properties of Asymmetric nuclear matter within Extended BHF Approach
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Transcript of properties of Asymmetric nuclear matter within Extended BHF Approach
properties of Asymmetric nuclear matter within Extended BHF Approach
Wei ZuoWei ZuoInstitute of Modern Physics, Chinese Institute of Modern Physics, Chinese
Academy of Sciences, LanzhouAcademy of Sciences, Lanzhou
Relativistic many-body problems forheavy and superheavy nuclei
Beijing, June 2009
U. Lombardo, I. Bombaci, G. Fiorela A. Lejeune, B. A. Li ,A. Li, Z. H. Li, J. F. Mathiot, H.-J. Schulze, C.W.Shen, L.G.Cao, H. F. Zhang
• Introduction (Motivation)• Theoretical approaches BHF approach, TBF• Results (TBF effects and TBF rearrangement) Bulk Properties: EOS of ANM, Symmetry enery, EOS at finite Tempertature, Liquid-gas phase Transition Single-particle (s.p.) Properties: Neutron and proton s.p. potentials and effective masses Isospin splitting of nucleon mean fields and effective masses • Summary and conclusion
Outline
MotivationsMotivations
EOS of asymmetric nuclear matter, especially High-density EOS of asymmetric nuclear matter, especially High-density behavior of symmetry energy---- New Challenge ! behavior of symmetry energy---- New Challenge ! P. Danielewicz P. Danielewicz et al., et al., Science 298(2002)1592; B.A.Li, PRL88(2002)192701Science 298(2002)1592; B.A.Li, PRL88(2002)192701
• Nuclear PhysicsNuclear Physics 1) The properties of neutron rich nuclei1) The properties of neutron rich nuclei I. Tanihata, NPA 616 (1997) 560; T. Glasmachet I. Tanihata, NPA 616 (1997) 560; T. Glasmachet et al., et al., PLB 395 (1997)PLB 395 (1997) 2) Strong correlation between the neutron skin thinkness and the slope 2) Strong correlation between the neutron skin thinkness and the slope of symmetry energyof symmetry energy 3) Heavy ion collisions 3) Heavy ion collisions B. A. Li B. A. Li et al., et al., Int. J. Mod. Phys. E7 (1998) 147Int. J. Mod. Phys. E7 (1998) 147
• Implications for astrophysicsImplications for astrophysics J.M. Lattimer and M. Prakash, Science 304 (2004) 536; M.Prakash et al., Phys. Rep. M.Prakash et al., Phys. Rep. 280(1997)1; C.J.Pethick, Rev. Mod. Phys. 64(1992)1133; Lect. Notes Phys., 578 (2001)280(1997)1; C.J.Pethick, Rev. Mod. Phys. 64(1992)1133; Lect. Notes Phys., 578 (2001)
1) Sturctures of neutron stars 1) Sturctures of neutron stars EOS of ANM is a basic input of the nutron star structure modelEOS of ANM is a basic input of the nutron star structure model 2) Chemical Compositions of neutron stars 2) Chemical Compositions of neutron stars determined by symmetry energy at high densitiesdetermined by symmetry energy at high densities 3) Cooling of neutron stars3) Cooling of neutron stars Fast cooling via direct URCA processFast cooling via direct URCA process
properties of Asymmetric Nuclear Matter
Effective NN interaction Effective NN interaction in nuclear mediumin nuclear medium
C. Fuchs and H. H. Wolter, EPJA30(2006)5 Dieperink et al., PRC67(2003)064307.
Symmetry energy predicted by various many-body Symmetry energy predicted by various many-body theories theories ---- ---- Extremely Large uncertainty at high densities!
Effective field theory
DBHF
BHFGreens function
Variational
Most recent results from BHF
Z.H. Li, U. Lombardo, H.-J. Schulze, Zuo et al., PRC74(2006)047304
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
Theoretical Approaches:
1. Brueckner-hartree-Fock Approach 2. Microscopic Three-Body Force
Bethe-Goldstone Theory
• Bethe-Goldstone equation and effective G-matrix
→ Nucleon-nucleon interaction:
★ Two-body interaction : AV18 (isospin dependent)
★ Effective three-body force
→ Pauli operator :
→ Single particle energy :
→ “Auxiliary” potential : continuous choice
);,()()(
),();,(
21 21
212121
Gikk
kkkkQkkvvG
kkNNNN
effNN Vvv 32
2veffV3
2121 11),( knknkkQ
)()2/()( 22 kUmkk
Ak
kkkkGkkknkU ')]'()(['Re)'()('
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
N
R ,
,
)(b )(c
N
N
N
N
N
N
N
, , , ,
N
N
,
,
R,
)(a
,
, ,
Z-diagram
• 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
Effective Microscopic Three-body Force
• Effective three-body force effV3
231333213213
23133*
3321213
11,,',','
'1'1''dd4
1,','
rrrrrrrrrW
rrrrrTrrrrrV
n
nn
eff
→ 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
TBF effect on the EOS of asymmetric nuclear matter
The TBF makes the the EOS much stiffer at high densities
β=0, 0.2, 0.4, 0.6, 0.8, 1
W. Zuo, A. Lejeune, U.Lombardo, J.F.Mothiot, NPA706(2002)418
Z-diagram
Full TBF
Saturation Mechanism
(fm-3) EA (MeV) K (MeV)
0.19 –15.0 210
0.26 –18.0 230
Saturation properties:
TBF is necessary for reproducing the empirical saturation property of nuclear matter in a non-relativistic microscopic framework.
Z-diagram
Full TBF
Relativistic effect in Dirac-BHF approach and TBF effect
W. Zuo et al. NPA706(2002)418
The other elementary processes can not be completely neglected especially at high densities
The comparison between the contribution of the 3BF derived from 2-NN exchange component and relativistic effect in DBHF approach
Z diagram 3BF contribution, Provide by Prof. U. Lombardo
Critical temperature for liquid-gas phase transition in warm nuclear matter
Z-diagram
Full TBF
SHF : 14-20 MeV RMT : 14 MeV DBHF: 10 MeV BHF(2BF): 16 MeVBHF(TBF): 13 MeVBHF(Z-d): 11 MeV
A possible explanation of the discrepancy between the
DBHF and BHF predictions
W. Zuo, Z.H.Li,A. Li, U.lombardo, NPA745(2004)34.
W. Zuo, A. Lejeune, U.Lombardo, J.F.Mothiot,
Parabolic law : linear dependence on β2
W. Zuo et al., PRC69(2004)064001
2( , , ) ( , ,0) ( , )A A symE T E T E T
The EOS of ANM is determined by the EOS of SNM and symmetry energy
sym4n p E
W. Zuo, A. Lejeune, U.Lombardo, J.F.Mothiot, NPA706(2002)418
Density dependence of symmetry energyDensity dependence of symmetry energy
W. Zuo et al. PRC 69(2004)064001
TBF effect Thermal effect
Decomposition of the EOS into various ST channels------ symmetric nuclear matter
squqres: SD
Decomposition of the EOS into various ST channels----- asymmetric nuclear matter
Squares: SDSolid: T=0Dash: ST=00Long-dash: ST=10
Dot: T=1Dot-dash:ST=01Double-dot-dash: ST=11
Single Particle Properties in neutron-rich matter
• Isosping splitting of effective mass• TBF rearrangement cobtribution
• neutron and proton s.p. potential • Isovector part : Symmetry potential
sym
( ) ( )( )
2n pU k U k
U k
Isospin splitting of nucleon mean field
W. Zuo, L.G. Gao, B.A. Li et al., Phys. Rev. C72 (2005)014005 .
In neutron rich matter : Up<Un at low momentaUp>Un at high enough momenta
Nuclear Symmetry Potential in Neutron-rich Matter
Isovector parts of neutron and proton s.p. potentials in neutron-rich matter
Comparison to DBHF predictions: Dalen et al., PRL95(05)022302
F. Sammarruca et al., nucl-th/0411053
BHF prediction: Momentum depndence Density dependence Isospin dependence
sym
( ) ( )( )
2n pU k U k
U k
Nuclear Symmetry Potential in Neutron-rich Matter : Lane potential
Predictions of Skyrme-like interactions
Extended BHF prediction :Comparison with empirical Lane potential
Comparison of the microscopic symmetry potential with the phenomenological ones
Our microscopic symmetry potential shows a strongly different density and momentum dependence from the phenomenological ones adopted in the dynamical simulations of HIC.
It is necessary to apply the
microscopic symmetry potential
in the calculations of HIC.
effective mass describes the non locality of the s.p. energy, which makes thelocal part less attractive. Starting from the energy-moment conservation
2
( , )2p p
pE E p
m
The effective mass is defined as:
*1 1
( )p
p
dEm m
m p p dp E p
effective mass is density and momentum dependent:
p ≤ pF m* > 1 (pairing?)
p > pF m* < 1
definition of m*
Neutron-proton effective mass splitting in neutron-rich matter
M*n > M*p
1* d1
dFk
m m U
m p k
neutrons
protons
Skyrme-like interactions:
mp* < mn* or mn* < mp*
B. A. Li et al., PRC69(2004)064602
Comparison to other predictions:
DBHF: mn* > mp*
Dalen et al., PRL95(2005)022302Z. Y. Ma et al., PLB 604 (2004)170F. Sammarruca et al., nucl-th/0411053
Microscopic origin of the isospin splittingMicroscopic origin of the isospin splitting
Neutron-proton effective masses is controlled by the isospin T=0 SD tensor component of the NN interaction
Neutron-proton effective masses is determined by the isospin splitting of k-mass.
( , ) ( ) ( )
( , ) ( ) ( )
nU U Usym
pU U Usym
BHF numerical prediction
Un-Up is linearly dependent on asymmetry in the consideredrange of asymmetry and momentum (energy)
at high energy Usym changes sign
Isospin splitting of effective mass can be extracted
Lane (1962)
( )* *m mMD MDU U En pm mn p
Provide by Prof. U. Lombardo
Isospin OMPcomparison with collisions p-A n-A
Provide by Prof. U. Lombardo
TBF effects on s.p. properties:1. TBF effect via G-matrix directly
eff3
TBF
1( )
2 i jij k A
Vk ij ij n n
n
3. TBF rearrangement
'
( ) ( ') Re ' [ ( ) ( ')] 'BHF Ak
U k n k kk G k k kk
);,()()(
),();,(
21 21
212121
Gikk
kkkkQkkvvG
kkNNNN
2. Ground state correlations
Full s.p. potential:2( ) ( ) ( ) ( )BHF TBFU k U k U k U k
TBF rearrangment effect on s.p. propertiesZuo, Lombardo, Schulze, Li, Phys. Rev. C74 (2006)017304
S.P. Potential : Ground state correlation and TBF rearrangement effect
TBF rearrangment contributions to the s.p. potentials
S.p. potentials in SNM in three cases: without the TBF; including the TBF effect only via G-matrix; including the full contribution of the TBF
TBF effects on s.p. properties :
1. TBF affects the s.p. properties via G-matrix
2. TBF rearrangement modifications of the s.p. properties
1. The TBF induces a strongly repulsive
and momentum-dependent rearrangement
modification of the neutron and proton s. p.
potentials at high densities and momenta.
2. The TBF rearrangement contribution is
much larger than that via G-matrix above
the Feimi momentum.
3. The TBF rearrangement strongly reduces
the attraction and enhances the
momentum-dependence of the s.p.
potential at high densities and momenta.
TBF rearrangment effect on 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.
3. Modification of the high-momentum
behavior at high
TBF rearrangment effect on neutron and proton 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.
Symmetric nuclear matter
Zuo, Lombardo, Schulze, Li, Phys. Rev. C74 (2006)017304
Implications for neutron stars
• Proton fraction in neutron star matter
• Kaon condensation
Proton fraction in β-stable neutron star matter
A. Lejeune, U.Lombardo, W. Zuo, Phys.Lett. B477(2000)45
Neutron Star Neutron Star StructureStructure
X.R.Zhou et al., PRC69(2004)018801
Kaon condensation in Kaon condensation in neutron starsneutron stars
Variational
BHF + 3BF
RMT
W. Zuo. A. Li, Z.H.Li, U. Lombardo,
PRC70(2004)055802.
Summary
• The TBF provides a repulsive contribution to the EOS and improves remarkably the predicted saturation properties.
• The TBF from the Z-diagram provides the saturation mechanism and gives the main relativistic effect in DBHF approach.
• The empirical parabolic law for the EOS of ANM can be extended
to the highest asymmetry and to the finite-temperature case.
• The TBF leads to a strong enhancement of symmetry energy and the proton fraction in β-stable matter at high density.
• The neutron-proton effective mass splitting is
• The neutron-proton effective mass splitting is determined by the splitting of the k-mass and essentially controlled by the nature of the NN interaction.
• The TBF induces a strongly repulsive and momentum-dependent rearrangement contribution to the s.p. potential at high densities.
m*n > m*p
谢谢 !THANK YOU!