非对称核物质性质
左维
中国科学院近代物理研究所
Outline:
1. Introduction (Motivation)
2. Theoretical approaches
3. Results
4. Summary and conclusion
北京，2010年6月
非对称核物质性质
原子核多体理论与核子-核子
有效相互作用
低密非对称核物质性质
关键性进展
Experiments at the NSCL/MSU ：
Sn+Sn， Ebeam/A=50 MeV
Iso-scaling
结论： 32(  / 0 )0.7  Esym (  )  32(  / 0 )1.1
Isospin diffusion
高密区对称能的密度依赖性
Z. G. Xiao etal, Phys. Rev. Lett. 102(2009)062502
Z.-Q. Feng, G.-M. Jin, Phys. Lett. B 683 (2010) 140
3.5
Elab=0.4A GeV
FOPI
IQMD (Nantes)
ImIQMD (stiff)
ImIQMD (linear)
ImIQMD (soft)
ImIQMD (supersoft)
Elab=1.5A GeV
Esym (MeV)
2
)
-
N/
Z
(N
/Z
)
-
2
2.0
31.6(/0)
80
+
1.5
 /
+
2.5
IQMD
2
(N
/Z
3.0
 /
100
2.0
hard
Ska
0.5
31.6(/0)
60
SLy6
40
soft
SkP
1.5
20
1.0
N/Z
SIII(supersoft)
1.0
0
1.0
1.1
1.2
1.3
(N/Z)sys
1.4
1.5
1.0
1.1
1.2
1.3
(N/Z)sys
1.4
1.5
0
1
2
/0
3
4
HIRFL-CSR in IMP, Lanzhou
SFC: several to 10 AMeV
SSC
North
Building
2#100 AMeV
SSC:
tens to
External Target
SFC
Building 6#
CSRe
CSRe Internal
Target
Cancer
Therapy
Nuclear Physics
CSRm
High Energy
• Reaction reduced by RIB
Density
• Effective strong interaction in dense matter
• EOS under extreme conditions (density, isospin,temperature)
• Isospin Physics and related
subjects in astrophysics
CSRm:520AMeV(238U72+), 1.1 AGeV(12C6+), 2.88 GeV(p)
• Structure of nuclei far from
stable line
CSRe: 520AMeV(238U72 ), 0.76 AGeV (12C6+)
CSRm Internal Target
与CSR相关的核物质相图
弱束缚核性质
核子核子有效相互作用
……….
同位旋非对称度β
高密区非对称核物质性质
中子星性质
中子星冷却
核子-核子相互作用
核微观多体理论 ……..
CSR能区高密非对称核物质的形成
Stiff Esym
Bao-An Li, Gao-Chan Yong, Wei Zuo, Phys. Rev. C71，014608(2005)
CSR能区高密非对称核物质状态方程的灵敏观测量
Stiff Esym
High-density behavior of
symmetry energy
(1232) resonance model:   /  
Thermal model:   /  
( N / Z )2
exp[( n   p ) / T ]
G.C.Yong, B.A.Li, W. Zuo,
PRC71(2006)014608; 044604
Double n/p ratio
B.A.Li, L.W.Chen,G.C.Yong, W. Zuo, PLB634(2006)378
Theoretical Approaches
• Skyrme-Hartree-Fock
• Relativistic Mean Field Theory, Relativistic
Hartree-Fock
•
•
•
•
•
Variational Approach
Green’s Function Theory
Brueckner Theory
Dirac-Brueckner Approach
Effective Field Theory
研究现状
唯像多体理论： SHF和RMF理论
B. A. Li， L. W. Chen， C. M. Ko，Phys. Rep. 464（2008）113
微观多体理论： 非相对论BHF理论
Z.H. Li, U. Lombardo, H.-J. Schulze, Zuo et al., PRC74(2006)047304
微观多体理论： 相对论Dirac-BHF理论
Krastev and Sammarruca
Nucl-th/0601065
Klahn et al.
Nucl-th/0602038
Brueckner-Hartree-Fock (BHF) 理论
Brueckner, Bethe, Goldstone et al., 1954--1967
重要进展：
① BHF理论方法的扩展(EBHF)：在单粒子性质中考虑基态关联效应，
改善其内在自洽性（Lejeune,Mahaux,Baldo,Bombaci,Lombardo,Zuo,…，
1970--2005)
② 同位旋相关的BHF与EBHF方法（Bombaci,Lombardo,Zuo,…)
③ 空穴线展开收敛性的证实(Song,Baldo,Lombardo,…,1998）√
④ 引入微观三体核力（Lejeune,Lombardo,Zuo…，1989-2002) √
⑤ 微观三体核力重排项的提出和实现（Zuo,Lombardo,…，2006)
Bethe-Goldstone Theory
•
Bethe-Goldstone equation and effective G-matrix
G (  ,  ;  )  v NN  v NN 
k1k 2
k1k 2 Q(k1 , k 2 ) k1k 2
   (k1 )   (k 2 )  i
G(  ,  ; )
→ Nucleon-nucleon interaction: v NN  v2  V3eff
★ Two-body interaction v2 : AV18 (isospin dependent)
★ Effective three-body force V eff
3
→ Pauli operator : Q(k , k )  1  nk 1  nk 
1 2
1
2
→ Single particle energy :  (k )   2 k 2 /( 2m)  U (k )
→ “Auxiliary” potential : continuous choice
U (k )   n(k ' ) Re kk' G[ (k )   (k ' )] kk'
A
k'
Confirmation of the hole-line expansion of the EOS under
the contineous chioce (Song,Baldo,Lombardo,et al,PRL(1998))
Brueckner Theory of Nuclear Matter
Microscopic Three-body Forces
• Based on meson exchange approach
• Be constructed in a consistent way with the adopted two-body
force---------microscopic TBF !
• Grange et.al PRC40(1989)1040
Z-diagram
, 
N

(b)
N
R
, 

, 
N
N
(c )
N
, 
N
N
 , ,
N
N
 , ,
N
(a )
, 

, 

, 
, R
Effective Microscopic Three-body Force
• Effective three-body force V3eff
eff
3
V
r ', r ' r , r 
1
2
1
2
 
1
 Tr   d r3d r3 ' n* r3 ' 1   r13 '1   r23 '
4
n

  
 W3 r1 ' , r2 ' , r3 ' r1 , r2 , r3  n r3 1   r13 1   r23 
→ Defect function: (r12)= (r12) – (r12)
★Short-range nucleon correlations (Ladder correlations)
★Evaluated self-consistently at each iteration
 Effective TBF ---- Density dependent
 Effective TBF ---- Isospin dependent for asymmetric
nuclear matter
EOS of Nuclear Matter
EOS of SNM & saturation properties
TBF is necessary for reproducing
the empirical saturation property of
nuclear matter in a non-relativistic
microscopic framework.
Saturation properties:
 (fm-3)
EA (MeV) K (MeV)
0.19
–15.0
210
0.26
–18.0
230
W. Zuo, A. Lejeune, U.Lombardo, J.F.Mothiot, NPA706(2002)418
Isospin dependence of the EOS
Parabolic law : linear dependence on  2
E A (  , T ,  )  E A (  , T , 0)  Esym (  , T )  2
W. Zuo, A. Lejeune, U.Lombardo, J.F.Mothiot,
Nucl.Phys.A706(2002)418
W. Zuo et al., Phys. Rev. C69
(2004) 064001
Density dependence of symmetry energy
TBF effect
Symmetry energy from
Thermal
effect
different
approaches
？
W. Zuo et al. PRC
69(2004)064001
W. Zuo, A. Lejeune, U.Lombardo,
J.F.Mothiot, EPJA 14(2002)469
C. Fuchs and H. H. Wolter,
EPJA30(2006)5
Critical temperature for liquid-gas
phase transition in warm nuclear matter
Z-diagram
SHF : 14-20 MeV
RMT : 14 MeV
DBHF: 10 MeV
BHF(2BF): 16 MeV
BHF(TBF): 13 MeV
BHF(Z-d): 11 MeV
Full TBF
A possible explanation of the
discrepancy between the DBHF
and BHF predictions
W. Zuo, Z.H.Li,A. Li, U.lombardo,
NPA745(2004)34.
Single Particle Properties
• Neutron and proton s.p. potential
• Isovector part : Symmetry potential
U sym (k ) 
U n (k )  U p (k )
2
• Isosping splitting of effective mass
• TBF rearrangement cobtribution
Single Particle Potential beyond the mean field approximation:
1. Single particle potential at lowest BHF level
G (  ,  ;  )  v NN  v NN 
k1k 2
k1k 2 Q(k1 , k 2 ) k1k 2
   (k1 )   (k 2 )  i
U BHF (k )   n(k ') Re kk ' G[ (k )   (k ')] kk '
G(  ,  ; )
A
k'
2. Ground state correlations
3. TBF rearrangement
 V3eff
1
 TBF (k )   ij
ij
2 ij
 nk
Full s.p. potential：
ni n j
A
U (k )  U BHF (k )  U 2 (k )  UTBF (k )
Single particle potential at the BHF level
In neutron rich matter :
Up<Un at low momenta
Up>Un at high enough momenta
W. Zuo, L.G. Gao, B.A. Li et al., Phys. Rev. C72 (2005)014005 .
Symmetry Potential: The isovector Part
U sym (k ) 
U n (k )  U p (k )
2
U n and U p depend linearly on  in the considered range of asymmetry and
momentum (Lane assumption):
U n (  ,  )  U (0,  )  U sym (  ), U p (  ,  )  U (0,  )  U sym (  )
Pauli rearrangement contribution: Ground state correlation
1. The Pauli rearrangement is repulsive
2. It affects maily the s.p. potential at low momenta and
vanishes repaidly above Fermi momentum
3. It distories the linear beta-dependence of the s.p. potential
W. Zuo, I. Bombaci, U. Lombardo, PRC 60 (1999) 024605
Neutron-proton effective mass splitting in neutron-rich matter
1
m  m dU 
 1 
m 
p dk  k
F
*
M*n > M*p
Comparison to other predictions:
DBHF: mn* > mp*
Dalen et al., PRL95(2005)022302
Z. Y. Ma et al., PLB 604 (2004)170
F. Sammarruca et al., nucl-th/0411053
Skyrme-like interactions:
mp* < mn* or mn* < mp*
B. A. Li et al., PRC69(2004)064602
neutrons
protons
TBF rearrangment contribution in symmetric nuclear matter
 V3eff
1
 TBF (k )   ij
ij
2 ij
 nk
ni n j
A
Effective mass
1. The TBF induces a strongly repulsive
rearrangement modification of the s. p.
potential at high densities and momenta.
2. The TBF rearrangement contribution is
strongly momentum dependent at high
densities and momenta.
Zuo, Lombardo, Schulze, Li, Phys. Rev. C74 (2006) 017304
Isospin dependence of the TBF rearrangment effect
Symmetry potential
1. Negligible at low densities around and
below the Fermi momentum.
2. Enhancement of the repulsion for
neutrons and the attraction for protons
at high densities
Effective masses
1. Remarkable reduction of the neutron
and proton effective masses.
2. Suppression of the isospin splitting
in neutron-rich matter at high
densities.
S.P. Potential：Ground state correlation and
TBF rearrangement effect
Proton fraction in β-stable neutron star matter
A. Lejeune, U.Lombardo, W. Zuo, Phys.Lett. B477(2000)45
Neutron Star
Structure
Kaon condensation in
neutron stars
Variational
RMT
BHF + 3BF
X.R.Zhou et al.,
PRC69(2004)018801
W. Zuo. A. Li, Z.H.Li, U.
Lombardo,
PRC70(2004)055802.
1S
0
neutron and proton gap in -stable
neutron star matter : TBF effect
nn
no significant effect since nn pairs are
embedded in low density neutron
background:
Vnn (3) ~ 0
pp
TBF suppresses strongly the 1S0 proton
superfluidity in neutron stars
1. It reduces the energy gap from ~1 to ~0.5
2. It suppresses largely the density region
W. Zuo et al., PLB 595(2004)44 of the superfluidity
3PF2 neutron pairing gap in a neutron star :
TBF effect
W. Zuo et al., Phys. Rev.
C78(2008)015805
总结:
1）发展和改进了微观三体核力模型和BHF理论方法，改善了BHF理论的内在热力学
自洽性及其对于核物质饱和点性质的描述
2）提出并在扩展的微观多体BHF理论框架内中实现了微观三体核力重排贡献的计算，
解决了非相对论BHF理论预言的光学势在高密度和高动量区域吸引性过强和动量
依赖性过弱的问题
3）在扩展的微观多体BHF理论框架内预言了非对称核物质中质子和中子单粒子势和
有效质量的同位旋劈裂性质，提出了有效质量同位旋劈裂的微观机制。
4）系统研究了非对称核物质的性质，预言了非对称核物质的状态方程对于非对称度
的依赖性满足平方规律并预言了对称能在低密度区域和高密度区域具有的不同
密度依赖关系
5）利用微观多体理论预言了微观三体核力对中子星物质中质子超流性具有强烈的抑
制作用，并预言了新的质子1S0态超流性强度参量。
谢谢!
THANK YOU!