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 worldwide. 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

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 GaoFeng Wei, Xi’an Jiao Tong University
Gao-Chan Yong, Institute of Modern Physics, Chinese Academy of Sciences

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

   
E sym

1
2


2

2

E
 pure neutron matter

E
 symmetric nuclear matter symmetry energy Isospin asymmetry δ
12
E (
 n
,
 p
12
)

E
0
(
 n
  p
)

E s ym
(

)


 n
 
 p
12


  
E (
  n p
)

Energy per nucleon in symmetric matter
18 18
3
Energy per nucleon in asymmetric matter
Normal density of nuclear matter

0
 
3
0 density
ρ=ρ n
+ ρ p
Isospin asymmetry

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) (QCD) n/p
 t/ 3 He
π / π +
K + /K 0
Isospin physics in
Terrestrial Labs isodiffusion isotransport isocorrelation isofractionation isoscaling

E sym
(ρ) predicted by microscopic many-body theories
BHF
Greens function
Variational many-body
Density
A.E. L. Dieperink et al., Phys. Rev. C68 (2003) 064307

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

Microphysics governing the E sym according to the Hugenholtz-Van Hove (HVH) theorem
U
  
U k
0
( ,

)

U sy m 1

U s ym 2
( k ,

)

2    
3    
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

Isaac Vidana
BHF
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.C82:054607,2010

• 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

Nusym13 constraints on E sym
( ρ
0
) 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. C86, 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
 
2 0
A
2
A
1
0
0
A i n i
Many interesting talks covering various topics including
• What is the EOS of clustered neutron-rich matter
   i n i
A i
A
 i

V 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

0

Joe Natowitz et al.

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:
ApJ v.772 (2013)
Independent of the masses of neutron stars
WFF1 (AV14+UVII)
WFF1 has a soft EOS: K
0
=209 MeV, E sym
≈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?

WFF: Wiringa, Fiks and Fabrocini (1988), Phys. Rev. C 38, 1010
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, R ns is most sensitive to the Esym in this region)

Extract the E sym
( ρ) at subnormal densities from isospin diffusion/transport
Degree of neutron-proton mixing
Experiment: 124 Sn+ 112 Sn, E beam
/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).

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)
MDI potential energy density
Transport model calculations
B.A. Li and L.W. Chen, PRC72, 064611 (05)
124 Sn+ 112 Sn
ρ ρ
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)

Formation of dense, asymmetric nuclear matter
E
  
E
 
E sym
2
Central density
Symmetry energy density
π / π + probe of dense matter
Stiff E sym n/p ratio at supra-normal densities

Circumstantial Evidence for a Super-soft Symmetry Energy at Supra-saturation Densities
Data:
W. Reisdorf et al.
NPA781 (2007) 459
Calculations: IQMD and IBUU04
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: K t
=

555 ± 75 MeV
The large uncertainty in L and Ksym explain why it is so hard to pink down K ԏ
Many ongoing and planned experiments studying various modes to give better constraints on K
0
, L and K sym
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 ρ
0 are the atomic masses: detailed statistical significance analysis for the L-Esym correlation possible,
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 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) x

0.048[ E sym
(

) / E sym
(

0
)] (
 
0
)( 1
 x
3

Why is it so hard to determine it?
Why L and E sym
(ρ
0
) 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 U sym
( 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 ,
Bao-An Li , Xiao-Hua Li , Chang Xu
PRC 85, 024305 (2012).
U
Need FRIB to determine
  
U k
0
( ,

)

U sy m 1

U s ym 2
( k ,

)

2    
3    

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 E sym
(ρ)=EOS(pnm)-EOS(snm)
PNM
sym
sym
0

PNM

Comments on the “symmetry energy” of clustered matter at very low densities
 
2 0
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”
A
2
0 for the clustered matter, what is needed are in-medium
A
1 properties of hot nuclei and their Esym
It is physically ambiguous to define and talk about the
“Esym” for clustered matter
0
A i
   i n i
A i
A
 i n i

V

0
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
 
0
E )

E
0

0 )

E s 1
E s 2
( E s 3
 
3       

Promising Probes of the E sym
(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
208
Pb 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/
3
He ratio and their differential flow
Towards supra-saturation densities

π
/π + ratio, K
+
/K
0
?

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-
3
He differential and difference transverse flow
(1) Correlations of m ulti-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
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

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)

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)

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)

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

(1) Effects of the symmetry POTENTIAL should be increased!
Heavy-ion reactions
Potential
Kinetic added in afterwards by hand using the Fermi gas model to fix the parameter Cs,p and gamma
3bf

(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

Nearthreshold π /
π + ratio as a probe of symmetry energy at supra-normal densities
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 corresponding t o E sym
 
100
8


0

(2
2 / 3 
1)
3
5
E
F
0
(


0
)
2 / 3
Need a symmetry energy softer than the above to make the pion production region more neutron-rich!
E
  
E
 
E sym
2 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 E sym
(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
208
Pb 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/
3
He ratio
Towards supra-saturation densities

π
/π + ratio, K
+
/K
0
?

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-
3
He differential and difference transverse flow
(1) Correlations of m ulti-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