1. 第十四届全国核结构大会暨第十次全国核结构专题讨论会 浙江 · 湖州 · 2012.4.12-16 Nuclear matter with chiral forces in Brueckner-Hartree-Fock approximation 李增花 复旦大学核科学与技术系（现代物理研究所）

2. Outline History of nuclear forces 3NF within the BHF method Results and discussion Summary

3. 1930’s Yukawa (1935): 1950’s “Pion Theories” Discovery of the pion in cosmic ray (1947) and in the Berkeley Cyclotron Lab (1948). 1940’s In analogy to Quantum-Electro-Dynamics (QED) which uses the photon, construct a Quantum Field Theory for the nuclear force which uses the pion. One-Pion-Exchange theory Meson Hypothesis 1960’s Heavy mesons (π ， σ ， ω ， ρ)are discovered, One-Boson-Exchange Model I. History of nuclear force

4. 1980’s Nijmegen: We need more precision!!! 1993: The high-precision Nijmegen phase shift analysis 1994-2001: High-precision NN potentials: Nijmegen I, II, 93, Reid93 (Stoks et al. 1994) Argonne V18 (Wiringa et al, 1995) CD-Bonn (Machleidt et al. 1996, 2001) 1990’s Sophisticated models for two-pion exchange: Paris Potential (Lacombe et al., PRC 21, 861 (1980)) Bonn potential (Machleidt et al., Phys. Rep. 149, 1 (1987)) 1970’s

5. Z. H. Li, U. Lombardo, H. J. Schulze, W. Zuo, et al., PRC74(2006)047304 The saturation points of nuclear matter obtained with the different pure two-body potentials in the framework of the BHF approach are all located on the Coester line, far from the empirical saturation point.

6. Z. H. Li, U. Lombardo, H. J. Schulze, W. Zuo, PRC77 (2008) 034316 Energy per particle obtained with Paris, Argonne V18, Nijmegen 93 and Bonn B 3NFs in BHF method.

7. 1990--- Nuclear physicists discover Effective Field Theory (EFT): Weinberg (1990); Ordonez, Ray, van Kolck (1994/96). Another pion theory constrained by chiral symmetry 1980’s Nuclear physicists discover QCD: Quark cluster models. N3LO Next-to-Next-to-Next-to Leading Order N3LO Next-to-Next-to-Next-to Leading Order D. R. Entem & R. Machleidt, PLB 524, (2002) 93 ; PRC 68 (2003) 041001

8. Two-nucleon force (2NF) and three-nucleon force (3NF) are created on an equal footing in a low- momentum expansion based on chiral symmetry. 3NF: N2LO R. Machleidt and D. R. Entem, Physics Reports 503 (2011) 1 2NF: N3LO

9. II. 3NF within the BHF method 3NF is reduced to an effective density-dependence: The effective two-nucleon potential with the operator structure:

10. The Bethe-Goldstone equation for the G-Matrix: The energy per nucleon is given by:

11. Propagator function:The cutoff: III. Results and Discussion

12. A. Lovato, O. Benhar, et al., Phys. Rev. C85 (2012) 024003; A. Kievsky, M. Viviani, et al., Phys. Rev. C81 (2010) 044003.

14. It is obvious that even for fairly large values of the parameters a realistic value B/A=-15 MeV cannot be reached.

15. The total 3NF contribution is attractive and no saturation is obtained. In the present approximation the main effective of chiral 3NF is provided by the attractive ππ -part, which parameters are fixed already at the two-body level. P. Navrátil, Few Body Syst., 41 (2007) 117; P. Navrátil, V. G. Gueorguiev, Et al., Phys. Rev. Lett. 99 (2007) 042501.

16. IV. Summary In conclusion, the binding energy of symmetric nuclear matter is computed in BHF approach using N3LO 2BF +N2LO 3BF. We find the strong over-binding cannot be remedied by the current version of N2LO 3BF. The reason is that, in the present version of chiral 3NF, the effects of heavier mesons are only partially included in the very rudimentary form of the D, E-contact term. It remains to be seen whether chiral 3NF of higher order are able to provide the missing contributions.

17. The End