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Higher-Order Effects on the Incompressibility of Isospin Asymmetric Nuclear Matter

Higher-Order Effects on the Incompressibility of Isospin Asymmetric Nuclear Matter. Collaborators ： Bao-Jun Cai and Chun Shen (SJTU) Che Ming Ko and Jun Xu (TAMU) Bao-An Li (TAMU-Commerce). Lie-Wen Chen ( 陈列文 )

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Higher-Order Effects on the Incompressibility of Isospin Asymmetric Nuclear Matter

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  1. Higher-Order Effects on the Incompressibility of Isospin Asymmetric Nuclear Matter Collaborators： Bao-Jun Cai and Chun Shen (SJTU) Che Ming Ko and Jun Xu (TAMU) Bao-An Li (TAMU-Commerce) Lie-Wen Chen (陈列文) (Institute of Nuclear, Particle, Astronomy, and Cosmology-INPAC, Department of Physics, Shanghai Jiao Tong University) The International Workshop on Nuclear Dynamics in Heavy-Ion Reactions and the Symmetry Energy (IWND09)August 23‐25, 2009, Shanghai

  2. Outline • Motivations • Formulism • Models • Saturation properties of asymmetric nuclear matter • Constraining the Ksat,2 of asymmetric nuclear matter • Summary Main Reference: L.W. Chen, B.J. Cai, C.M. Ko, B.A. Li,C. Shen, and J. Xu, Phys. Rev. C 80, 014322 (2009) [arXiv:0905.4323]

  3. On Earth!!! Transport Theory In Heaven!!! General Relativity EOS for Asymmetric Nuclear Matter Isospin Effects in HIC’s … Neutron Stars … Many-Body Theory Nuclear Force Many-Body Theory Structures of Radioactive Nuclei, SHE … I. Motivations Isospin Physics in medium energy nuclear physics HIC’s induced by neutron-rich nuclei (CSR/Lanzhou,FRIB,GSI, RIKEN……) Most uncertain property of an asymmetric nuclear matter Density Dependence of the Nuclear Symmetry Energy What is the isospin dependence of the in-medium nuclear effective interactions???

  4. Giant Monopole Resonance • It is generally believed that the incompressibility of ANM at saturation can be extracted experimentally by measuring the GMR in finite nuclei (see, e.g., J. P. Blaizot, Phys. Rep. 61, 171 (1980)) Incompressibility of ANM Incompressibility of ANM around the saturation density ρ0 • The incompressibility of ANM is a basic property of ANM, and its isospin dependence carries important information on the density dependence of symmetry energy • The incompressibility of ANM plays an important role for explosions of supernova (see, e.g., E. Baron, J. Cooperstein, and S. Kahana, PRL55, 126(1985))

  5. K0=231±5 MeV PRL82, 691 (1999) Recent results: K0=240±20 MeV G. Colo et al., U. Garg et al., S. Shlomo et al.,…… __ Incompressibility of ANM Incompressibility of SNM around the saturation density ρ0 Giant Monopole Resonance

  6. Too stiff! Big error bars! Incompressibility of ANM Incompressibility of ANM around the saturation density ρ0

  7. Incompressibility of ANM Incompressibility of ANM around the saturation density ρ0 depending on the mass region of nuclei and the number of parameters used in parametrizing the incompressibility of finite nuclei.

  8. Incompressibility of ANM Incompressibility of ANM around the saturation density ρ0

  9. Questions • What determine the incompressibility of ANM? • What can we know about the incompressibility of ANM from the present nuclear data? • Are the higher-order isospin asymmetry/density terms important? • Can the high density properties of ANM be predicted based on the information around the saturation density? • Is the isospin dependent surface term of the incompressibility of neutron-rich nuclei important?

  10. II. Formulism EOS of isospin asymmetric nuclear matter The Nuclear Symmetry Energy The 4th-order Nuclear Symmetry Energy Parabolic Law of EOS for isospin asymmetric nuclear matter

  11. Parabolic Approximation of EOS for symmetric nuclear matter II. Formulism EOS of symmetric nuclear matter

  12. II. Formulism The Nuclear Symmetry Energy

  13. II. Formulism The 4th-Order Nuclear Symmetry Energy

  14. II. Formulism Characteristic Parameters of asymmetric nuclear matter around the normal nuclear matter density

  15. II. Formulism Saturation density of asymmetric nuclear matter Binding energy at the saturation density

  16. II. Formulism Incompressibility at the saturation density (At saturation, P=0 Isobaric incompressibility) The above expressions are exact and higher-order terms have no contribution!

  17. II. Formulism The Ksat,2 of asymmetric nuclear matter

  18. III. Models Many-Body Approaches to Nuclear Matter EOS • Microscopic Many-Body Approaches Non-relativistic Brueckner-Bethe-Goldstone (BBG) Theory Relativistic Dirac-Brueckner-Hartree-Fock (DBHF) approach Self-consistent Green’s Function (SCGF) Theory Variational Many-Body (VMB) approach …… • Effective Field Theory Density Functional Theory (DFT) Chiral Perturbation Theory (ChPT) …… • Phenomenological Approaches Relativistic mean-field (RMF) theory • Relativistic Hartree-Fock (RHF) • Non-relativistic Hartree-Fock (Skyrme-Hartree-Fock) Thomas-Fermi (TF) approximations • Phenomenological potential models ……

  19. III. Models Isospin- and momentum-dependent potential (MDI) Das/Das Gupta/Gale/Li, PRC67,034611 (2003) Chen/Ko/Li, PRL94,032701(2005) Li/Chen, PRC72, 064611 (2005)

  20. III. Models Isospin- and momentum-dependent potential (MDI)

  21. III. Models Isospin- and momentum-dependent potential (MDI)

  22. III. Models Isospin- and momentum-dependent potential (MDI)

  23. _________ III. Models Skyrme-Hartree-Fock approach Standard Skyrme Interaction:

  24. III. Models Skyrme-Hartree-Fock approach

  25. III. Models Skyrme-Hartree-Fock approach

  26. III. Models Modified Skyrme-Like (MSL) model

  27. III. Models Modified Skyrme-Like (MSL) model All the expressions from the above 3 models are analytical! Especially, the Skyrme force parameters can be expressed analytically by a number of physical quantities via the MSL model!

  28. IV. Saturation properties of ANM Characteristic parameters and EOS of Asymmetric Nuclear matter It is very difficult to obtain information on the nuclear matter EOS at higher densities from nuclear properties around normal density which can be extracted from nuclear structure of finite nuclei and nuclear excitation! Heavy-Ion Collisions provide an important tool to study the high density EOS!

  29. IV. Saturation properties of ANM Characteristic parameters and EOS of Asymmetric Nuclear matter The 4-th order symmetry energy is small!

  30. IV. Saturation properties of ANM Saturation properties of Asymmetric Nuclear matter • By adjusting only one single parameter y, the MSL model can give good • description of the symmetry energy predicted by the MDI interaction • The saturation properties depend on the density dependence of • the nuclear symmetry energy.

  31. IV. Saturation properties of ANM Saturation density of Asymmetric Nuclear matter • More neutron-rich nuclear matter has a smaller saturation density • The higher-order terms are only important for extremely neutron-rich nuclear matter

  32. IV. Saturation properties of ANM Binding energy at the saturation density • More neutron-rich nuclear matter has a smaller binding energy • The higher-order terms are only important for extremely neutron-rich nuclear matter with a stiff symmetry energy

  33. IV. Saturation properties of ANM Incompressibility at the saturation density • More neutron-rich nuclear matter has a smaller incompressibility • The higher-order terms are only important for extremely neutron-rich nuclear matter with a stiff symmetry energy

  34. V. Constraining the Ksat,2 parameter Ksat,2,Kasy, and Ksat,4 • The higher-order Ksat,4 are only important for very stiff symmetry energies • The higher-order J0 contribution generally cannot be neglected!

  35. V. Constraining the Ksat,2 parameter Correlation between K0 and J0 K0 J0/K0 • The J0/K0 displays a good linear correlation with K0

  36. V. Constraining the Ksat,2 parameter Correlation between Ksym and L LKsym • The Ksym displays a good linear correlation with L

  37. V. Constraining the Ksat,2 parameter Constraining Ksat,2 Only 5 Skyrme forces in the 63 Skyrme forces used are consistent with all empirical constraint: SKM, Gs,Rs,SKO,SKO* K0 J0/K0 LKsym

  38. V. Constraining the Ksat,2 parameter Isospin surface contribution to the incompressibility of finite nuclei Compressed semi-infinite nuclear matter Surface tension: M. Brack and W. Stocker, Nucl. Phys. A388 (1982) 230-242

  39. V. Constraining the Ksat,2 parameter Isospin surface contribution to the incompressibility of finite nuclei -537 -702 -526 -522 KτS: 20-30% contribution Including isospin surface term in the incompressibility of finite nuclei can describe Notre Dame data very well!

  40. IV. Summary • The higher-order Ksat,4 parameter is usually very small compared with the Ksat,2 parameter • The higher-order contribution from J0 generally cannot be neglected • The Ksat,2 can be constrained to be -370±120 MeV from present empirical information based on the MSL model • The isospin dependent surface term of the incompressibility of neutron-rich nuclei is important • More precise constraint on the symmetry energy even around saturation density still remains a big challenge

  41. Thanks！

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