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Probing the Incompressibility of Neutron-Rich Matter from Heavy-Ion Reactions

Probing the Incompressibility of Neutron-Rich Matter from Heavy-Ion Reactions. Collaborators : Lie-Wen Chen, Shanghai Jiao Tong University Che Ming Ko, Texas A&M University. Andrew W. Steiner, Los Alamos National Laboratory.

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Probing the Incompressibility of Neutron-Rich Matter from Heavy-Ion Reactions

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  1. Probing the Incompressibility of Neutron-Rich Matter from Heavy-Ion Reactions Collaborators:Lie-Wen Chen, Shanghai Jiao Tong University Che Ming Ko, Texas A&M University Andrew W. Steiner, Los Alamos National Laboratory • Symmetry Energy and Incompressibility of Neutron-Rich Matter • Current status and major issues • Importance in astrophysics and nuclear physics • A Transport Model for Nuclear Reactions Induced by Neutron-Rich Nuclei • Some details of the IBUU04 model • Momentum dependence of the symmetry potential and neutron-proton effective mass splitting • in neutron-rich matter • Experimental Probes • Examples:isospin transport, n/p, π-/π+ ratio, and neutron-proton differential flow • 4. Summary Bao-An Li Arkansas State University

  2. Equation of State of neutron-rich matter at T=0, density ρ and isospin asymmetry is: The key messages:A great deal of information about the EOS of symmetric matter E(ρ,0) has been obtained from studying heavy-ion reactions for almost 30 years. The field has come to the point that further progress on determining the E(ρ,0) and K∞ requires a better determination of the Esym(ρ) and Kasy. The symmetry energy itself is very important for many interesting questions in both nuclear physics and astrophysicsMomentum dependence of the symmetry potential and the correspondingneutron-proton effective mass splitting in neutron-rich matter are critically important for extracting novel properties of neutron-rich matter.Nuclear reactions induced by neutron-rich nuclei provide a unique opportunity to constrain the symmetry energy Esym(ρ) and the n-p effective mass splitting in neutron-rich matter in a broad density range, -550 < Kasy < -450 MeV from MSU isospin diffusion data

  3. Esym (ρ)predicted by microscopic many-body theories Symmetry energy (MeV) DBHF RMF BHF Effective field theory Greens function Variational Density A.E. L. Dieperink et al., Phys. Rev. C68 (2003) 064307

  4. The major remaining uncertainty in determining theEOS of symmetric matter is the poor knowledge about Esym(ρ) Example 1:On extracting the incompressibility K∞ of symmetric nuclear matter at ρ0 from giant monopole resonance, J. Piekarewicz, PRC 69, 041301 (2004); G. Colo, N. Van Giai, J. Meyer, K. Bennaceur and P. Bonche, PRC 70, 024307 (2004). , KA= m<r2>0E2ISGMR = K (1+cA-1/3) + Kasyδ2 + KCoul Z2 A-4/3 Kasy depends on the density dependence of the symmetry energy ! K∞=250 K∞=240 The latest conclusion: K =230-240 MeV for 26 < Esym(ρ0) < 40 MeV data range K∞=230 -566 ± 1350 < Kasy < 139 ±1617 MeV Shlomo and Youngblood, PRC 47, 529 (1993) (Kasy ??) Symmetry energy at ρ0

  5. Themultifaceted influence of symmetry energy in astrophysics and nuclear physicsJ.M. Lattimer and M. Prakash, Science Vol. 304 (2004) 536-542.A.W. Steiner, M. Prakash, J.M. Lattimer and P.J. Ellis, Phys. Rep. (2005). isodiffusion n/p π-/π+ Isospin physics isotransport isocorrelation isofractionation t/3He K+/K0 Expanding fireball and gamma-ray burst (GRB) from the superdene neutron star (magnetar) SGR 1806-20 on 12/27/2004. RAO/AUI/NSF isoscaling GRB and nucleosynthesis in the expanding fireball after an explosion of a supermassive object depends on the n/p ratio In pre-supernova explosion of massive stars is easier with smaller symmetry energy

  6. Promising Probes of the Esym(ρ) in Nuclear Reactions (an incomplete list !) Detecting neutrons simultaneously with charged particles is critical ! Most probes in heavy-ion collisions are based on transport model studies

  7. Hadronic transport equations for the reaction dynamics: Ub is the mean-field potential for baryons Baryons: Mesons: The phase space distribution functions, mean fields and collisions integrals are all isospin dependent An example: Simulate solutions of the coupled transport equations using test-particles and Monte Carlo: The evolution of is followed on a 6D lattice (gain) (loss)

  8. Isospin splitting of nucleon mean field within the BHF approach W. Zuo, L.G. Gao, B.A. Li, U. Lombardo and C.W. Shen, Phys. Rev. C (2005) in press. The momentum dependence of the nucleon potential is a result of the non-locality of nuclear effective interactions and the Pauli exclusion principle

  9. Neutron-proton effective k-mass splitting BHF vs. EBHF (with 3-bodt force) e is the energy density M*n > M*p neutrons protons with Without 3-body force W. Zuo, L.G. Gao, B.A. Li, U. Lombardo and C.W. Shen, Phys. Rev. C (2005) in press. Some Skyrme interactions gave mn* < mp* !

  10. Symmetry energy and single nucleon potential used in the IBUU04 transport code for reactions with radioactive beams stiff ρ soft density HF using a modified Gogny force: B.A. Li, C.B. Das, S. Das Gupta and C. Gale, PRC 69, 034614; NPA 735, 563 (2004).

  11. Momentum and density dependence of the symmetry potential δ δ Density ρ/ρ0 momentum Lane potential extracted from n/p-nucleus scatterings and (p,n) charge exchange reactions provides only a constraint at ρ0: Although the uncertainities are large, NOT a single experiment was analyzed assuming the symmetry potential would INCREASE with energy because then the errors will be even larger for Ekin < 100 MeV P.E. Hodgson, The Nucleon Optical Model, World Scientific, 1994 G.W. Hoffmann et al., PRL, 29, 227 (1972). G.R. Satchler, Isospin Dependence of Optical Model Potentials, 1968

  12. Neutron-proton effective k-mass splitting in neutron-rich matter With the modified Gogny effective interaction B.A. Li, C.B. Das, S. Das Gupta and C. Gale, PRC 69, 034614 (2004); NPA 735, 563 (2004).

  13. Probing the isospin-dependence of in-medium NN cross sectionsHow does the ratio change in neutron-rich medium? • All published results are for symmetric matter • Conflicting conclusions • Need experimental constraints NN cross section in free-space G.Q. Li and R. Machleidt, Phys. Rev. C48, 11702 and C49, 566 (1994). Opposing conclusions with other models: 1. Q. Li et al., PRC 62, 014606 (2000) 2. G. Giansiracusa et al., PRC 53, R1478 (1996) 3. H.-J. Schulze et al., PRC 55, 3006 (1997) 4. M. Kohno et al., PRC 57, 3495 (1998)

  14. Nucleon-nucleon crosssections and nuclear stopping power in neutron-rich matter in neutron-rich matter is the reduced mass of the colliding pair NN in medium Effects on the nuclear stopping power and nucleon mean free-path in n-rich matter J.W. Negele and K. Yazaki, PRL 47, 71 (1981) V.R. Pandharipande and S.C. Pieper, PRC 45, 791 (1992) M. Kohno et al., PRC 57, 3495 (1998) D. Persram and C. Gale, PRC65, 064611 (2002). • In-medium xsections are reduced • nn and pp xsections are splitted • due to the neutron-proton effective mass slitting in neutron-rich matter

  15. Isospin transport (diffusion) in heavy-ion collisions as a probe of Esym (ρ) at subnormal densities Particle Flux: Isospin Flow: The isospin diffusion coefficient DI depends on both the symmetry energy and the neutron-proton scattering cross section Schematicaly for simplified situations: time Isospin asymmetric force L. Shi and P. Danielewicz, Phys. Rev. C68, 017601 (2003).

  16. Extract the Esym(ρ) at subnormal densities from isospin transport A quantitative measure of the isospin non-equilibrium and stopping using any isospin tracer X, F. Rami (FOPI/GSI), PRL, 84, 1120 (2000). if complete isospin mixing ρ ρ MSU experiments: 124Sn+112Sn at Ebeam/A=50 MeV Use X=7Li/7Be or δ of the projectile residue. M.B. Tsang et al. PRL 92, 062701 (2004)

  17. Comparing momentum-dependent IBUU04 calculations using free NN xsections with data on isospin transport from NSCL/MSU Experiments favors: Esym()=32 (/ρ0 )1.1 for ρ<1.2ρ0 Kasy(ρ0)~-550 MeV L.W. Chen, C.M. Ko and B.A. Li, PRL 94, 32701 (2005). Strength of isospin transport Next step: 1. Reduce the error bars of the data and the calculations 2. Compare with results using other observables 3. Exam effects of in-medium cross sections Isobaric incompressibility of asymmetric nuclear matter

  18. Correlation between isospin diffusion and n-skin in 208Pbusing the same EOS------- a more stringent constraint on the symmetry energy Softer symmetry energy than IBUU04 corresponding to x=-1 is needed. The way out: using reduced and isospin dependent in-medium NN cross sections would require a softer symmetry energy to obtain the same value of isospin diffusion at subnormal densities MSU data N-skin in 208Pb within HF Andrew W. Steiner and Bao-An Li, nucl-th/0505051

  19. Effects of the in-medium nucleon-nucleon cross sections б б Free-space xsection -550 < Kasy < -450 MeV close to that extracted from Osaka giant resonsnces data by Fujiwara et al. 0.7 <  < 1.1 in fitting Esym=32(ρ/ρ0) in-medium xsection

  20. Strength of the symmetry potential with and without momentum dependence ρ ρ

  21. The ultimate goal and major questions of studying heavy-ion reactions induced by neutron-rich (stable and/or radioactive) nuclei To understand the isospin dependence of the nuclear Equation of State, extract the isospin dependence of thermal, mechanical and transport properties of asymmetric nuclear matter playing important roles in nuclei, neutron stars and supernove. Among the currently most interesting topics in isospin physics • EOS of neutron-rich matter, especially the density dependence of symmetry energy Esym(ρ) at abnormal densities. 2. Momentum-dependence of the symmetry potential and the neutron-proton effective mass splitting mn*-mp* in neutron-rich matter • Isospin-dependence of in-medium nucleon-nucleon cross sections and the nuclear stopping power in neutron-rich matter • Explore the phase diagram (T-ρ-δ) of neutron-rich matter along the isospin asymmetry δ axis (e.g, neutron distillation, n-Λ phase transition) • Isospin mixing of vector mesons (ρ0-ω) and charge symmetry breaking in neutron-rich matter The most important question relevant to all of the above: What is the isospin dependence of the in-medium nuclear effective interactions

  22. Evolution of isospin diffusion б

  23. Predictions for reactions with high energy neutron-rich beamsat CSR/Lanzhou up to 500 MeV/A for 238U at RIA/USA up to 400 MeV/A for 132Snat FAIR/GSI up to 2 GeV/A for 132Sn Examples: • Isospin distillation/fractionation • π- yields and π-/π+ ratio • Neutron-proton differential transverse flow Besides many other interesting physics, it allows the determination of nuclear equation of state for neutron-rich matter at high densities where it is most uncertain and most important for several key questions in astrophysics.

  24. Formation of dense, asymmetric nuclear matter at CSR, RIA and GSI Soft Esym Soft Esym Stiff Esym Stiff Esym n/p ratio of the high density region B.A. Li, G.C. Yong and W. Zuo, PRC 71, 014608 (2005)

  25. Isospin fractionation (distillation): at isospin equilibrium EOS requirement: low(high)density region is more neutron-rich with stiff (soft)symmetry energy Isospin asymmetry of free nucleons Symmetry enengy stiff soft ρ0 density

  26. Near-threshold pion production with radioactive beams at RIA and GSI ρ density stiff soft yields are more sensitive to the symmetry energy Esym(ρ)since they are mostly produced in the neutron-rich region formed preferentially with the soft symmetry energy However, pion yields are also sensitive to the symmetric part of the EOS

  27. Pion ratio probe of symmetry energy

  28. Time evolution of π-/π+ ratio in central reactions at RIA and GSI From the overlapping n-skins of the colliding nuclei soft stiff

  29. Differential ratios

  30. Transverse flow as a probe of the nuclear EOS: px y Neutron-proton differential flow as a probe of the symmetry energy: for n and p symmetry potential is generally repulsive for neutrons and attractive for protons Bao-An Li, PRL 85, 4221 (2000). G.C. Yong, B.A. Li, W. Zuo, High energy physics and nuclear physics (2005).

  31. Summary • The EOS of n-rich matter, especially the Esym(ρ) is very important for many interesting questions in both astrophysics and nuclear physics • Transport models are invaluable tools for studying the EOS of neutron-rich matter • Isospin transport experiments at intermediate energies allowed us to extract Esym()=32 (/ρ0 )1.1 for ρ<1.2ρ0, and Kasy(ρ0)~-550 MeV • High energy radioactive beams at RIA and FAIR/GSI will allow us to study the EOS of n-rich matter up to 3ρ0 using several sensitive probes of the symmetry energy Esym().

  32. Extract the Esym(ρ) from isospin transport A quantitative measure of the isospin non-equilibrium and stopping power In A+B using any isospin tracer X, F. Rami (FOPI), PRL, 84, 1120 (2000). If complete isospin mixing/ equilibrium MSU experiments: R=0.42-0.52 in 124Sn+112Sn at Ebeam/A=50 MeV mid-central collisions. With 112Sn+112Sn and 124Sn+124Sn as references. Use X=7Li/7Be or δ of the projectile residue, etc. M.B. Tsang et al. PRL 92, 062701 (2004) SBKD: momentum-independent Soft Bertsch-Kruse-Das Gupta EOS MDI: Momentum-Dependent Interaction Momentum-independent Momentum-dependent All having the same Esym (ρ)=32 (ρ/ρ0)1.1

  33. Coulomb effects on π-/π+ ratio is well known

  34. The n/p ratio of pre-equilibrium nucleons is one of the most sensitive observables to the Esym(ρ) as expected from the statistical consideration and predicted by several dynamical models • Experimental situation: (several examples) • Unusually high n/p ratio of pre-equilibrium nucleons beyond the Coulomb • effect was observed by Dieter Hilscher et al. using the Berlin neutron-ball • in both heavy-ion and pion induced reactions around 1987 • Similar phenomenon was observed in heavy-ion experiments at MSU • using the Rochester neutron-ball by Udo Schröder et al. around 1997 • More recent experiments dedicated to the study of n/p ratio of pre- • equilibrium nucleons are being analyzed by the MSU-UW collaboration • Generally, a high n/p ratio of pre-equilibrium nucleons emitted from subnormal densities requires a soft symmetry energy. However, no model comparison has been made, thus no indication on the Esym(ρ) has been obtained yet.

  35. Symmetry potential The n/p ratio of pre-equilibrium nucleons as a probe of Esym(ρ) Symmetry energy soft Statistically one expects: Dynamical simulations B.A. Li, C.M. Ko and. Z. Ren, PRL 78 (1997) 1644 B.A. Li, PRL 85 (2000) 4221 soft (N/Z)free/(N/Z)bound at 100 fm/c stiff

  36. t/3He ratio as a probe of the symmetry energy X=1 X=-2

  37. Correlation between n/p and t/3He ratios in advanced coalescence model • It is expected to be linear ONLY within the simplified momentum-space coalescence model • In more advanced coalescence models where the overlap between the product of the neutron and • proton phase space distribution functions at freeze-out and the Wigner functions of light clusters • are used, this correlation is NOT NECESSARILY linear • Can we use this correlation itself as a probe of the symmetry energy? X=1 X=-2

  38. Jorge Piekarewicz et al., RMF with FSU-Gold parameter set (NL3 with two additional couplings). It reproduce the GMR in 90Zr and 208Pb, and the isovector giant dipole resonance of 208Pb. The symmetry energy is significantly softer than what is extracted from the isospin diffusion.

  39. Isospin mixing of vector mesons (ρ0-ω) and charge symmetry breaking (CSB) in neutron-rich matter proton neutron + ρ0 ω ρ0 ω Anti-neutron Anti-proton Vertex (ρpp)= - Vertex (ρnn), Vertex (ωpp)= Vertex (ωnn) the two contributions almost cancel out in symmetric matter, the small remains due to Mn > Mp is enough to explain the CSB in vacuum and the Nolen-Schiffer effect in mirror nuclei. In neutron-rich matter due to both N > Z and the neutron-proton effective mass splitting Mn* - Mp*, there is a large (ρ0-ω)mixing. The consequences of the mixing are: (1) Separation ofρ0 and ω increases from about 12 MeV in vacuum to about 150 MeV in dense neutron-rich matter; (2) additional reduction of the ρ mass besides that due to the chiral symmetry restoration which happens also in symmetric matter

  40. Probing the Neutron-Proton Effective Mass Splitting in Neutron-Rich Matter at CSR? Collaborators:Lie-Wen Chen, Shanghai Jiao Tong University Che Ming Ko, Texas A&M University Pawel Danielewicz and Bill Lynch, Michigan State University Gaochan Yong and Wei Zuo, IMP, Lanzhou, Chinese Academy of Science Andrew W. Steiner, Los Alamos National Laboratory Champak B. Das, Charles Gale and Subal Das Gupta, McGill University Bao-An Li Arkansas State University, USA and Institute of Modern Physics, Chinese Academy of Science • The ultimate goal and major issues of studying heavy-ion reactions induced by • neutron-rich (stable and/or radioactive) nuclei • 2. Determining the momentum dependence of the symmetry potential and neutron-proton effective mass splitting in neutron-rich matter • 3. Determining the symmetry energy of neutron-rich matter at abnormal densities

  41. Isospin- asymmetric nuclear matter with Three Body Force Zuo Wei and U. Lombardo with 3-body force without

  42. Use constrained mean fields to predict the EOS for symmetric matter Width of pressure domain reflects uncertainties in comparison and of assumed momentum dependence. Corresponding EOS for neutron matter - Two regions correspond to two different Esym(ρ), the width is completely due to the uncertainty in Esym(ρ). (2) Present constraints on the EOS of symmetric and pure neutron matter for 2ρ0< ρ < 5ρ0 using flow data from BEVALAC, SIS/GSI and AGS P. Danielewicz, R. Lacey and W.G. Lynch, Science 298, 1592 (2002)

  43. Simulation as the Third Branch of Science(experiment/observation, theory, simulation) • Applications of transport models • Transport models have been widely used in astrophyics, plasma physics, • semiconductor and nanostructures, particle and nuclear physics. • 2.Development of transport models • Transport codes often implement extra physical assumptions and dynamical • mechanisms which go beyond the equations used to motivate their designs. These • algorithms often undergo evolutions with time as we make progresses in our R&D • efforts and also as our needs for including new processes arise. They may involve • many phenomenological parameters which are not all well experimentally constrained • yet because of the lack of the relevant experimental data, and some of them • are exactly what we want to learn. • 3. Challenges of transport models for reactions involving radioactive beams • Develop practically implementable quantum transport theories ( the de Broglie • wavelenght may be comparable to the nucleon mean free path in energetic central • reactions, and the uncertainty principle imposes a strong correlation between • delocalization of nucleons and their momentum distribution) • Include more structure information in the initial state especially for peripheral reactions. • Use consistently all inputs (initial state, mean field and бNN) from the same interactions

  44. Initialization procedures: • r-space: distribute n and p according to • predictions by structure models**, e.g., RMF • (2) p-space: using local Thomas-Fermi • (3) check stability • ** Trade-off: drawbacks/advantages • The initial state may not be the ground state corresponding to the effective interactions used in the subsequent reactions. This is, however, not a serious problem for high energy central reactions. • None of the existing transport models can generate the initial nucleon density profiles BETTER than dedicated structure models for radioactive nuclei, and there is no data to constrain the neutron density profiles. • If one insists on using the same effective interactions in generating the initial state and carrying out the subsequent reactions, it is then hard to tell whether differences in final observables obtained from using different interactions, e.g., symmetry energies, are from the different initial states or from the reaction dynamics. • A compromise has to be made RMF (TM1)

  45. Sensitivity of the Various Structure Measurements Iso Tanihata Radii Density Skin

  46. Equation of State of Neutron-Rich Matter: K. Oyamatsu, I. Tanihata, Y. Sugahara, K. Sumiyoshi and H. Toki, NPA 634 (1998) 3. Isospin asymmetry (TM1) saturation lines N/Z

  47. Esym(ρ)from Hartree-Fock approach using different effective interactions B. Cochet, K. Bennaceur, P. Bonche, T. Duguet and J. Meyer, Nucl. Phys. A731, 34 (2004). J. Stone, J.C. Miller, R. Koncewicz, P.D. Stevenson and M.R. Strayer, PRC 68, 034324 (2003). Bao-An Li, PRL 88, 192701 (2002) (where paramaterizations of Easym and Ebsym are given) New Skyrme interactions Easym HF predictions using 90 effective interactions scatter between Easym and Ebsym Amplication around normal density Ebsym

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