原子核多体理论
左维
中国科学院近代物理研究所
湖州, 2012年4月
1. Skyrme-Hartree-Fock理论
2. 相对论平均场理论
3. Bruekner-Hartree-Fock理论
Skyrme-Hartree-Fock理论
 张量力效应（张焕乔，白春林，曹李刚, 顾建中，董建敏, 左维,Tanihata,
Sagawa,Otsuka,Colo…)
 基于微观多体理论预言的Skyrme参数 (U.Lombardo,曹李刚,左维…）
 非对称核物质等(陈列文,李宝安…)
 重离子碰撞输运理论模型(李祝霞，李庆峰，冯兆庆 …)
奇异核, 超核与 K介子核的性质 (任中洲, 周先荣….)
…………………
相对论平均场理论
 奇特核性质(孟杰，周善贵，任中洲，张双全…)
 超重核结构性质和形变（任中洲,张鸿飞…）
 反核子谱的自旋对称性(周善贵，孟杰，…)
 单粒子共振态(孟杰，马中玉…)
 Woods-Saxon基展开的相对论平均场理论(周善贵，孟杰…）
 密度依赖的相对论平均场理论和相对论性HF理论(龙文辉，孟杰，
任中洲 ，…)
 三维角动量投影+生成坐标(姚江明…)
 基于RMF的振动转动耦合（李志攀…）
 倾斜轴推转的RMF（彭婧，张双全…)
 RMF+RPA（梁豪兆…)
 形变的相对论连续谱Hartree-Bogoliubov理论(周善贵, 孟杰，李璐
璐…)
 超核性质 (周善贵，赵恩广，…)
…………………….
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,…，70--05)
② 同位旋相关的BHF与EBHF方法（Bombaci,Lombardo,Zuo,…)
③ 收敛性的证实(Song,Baldo,Lombardo,…,1998）√
④ 引入微观三体核力（Lejeune,Lombardo,Zuo,…，2002) √
⑤ 将包含微观三体核力的BHF理论方法推广到有限温（Li,Zuo,…，
2004)
⑥ 三体核力重排贡献(Zuo, Lombardo, …2005-2006)
Brueckner Theory of Nuclear Matter
Bethe-Goldstone Theory
•
Bethe-Goldstone equation and effective G-matrix
G(  ,  ; )  vNN  vNN 
k1k 2
k1k2 Q(k1 , k2 ) k1k2
   (k1 )   (k2 )  i
G(  ,  ;  )
→ Nucleon-nucleon interaction: vNN  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))
Problems of BHF approach for predicting nuclear EOS
and s.p. properties of nuclear matter
1. Within the non-relativistic BHF framework, the empirical
nuclear matter saturation properties can not be reproduced by
two-body NN interaction. Coestor et al., PRC1(1970)765
2. At densities around the saturation density, the predicted
optical potential depth is too deep as compared to the
empirical value, and it destroy the Hugenholtz-Van Hove
(HVH) theorem.
Solution: to include the effect of ground state correlations
J. P. Jeukenne et al., Phys. Rep. 25 (1976) 83
M. Baldo et al., Phys. Lett. 209 (1988) 135; 215 (1988) 19
3. At high densities, the predicted potential is too attractive and
its momentum dependence turns out to be too weak for
describing the experimental elliptic flow data.
P. Danielewicz, Nucl. Phys. A673 (2000) 375
Nuclear Matter Saturation
Problem
The model of rigid nucleons interacting via realistic two-body forces fitting
in-vacuum nucleon-nucleon scattering data can not reproduce the
empirical saturation properties of nuclear matter (Coestor band,
Coestor et al., PRC1(1970)765)
Optical potential at the lowest order BHF level
At high densities, the BHF
potential is too attractive and its
momentum dependence turns out to
be too weak for describing the
experimental elliptic flow data.
P. Danielewicz, Nucl. Phys. A673 (2000)375
Improvement in three aspects:
1. Include a microscopic three-body force (TBF) to improve the
prediction of the saturation properties with BHF approach
W. Zuo et al., NPA706 (2002) 418; Z. H. LI, et al., PRC 77,
034316 (2008)
2. Extend the calculation of the effect of ground state correlations
to asymmetric nuclear
W. Zuo et al., PRC 60 (1999) 024605
2. The TBF-induced rearrangement contribution in calculating the
s.p. properties
W. Zuo, et al., PRC 74 (2006) 014317
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)
(c)
N
N
R
,

, 
N
N
, 
N
N
 ,  ,
N
N
 ,  ,
N
(a )
, 

, 

, 
, R
Effective Microscopic Three-body Force
• Effective three-body force V eff
3
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 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
TBF based on Bonn B interaction
李增花, ，H. J. Schulze, U. Lombardo, 左维， PRC 77, 034316 (2008)
Single Particle Potential beyond the mean field approximation:
1. Single particle potential at lowest BHF level
G(  ,  ; )  vNN  vNN 
k1k 2
k1k2 Q(k1 , k2 ) k1k2
   (k1 )   (k2 )  i
G(  ,  ;  )
U BHF (k )   n(k ') Re kk ' G[ (k )   (k ')] kk '
A
k'
2. Ground state correlations
3. TBF rearrangement
 V3eff
1
U TBF (k )   ij
ij
2 ij
 nk
Full s.p. potential：
ni n j
A
U (k )  U BHF (k )  U2 (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 .
Pauli rearrangement contribution: Ground state correlations
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
TBF rearrangment contribution to s.p. potential in
symmetric nuclear matter
 V3eff
1
U 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
S.p. potential including the TBF rearrangment contribution
三体核力重排贡献在很大程度上解决了高密BHF单核子势吸引性
过强和动量相关性过弱的问题
W. Zuo, L.G. Gao, B.A. Li et al., Phys. Rev. C72 (2005)014005 .
总结
• 简要介绍了Skyrme-Hartree-Fock理论和相对论平均场理论
的进展
• 简要报告了我们在扩展和改进BHF理论方法方面取得的进展
Thanks!
谢谢!