properties of Asymmetric nuclear matter within Extended BHF Approach Wei Zuo Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou Relativistic many-body problems for heavy 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

Motivations 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 et al., Science 298(2002)1592; B.A.Li, PRL88(2002) P. Danielewicz et al., Science 298(2002)1592; B.A.Li, PRL88(2002) Nuclear Physics 1) The properties of neutron rich nuclei 1) The properties of neutron rich nuclei I. Tanihata, NPA 616 (1997) 560; T. Glasmachet et al., PLB 395 (1997) I. Tanihata, NPA 616 (1997) 560; T. Glasmachet et al., 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 energy of symmetry energy 3) Heavy ion collisions 3) Heavy ion collisions B. A. Li et al., Int. J. Mod. Phys. E7 (1998) 147 B. A. Li et al., Int. J. Mod. Phys. E7 (1998) 147 Implications for astrophysics Implications for astrophysics M.Prakash et al., Phys. Rep. J.M. Lattimer and M. Prakash, Science 304 (2004) 536; 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 model EOS 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 densities determined by symmetry energy at high densities 3) Cooling of neutron stars 3) Cooling of neutron stars Fast cooling via direct URCA process Fast cooling via direct URCA process

properties of Asymmetric Nuclear Matter Effective NN interaction in nuclear medium

C. Fuchs and H. H. Wolter, EPJA30(2006)5 Dieperink et al., PRC67(2003) Symmetry energy predicted by various many-body theories ---- Symmetry energy predicted by various many-body theories ---- Extremely Large uncertainty at high densities! Effective field theory DBHF BHF Greens 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 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 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 → Defect function:  (r 12 )=  (r 12 ) –  (r 12 ) ★ 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 ) E A (MeV) K (MeV) 0.19– – 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 s - 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 : MeV RMT : 14 MeV DBHF: 10 MeV BHF(2BF): 16 MeV BHF(TBF): 13 MeV BHF(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 β 2 W. Zuo et al., PRC69(2004) The EOS of ANM is determined by the EOS of SNM and symmetry energy

W. Zuo, A. Lejeune, U.Lombardo, J.F.Mothiot, NPA706(2002)418 Density dependence of symmetry energy W. Zuo et al. PRC 69(2004) 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: SD Solid: T=0 Dash: ST=00 Long-dash: ST=10 Dot: T=1 Dot-dash:ST=01 Double-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

Isospin splitting of nucleon mean field W. Zuo, L.G. Gao, B.A. Li et al., Phys. Rev. C72 (2005) In neutron rich matter : U p <U n at low momenta U p >U n 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) F. Sammarruca et al., nucl-th/ BHF prediction: Momentum depndence Density dependence Isospin dependence

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 the local part less attractive. Starting from the energy-moment conservation The effective mass is defined as: effective mass is density and momentum dependent: p ≤ p F m* > 1 (pairing?) p > p F m* < 1 definition of m *

Neutron-proton effective mass splitting in neutron-rich matter M* n > M* p neutrons protons Skyrme-like interactions: m p * < m n * or m n * < m p * B. A. Li et al., PRC69(2004) Comparison to other predictions: DBHF: m n * > m p * Dalen et al., PRL95(2005) Z. Y. Ma et al., PLB 604 (2004)170 F. Sammarruca et al., nucl-th/

Microscopic 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.

BHF numerical prediction Un-Up is linearly dependent on asymmetry in the considered range of asymmetry and momentum (energy) at high energy Usym changes sign Isospin splitting of effective mass can be extracted Lane (1962) Provide by Prof. U. Lombardo

Isospin OMP comparison with collisions p-A n-A Provide by Prof. U. Lombardo

TBF effects on s.p. properties ： 1. TBF effect via G-matrix directly 3. TBF rearrangement 2. Ground state correlations Full s.p. potential ：

TBF rearrangment effect on s.p. properties Zuo, 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 Structure X.R.Zhou et al., PRC69(2004) Kaon condensation in neutron stars Variational BHF + 3BF RMT W. Zuo. A. Li, Z.H.Li, U. Lombardo, PRC70(2004)

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!