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properties of Asymmetric nuclear matter within Extended BHF Approach

properties of Asymmetric nuclear matter within Extended BHF Approach. Wei Zuo Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou. 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.

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properties of Asymmetric nuclear matter within Extended BHF Approach

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  1. properties of Asymmetric nuclear matter within Extended BHF Approach • Wei Zuo • Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 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 Relativistic many-body problems for heavy and superheavy nuclei Beijing, June 2009

  2. Outline • 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

  3. Motivations • EOS of asymmetric nuclear matter, especially High-density • behavior of symmetry energy---- New Challenge ! • P. Danielewicz et al., Science 298(2002)1592; B.A.Li, PRL88(2002)192701 • Nuclear Physics • 1) The properties of neutron rich nuclei • I. Tanihata, NPA 616 (1997) 560; T. Glasmachet et al., PLB 395 (1997) • 2) Strong correlation between the neutron skin thinkness and the slope • of symmetry energy • 3) Heavy ion collisions • B. A. Li et al., Int. J. Mod. Phys. E7 (1998) 147 • Implications for astrophysics • 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) 1) Sturctures of neutron stars EOS of ANM is a basic input of the nutron star structure model • 2) Chemical Compositions of neutron stars • determined by symmetry energy at high densities 3) Cooling of neutron stars Fast cooling via direct URCA process

  4. properties of Asymmetric Nuclear Matter Effective NN interaction in nuclear medium

  5. Symmetry energy predicted by various many-body theories ---- Extremely Large uncertainty at high densities! DBHF BHF Effective field theory Greens function Variational C. Fuchs and H. H. Wolter, EPJA30(2006)5 Dieperinket al., PRC67(2003)064307.

  6. Most recent results from BHF Z.H. Li, U. Lombardo, H.-J. Schulze, Zuo et al., PRC74(2006)047304

  7. 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

  8. Theoretical Approaches:1. Brueckner-hartree-Fock Approach 2. Microscopic Three-Body Force

  9. 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))

  10. Brueckner Theory of Nuclear Matter

  11. 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

  12. Effective Microscopic Three-body Force • Effective three-body force • →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

  13. EOS of Nuclear Matter

  14. TBF effect on the EOS of asymmetric nuclear matter β=0, 0.2, 0.4, 0.6, 0.8, 1 The TBF makes the the EOS much stiffer at high densities

  15. Saturation Mechanism TBF is necessary for reproducing the empirical saturation property of nuclear matter in a non-relativistic microscopic framework. Z-diagram Full TBF Saturation properties: W. Zuo, A. Lejeune, U.Lombardo, J.F.Mothiot, NPA706(2002)418

  16. Relativistic effect in Dirac-BHF approach and TBF effect The other elementary processes can not be completely neglected especially at high densities W. Zuo et al. NPA706(2002)418 Z-diagram Full TBF

  17. The comparison between the contribution of the 3BF derived from 2s-NN exchange component and relativistic effect in DBHF approach Z diagram 3BF contribution, Provide by Prof. U. Lombardo

  18. Critical temperature for liquid-gas phase transition in warm nuclear matter SHF : 14-20 MeV RMT : 14 MeV DBHF: 10 MeV BHF(2BF): 16 MeV BHF(TBF): 13 MeV BHF(Z-d): 11 MeV Z-diagram 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.

  19. Parabolic law : linear dependence on β2 The EOS of ANM is determined by the EOS of SNM and symmetry energy W. Zuo, A. Lejeune, U.Lombardo, J.F.Mothiot, W. Zuo et al., PRC69(2004)064001

  20. Density dependence of symmetry energy Thermal effect TBF effect W. Zuo, A. Lejeune, U.Lombardo, J.F.Mothiot, NPA706(2002)418 W. Zuo et al. PRC 69(2004)064001

  21. Decomposition of the EOS into various ST channels------ symmetric nuclear matter squqres: SD

  22. 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

  23. Single Particle Properties in neutron-rich matter • neutron and proton s.p. potential • Isovector part : Symmetry potential • Isosping splitting of effective mass • TBF rearrangement cobtribution

  24. Isospin splitting of nucleon mean field 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 .

  25. 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

  26. Nuclear Symmetry Potential in Neutron-rich Matter : Lane potential Predictions of Skyrme-like interactions Extended BHF prediction : Comparison with empirical Lane potential

  27. 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.

  28. definition of m* 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 ≤ pF m* > 1 (pairing?) p > pF m* < 1

  29. Neutron-proton effective mass splitting in neutron-rich matter neutrons M*n > M*p protons 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

  30. Microscopic origin of the isospin splitting Neutron-proton effective masses is determined by the isospin splitting of k-mass. Neutron-proton effective masses is controlled by the isospin T=0 SD tensor component of the NN interaction

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

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

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

  34. TBF rearrangment effect on s.p. properties Zuo, Lombardo, Schulze, Li, Phys. Rev. C74 (2006)017304

  35. S.P. Potential：Ground state correlation and TBF rearrangement effect

  36. TBF rearrangment contributions to the s.p. potentials 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. 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

  37. 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

  38. TBF rearrangment effect on neutron and proton effective masses Symmetric nuclear matter 1. Remarkable reduction of the neutron and proton effective masses. 2. Suppression of the isospin splitting in neutron-rich matter at high densities. Zuo, Lombardo, Schulze, Li, Phys. Rev. C74 (2006)017304

  39. Implications for neutron stars • Proton fraction in neutron star matter • Kaon condensation

  40. Proton fraction in β-stable neutron star matter A. Lejeune, U.Lombardo, W. Zuo, Phys.Lett. B477(2000)45

  41. Neutron Star Structure Kaon condensation in neutron stars Variational RMT BHF + 3BF W. Zuo. A. Li, Z.H.Li, U. Lombardo, PRC70(2004)055802. X.R.Zhou et al., PRC69(2004)018801

  42. 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

  43. 谢谢!THANK YOU!

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