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Three-body Force Effects on the Properties of Asymmetric Nuclear Matter

Three-body Force Effects on the Properties of Asymmetric Nuclear Matter. Zuo Wei Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, China.

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Three-body Force Effects on the Properties of Asymmetric Nuclear Matter

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  1. Three-body Force Effects on the Properties of Asymmetric Nuclear Matter • Zuo Wei • Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, China I. Bombaci, G.F.Burgio, U. Lombardo, H.-J. Schulze, A. Lejeune, J. F. Mathiot, B. A. Li , A. Li, Z. H. Li, L.G.Cao, C.W.Shen, J.M.Dong, H.F. Zhang, W. Scheid From nucleon structure to nuclear structure and compact astrophysical objects KITPC/ITP-CAS, Beijing, June 10 – July 20, 2012

  2. Outline: 1. Introduction (Motivation) 2. Theoretical approaches 3. Results 4. Summary and conclusion

  3. Properties of Asymmetric Nuclear Matter

  4. Composition of neutron star& Cooling of neutron stars Lattimer and Prakash, Science 304(2004)536. Lattimer et al., PRL66(1991)2701.

  5. Double n/p ratio in HIC B.A.Li, L.W.Chen,G.C.Yong, W. Zuo, PLB634(2006)378

  6. Asymmetric nuclear matter at low densities extracted from HIC Isospin diffusion Experiments at the NSCL/MSU：Sn+Sn， Ebeam/A=50 MeV Iso-scaling Conclusion:

  7. Asymmetric nuclear matter at high densities from HIC FOPI Experiments at GSI：Au+Au P. Russotto etal, PLB. 697(2011)471 Z. G. Xiao etal, PRL 102(2009)062502 Super-soft Z.-Q. Feng etal, PLB 683 (2010) 140 Stiff Between soft and stiff: γ=0.90.4 Conclusion: ?????

  8. 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

  9. RMF SHF Symmetry energy predicted by SHF and RMF approaches L.W. Chen, C.M. Ko, B.A. Li, Phys. Rev. Lett. 94 (2005) 032701. B. A. Li， L. W. Chen， C. M. Ko，Phys. Rep. 464（2008）113

  10. 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.

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

  12. 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))

  13. 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)

  14. Effective NN interaction • Dirac-Brueckner approach [R.Machleidt, Adv. Nucl. Phys. 16 (1989) 189; Serot andWalecka, Int. Journ. Mod. Phys. E6(1997) 515] • There are on the market different ways on how to introduce the medium effects: ◆ Phenomenologocal three-body force --- Two or few adjustable parameters, which are adjusted simultaneously on nuclear saturation point and light nuclei (3He)properties. --- Extensively applied to neutron star physics within both variational approach [Wiringa et al., PRC38(1988) 1010; Akmal et al., PRC56 (1997)2261; C58(98) 1804.] and BHF approach [Baldo et al., Astron. Astrophys. 328(1997) 274.] ◆ Microscopic three-body force

  15. 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; W. Zuo etal., NPA706(2002)418 Z-diagram

  16. 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

  17. 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: W. Zuo, A. Lejeune, U.Lombardo, J.F.Mothiot, NPA706(2002)418

  18. TBF based on Bonn B interaction Li ZengHua，H. J. Schulze, U. Lombardo, Wei Zuo， PRC 77, 034316 (2008)

  19. Isospin dependence of the EOS of asymmetric nuclear matter Parabolic law W. Zuo, A. Lejeune, U.Lombardo, J.F.Mothiot, EPJA 14 (2002) 469 W. Zuo, Z.H.Li,A. Li, G.C.Lu, PRC 69(2004)064001

  20. Density dependence of symmetry energy Thermal effect TBF effect

  21. Incompressibility of asymmetric nuclear matter BHF(two-body force) BHF(two-body force + TBF) M3Y interaction (Dao T. Khoa etal, NPA602(1996)98)

  22. At the lowest mean field approximation, two problems of BHF approach for predicting nuclear s.p. properties: 1. 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 2. 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

  23. Improvement in two aspects: 1. Extend the calculation of the effect of ground state correlations to asymmetric nuclear W. Zuo et al., PRC 60 (1999) 024605 2. Include a microscopic three-body force (TBF) and the TBF-induced rearrangement contribution in calculating the s.p. properties W. Zuo et al., NPA706 (2002) 418; PRC 74 (2006) 014317

  24. Single Particle Potential beyond the mean field approximation: 1. Single particle potential at lowest BHF level 2. Ground state correlations 3. TBF rearrangement Full s.p. potential：

  25. Single particle potential at the BHF level In neutron rich matter : Up<Un at low momenta Up>Un at high enough momenta W. Zuo, I. Bombaci and U. Lombardo, PRC60(1999)024605 W. Zuo, L.G. Gao, B.A. Li et al., Phys. Rev. C72 (2005)014005 .

  26. 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

  27. 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 W. Zuo, L.G. Gao, B.A. Li et al., Phys. Rev. C72 (2005)014005 .

  28. TBF rearrangment contribution to s.p. potential in symmetric nuclear matter 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

  29. The s. p. potentials at three different aproximations S.p. potentials in SNM in three cases: 1. without the TBF; 2. including the TBF effect only via G-matrix; 3. including the full contribution of the TBF

  30. S.p. potential including the TBF rearrangment contribution W. Zuo, L.G. Gao, B.A. Li et al., Phys. Rev. C72 (2005)014005 .

  31. Isospin dependence of the TBF rearrangment effect Symmetry potential Effective masses 1. Negligible at low densities around and below the Fermi momentum. 2. Enhancement of the repulsion for neutrons and the attraction for protons at high densities 1. Remarkable reduction of the neutron and proton effective masses. 2. Suppression of the isospin splitting in neutron-rich matter at high densities.

  32. Momentum distribution in asymmetric nuclear matter As the asymmetry increases, the neutron depletion becomes smaller, while the proton becomes larger, indicting that at a higher asymmetry, the many-body correlations induced by the nucleon-nucleon interaction becomes stronger on protons and weaker on neutrons.

  33. W. Zuo et al., PLB 595(2004)44 TBF effect on the 1S0 proton gap in neutron star matter TBF suppresses strongly the 1S0 proton superfluidity in neutron stars 1. It reduces the energy gap from ~1 to ~0.5 2. It suppresses largely the density region of the superfluidity Proton superfludity: Going from SNM to PNM, the maximum gap value decreases and the density domain enlarges remarkably W. Zuo et al., PRC75(2007)045806

  34. 3PF2 proton and neutron superfluidity in asymmetric nuclear matter Proton Neutron W. Zuo et al.,EurPhys. Lett. 84(2008)32001

  35. TBF effect on the 3PF2 neutron gap in neutron star matter and neutron stars TBF enhances remarkably the 3PF2 neutron superfluidity in neutron star matter and in neutron stars 3PF2 gap in Neutron star matter 3PF2 gap in Neutron stars W. Zuo et al., Phys. Rev. C78(2008)015805

  36. Isospin dependence of Alpha-decay energies of SHN A simple formula has been proposed for accurately predicting the Qα values of SHN The increased stability of these SHN against alpha-decay with larger neutron number is primarily attributed to the effect of the symmetry energy.

  37. Summary • The TBF provides a repulsive contribution to the EOS of nuclear matter and improves remarkably the predicted saturation properties. • 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 the stiffness of symmetry energy at high densities. • The neutron-proton effective mass splitting in neutron-rich matter is • The TBF induces a strongly repulsive and momentum-dependent rearrangement contribution to the s.p. potential at high densities. m*n > m*p

  38. Thank you !

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