Post on 28-Jan-2016
description
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
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ii i
i
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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!