1. 陈融 导师：陈列文教授 合作者：蔡宝军，许昌，李宝安，李小华 Single-nucleon potential decomposition of the nuclear symmetry energy the nuclear symmetry energy Shanghai Jiao Tong University Huzhou, 2012-4

2. Symmetry energy and its density slope Single-nucleon potential decomposition Discussions Summary

5. Also,single-nucleon potential can be expanded as: C. Xu, B.A. Li, L.W. Chen, and C.M. Ko, Nucl. Phys. A (2011)

6. Yes, we can

7. HVH theorem We consider here non-relativistic situation Right-hand side Left-hand side N.M.Hugenholtz and L.Van.Hove, Physica XXIV 363-376 (1958)

8. plus them we have: Right-hand side: minus them we have

9. Take left-hand side into consideration, that is and

11. and have:

12. We have:

13. So that

14. So now we write further into:

15. For convenience,we write with

18. 3 non-relativistic phenomenological models (10 sets of parameters) are used here in discussions: MDI (x=-1,0,1) L.W. Chen, C.M. Ko, and B.A. Li, Phys. Rev. Lett (2005) B.A. Li and L.W. Chen, Phys. Rev. C (2005) Skyrme-Hartree-Fock (MSL0,SKM*,SLy4) L.W. Chen, C.M. Ko, B.A. Li, and J. Xu, Phys. Rev. C (2010) J. Bartel et al., Nucl. Phys. A386, 79 (1982) E. Chabanat et al., Nucl. Phys. A635, 231 (1998 Gogny-Hartree-Fock (D1,D1S,D1N,D1M) J. Decharge and D. Gogny, Phys. Rev. C 21, 1568(1980) J.F. Berger, M. Girod, and D. Gogny, Comp. Phys. Comm. 63, 365 (1991) F. Chappert, M. Girod, and S. Hilaire, Phys. Lett. B 668, 420 (2008) S. Goriely, S. Hilaire, M. Girod, and S. Peru, Phys. Rev. Lett. 102, 242501 (2009)

19. MDI Potential energy density: Single-nucleon potential:

20. Skyrme-Hartree-Fock Skyrme interaction Single-nucleon potential:

21. Gogny-Hartree-Fock Gogny interaction Single-nucleon potential: here

22. Discussions

23. Symmetry energy decomposition

24. Density slope decomposition

26. Density slope correlations

29. Summary Within the framework of HVH theorem, symmetry energy and its density slope can be decomposed into terms of single-nucleon potential.

30. ¡Mucho Gracias !