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Cyclotron aggies at IWND2009, Shanghai, China

It is my great pleasure to say s ome words on this occasion to c elebrate Prof. J oe. Natowitz’s achievement on this workshop. B ecause un expected delay for my visa process, I am sorry unable to join this special workshop.

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Cyclotron aggies at IWND2009, Shanghai, China

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  1. Itismygreat pleasure to say some words on this occasion to celebrate Prof. Joe. Natowitz’sachievementonthisworkshop.Becauseunexpecteddelayformyvisaprocess,Iamsorryunabletojointhisspecialworkshop. It was my honor to have been associated withJoe when I joined hisgroupat Cyclotron Institute as a post-doc fellow for abouttwo years fromearlier2001. Since then I have opportunitiestoworkwithJoewithfullofpleasure.Heisnotonlyanexcellenttutoralsoaverynicefriend. HeandKarinarealwayssokind.Inthe1stdaywhenIarrivedatCollegeStation,itwasJoetotakemetogotodifferentstoresforpreparingmylivingstuffs,evenmattressandchairsetc.Also,inacoupleofmyrecentshortvisitstoTAMU,JoeandKarininvitedmetoliveinhishouse.Thisisalsoamemorableexperienceinmylife. Inmyfeeling,Joealwayshasalotofnewidealsandkeepexcitingeverydayfornuclearphysicsresearches.Hedoesnotliketofollow so-calledhottopic,butincontraryheoftentriedtoproposenewobservablesandmethods.Hissteadfastenthusiasm and dedicationmadehimbecomeafamousnuclearphysicistworld-wide. That’sthereasonwhywecanoftenreadhispublicationinPhysicalReviewLetters. HealsoverysupportnuclearphysicsdevelopmentinChina.Underhissupervising,manyChinesepostodcshaveworkedwithhimandmostofthemwentbackChinaandcontinueworkinthefieldwithsuccess. Joe&Karin,thank you verymuch.IbelieveyouhaveawonderfultimewithsomanyfriendsinCollegeStation! Yu-GangMa(& family) Nationaldistinguishedyoungscholar and HeadofNuclear Physics Div., ShanghaiInstituteofAppliedPhysics,ChineseAcademyofSciences

  2. Cyclotron aggies at IWND2009,Shanghai,China

  3. Cyclotron Aggies at IWND2012,Shenzhen, China Shanghai,2005

  4. Bao-An Li Texas A&M University-Commerce Collaborators: F. Fattoyev, J. Hooker, W. Newton, TAMU-Commerce Lie-Wen Chen, Rong Chen, Xiao-Hua Li and Bao-Jun Chai, Shanghai Jiao Tong University Chang Xu, Nanjing University Jun Xu, Shanghai Institute of Applied Physics Andrew Steiner, INT, University of Washington Che Ming Ko, Texas A&M University Xiao Han and Gao-Feng Wei, Xi’an Jiao Tong University Gao-Chan Yong, Institute of Modern Physics, Chinese Academy of Sciences A brief overview: probing nuclear symmetry energy with nuclear reactions

  5. Outline: 1. What is the symmetry energy problem? 2. Recent community effort and progress made in constraining the symmetry energy 3. Major current challenges

  6. What is the Equation of State of neutron-rich nucleonic matter? symmetry energy Isospin asymmetry δ 12 12 12 Energy per nucleon in symmetric matter 18 18 3 Energy per nucleon in asymmetric matter Symmetric matter ρn=ρp density ??? 0 ρ=ρn+ρp ??? The axis of new opportunities ??? 1 Isospin asymmetry ???

  7. The multifaceted influence of the isospin dependence of strong interactionand symmetry energy in nuclear physics and astrophysicsJ.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. 411, 325 (2005). (Effective Field Theory) (QCD) isodiffusion n/p Isospin physics π-/π+ isotransport in isocorrelation Terrestrial Labs isofractionation t/3He K+/K0 isoscaling

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

  9. Examples: Skyrme Hartree-Fock and Relativistic Mean-Field predictions 23 RMF models ρ Density L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. C72, 064309 (2005); C76, 054316 (2007).

  10. Characterization of symmetry energy near normal density The physical importance of L In npe matter in the simplest model of neutron stars at ϐ-equilibrium In pure neutron matter at saturation density of nuclear matter Many other astrophysical observables, e.g., radii, core-crust transition density, cooling rate, oscillation frequencies and damping rate, etc of neutron stars

  11. C. Xu, B.A. Li, L.W. Chen and C.M. Ko, NPA 865, 1 (2011) R. Chen et al., PRC 85, 024305 (2012).

  12. Symmetry (isovector) potential and its major uncertainties Within an interacting Fermi gas model, schematically, Structure of the nucleus, M.A. Preston and R.K. Bhaduri (1975) NN correlation functions • Spin-isospin dependence of 3-body forces • Short-range tensor force due to rho meson exchange • Isospin-dependence of NN correlations and the tensor force

  13. Usym,1 (ρ,p) in several models BHF Isaac Vidana R. Chen et al., PRC 85, 024305 (2012).

  14. Symmetry potential near saturation density from global nucleon optical potentials • Systematics based on world data accumulated since 1969: • Single particle energy levels from pick-up and stripping reaction • Neutron and proton scattering on the same target at about the same energy • Proton scattering on isotopes of the same element • (p,n) charge exchange reactions Chang Xu, Bao-An Li, Lie-Wen Chen Phys.Rev.C82:054607,2010

  15. Examples of community efforts • Newly formed collaborations and constructions of new detectors • Topical workshops and symposia on symmetry energy RIKEN 2010, Smith College 2011, MSU 2013, Liverpool 2014, …., besides sessions at other meetings • 1-month program on symmetry energy in summer 2013 at MSU with about 70 participants, the first program of the ICNT (International Collaboration in Nuclear Theory jointly funded by MSU+RIKEN+GSI) • EPJA Topical Issue in 2013 on Nuclear Symmetry Energy including 42 papers

  16. Thanks to the hard work of many of you, your postdocs and students as well as supports of your funding agencies

  17. Nusym13 constraints on Esym(ρ0) and L based on 29 analyses of some data V2np Currently impossible to estimate a physically meaningful error bar V2np

  18. Approximate & model-dependent constraints around/below normal density ? ? ? ? ? • Constraints on the symmetry energy and neutron skins from experiments and theory • M. B. Tsang, J. R. Stone, F. Camera, P. Danielewicz, S. Gandolfi, K. Hebeler, C. J. Horowitz, Jenny Lee, W. G. Lynch, Z. Kohley, R. Lemmon, P. Moller, T. Murakami, S. Riordan, X. Roca-Maza, F. Sammarruca, A. W. Steiner, I. Vidaña, S. J. Yennello, • Phys. Rev. C86, 015803 (2012)

  19. Some basic issues on low density, hot neutron-rich matter neutron +proton uniform matter at density ρ and isospin asymmetry as density decreases Many interesting talks covering various topics including • What is the EOS of clustered neutron-rich matter • with pairing and its astrophysical ramifications • In-medium properties of finite nuclei, Mott points, • isospin dependence of the Caloric curve… • Symmetry energy of hot nuclei and the meaning of • isoscaling coefficients • The origin of the Wigner term or linear symmetry energy At finite Temperature T

  20. Joe Natowitz et al.

  21. Experimental extraction of the symmetry energy of clustered matter at very low densities J.B. Natowitz, G. Ropke, S. Typel, D. Blaschke, A. Bonasera, K. Hagel, T. Klahn, S. Kowalski, L. Qin, S. Shlomo, R. Wada, H.H. Wolter Phys.Rev.Lett.104:202501,2010

  22. How to determine the high-density Esym ? ?

  23. Rutledge+Guillot: ApJ v.772 (2013) Independent of the masses of neutron stars WFF1 (AV14+UVII) WFF1 has a soft EOS: K0=209 MeV, Esym ≈26 MeV, L ≈ 60 MeV (estimates) WFF: Wiringa, Fiks and Fabrocini (1988), Phys. Rev. C 38, 1010 The L is not so different from those studies giving significantly larger radii, is the high density Esym rather than L more important here?

  24. WFF: Wiringa, Fiks and Fabrocini (1988), Phys. Rev. C 38, 1010 WFF1 WFF1 (AV14+UVII) WFF1 has a rather soft Esym in the density range of 2-3rho_0 (according to a study by Lattimer and Prakash, Rns is most sensitive to the Esym in this region)

  25. Summary • Significant progress has been made in constraining the symmetry energy around normal density • Interesting new features about the EOS of low-density neutron-rich matter have been found • Major challenges remain in constraining the symmetry energy at supra-saturation densities

  26. Extract the Esym(ρ) at subnormal densities from isospin diffusion/transport Degree of neutron-proton mixing Experiment: 124Sn+112Sn, Ebeam/A=50 MeV National Superconducting Cyclotron Lab. M.B. Tsang et al., Phys. Rev. Lett. 92, 062701 (2004) Transport model analysis: L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. Lett 94, 32701 (2005); Bao-An Li and Lie-Wen Chen, Phys. Rev. C72, 064611 (2005).

  27. Constraints from both isospin diffusion and n-skin in 208Pb Isospin diffusion data: M.B. Tsang et al., PRL. 92, 062701 (2004); T.X. Liu et al., PRC 76, 034603 (2007) MDI potential energy density Transport model calculations B.A. Li and L.W. Chen, PRC72, 064611 (05) X=1 124Sn+112Sn X=0 x=-1 ρρ Hartree-Fock calculations A. Steiner and B.A. Li, PRC72, 041601 (05) Neutron-skin from nuclear scattering: V.E. Starodubsky and N.M. Hintz, PRC 49, 2118 (1994); B.C. Clark, L.J. Kerr and S. Hama, PRC 67, 054605 (2003)

  28. Formation of dense, asymmetric nuclear matter Symmetry energy Stiff Central density Soft density π-/ π+ probe of dense matter Soft Esym Stiff Esym n/p ratio at supra-normal densities

  29. Circumstantial Evidence for a Super-soft Symmetry Energy at Supra-saturation Densities A super-soft nuclear symmetry energy is favored by the FOPI data!!! Z.G. Xiao, B.A. Li, L.W. Chen, G.C. Yong and M. Zhang, Phys. Rev. Lett. 102 (2009) 062502 W. Reisdorf et al. NPA781 (2007) 459 Data: Calculations: IQMD and IBUU04

  30. Umesh Garg: Kt = -555 ± 75 MeV The large uncertainty in L and Ksym explain why it is so hard to pink down Kԏ Many ongoing and planned experiments studying various modes to give better constraints on K0, L and Ksym Existing estimates are consistent M. Centelleset al., Phys. Rev. Lett. 102, 122502 (2009)

  31. The most accurate and abundant data available for either global or nucleus-by-by nucleus analysis of Esym and L at ρ0 are the atomic masses: detailed statistical significance analysis for the L-Esym correlation possible, Danielewicz+Lee, 2013 Lattimer+Lim, 2013 leading to so far the most accurate extraction (FRDM12): J=32.5±0.5  MeV and L=70±15  Peter Möller, William D. Myers, Hiroyuki Sagawa, and Satoshi Yoshida Mostly consistent conclusions, necessary to use L-Esym correlations from other observables to pin down the Esym and L more accurately

  32. Can the symmetry energy become negative at high densities? Yes, it happens when the tensor force due to rho exchange in the T=0 channel dominates Making the EOS of symmetric matter increases faster than the EOS for pure n-matter Example: proton fractions with interactions/models leading to negative symmetry energy M. Kutschera et al., Acta Physica Polonica B37 (2006)

  33. Some questions about Esym(ρ) Why is it so hard to determine it? Why L and Esym(ρ0) are correlated? Some hints and possible answers at the mean-field level

  34. Relationship between the symmetry energy and the mean-field potentials Lane potential Both U0 (ρ,k) and Usym(ρ,k) are density and momentum dependent kinetic isoscalar isovector Symmetry energy Isoscarlar effective mass Using K-matrix theory, the conclusion is independent of the interaction

  35. Rong Chen, Bao-Jun Cai, Lie-Wen Chen, Bao-An Li, Xiao-Hua Li, Chang Xu PRC 85, 024305 (2012). Need FRIB to determine

  36. A major issue near saturation density Possible experimental tests: Esym and the effective mass splitting are NOT 2 independent issues/quantities! The effective mass splitting is an Important part of the L and mainly responsible for its uncertainty!

  37. Comments on the EOS of pure neutron matter and its role in constraining the Esym(ρ)=EOS(pnm)-EOS(snm) • Impressive progress made in calculating the EOSPNM providing a theoretical boundary condition to calibrate the EOS of asymmetric matter • It does constrain the Esym(ρ) around saturation point assuming the EOS of symmetric matter is well understood • It does NOT constrain the Esym(ρ) away from ρ0 where it is harder to calculate the EOS of SNM due to the tensor force, etc

  38. EOSPNM provides a theoretical boundary condition to calibrate the EOS of asymmetric matter

  39. Comments on the “symmetry energy” of clustered matter at very low densities To my best knowledge, for all practical purposes of calculating the EOS for supernovae simulation and neutron star properties, it is Unnecessary to define a “Esym” for the clustered matter, what is needed are in-medium properties of hot nuclei and their Esym It is physically ambiguous to define and talk about the “Esym” for clustered matter

  40. Promising Probes of the Esym(ρ) in Nuclear Reactions • Correlations of multi-observableare important • (2) Detecting neutrons simultaneously with charged particles is critical B.A. Li, L.W. Chen and C.M. Ko, Physics Reports 464, 113 (2008)

  41. Probing the symmetry energy at supra-saturation densities • π -/π +, K+/K0, η • Neutron-proton differential or relative flows • Neutrino flux of supernova explosions (Luke Roberts) • Strength and frequency of gravitational waves (Will Newton) U. Mosel, Ann. Rev. Nucl. Part. Sci. 41, (1991) 29

  42. Xiao et al. 2008 Yong and Li, 2013

  43. Tensor force induced (1) high-momentum tail in single-particle momentum distribution and (2) isospin dependence of NN correlation Theory of Nuclear matter H.A. Bethe Ann. Rev. Nucl. Part. Sci., 21, 93-244 (1971) Fermi Sphere

  44. Variational many-body calculations including 2b tensor Fourier transform of single-particle wf Jastrow wf • Universal shape of high-momentum tail • due to short-range interaction of two • nearby nucleons • scaling of weighted (e,e’) inclusive • xsections from light to heavy nuclei: • the ratio of weighted xsection should be • independent of the scattering variables Tensor force dominance: 270 MeV/c < P < 600 MeV/c 3N correlations, repulsive core and nucleon resonances start playing a role at higher momentum

  45. Isospin-dependence of Short Range NN Correlations and Tensor Force Two-nucleon knockout by a p or e A.Tang et al, PRL 90, 042301 (2003) R. Subedi et al. Science 320, 1475 (2008) Triggered on nucleon pairs with zero total momentum np pp At finite total momentum, the effect is reduced, H. Baghdasaryan et al. (CLAS) PRL 105, 222501 (2010)

  46. 2n SRC 3n SRC Absolute probability per nucleon in the high momentum tail due to n-p short-range tensor force Four-momentum transfer Energy transfer K.S. Egiyan et al (CLAS), PRL96, 082501 (2006)

  47. 420, 012190 (2013). Kinetic part of the symmetry energy can be negative While the Fermi momentum for PNM Is higher than that for SNM at the same density in the mean-field models, if more than 15% nucleons are in the high-momentum tail of SNM due to the tensor force for n-p T=0 channel, the symmetry energy becomes negative Chang Xu, Ang Li, Bao-An Li J. of Phys: Conference Series, 420, 012190 (2013)

  48. Confirmation by Microscopic Many-Body Theories 1. Nuclear symmetry energy and the role of the tensor force Isaac Vidana, Artur Polls, Constanca Providencia, arXiv:1107.5412v1, PRC84, 062801(R) (2011) Brueckner--Hartree--Fock approach using the Argonne V18 potential plus the Urbana IX three-body force 2. High momentum components in the nuclear symmetry energy Arianna Carbone, Artur Polls, Arnau Rios, arXiv:1111.0797v1 Euro. Phys. Lett. 97, 22001 (2012). Self-Consistent Green’s Function Approach with Argonne Av18, CDBonn, Nij1, N3LO interactions 3. Alessandro Lovato, Omar Benhar et al., extracted from results already published in Phys. Rev. C83:054003,2011 Using Argonne V’6 interaction Fermi gas Kinetic symmetry E with tensor correlation They all included the tensor force and many-body correlations using different techniques

  49. Two Consequences of small kinetic contribution to the total Esym (1) Effects of the symmetry POTENTIAL should be increased! Can be zero! But ~ 25 MeV is currently used in all transport models Heavy-ion reactions probing Potential Kinetic added in afterwards by hand using the Fermi gas model to fix the parameter Cs,p and gamma 3bf

  50. (2) Effects on sub-threshold pion ratio, etc n-rich matter with Xp=1/9. 2012 Fraction of high-momentum nucleons in neutron-rich matter Distribution of the available energy for particle production in 2-colliding extended Fermi spheres Percentage of high-momentum nucleons Bao-An Li et al., 2013

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