It is my great pleasure to say some

It is my great pleasure to say some words on this occasion to celebrate Prof. Joe. Natowitz’s achievement on this workshop. Because unexpected delay for my visa process, I am sorry unable to join this special workshop. It was my honor to have been associated with Joe when I joined his group at Cyclotron Institute as a post-doc fellow for about two years from earlier 2001. Since then I have opportunities to work with Joe with full of pleasure. He is not only an excellent tutor also a very nice friend. He and Karin are always so kind. In the 1 st day when I arrived at College Station, it was Joe to take me to go to different stores for preparing my living stuffs, even mattress and chairs etc. Also, in a couple of my recent short visits to TAMU, Joe and Karin invited me to live in his house. This is also a memorable experience in my life. In my feeling, Joe always has a lot of new ideals and keep exciting everyday for nuclear physics researches. He does not like to follow so-called hot topic, but in contrary he often tried to propose new observables and methods. His steadfast enthusiasm and dedication made him become a famous nuclear physicist world-wide. That’s the reason why we can often read his publication in Physical Review Letters. He also very support nuclear physics development in China. Under his supervising, many Chinese postodcs have worked with him and most of them went back China and continue work in the field with success. Joe & Karin, thank you very much. I believe you have a wonderful time with so many friends in College Station!

Cyclotron aggies at IWND 2009, Shanghai, China

Cyclotron Aggies at IWND 2012, Shenzhen, China Shanghai, 2005

A brief overview: probing nuclear symmetry energy with nuclear reactions 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

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

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 r tte a m ic etr =ρ p m ρn ym S density 0 ies ρ=ρn+ρp it un rt po p Energy per nucleon in asymmetric matter ? ? ? Isospin asymmetry 1 Th i ax e o ew n of s ? ? ?

The multifaceted influence of the isospin dependence of strong interaction and symmetry energy in nuclear physics and astrophysics J. 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) n/p π-/π+ t/3 He K+/K 0 (QCD) Isospin physics in Terrestrial Labs isodiffusion isotransport isocorrelation isofractionation isoscaling

Symmetry energy (Me. V) Esym (ρ) predicted by microscopic many-body theories y eor th ld fie. ) e ctiv et al e Eff iser (Ka H DB F F RM BHF Greens function Variational many-body Density A. E. L. Dieperink et al. , Phys. Rev. C 68 (2003) 064307

Examples: Skyrme Hartree-Fock and Relativistic Mean-Field predictions ρ 23 RMF models Density L. W. Chen, C. M. Ko and B. A. Li, Phys. Rev. C 72, 064309 (2005); C 76, 054316 (2007).

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

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

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

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

Symmetry potential near saturation density from global nucleon optical potentials Systematics based on world data accumulated since 1969: (1) Single particle energy levels from pick-up and stripping reaction (2) Neutron and proton scattering on the same target at about the same energy (3) Proton scattering on isotopes of the same element (4) (p, n) charge exchange reactions Chang Xu, Bao-An Li, Lie-Wen Chen Phys. Rev. C 82: 054607, 2010

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 a 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

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

Nusym 13 constraints on Esym(ρ0) and L based on 29 analyses of some data V 2 np Esym L average of the means 31. 55415 58. 88646 standard deviation 0. 915867 16. 52645 Currently impossible to estimate a physically meaningful error bar V 2 np

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. C 86, 015803 (2012)

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 At finite Temperature T • 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

Joe Natowitz et al.

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

How to determine the high-density Esym ? ?

Rutledge+Guillot: Ap. J v. 772 (2013) Independent of the masses of neutron stars WFF 1 (AV 14+UVII) WFF 1 has a soft EOS: K 0=209 Me. V, Esym ≈26 Me. V, L ≈ 60 Me. V (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?

WFF: Wiringa, Fiks and Fabrocini (1988), Phys. Rev. C 38, 1010 1 FF W WFF 1 (AV 14+UVII) WFF 1 has a rather soft Esym in the density range of 2 -3 rho_0 (according to a study by Lattimer and Prakash, Rns is most sensitive to the Esym in this region)

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

Extract the Esym(ρ) at subnormal densities from isospin diffusion/transport Degree of neutron-proton mixing Experiment: 124 Sn+112 Sn, Ebeam/A=50 Me. V 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. C 72, 064611 (2005).

Constraints from both isospin diffusion and n-skin in 208 Pb Isospin diffusion data: M. B. Tsang et al. , PRL. 92, 062701 (2004); T. X. Liu et al. , PRC 76, 034603 (2007) X= 1 MDI potential energy density Transport model calculations B. A. Li and L. W. Chen, PRC 72, 064611 (05) X= 0 124 Sn+112 Sn x= -1 ρ ρ Hartree-Fock calculations A. Steiner and B. A. Li, PRC 72, 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)

Symmetry energy Sti ff Formation of dense, asymmetric nuclear matter Central density So ft density π-/ π+ probe of dense matter ym s ft E So Stiff Esym n/p ratio at supra-normal densities

Circumstantial Evidence for a Super-soft Symmetry Energy at Supra-saturation Densities Data: W. Reisdorf et al. NPA 781 (2007) 459 Calculations: IQMD and IBUU 04 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

Umesh Garg: Kt = -555 ± 75 Me. V 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 K 0, L and Ksym Existing estimates are consistent M. Centelles et al. , Phys. Rev. Lett. 102, 122502 (2009)

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 3 Lim 1 20 , + er im att L leading to so far the most accurate extraction (FRDM 12): J=32. 5± 0. 5  Me. V 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

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 B 37 (2006)

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

Relationship between the symmetry energy and the mean-field potentials Lane potential Both U 0 (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

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

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!

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

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

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

Promising Probes of the Esym(ρ) in Nuclear Reactions (1) Correlations of multi-observable are 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)

Probing the symmetry energy at supra-saturation densities • π -/π +, K+/K 0, 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

Xiao et al. 2008 Yong and Li, 2013

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

Variational many-body calculations inclu Fo u si rier ng tra le- ns pa fo rti rm cle w f ding 2 b t enso r of Universal shape of high-momentum tail àdue to short-range interaction of two nearby nucleons à scaling of weighted (e, e’) inclusive xsections from light to heavy nuclei: the ratio of weighted xsection should be independent of the scattering variables Jas trow wf Tensor force dominance: 270 Me. V/c < P < 600 Me. V/c 3 N correlations, repulsive core and nucleon resonances start playing a role at higher momentum

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)

2 n SRC 3 n 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), PRL 96, 082501 (2006)

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)

Confirmation by Microscopic Many-Body Theories 1. Nuclear symmetry energy and the role of the tensor force Isaac Vidana, Artur Polls, Constanca Providencia, ar. Xiv: 1107. 5412 v 1, PRC 84, 062801(R) (2011) Brueckner--Hartree--Fock approach using the Argonne V 18 potential plus the Urbana IX three-body force 2. High momentum components in the nuclear symmetry energy Arianna Carbone, Artur Polls, Arnau Rios, ar. Xiv: 1111. 0797 v 1 Euro. Phys. Lett. 97, 22001 (2012). Self-Consistent Green’s Function Approach with Argonne Av 18, CDBonn, Nij 1, N 3 LO interactions 3. Alessandro Lovato, Omar Benhar et al. , extracted from results already published in Phys. Rev. C 83: 054003, 2011 Using Argonne V’ 6 interaction They all included the tensor force and many-body correlations using different techniques gas Fermi E metry sym Kinetic relation ensor cor with t

Two Consequences of small kinetic contribution to the total Esym (1) Effects of the symmetry POTENTIAL should be increased! rt mo transpo in all ly used current e. V is 25 M ro! But ~ ze Can be Kinetic Potential dels Heavy-ion reactions ng i b o pr added in afterwards by hand using the Fermi gas model to fix the parameter Cs, p and gamma 3 bf

(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 Bao-An Li et al. , 2013 Per hig centa h-m ge om of ent um n ucl eon s

Near-threshold π-/π+ ratio as a probe of symmetry energy at supra-normal densities W. Reisdorf et al. for the FOPI collaboration , NPA 781 (2007) 459 IQMD, modelling the many-body dynamics of heavy ion collisions: Present status and future perspective C. Hartnack, Rajeev K. Puri, J. Aichelin, J. Konopka, S. A. Bass, H. Stoecker, W. Greiner Eur. Phys. J. A 1 (1998) 151 -169 Need a symmetry energy softer than the above to make the pion production region more neutron-rich! low (high) density region is more neutron-rich with stiff (soft) symmetry energy Or: effectively reduce/increase the pion-/pion+ threshold with different n/p self-energies (M. Di Toro et al)

Promising Probes of the Esym(ρ) in Nuclear Reactions (1) Correlations of multi-observable are 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)

Collaborations are essential to move forward! Esym s D ilitie s ac lite -QM f X U el FRIB satel ls Y-BU mod l y r X-ra and n-ba you X ZTPCs I&II, CRE PREX Thanks!