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 1st 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!

Yu-Gang Ma (& family)

National distinguished young scholar and Head of Nuclear Physics Div., Shanghai Institute of Applied Physics, Chinese Academy of Sciences

Cyclotron aggies at IWND2009, Shanghai, China

Cyclotron Aggies at IWND2012, Shenzhen, China

Shanghai, 2005

Bao-An Li Texas A&M University-Commerce

Collaborators:F. Fattoyev, J. Hooker, W. Newton, TAMU-CommerceLie-Wen Chen, Rong Chen, Xiao-Hua Li and Bao-Jun Chai, Shanghai Jiao Tong UniversityChang Xu, Nanjing UniversityJun Xu, Shanghai Institute of Applied PhysicsAndrew Steiner, INT, University of WashingtonChe Ming Ko, Texas A&M UniversityXiao Han and Gao-Feng Wei, Xi’an Jiao Tong UniversityGao-Chan Yong, Institute of Modern Physics, Chinese Academy of Sciences

A brief overview: probing nuclear symmetry energy

with nuclear reactions

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?

18 18

12

12

12

3

0 )) (, (( ) sn ymp

nn

p pE E E

( , )n pE

symmetry energy

ρ=ρn+ρp0

1

density

Isospin asymmetry

Symmetric m

atter

ρ n=ρ p

Energy per nucleon in symmetric matter

Energy per nucleon in asymmetric matter

δIsospin asymmetry

???

2

pure neutron matter symmetric nuclear matter2

1( ) ( ) ( )

2sym

EE E E

The axis of new opportu

nities

???

???

???

14 30Normal density of nuclear matter 2.7 10 g/cm

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).

Isospin physicsIsospin physicsn/p n/p

isoscaling isoscaling

isotransportisotransport isodiffusionisodiffusion

t/t/33HeHe isofractionationisofractionation

KK++/K/K00

isocorrelation isocorrelation

ππ--//ππ++

inTerrestrial Labs

(QCD)(Effective Field Theory)

Esym (ρ) predicted by microscopic many-body theories

Sym

met

ry e

ner

gy

(MeV

)

Density

Effective field theory

(Kaiser et al.) DBHF

RMF BHF

Greens function

Variational many-body

A.E. L. Dieperink et al., Phys. Rev. C68 (2003) 064307

Examples: Skyrme Hartree-Fock and Relativistic Mean-Field predictions

23 RMFmodels

ρ

L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. C72, 064309 (2005); C76, 054316 (2007).

Density

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

Microphysics governing the E ( ) and L( ) sym

according to the Hugenholtz-Van Hove (HVH) theorem

C. Xu, B.A. Li, L.W. Chen and C.M. Ko, NPA 865, 1 (2011)

R. Chen et al., PRC 85, 024305 (2012).

03

/2

21( ,( , , ) ( ( )), ,) sy ymm sn p UU U k kk U k

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)

• Isospin-dependence of NN correlations and the tensor force

• Spin-isospin dependence of 3-body forces• Short-range tensor force due to rho meson exchange

NN correlation functions

Usym,1 (ρ,p) in several models

R. Chen et al., PRC 85, 024305 (2012).

Isaac Vidana

BHF

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.C82:054607,2010

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 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

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

funding agencies

Esym L

average of the means 31.55415 58.88646standard deviation 0.915867 16.52645

Currently impossible to estimate a physically meaningful error bar

Nusym13 constraints on Esym(ρ0) and L based on 29 analyses of some data

V2np

V2np

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)

Approximate & model-dependent constraints around/below normal density

?

?

?

?

?

Some basic issues on low density, hot neutron-rich matter

neutron +proton uniform matter at density ρ and isospin asymmetry as density decreases

0

1

,

A

2 0

2

,

A

in

0,

i

i

A

ii i

i

AnA

0

A

V

• 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

Many interesting talks covering various topics including

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

?

?

WFF1 (AV14+UVII)

Rutledge+Guillot:

WFF: Wiringa, Fiks and Fabrocini (1988), Phys. Rev. C 38, 1010 WFF1 has a soft EOS: K0=209 MeV, Esym ≈26 MeV, L ≈ 60 MeV (estimates)

The L is not so different from those studies giving significantly larger radii, is the high density Esym rather than L more important here?

Independent of the masses of neutron starsApJ v.772 (2013)

WFF1 (AV14+UVII)

WFF1

WFF: Wiringa, Fiks and Fabrocini (1988), Phys. Rev. C 38, 1010

WFF1 has a rather soft Esym in the density range of 2-3rho_0 (according to astudy 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 low-

density neutron-rich matter have been found• Major challenges remain in constraining the

symmetry energy at supra-saturation densities

Extract the EExtract the Esymsym((ρρ) at subnormal densities from isospin diffusion/transport) at subnormal densities from isospin diffusion/transport

Degree of neutron-proton mixing

Experiment: Experiment: 124124Sn+Sn+112112Sn, ESn, Ebeambeam/A=50 MeV/A=50 MeV

National Superconducting Cyclotron Lab.National Superconducting Cyclotron Lab.M.B. Tsang et al., Phys. Rev. Lett. 92, 062701 (2004)

Transport model analysis:Transport model analysis:L.W. Chen, C.M. Ko and B.A. Li,L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. Lett 94, 32701 (2005);Phys. Rev. Lett 94, 32701 (2005);Bao-An Li and Lie-Wen Chen, Bao-An Li and Lie-Wen Chen, Phys. Rev. C72, 064611 (2005).Phys. Rev. C72, 064611 (2005).

Constraints from both isospin diffusion and n-skin in 208Pb

ρ ρ

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)

Isospin diffusion data:M.B. Tsang et al., PRL. 92, 062701 (2004); T.X. Liu et al., PRC 76, 034603 (2007)

Hartree-Fock calculationsA. Steiner and B.A. Li, PRC72, 041601 (05)

Transport model calculationsB.A. Li and L.W. Chen, PRC72, 064611 (05)

124Sn+112Sn

X=1

X=0

x=-1

MDI potential energy density

Formation of dense, asymmetric nuclear matter

SoftSoft

Stif

fS

tiff

Soft Esym

Stiff Esym

density

Symmetry energy

n/p ratio at supra-normal densities

Central density

π-/ π+ probe of dense matter

2( , ) ( ,0) ( )symE E E

Circumstantial Evidence for a Super-soft Symmetry Energy at Supra-saturation Densities

Z.G. Xiao, B.A. Li, L.W. Chen, G.C. Yong and M. Zhang, Phys. Rev. Lett. 102 (2009) 062502

A super-soft nuclear symmetry energy is favored by the FOPI data!!!

W. Reisdorf et al. NPA781 (2007) 459 Data:

Calculations: IQMD and IBUU04

M. Centelles et al., Phys. Rev. Lett. 102, 122502 (2009)M. Centelles et al., Phys. Rev. Lett. 102, 122502 (2009)

Umesh Garg: K = 555 ± 75 MeV

Many ongoing and planned experimentsstudying various modes to give betterconstraints on K0, L and Ksym

The large uncertainty in L and Ksymexplain why it is so hard to pink down Kԏ

Existing estimates are consistent

The most accurate and abundant data available for either global or nucleus-by-by nucleusanalysis of Esym and L at ρ0 are the atomic masses: detailed statistical significance analysis for the L-Esym correlation possible,

Lattimer+Lim

, 2013

Danielewicz+Lee, 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

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 dominatesMaking 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

3 30 0(0.048[ / ( )] ( / )() 1 2 )symsymE Ex x

M. Kutschera et al., Acta Physica Polonica B37 (2006)

Some hints and possible answers at the mean-field level

Some questions about Esym(ρ)

Why is it so hard to determine it? Why L and Esym(ρ0) are correlated?

Relationship between the symmetry energy and the mean-field potentials

Lane potential

Symmetry energy

Isoscarlar effective mass

kinetic isoscalar isovector

Using K-matrix theory, the conclusion is independent of the interaction

Both U0 (ρ,k) and Usym(ρ,k) are density and momentum dependent

PRC 85, 024305 (2012).

03

/2

21( ,( , , ) ( ( )), ,) sy ymm sn p UU U k kk U k

Need FRIB to determine

Rong Chen, Bao-Jun Cai, Lie-Wen Chen, Bao-An Li, Xiao-Hua Li, Chang Xu

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 mainlyresponsible 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

0

1

,

A

2 0

2

,

A

in

0,

i

i

A

ii i

i

AnA

0

A

V

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

For clustered matter there is no more n p invariance because of the Coulmb term

in the binding energies of nuclei, interactions among them and the asymmetry between proton

and neutron driplines, the E

102 3

2 3

OS can have odd terms in and it does NOT minimize at =

( , (( , 0

0

) )) ( )( ) ss sE E E EE

It is physically ambiguous to define and talk about the“Esym” for clustered matter

Promising Probes of the Esym(ρ) in Nuclear Reactions

At sub-saturation densities

Global nucleon optical potentials from n/p-nucleus and (p,n) reactions

Thickness of n-skin in 208Pb measured using various approaches and sizes of n-skins of unstable nuclei from total reaction cross sections

n/p ratio of FAST, pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusion/transport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t/3He ratio and their differential flow

Towards supra-saturation densities π -/π + ratio, K+/K0 ? Neutron-proton differential transverse flow n/p ratio of squeezed-out nucleons perpendicular to the reaction plane Nucleon elliptical flow at high transverse momentum t-3He differential and difference transverse flow

(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+/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

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 matterH.A. BetheAnn. Rev. Nucl. Part. Sci., 21, 93-244 (1971)

Fermi Sphere

Universal shape of high-momentum taildue 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/c3N correlations, repulsive core and nucleon resonances start playing a role at higher momentum

Variational many-body calculations

Fourier transform

of single-particle wf

Jastrow wf

including 2b tensor

A.Tang et al, PRL 90, 042301 (2003) R. Subedi et al. Science 320, 1475 (2008)

Isospin-dependence of Short Range NN Correlations and Tensor ForceIsospin-dependence of Short Range NN Correlations and Tensor Force

Two-nucleon knockout by a p or e

np

pp

Triggered on nucleon pairs with zero total momentum

At finite total momentum, the effect is reduced, H. Baghdasaryan et al. (CLAS)PRL 105, 222501 (2010)

K.S. Egiyan et al (CLAS), PRL96, 082501 (2006)

2n SRC

3n SRC

Absolute probability per nucleon in the highmomentum tail due to n-p short-range tensor force

Four-momentum transfer

Energy transfer

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 thetensor 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)

420, 012190 (2013).

Confirmation by Microscopic Many-Body Theories

2. High momentum components in the nuclear symmetry energyArianna Carbone, Artur Polls, Arnau Rios, arXiv:1111.0797v1Euro. Phys. Lett. 97, 22001 (2012).Self-Consistent Green’s Function Approach with Argonne Av18, CDBonn, Nij1, N3LO interactions

1. Nuclear symmetry energy and the role of the tensor forceIsaac 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

3. Alessandro Lovato, Omar Benhar et al., extracted from results already published inPhys. Rev. C83:054003,2011

Using Argonne V’6 interaction

Fermi gas

with tensor correlationKinetic symmetry E

They all included the tensor force and many-body correlations using different techniques

Two Consequences of small kinetic contribution

to the total Esym

Heavy-ion reactions

probing

added in afterwards by hand using the Fermi gas model to fix theparameter Cs,p and gamma

KineticPotential

(1) Effects of the symmetry POTENTIAL should be increased!

3bf

Can be zero! But ~ 25 MeV is currently used in all transport models

(2) Effects on sub-threshold pion ratio, etc

n-rich matter with Xp=1/9.

Fraction of high-momentum nucleons in neutron-rich matter

2012

Bao-An Li et al., 2013

Distribution of the available energy for particle production in 2-colliding extended Fermi spheres

Percentage of

high-momentum nucleons

W. Reisdorf et al. for the FOPI collaboration , NPA781 (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. A1 (1998) 151-169

Near-threshold π-/π+ ratio as a probe of symmetry energy at supra-normal densities

lowlow (high)(high) density region is more neutron-rich density region is more neutron-rich withwith stiff stiff (soft)(soft) symmetry energysymmetry energy

2( , ) ( ,0) ( )symE E E

Need a symmetry energy softer than the above to make the pion production region more neutron-rich!

2/3 0

00

2/3100 3(2corresponding t 1) ( )

5o ( )

8 FsymE E

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

At sub-saturation densities

Global nucleon optical potentials from n/p-nucleus and (p,n) reactions

Sizes of n-skins of unstable nuclei from total reaction cross sections Parity violating electron scattering studies of the n-skin in 208Pb at JLab n/p ratio of FAST, pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusion/transport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t/3He ratio

Towards supra-saturation densities π -/π + ratio, K+/K0 ? Neutron-proton differential transverse flow n/p ratio of squeezed-out nucleons perpendicular to the reaction plane Nucleon elliptical flow at high transverse momentum t-3He differential and difference transverse flow

(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)

FRIB facilities

X-ray satellites

TPCs and n-

balls

PREX I&II, CREX

Collaborations are essential to move forward!

X-QMD

Y-BUU

Z-your

model

Esym

Thanks!