Constraints on the Density dependence of Symmetry Energy in Heavy Ion Reactions 5th ANL/MSU/JINA/I NT FRIB Workshop on S(r) Bulk Nuclear Properties Nov 19-22, 2008 MSU Betty Tsang The National Superconducting Cyclotron Laboratory Michigan.
Download ReportTranscript Constraints on the Density dependence of Symmetry Energy in Heavy Ion Reactions 5th ANL/MSU/JINA/I NT FRIB Workshop on S(r) Bulk Nuclear Properties Nov 19-22, 2008 MSU Betty Tsang The National Superconducting Cyclotron Laboratory Michigan.
Constraints on the Density dependence of Symmetry Energy in Heavy Ion Reactions 5th ANL/MSU/JINA/I NT FRIB Workshop on S(r) Bulk Nuclear Properties Nov 19-22, 2008 MSU Betty Tsang The National Superconducting Cyclotron Laboratory Michigan State University 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 Micha Kilburn HIC provides a range of density determined from incident energy and impact parameter Bulk nuclear matter properties from Heavy Ion Central Collisions E/A=1600 MeV 200 MeV 50 MeV Highest density reached by central collisions depends on incident beam energy. Pions, n, p fragments Types of particles formed depend on emission times and density. Danielewicz, Lacey, Lynch, Science 298,1592 (2002) pressure contours density contours • 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. Equation of State of Nuclear Matter E/A(r,) = E/A(r,0) + 2S(r) ; = (rn- rp)/ (rn+ rp) = (N-Z)/A Danielewicz, Lacey, Lynch, Science 298,1592 (2002) symmetric matter -3 P (MeV/fm ) 100 10 RMF:NL3 Akmal Fermi gas Flow Exp. 1 1 1.5 2 2.5 3 r/r 3.5 0 4 4.5 5 Equation of State of Nuclear Matter E/A(r,) = E/A(r,0) + 2S(r) ; = (rn- rp)/ (rn+ rp) = (N-Z)/A ?? Danielewicz, Lacey, Lynch, Science 298,1592 (2002) symmetric matter •Newer calculation and experiment are consistent with the constraints. •Transport model includes constraints in momentum dependence of the mean field and NN cross-sections -3 P (MeV/fm ) 100 RMF:NL3 Akmal Fermi gas Flow Experiment Kaons Experiment FSU Au 10 1 1 1.5 2 2.5 3 r/r 3.5 0 4 4.5 5 Experimental Techniques to probe the symmetry energy with heavy ion collisions at E/A<100 MeV Isospin degree of freedom Z ( Z 1) B aV A aS A aC A1/ 3 2 ( A 2Z ) a sym A Proton Number Z 2/ 3 • Vary the N/Z compositions of projectile and targets 124Sn+124Sn, 124Sn+112Sn, 112Sn+124Sn, 112Sn+112Sn • Measure N/Z compositions of emitted particles n & p isotopes p+ & p- at higher incident energy Neutron Number N Hubble ST Crab Pulsar Heavy Ion collision: 124Sn+124Sn, E/A=50 MeV Around incident energy: E/A<100 MeV: Reaction mechanism depends on impact parameters n & p are emitted throughout b=0 fm multifragmentation b=7 fm Neck fragments Charged fragments (Z=3-20) are formed at subnormal density gi Esym=12.7(r/ro)2/3 + 19(r/ro) Classes of models used to interpret experimental results 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. II. Statistical models: Describe longer time scale decays from single source. •nuclear mass, •level densities, •decay rates Uncertainties Source parameters: Ao, Zo, Eo, Vo, J Information obtained is for finite nuclei, not for infinite nuclear matter Symmetry energy included in the nuclear EOS for infinite nuclear matter at various density from the beginning of collision. Symmetry energy included in the form of fragment masses – finite nuclei & valid for ro only. EOS extrapolated using statistical model is questionable. Theory must predict how reaction evolves from initial contact to final observables Experimental Observable : Isospin Diffusion Isospin diffusion occurs only in asymmetric systems A+B No isospin diffusion between symmetric systems --Isospin Transport Ratio 124 112 124 R =1 112 124 Ri = -1 112 i 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”?? x AB ( x AA xBB ) / 2 Ri 2 x AA xBB Rami et al., PRL, 84, 1120 (2000) xAB, yAB experimental or theoretical observable for AB yAB= a xAB+b Ri(xAB )= Ri(yAB ) Experimental Observable : Isospin Diffusion Probe the symmetry energy at subsaturation densities in peripheral collisions, e.g. 124Sn + 112Sn Isospin “diffuse” through low-density neck region x AB ( x AA xBB ) / 2 Ri 2 x AA xBB Projectile 124Sn Target 112Sn stiff x(calc)= Symmetry energy drives system towards equilibrium. •stiff EOS small diffusion; |Ri|>>0 •soft EOS fast equilibrium; Ri0 soft Constraints from Isospin Diffusion Dataof calculation! g pBUU: S=12.7(r/ro)2/3 + 12.5 (r/ro) i gi ~2 IBUU04 : S~31.6(r/ro)g 0.69g 1.05 stiffness stiffness M.B. Tsang et. al., PRL 92, 062701 (2004) L.W. Chen, … B.A. Li, PRL 94, 032701 (2005) Observable in HIC is sensitive to r dependence of S and should provide constraints to symmetry energy Experimental Observables: n/p yield ratios Li et al., PRL 78 (1997) 1644 100 F2 F1 =0.3 stiff F3 50 S=12.7(r/ro)2/3 + 17.6(r/ro)gi soft Neutron Proton 0 ImQMD -50 Y(n)/Y(p) (MeV) UVasyasy(MeV) •n and p potentials have opposite sign. •n & p energy spectra depend on the symmetry energy softer density dependence emits more neutrons. F1=2u2/(1+u) F2=u F3=u -100 0 0.5 1 u = r / ro 1.5 2 •More n’s are emitted from the nrich system and softer iso-EOS. n/p Double Ratios (central collisions) Double Ratio 124Sn+124Sn;Y(n)/Y(p) 112Sn+112Sn;Y(n)/Y(p) minimize systematic errors Will repeat experiment for better accuracy Data : Famiano et al. PRL 97 (2006) 052701 n/p Double Ratios (central collisions) 112Sn+112Sn;Y(n)/Y(p) minimize systematic errors Double Ratio Double Ratio 124Sn+124Sn;Y(n)/Y(p) Center of mass Energy Famiano et al. RPL 97 (2006) 052701 •Effect is much larger than IBUU04 predictions inconsistent with conclusions from isospin diffusion data. Nuclear Collisions simulations with Transport Models – Nuclear EOS included from beginning of collisions BUU models: Semiclassical solution of onebody 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 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 g Esym=12.5(r/ro)2/3 + 17.6 (r/ro)i 0.4gi 1.05 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 x AB ( x AA xBB ) / 2 Ri 2 x AA xBB S=12.5(r/ro)2/3 + gi 17.6 (r/ro) x(data)=a x(QMD)= Equilibrium Ri=0 0.4gi 1 No diffusion Ri =1; Ri =-1 b~5.8 – 7.2 fm Impact parameter is not well determined in the experiment Analysis of rapidity dependence of Ri with ImQMD model x AB ( x AA xBB ) / 2 Ri 2 x AA xBB S=12.5(r/ro)2/3 + 17.6 (r/ro) x(data) =f(7Li/7Be) x(QMD)= Equilibrium Ri=0 0.4gi 1 No diffusion Ri =1; Ri =-1 gi b~5.8 – 7.2 fm New analysis on rapidity dependence of isospin diffusion ratios – not possible with BUU type of simulations due to lack of fragments. For the first time, we have a transport model that describes np ratios and two isospin diffusion measurements 0.4gi 1.05 0.4gi 1 0.45gi 0.95 Consistent constraints from the 2 analysis of three observables S=12.5(r/ro)2/3 + gi 17.6 (r/ro) 0.4gi 1 How to connect different representations of the symmetry energy IBUU04 : S~31.6(r/ro)g approximation 0.69g 1.05 g S=12.5(r/ro)2/3 + 17.6 (r/ro) i IBUU04 IQMD Expansion around r0: slope L & curvature Ksym L r r0 S S o B 3 r0 K sym 18 r B r0 r0 S~31.6(r/ro) LSymmetry pressure Psym 2 ... L 3r 0 Esym r B r B r0 3 r0 Psym g g S=12.5(r/ro)2/3 + 17.6 (r/ro) i S~31.6(r/ro) Rnp=0.04 fm IBUU04 IQMD L r r0 S S o B 3 r0 K sym 18 r B r0 r0 2 ... L 3r 0 Esym r B r B r0 3 r0 Psym g g S=12.5(r/ro)2/3 + Cs,p(r/ro) i Vary Cs,p and gi 2 2 analysis No constraints on So L r r0 S S o B 3 r0 K sym 18 r B r0 r0 2 ... L 3r 0 Esym r B r B r0 3 r0 Psym g Esym=12.5(r/ro)2/3 + Cs,p(r/ro) i Constraints from masses and Pygmy Dipole Resonances E sym L r r0 S o B 3 r0 K sym 18 r B r0 r0 2 ... L 3r 0 Esym r B r B r0 3 r0 Psym g Esym=12.5(r/ro)2/3 + Cs,p(r/ro) i Constraints from masses and Pygmy Dipole Resonances E sym L r r0 S o B 3 r0 K sym 18 r B r0 r0 2 ... L 3r 0 Esym r B r B r0 3 r0 Psym g Esym=12.5(r/ro)2/3 + Cs,p(r/ro) i Current constraints on symmetry energy from HIC E sym L r r0 S o B 3 r0 K sym 18 r B r0 r0 2 ... L 3r 0 Esym r B r B r0 3 r0 Psym Constraints on the density dependence of symmetry energy ? FRIB Au+Au No constraints between r0 and 2 r0 Outlook 2020? FRIB FAIR Precision measurements in FRIB Outlook FRIB MSU FAIR MSU (2009-2012) : E/A<100 MeV measure isospin diffusion, fragments, residues, p,n spectra ratios and differential flow improve constraints on S(r), m*, nn, pp, np at r<ro MSU (~2013) : E/A>120 MeV measure p+, p- spectra ratios constraints at ro< r<1.7ro -- Bickley Outlook FRIB MSU ? GSI FAIR GSI (2011) : E/A~400 – 800 MeV measure p,n spectra ratios and differential flow determine constraints S(r), m*, nn, pp, np at 2.5ro< r<3ro Lemmon, Russotto et al, experimental proposal to GSI PAC Outlook Riken FRIB MSU ? GSI FAIR Riken (2013-2017) : E/A=200-300 MeV measure p+, p- spectra ratios, p,n, t/3He spectra ratios and differential flow determine S(r), m*, nn, pp, np at r~2ro Riken (2011) : E/A>50 MeV measure isospin diffusions for fragments and residues determine S(r) at r<2ro. 108Sn+112,124Sn – RI beam used to increase . Detectors needed: n detectors: NSCL/pre-FRIB; GSI; RIBF/Riken Pions/kaons & p, t, 3He 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 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 rr0, -- refinement in constraints foreseen in near future with improvement in calculations and experiments at MSU, GANIL & Riken – p+ vs. p- production, n/p, t/3He spectra and differential flows may provide constraints at r2r0 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 Y.X. Zhang (ImQMD), P. Danielewicz, M. Famiano, W.A. Friedman, W.G. Lynch, L.J. Shi, Jenny Lee, 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) 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 How to connect different symmetry energy representations 50 Expansion around r0: Symmetry slope L & curvature Ksym Total Symmetry Energy 40 E sym (MeV) Esym 30 L r r 0 K sym a4 B 3 r 0 18 r B r0 r 0 2 Symmetry pressure Psym L 3r 0 g =0.5 20 Esym r B r B r0 3 r0 Psym i g =2.0 i FSU GOLD AV18 skm* NL3 10 0 0 0.2 0.4 0.6 0.8 r/r0 1 1.2 1.4 Value of symmetry energy at saturation Esym ( r0 ) a4 Riken Samurai TPC Density region sampled depends on collision observable & beam energy • r>r0 examples: – Pion energy spectra – Pion production ratios – Isotopic spectra – Isotopic flow – With NSCL beams, densities up to 1.7 0 are accessible – Beams: 50-150 MeV, 50,000pps 106Sn-126Sn, 37Ca-49Ca Riken Samurai TPC Density region sampled depends on collision observable & beam energy • r>r0 examples: – Pion energy spectra – Pion production ratios – Isotopic spectra – Isotopic flow – With NSCL beams, densities up to 1.7 0 are accessible – Beams: 50-150 MeV, 50,000pps 106Sn-126Sn, 37Ca-49Ca Projectile Isospin Diffusion 124Sn No diffusion Target 112Sn from isoscaling Complete mixing from Y(7Li)/Y(7Be) Laboratory experiments to study properties of neutron stars r/r0 ye T(MeV) n-star HI collisions ~ 0.1 - 10 ~ 0.1-5 ~0.1 ~1 ~0.38-0.5 ~ 4-50 Extrapolate information from limited asymmetry and temperature to neutron stars! Laboratory experiments to study properties of neutron stars 208Pb extrapolation from 208Pb radius to n-star radius N/Z ratios from bound fragments (Z=3-8) complementary to n/p ratios Effects are small Hot fragments produced in calculations. EC.M. P Esym=12.7(r/ro)2/3 + 19(r/ro)gi T N/Z ratios from bound fragments (Z=3-8) complementary to n/p ratios Sequential decay effects are important Data consistent with soft EOS P Esym=12.7(r/ro)2/3 + 19(r/ro)gi T Experimental Observables to probe the symmetry energy E/A(r,) = E/A(r,0) + 2S(r) ; = (rn- rp)/ (rn+ rp) = (N-Z)/A • Collision systems: 124Sn+124Sn, 124Sn+112Sn, 112Sn+124Sn, 112Sn+112Sn • E/A=50 MeV • Low densities (r<r0): – n/p spectra and flows; Y(n)/Y(p), Y(t)/Y(3He), – Fragment isotopic distributions, • Isoscaling: interpretation with statistical model is incorrect • <N>/<Z> of Z=3-8 fragments • Isospin diffusion – Correlation function, C(q) – Neutron, proton radii, E1 collective modes. • High densities (r2r0) – Neutron/proton spectra and flows; C(q) – p+ vs. p- production, k, hyperon production. Exploring Bulk properties of Nuclear Matter with Heavy Ion Collisions asystiff asysoft Low density/energy High density/energy Tsang, HW • fragments, ratios • differential flow QF Li, Di Toro BA Li, HW • isospin diffusion • n/p, LIF ratios Di Toro, Lukasic Tsang • isoscaling • pions ratios DiToro, Reisdorf, QF Li Di Toro • migration/fractionat. • kaon ratios Prassa, QF Li Aumann, Ducoin • collective excitations • neutron stars Danielewicz • surface phenomena Lehaut • phase transitions BA Li, Kubis Hermann Wolter Constraints from Isospin Diffusion Data x=-1 124Sn+112Sn data x=0 x=1(soft) x=-2 Data: IBUU04: •Collisions of Sn+Sn isotopes at E/A=50 MeV Collisions of Sn+Sn isotopes at E/A=50 MeV •b/bmax>0.8 <b>~7.2 fm from multiplicity gates. b=6 fm •y/yb>0.7 •Results obtained with clusters Projectile-like residue determined from density & y/yb>0.5 No clusters Isospin diffusion in the projectile-like region Basic ideas: • Peripheral reactions • Asymmetric collisions 124Sn+112Sn, 112Sn+124Sn -- diffusion • Symmetric Collisions 124Sn+124Sn, 112Sn+112Sn -- no diffusion • Relative change between target and projectile is the diffusion effect Projectile Target Density region sampled depends on collision observable & beam energy • r>r0 examples: – Pion energy spectra – Pion production ratios – Isotopic spectra – Isotopic flow – With NSCL beams, densities up to 1.7 0 are accessible – Beams: 50-150 MeV, 50,000pps 106Sn-126Sn, 37Ca-49Ca 30 Isospin Dependence of the Nuclear Equation Neutron of State matter EOS PAL: Prakash et al., PRL 61, (1988) 2518. forPhys. Asymmetric Matter ColonnaEOS et al., Rev. C57, (1998) 1410. Soft (=0, K=200 MeV) asy-soft, =1/3 (Colonna) asy-stiff, =1/3 (PAL) =(r -r )/(r +r ) 20 E/A (MeV) Brown, Phys. Rev. Lett. 85, 5296 (2001) 10 n p n p 0 -10 -20 0 0.1 0.2 0.3 0.4 0.5 0.6 r (fm ) -3 E/A (r,) = E/A (r,0) + 2S(r) = (rn- rp)/ (r n+ rp) = (N2 E / A ) P r Z)/A r s/a • The density dependence of symmetry energy is largely unconstrained. • Pressure, i.e. EOS is rather uncertain even at r0. • r<r0 – created in multifragmentation process Observables: – n/p ratios – Isotopic spectra – Beams: 50 MeV, 112Sn-124Sn dailygalaxy.com Transport description of heavy ion collisions: non-relativistic: BUU f p f U p f I coll f , t m Vlasov eq.; mean field EOS 3 2-body hard collisions 1 (2p ) 3 2 dp dp dp 2 3 4 v12 gain term effective mass Kinetic momentum Field tensor mean px(y0) [MeV] Simulation with Test Particles: 1 f f 2 (1 f 3 )(1 f 4 ) Relativistic BUU I coll ( f , ) 1 2 1 d ( p1 p2 p3 p4 ) d 1234 (1 f )(1 f 2 ) f 3 f 4 loss term 1 4 Analysis of rapidity dependence of Ri with ImQMD model g Esym=12.5(r/ro)2/3 + 17.6 (r/ro)i 0.45gi 0.95 New analysis on rapidity dependence of isospin diffusion ratios – not possible with BUU type of simulations due to lack of fragments.