o )  i Constraints from masses and Pygmy Dipole Resonances

E sym =12.5(  /  o ) 2/3 + C s,p (  /  o )  i Current constraints on symmetry energy from HIC

Constraints on the density dependence of symmetry energy Au+Au ? No constraints between  0 and 2  0 FRIB

2020? FRIB FAIR Outlook Precision measurements in FRIB

MSU FRIB FAIR MSU ( ) : E/A<100 MeV  measure isospin diffusion, fragments, residues, p,n spectra ratios and differential flow  improve constraints on S( , m*,  nn,  pp,  np at  <  o MSU (~2013) : E/A>120 MeV  measure  +,  - spectra ratios  constraints at  o <  <1.7  o -- Bickley Outlook

? MSU GSI FRIB FAIR GSI (2011) : E/A~400 – 800 MeV  measure p,n spectra ratios and differential flow  determine constraints S( , m*,  nn,  pp,  np at 2.5  o <  <3  o Lemmon, Russotto et al, experimental proposal to GSI PAC Outlook

? MSU Riken GSI FRIB FAIR Riken ( ) : E/A= MeV  measure  +,  - spectra ratios, p,n, t/3He spectra ratios and differential flow  determine S(  ), m*,  nn,  pp,  np at  ~2  o Riken (2011) : E/A>50 MeV  measure isospin diffusions for fragments and residues  determine S(  ) at  <2  o. 108 Sn+ 112,124 Sn – RI beam used to increase . Outlook

n detectors: NSCL/pre-FRIB; GSI; RIBF/Riken Pions/kaons & p, t, 3 He detectors: TPC NSCL Dual purpose AT-TPC: proposal to be submitted to DOE RIBF TPC: SUMARAI magnet funded, TPC – Japan-US collaboration: proposal to be submitted to DOE. AT-TPC: FRIB ~ 1.2 M TPC ~ 0.78 M Travel: 0.37 M Detectors needed:

Summary The density dependence of the symmetry energy is of fundamental importance to nuclear physics and neutron star physics. Observables in HI collisions provide unique opportunities to probe the symmetry energy over a range of density especially for dense asymmetric matter Calculations suggest a number of promising observables that can probe the density dependence of the symmetry energy. –Isospin diffusion, isotope ratios, and n/p spectral ratios provide some constraints at  0, -- refinement in constraints foreseen in near future with improvement in calculations and experiments at MSU, GANIL & Riken –  + vs.  - production, n/p, t/ 3 He spectra and differential flows may provide constraints at  2  0 and above, MSU, GSI, Riken The availability of intense fast rare isotope beams at a variety of energies at RIKEN, FRIB & FAIR allows increased precisions in probing the symmetry energy at a range of densities.

Acknowledgements NSCL Transport simulation group Brent Barker, Abby Bickley, Dan Coupland, Krista Cruse, Pawel Danielewicz, Micha Kilburn, Bill Lynch, Michelle Mosby, Scott Pratt, Andrew Steiner, Josh Vredevooqd, Mike Youngs, YingXun Zhang Experimenters Michigan State University T.X. Liu (thesis), W.G. Lynch, Z.Y. Sun, W.P. Tan, G. Verde, A. Wagner, H.S. Xu L.G. Sobotka, R.J. Charity (WU) R. deSouza, V. E. Viola (IU) M. Famiano: (Westen Michigan U) Y.X. Zhang (ImQMD), P. Danielewicz, M. Famiano, W.A. Friedman, W.G. Lynch, L.J. Shi, Jenny Lee,

How to connect different symmetry energy representations Value of symmetry energy at saturation Expansion around  0 :  Symmetry slope L & curvature K sym  Symmetry pressure P sym

Density region sampled depends on collision observable & beam energy  >  0 examples: – Pion energy spectra – Pion production ratios – Isotopic spectra – Isotopic flow – With NSCL beams, densities up to 1.7  0 are accessible – Beams: MeV, 50,000pps 106Sn-126Sn, 37Ca-49Ca Riken Samurai TPC

Density region sampled depends on collision observable & beam energy  >  0 examples: – Pion energy spectra – Pion production ratios – Isotopic spectra – Isotopic flow – With NSCL beams, densities up to 1.7  0 are accessible – Beams: MeV, 50,000pps 106Sn-126Sn, 37Ca-49Ca Riken Samurai TPC

Isospin Diffusion Degree of Asymmetry from isoscalingfrom Y( 7 Li)/Y( 7 Be) Projectile Target 124 Sn 112 Sn No diffusion Complete mixing

n-star HI collisions /0/0 ~ ~ yeye ~0.1~ T(MeV) ~1 ~ 4-50 Extrapolate information from limited asymmetry and temperature to neutron stars! Laboratory experiments to study properties of neutron stars

208 Pb extrapolation from 208 Pb radius to n-star radius

N/Z ratios from bound fragments (Z=3-8)  complementary to n/p ratios E C.M. E sym =12.7(  /  o ) 2/3 + 19(  /  o ) ii Effects are small Hot fragments produced in calculations.

Sequential decay effects are important Data consistent with soft EOS N/Z ratios from bound fragments (Z=3-8)  complementary to n/p ratios E sym =12.7(  /  o ) 2/3 + 19(  /  o ) ii

Experimental Observables to probe the symmetry energy E/A( ,  ) = E/A( ,0) +  2  S(  ) ;  = (  n -  p )/ (  n +  p ) = (N-Z)/A Collision systems: 124 Sn+ 124 Sn, 124 Sn+ 112 Sn, 112 Sn+ 124 Sn, 112 Sn+ 112 Sn E/A=50 MeV Low densities (  <  0 ): –n/p spectra and flows; Y(n)/Y(p), Y(t)/Y( 3 He), –Fragment isotopic distributions, Isoscaling: interpretation with statistical model is incorrect / of Z=3-8 fragments Isospin diffusion –Correlation function, C(q) –Neutron, proton radii, E1 collective modes. High densities (  2  0 )  –Neutron/proton spectra and flows; C(q) –  + vs.  - production, k, hyperon production.

asy- stiff asy- soft Exploring Bulk properties of Nuclear Matter with Heavy Ion Collisions High density/energy differential flow n/p, LIF ratios pions ratios kaon ratios neutron stars Low density/energy fragments, ratios isospin diffusion isoscaling migration/fractionat. collective excitations surface phenomena phase transitions QF Li, Di Toro Di Toro, Lukasic DiToro, Reisdorf, QF Li Prassa, QF Li BA Li, Kubis Tsang, HW BA Li, HW Tsang Di Toro Aumann, Ducoin Lehaut Danielewicz Hermann Wolter

Constraints from Isospin Diffusion Data 124 Sn+ 112 Sn data Data: Collisions of Sn+Sn isotopes at E/A=50 MeV b/b max >0.8 ~7.2 fm  from multiplicity gates. y/yb>0.7 Results obtained with clusters IBUU04:  Collisions of Sn+Sn isotopes at E/A=50 MeV  b=6 fm  Projectile-like residue determined from density &  y/yb>0.5  No clusters x=0 x=1( soft) x=-1 x=-2

Isospin diffusion in the projectile-like region Basic ideas: Peripheral reactions Asymmetric collisions 124 Sn+ 112 Sn, 112 Sn+ 124 Sn -- diffusion Symmetric Collisions 124 Sn+ 124 Sn, 112 Sn+ 112 Sn -- no diffusion Relative change between target and projectile is the diffusion effect Projectile Target

Density region sampled depends on collision observable & beam energy  >  0 examples: – Pion energy spectra – Pion production ratios – Isotopic spectra – Isotopic flow – With NSCL beams, densities up to 1.7  0 are accessible – Beams: MeV, 50,000pps 106Sn-126Sn, 37Ca-49Ca

The density dependence of symmetry energy is largely unconstrained. Pressure, i.e. EOS is rather uncertain even at  0. The density dependence of symmetry energy is largely unconstrained. Pressure, i.e. EOS is rather uncertain even at  0. Isospin Dependence of the Nuclear Equation of State E/A ( ,  ) = E/A ( ,0) +  2  S(  )  = (  n -  p )/ (  n +  p ) = (N- Z)/A PAL: Prakash et al., PRL 61, (1988) Colonna et al., Phys. Rev. C57, (1998) Brown, Phys. Rev. Lett. 85, 5296 (2001) Neutron matter EOS

dailygalaxy.com  <  0 – created in multifragmentation process Observables: – n/p ratios – Isotopic spectra – Beams: 50 MeV, 112Sn-124Sn

Transport description of heavy ion collisions: 2-body hard collisions loss termgain term non-relativistic: BUU effective mass Kinetic momentum Field tensor Relativistic BUU Vlasov eq.; mean field EOS Simulation with Test Particles: mean p x (y 0 ) [MeV]

Analysis of rapidity dependence of Ri with ImQMD model E sym =12.5(  /  o ) 2/ (  /  o ) ii New analysis on rapidity dependence of isospin diffusion ratios – not possible with BUU type of simulations due to lack of fragments.  i 