recent progress on the determination of the symmetry energy

Recent progress on the determination of the symmetry Energy

Lie-Wen Chen ( 陈列文 )

INPAC, Department of Physics, Shanghai Jiao Tong [email protected]

“ 第十四届全国核结构大会暨第十次全国核结构专题讨论会” , 湖州，浙江， 2012 年 4 月 12-16 日

Collaborators ：Wei-Zhou Jiang (SEU)Che Ming Ko (TAMU)Bao-An Li and Jun Xu (TAMU-Commerce)De-Hua Wen (SCUT) Zhi-Gang Xiao (Tsinghua) Chang Xu (NJU)Gao-Chan Yong (IMP)Xin Wang, Xiao-Hua Li, Bao-Jun Cai, Rong Chen, Peng-Cheng Chu, Zhen Zhang , Kai-Jia Sun, Hao Zheng, Rui Wang (SJTU)

目录

核物质的状态方程与对称能约束核物质的对称能 :

(1) 饱和密度附近的行为 (2) 低密行为 (3) 高密行为

对称能的效应： (1) 核的有效相互作用 (2) 原子核的“中子皮” (3) 中子星的“壳 - 芯”边界 ( 见郑皓报

告 ) (4) “ 第五种力” ( 见郑皓报告 )

总结和展望

状态方程 (Equation of State): a relationship among several state variables

Van der Waals EOS: 2[ ( ) ](v )v

np a nb nRT

• The EOS depends on the interactions and properties of the particles in the matter.

• It describes how the state of the matter changes under different conditions

物质的状态方程

核物质的状态方程

-

The in a nuclear matter with density , temperature , and

isospin asymmetry

T

energ

( ) can be expressed as

T

/

y of per nucleon

( , Nuclear Ma, ) ( tter EO )S

he

n p

E A T

2

, constant

pressure of the nuclear matter can be expresse P

incompessibi

d as

The of the nucl

( , , )

ear mattlty K er can be expressed a

s

T N

P T

, constant

30

14Water

Empirical values about the nuclear mat

ofSaturation density

sy

mmetric nuclear

Pressur

matter

a

ter EOS:

t T=0 Me

V:

( , , ) 9

0.16 fm ( 1 )0

T N

PK T

3

0 0

0

0

of symmetric nuclear matter at T=0 MeV:

The of symmetric nuclear matter at and T=0 MeV:

( ) 0 MeVfm

16 MeV/nu

e

energy of per nucleon

Inco

of symmetric nuclear matter at mpess T=0 ibilty

cleon

P

0 200MeV: 40 V 0 MeK

EOS of Isospin Asymmetric Nuclear Matter

s2 4

ym ( )( , ) ( ), ( ),0) /( n pE OE E

(Parabolic law)

The Nuclear Symmetry Energy2

sym 2

1 ( , )( )

2

EE

核物质的对称能

Symmetry energy term(poorly known)

Symmetric Nuclear Matter(relatively well-determined)

Isospin asymmetry

0

2

s

sym

ym

0 0

0 0

sym

sym y 0

0

0s

0

m , ( )3 18

30 MeV (LD mass formula: )

( )3 (Many 50-Bo 2

(

0dy 0 M eTheor

( )

y: : ;

(

)

V Ex

)

p

E My

E

ers & Swiatecki, NPA81; Pomorski & Dudek, PRC67

EEL

L

K

L

0

sy

2sym2

0 sym2m

: ???)

( )9 (Many-Body Theory: : ; Exp: ??700 466 M ?e )V

EK K

为什么研究对称能？The multifaceted influence of the nuclear symmetry energy

A.W. Steiner, M. Prakash, J.M. Lattimer and P.J. Ellis, Phys. Rep. 411, 325 (2005).

The symmetry energy is also related to some issues of fundamental physics:1. The precision tests of the SM through atomic parity violation observables (Sil et al., PRC05)2. Possible time variation of the gravitational constant (Jofre et al. PRL06; Krastev/Li, PRC07)3. Non-Newtonian gravity proposed in the grand unified theories (Wen/Li/Chen, PRL09)

Symmetry Energy

Nuclear Physics on the Earth

Astrophysics and Cosmology in Heaven

QCD Phase Diagram in 3D: density, temperature, and isospin

同位旋核物理致密星体物理

夸克胶子等离子体物理

理解极端条件下强相互作用物质的性质，尤其是它的状态方程 1. 放射性核结构及重离子碰撞 ( 地球上加速器实验 ); 2. 致密星体 ( 天文观测 );

…

V.E. Fortov, Extreme States of Matter – on Earth and in the Cosmos, Springer-Verlag Berlin Heidelberg 2011

强相互作用物质相图

Holy Grail of Nuclear Physics

Nuclear Matter EOS: Many-Body Approaches

Microscopic Many-Body Approaches Non-relativistic Brueckner-Bethe-Goldstone (BBG) Theory Relativistic Dirac-Brueckner-Hartree-Fock (DBHF) approach Self-Consistent Green’s Function (SCGF) Theory Variational Many-Body (VMB) approach Green’s Function Monte Carlo Calculation Vlowk + Renormalization Group Effective Field Theory Density Functional Theory (DFT) Chiral Perturbation Theory (ChPT) QCD-based theory Phenomenological Approaches Relativistic mean-field (RMF) theory Quark Meson Coupling (QMC) Model Relativistic Hartree-Fock (RHF) Non-relativistic Hartree-Fock (Skyrme-Hartree-Fock) Thomas-Fermi (TF) approximations

The nuclear EOS cannot be measured experimentally, its determination thus depends on theoretical approaches

核物质的对称能

Chen/Ko/Li, PRC72, 064309(2005) Chen/Ko/Li, PRC76, 054316(2007)

Z.H. Li et al., PRC74, 047304(2006) Dieperink et al., PRC68, 064307(2003)

BHF

Broad applications of transport modelsin astrophysics, plasma physics, electron transport in semiconductor and nanostructures, particle and nuclear physics, ……

Transport Models for HIC’s at intermediate energies:

N-body approachesCMD, QMD,IQMD,IDQMD,ImQMD,ImIQMD,AMD,FMD

One-body approachesBUU/VUU, BNV, LV, IBL

Relativistic covariant approachesRVUU/RBUU,RQMD…

Transport Models

Central collisions

Ni + Au, E/A = 45 MeV/A

Nuclear Matter EOS: Transport Theory

放射性核束装置 Cooling Storage Ring (CSR) Facility at HIRFL/Lanzhou in China (2008) up to 500 MeV/A for 238U http://www.impcas.ac.cn/zhuye/en/htm/247.htm Beijing Radioactive Ion Facility (BRIF-II) at CIAE in China (2012) http://www.ciae.ac.cn/ Radioactive Ion Beam Factory (RIBF) at RIKEN in Japan (2007) http://www.riken.jp/engn/index.html Facility for Antiproton and Ion Research (FAIR)/GSI in Germany (2016) up to 2 GeV/A for 132Sn (NUSTAR - NUclear STructure, Astrophysics and Reactions ) http://www.gsi.de/fair/index_e.html SPIRAL2/GANIL in France (2013) http://pro.ganil-spiral2.eu/spiral2 Selective Production of Exotic Species (SPES)/INFN in Italy (2015) http://web.infn.it/spes Facility for Rare Isotope Beams (FRIB)/MSU in USA (2018) up to 400(200) MeV/A for 132Sn http://www.frib.msu.edu/The Korean Rare Isotope Accelerator (KoRIA) (Planning) up to 250 MeV/A for 132Sn, up to 109 pps

http://pro.ganil-spiral2.eu/spiral2

http://pro.ganil-spiral2.eu/spiral2

http://www.frib.msu.edu/

目录





总结和展望

(1) EOS of symmetric matter around the saturation density ρ0

GMR 0Frequency f K

Giant Monopole Resonance

K0=231±5 MeVYongblood/Clark/Lui, PRL82, 691 (1999)Recent results:K0=240±20 MeVG. Colo et al. U. Garg et al.S. Shlomo et al.

0

22

0 0 2Incompressibility: K =9 ( )

d E

d

“ 对称核物质”的状态方程

Uncertainty of the extracted K0 is mainly due to the uncertainty ofL (slope parameter of the symmetry energy) and m*0 (isoscalar nucleon effective mass)(See, e.g., L.W. Chen/J.Z. Gu, JPG39, 035104(2012))

(2) EOS of symmetric matter for 1ρ0< ρ < 3ρ0 from K+ production in HIC’sJ. Aichelin and C.M. Ko,

PRL55, (1985) 2661C. Fuchs,

Prog. Part. Nucl. Phys. 56, (2006) 1

Transport calculations indicate that “results for the K+ excitation function in Au + Au over C + C reactions as measured by the KaoS Collaboration strongly support the scenariowith a soft EOS.”

C. Fuchs et al, PRL86, (2001) 1974

See also: C. Hartnack, H. Oeschler, and J. Aichelin,

PRL96, 012302 (2006)


(3) Present constraints on the EOS of symmetric nuclear matter for 2ρ0< ρ < 5ρ0 using flow data from BEVALAC, SIS/GSI and AGS

Use constrained mean fields to predict the EOS for symmetric matter

• Width of pressure domain reflects uncertainties in comparison and of

assumed momentum dependence.

P. Danielewicz, R. Lacey and W.G. Lynch, Science 298, 1592 (2002)

2Pressure P( )s

E

The highest pressure recorded under laboratory controlled conditions in nucleus-nucleus collisions

y

px

High density nuclear matter2 to 5ρ0


Promising Probes of the Esym(ρ)(an incomplete list !)

对称能的实验探针

At sub-saturation densities (亚饱和密度行为) Sizes of n-skins of unstable nuclei from total reaction cross sections Proton-nucleus elastic scattering in inverse kinematics Parity violating electron scattering studies of the n-skin in 208Pb 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 Hard photon production

Towards high densities reachable at CSR/Lanzhou, FAIR/GSI, RIKEN, GANIL and, FRIB/MSU (高密度行为) π -/π + ratio, K+/K0 ratio? Neutron-proton differential transverse flow n/p ratio at mid-rapidity Nucleon elliptical flow at high transverse momenta n/p ratio of squeeze-out emission

Pigmy/Giant resonances Nucleon optical potential

B.A. Li, L.W. Chen, C.M. KoPhys. Rep. 464, 113(2008)

“ 同位旋核物理”的综述性文章

已成为目前国际上关于对称能研究的标准参考文献之一

被引用 : >248 (SCIE) 在 SPIRES 数据库“ The 100 most highly cited papers during 2010 in the nucl-th archive )” 排名第 5入选“ ESI 高被引用论文” (Most Cited Papers in Essential Science Indicators)

PRL papers about Esym in 2010-2012

J.B. Natowitz et al, Symmetry Energy of Dilute Warm Nuclear Matter, PRL104, 202501 (2010)

J. Dong, W. Zuo, and W. Scheid, Correlation between -Decay Energies of Superheavy Nuclei Involving the Effects of Symmetry Energy, PRL 107, 012501 (2011)

S. S. Henshaw et al., New Method for Precise Determination of the Isovector Giant Quadrupole Resonances in Nuclei, PRL 107, 222501 (2011)

X. Roca-Maza et al., Neutron Skin of 208Pb, Nuclear Symmetry Energy, and the Parity Radius Experiment, PRL 106, 252501 (2011)

A. Tamii et al., Complete Electric Dipole Response and the Neutron Skin in 208Pb, PRL 107, 062502 (2011)

P. Moller et al., New Finite-Range Droplet Mass Model and Equation-of-State Parameters, PRL 108, 052501 (2012)

F.L.Roberts et al., Protoneutron Star Cooling with Convection: The Effect of the Symmetry Energy, PRL 108, 061103 (2012)

A.W. Steiner and S. Gandolfi, Connecting Neutron Star Observations to Three-Body Forces in Neutron Matter and to the Nuclear Symmetry Energy, PRL 108, 081102 (2012)

L. Qin et al., Laboratory Tests of Low Density Astrophysical Equations of State, PRL (2012), in press

2010: 1 2011: 4 2012: 4 (2009: 7)

How to measure Isospin Diffusion?

PRL84, 1120 (2000)

______________________________________

A+A,B+B,A+BX: isospin tracer

Isospin Diffusion/Transport

(1) Esym: Isospin Diffusion in HIC’s

Li/ Chen, PRC72, 064611(2005)

Symmetry energy, isospin diffusion, in-medium cross section

Isospin Diffusion Data Esym(ρ0)=31.6 MeVL=88±25 MeV

0

0

( ) 31.6( / ) MeV

(From 0 ), we ob

Fit the symmetry ener

tain

0.69 for1. 005

gy with

for 1 n

:

a d

symE

x x

Chen/Ko/Li, PRC72,064309 (2005)

(1) Esym: Isospin Diffusion in HIC’s

Chen/Ko/Li, PRL94,032701 (2005)

Isoscaling in HIC’sIsoscaling observed in many reactions

2 1

( ) /

Y / Yn pN Z Te

M.B. Tsang et al. PRL86, 5023 (2001)

(2) Esym: Isoscaling in HIC’s

Consistent with isospin diffusion data!

Constraining Symmetry Energy by Isocaling: TAMU DataShetty/Yennello/Souliotis, PRC75,034602(2007); PRC76, 024606 (2007)

(2) Esym: Isoscaling in HIC’s

Isoscaling Data Esym(ρ0)=31.6 MeVL=65 MeV

ImQMD: n/p ratios and two isospin diffusion measurementsTsang/Zhang/Danielewicz/Famiano/Li/Lynch/Steiner, PRL 102, 122701 (2009)

(3) Esym: Isospin diffusion and double n/p ratio in HIC’s

ImQMD: Isospin Diffusion and double n/p ratio Esym(ρ0)~28 - 34 MeV?L=38 - 103 MeV

(4) Esym: Nuclear Mass in Thomas-Fermi Model

Thomas-Fermi Model + Nuclear Mass Esym(ρ0)=32 .65 MeV L=49.9 MeV

Myers/Swiatecki, NPA 601, 141 (1996)Thomas-Fermi Model analysis of 1654 ground state mass of nuclei with N,Z≥8

Droplet Model + N-skin Esym(ρ0)=28 - 35 MeV, L=55 ± 25 MeV

(5) Esym: Droplet Model Analysis on Neutron Skin

N-Skin data measured in antiprotonic atoms

Neutron skin constraints on L and Esym(ρ0) are insensitive tothe variations of other macroscopic quantities.

Esym(ρ0)=30 MeV

Chen/Ko/Li/XuPRC82,

024321(2010)

(6) Esym: Skyrme-HF Analysis on Neutron Skin

N-Skin data of Sn isotopes

Electric dipole strength in atomic nuclei

By Deniz Savran

(7) 、 (8) Esym: Pygmy Dipole Resonances

(7) 、 (8) Esym: Pygmy Dipole Resonances

Pygmy Dipole Resonances of 130,132Sn Esym(ρ0)=32 ± 1.8 MeV L=43.125 ± 15 MeV

Pygmy Dipole Resonances of 68Ni and 132Sn Esym(ρ0)=32.3 ± 1.3 MeV, L=64.8 ± 15.7 MeV

Esym from Isobaric Analog States + Liquid Drop model with surface symmetry energy

IAS+Liquid Drop Model with Surface Esym Esym(ρ0)=32.5 ± 1 MeV L=94.5 ± 16.5 MeV

Danielewicz/Lee, NPA 818, 36 (2009)

(9) Esym: IAS+LDM

Esym from Liquid Drop model with surface symmetry energy

Liquid Drop Model with Surface Esym Esym(ρ0)=31.1 ± 1.7 MeV L=66.0 ± 13 MeV

(10) Esym: LDM

=26.11 MeV

Xu/Li/Chen, PRC82, 054607 (2010)

(11) Esym: Global nucleon optical potential

(11) Esym: Global nucleon optical potential

Xu/Li/Chen, PRC82, 054607 (2010)

Esym from FRDM-2011 + Nuclear Mass (AME2003)

FRDM+Nuclear Mass (AME2003) Esym(ρ0)=32.5 ± 0.5 MeV L=70 ± 15 MeV

(12) Esym: FRDM

Nuclear matter symmetry energy aroundρ0

Current constraints on Esym (ρ0) and L from nuclear reactions and structures(1) TF+Nucl. Mass (1996) Myers/Swiatecki, NPA 601, 141 (1996)

(2) Iso. Diff. (IBUU04, 2005) L.W. Chen et al., PRL94, 032701 (2005); B.A. Li/L.W. Chen, PRC72, 064611(2005)(3) Isoscaling (2007) D. Shetty et al., PRC76, 024606 (2007)

(5) Iso. Diff. & double n/p (ImQMD, 2009) M.B. Tsang et al., PRL102, 122701 (2009);

(4) PDR in 130,132Sn (2007) (LAND/GSI) A. Klimkiewicz et al., PRC76, 051603(R)(2007)

(6) IAS+LDM (2009) Danielewicz/J. Lee, NPA818, 36 (2009)

(7) DM+N-Skin (2009) M. Centelles et al., PRL102, 122502 (2009); M. Warda et al., PRC80, 024316 (2009)

(9) SHF+N-Skin (2010) L.W. Chen et al., PRC82, 024321 (2010)

(10) Opt. Pot. (2010) C. Xu et al., PRC82, 054607 (2010)(11) Nucl. Mass (2010) M. Liu et al., PRC82, 064306 (2010)

(8) PDR in 68Ni and 132Sn (2010) A. Carbon et al., PRC81, 041301(R)(2010)

(12) FRDM (2012) P. Moller et al., PRL108, 052501 (2012)

对称能：饱和密度附近行为

Esym(ρ0)=27 - 36 MeVL=30 - 90 MeV

Current constraints on Esym (ρ0) and L from nuclear reactions and structures

More accurate data are needed to

obtain more stringent constraints!

Chen/Ko/Li/Xu, PRC82, 024321(2010)

Esym(ρ0)=30±5 MeVL=58±18 MeV

L.W. Chen, PRC83, 044308(2011)

Esym: Neutron Skin + Esym(ρ=0.1 fm-3)

•IVGDR of 208Pb/SHF: Trippa/Colo/Vigezzi, PRC77, 061304(R)(2008)•IVGDR of 132Sn/RMF: Cao/Ma, CPL25, 1625(2008)•Nuclear Mass: Liu/Wang/Li/Zhang, PRC82, 064306(2010)

Chen/Ko/Li/Xu, PRC82, 024321(2010)

Based on the same SHF approach!

Esym(ρ0) = 30.5±3 MeVL = 52.5±20 MeV

Linear L-Esym corr.

一种新的思路 ??? 基于同样的理论框架，使用不同的实验探针 :交叉约束！

Neutron-Skin of Tin isotopes

目录





总结和展望

极端低密时的对称能：结团效应

S. Kowalski, et al., PRC 75 (2007) 014601.

Horowitz and Schwenk, Nucl. Phys. A 776 (2006) 55

极端低密时的对称能：结团效应

目录





总结和展望

对称能的高密行为：重离子碰撞

Xu/Tsang et al. PRL85, 716 (2000)

Isospin fractionation!

Heavy-Ion Collisions at Higher EnergiesIBUU simu.

n/p ratio of the high density region

粒子产生阈能

: 289 MeV ( )

( , ) : 1583 MeV ( )

: 2513 MeV ( )

: 3740 MeV ( )

NN NN

K NN NYK

K NN NNK K

NN N K K

实验发现在低于阈能时，重离子碰撞中仍能产生以上粒子，称为阈下产生。重离子碰撞中粒子的阈下产生为研究高温高密核介质中强子的性质以及核介质的性质提供了实验基础。

IBUU04, Xiao/Li/Chen/Yong/Zhang, PRL102,062502(2009)

对称能高密探针 :pion 比率 A Quite Soft Esym at supra-saturation densities ???

Zhang et al.,PRC80,034616(2009)

ImIQMD, Feng/Jin, PLB683, 140(2010)

Softer

StifferPion Medium Effects?

Xu/Ko/OhPRC81, 024910(2010)

Threshold effects?Δ resonances?

……

A Soft or Stiff Esym at supra-saturation densities ???P. Russotto,W. Trauntmann, Q.F. Li et al., PLB697, 471(2011)

对称能高密探针 :n/p 椭圆流 v2

对称能高密行为 :Ksym 参数？

L.W. Chen, Sci. China Phys. Mech. Astron. 54, suppl. 1, s124 (2011) [arXiv:1101.2384]

对称能高密行为 :Ksym 参数？

L.W. Chen, Sci. China Phys. Mech. Astron. 54, suppl. 1, s124 (2011) [arXiv:1101.2384]

L.W. Chen, PRC83,

044308(2011)

The Skyrme HF Energy Density Functional

Standard Skyrme Interaction:

_________

9 Skyrme parameters:

9 macroscopic nuclear properties:

There are more than 120 sets of Skyrme- like Interactions in

the literature

Agrawal/Shlomo/Kim AuPRC72, 014310 (2005)

Yoshida/SagawaPRC73, 044320 (2006)

Chen/Ko/Li/XuPRC82,

024321(2010)

目录





总结和展望

Chen/Ko/Li, PRC72,064309 (2005) Chen/Ko/Li, PRC76, 054316(2007)

Esym(ρ0)= 31.5 ±4.5 MeV and L=55 ± 25 MeV: only 55/118

Esym(ρ0)= 31.5 ±4.5 MeV and L=55 ± 25 MeV: only 8/23

对称能与核的有效相互作用

目录





总结和展望

208( Pb) varies from 0.04 fm to 0.24 fm

depending on the Skyrme interaction !

S

Good linear Correlation: S-L

Chen/Ko/Li, PRC72,064309 (2005)

Oyamatsu et al., NPA634, 3 (1998); Brown, PRL85,5296 (2000); Horowitz/Piekarewicz, PRL86, 5647 (2001); Furnstahl, NPA706, 85 (2002); Yoshida/Sagawa, PRC73, 044320 (2006)

2 2

Neutron-Skin Thickness:

(fm)n pr rS

(5) Esym: Droplet Model Analysis on Neutron Skin

208Pb 的“中子皮”

A quite stringent constraint on Δrnp of 208Pb:

Jefferson Lab (JLab):208Pb Radius EXperiments - PREX

The Lead Radius Experiment ("PREX"), experiment number E06002, uses the parity violating weak neutral interaction to probe the neutron distribution in a heavy nucleus, namely 208Pb, thus measuring the RMS neutron radius to 1% accuracy, which has an important impact on nuclear theory.

Chen/Ko/Li/Xu, PRC82, 024321 (2010)

PRL108, 112502(2012):

目录





总结和展望

通过重离子碰撞，原子核结构性质 (mass, neutron skin, GR/PG…), 以及核子光学势的研究，我们对饱和密度附近及低密核物质对称能的行为有了一定的认识 : Esym(ρ0) =31±3 MeV and L=60±30 MeV 更精确的约束需要更精确的实验数据和更可靠的理论方法 !

对称能对于理解核的有效相互作用、丰中子核的中子皮结构、中子星的结构性质以及引力的短距离行为有重要意义决定对称能的高密行为依然是一个巨大的挑战 (Many-body forces, Short range tensor forces, Short range NN correlations( 许昌报告 ), Model cross check, more data,……). 丰中子核引起的高能重离子碰撞的实验数据将变得非常重要 ! 对称能高阶系数 (Ksym,Jsym,…) ？直接由 QCD 出发计算对称能？ QCD sum rule → Lorentz Covariant Nucleon Self-Energies → Esym ( 蔡宝军报告 )

总结和展望

重离子碰撞物理 @SJTU

Dr. Xin Wang( 王欣 )

Dr. Xiao-Hua Li ( 李小华 ) Mr. Bao-Jun Cai ( 蔡宝军 ) Mr. Peng-Cheng Chu ( 初鹏程 )

Mr. Rong Chen ( 陈融 ) Mr. Zhen Zhang ( 张振 ) Mr. Kai-Jia Sun (孙开佳 ) Mr. Hao Zheng ( 郑皓 )

Dr. Lie-Wen Chen ( 陈列文 )

谢谢！Thanks!

recent progress on the determination of the symmetry energy

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