1. Ning Wang An improved nuclear mass formula Guangxi Normal University, Guilin, China KITPC 2012.6.11-29, Beijing

2. KITPC, 2012.6.11-29, Beijing Introduction An improved nuclear mass formula Tests and applications Summary and discussion

3. KITPC, 2012.6.11-29, Beijing Hendrik Schatz, Klaus Blaum Nuclear mass formulas are important for study of super-heavy nuclei and nuclear astrophysics Wang et al., PRC 82 (2010) 044304 SHE

4. KITPC, 2012.6.11-29, Beijing Some nuclear mass formulas 1 ） Macro-micro ： FRDM （ 1995 ） 656 keV FRDM （ 2012 ） 570 keV 2 ） HFB 、 RMF ： HFB17 （ 1999 ） 581 keV PC-PK1 （ 2010 ） 1400 keV 3 ） Duflo-Zuker ： DZ28 （ 1995 ） 360 keV 4 ） Weizsäcker-Skyrme ： WS3 （ 2011 ） 336 keV Y. M. Zhao, PRC82-054317; PRC84-034311 ☺ Global nuclear mass formulas ： ۞ Local mass formulas ： 1 ） Garvey-Kelson, n-p residual interaction 2 ） Isobaric Multiplet Mass Equation (IMME) J. Barea, et al, PRC77 041304(R) (2008) ☻ Systematic approaches ： Audi 、 CLEAN 、 RBF

5. KITPC, 2012.6.11-29, Beijing Morales, NPA 828 (2009) 113 Mass predictions from local mass equations by using iterations errors increase rapidly with iterations 1 ） error of local mass equations, ~100keV 2 ） predicted masses are used in new iteration Zhao, PRC 84, 034311 (2011) MeV

6. KITPC, 2012.6.11-29, Beijing WS ： PRC 81 (2010) 044322 WS* ： PRC 82 (2010) 044304 Skyrme EDF Duflo-Zuker Liquid drop Deformation corr. Shell corr. WS3 ： PRC 84 (2011) 014333 +… Other corr.

7. KITPC, 2012.6.11-29, Beijing Symmetry energy coefficient of finite nuclei Wang, Liu, Phys. Rev. C 81 (2010) 067302 Para. are stable for different mass region, J. Phys. Conf. Seri. 322, 012017 (2011) Form of a sym I=(N-Z)/A NPA818 (2009) 36

8. KITPC, 2012.6.11-29, Beijing Skyrme EDF plus extended Thomas-Fermi approach, significantly reduces CPU time Influence of nuclear deformations on liquid-drop energy (parabolic approx.)

9. KITPC, 2012.6.11-29, Beijing Single-particle levels Shell correction

10. KITPC, 2012.6.11-29, Beijing Constraint from mirror nuclei reduces rms error by ~10% with the same mass but with the numbers of protons and neutrons interchanged charge-symmetry / independence of nuclear force

11. KITPC, 2012.6.11-29, Beijing 1 ） Wigner effect of heavy nuclei K. Mazurek, J. Dudek ， et al., J. Phys. Conf. Seri. 205 (2010) 012034 Other residual corrections N=Z (N,Z)

12. KITPC, 2012.6.11-29, Beijing Improve the accuracy by ~10% - 40% Revised masses 2 ） Radial basis function corr. Ning Wang, Min Liu, PRC 84, 051303(R) (2011); leave-one-out cross-validation

13. KITPC, 2012.6.11-29, Beijing Liu, Wang, Deng, Wu, PRC 84, 014333 (2011) keV # 2149 1988 46 2149 Model parameters: FRDM : ~30 WS : ~15 HFB17 : ~24 DZ28 : ~28

14. KITPC, 2012.6.11-29, Beijing Model errors for different region prolate oblate Quadrupole deformation

15. KITPC, 2012.6.11-29, Beijing Predictive power for new masses in keV 154 new data in Audi 2011 53 new masses in GSI FRDM / 2012 723 / 562 600 HFB17693582 DZ28622504 WS3433360 Audi 2011: G. Audi and M. Wang (private communication) NPA 882 (2012) 71

16. KITPC, 2012.6.11-29, Beijing rms deviation with respect to 2149 known masses （ in keV ） AME95-03 test （ 389 ） in keV 154 new masses in Audi 2011 53 new masses in GSI Model with RBF Model with RBF FRDM723475600193 HFB17693596582250 DZ28622442504287 WS3433397360229 Ning Wang, Min Liu, PRC 84, 051303(R) (2011)

17. KITPC, 2012.6.11-29, Beijing RBF corrections

18. KITPC, 2012.6.11-29, Beijing Alpha decay energies of super-heavy nuclei Alpha decay data are not used for para. fit

19. KITPC, 2012.6.11-29, Beijing Zhang, et al., Phys. Rev. C 85, 014325 (2012) N=178 WS* N=178 WS* N=162N=178 WS*

20. KITPC, 2012.6.11-29, Beijing Fission barrier: Phys. Rev. C 82 (2010) 014303 M. Kowal, P. Jachimowicz, and A. Sobiczewski

21. KITPC, 2012.6.11-29, Beijing Wang,Tian, Scheid, PRC84, 061601(R) (2011)

22. KITPC, 2012.6.11-29, Beijing 被选为 2012 年第 7 期的优秀论文 Classical r-Process

23. KITPC, 2012.6.11-29, Beijing excitation energy of the 2+ level above 4.7 MeV PLB672 （ 2009 ） 17 Shell corr.

24. KITPC, 2012.6.11-29, Beijing Shell gaps Shell gap: Rev. Mod. Phys. 75 (2003)1021 A~190

25. KITPC, 2012.6.11-29, Beijing rms deviation to 2149 masses rms deviation to GK estimates rms deviation to b fit for neutron drip line nuclei Fulfilling both the Isobaric Multiplet Mass Equation and the Garvey- Kelson relations seem to be two necessary conditions for improving the quality of the model prediction. Two constraints 17 mass models Ormand, PRC 55, 2407

26. KITPC, 2012.6.11-29, Beijing Based on the Skyrme EDF and macro-micro method, we proposed a global nuclear mass formula with high accuracy and reliability Shell effect and isospin effect, especially isospin symmetry play a crucial role for improving the nuclear mass formula The neutron separation energies, alpha-decay energies of SHN, shell gaps, Gavey-Kalson relations and IMME can also be reproduced remarkably well Radial basis function (RBF) approach is an efficient and powerful systematic method for improving the accuracy and predictive power of global nuclear mass models Conclusion and discussion

27. KITPC, 2012.6.11-29, Beijing Thanks for your attention! Nuclear mass tables ： www.ImQMD.com www.ImQMD.com Collaborators: Guilin ： Min Liu CIAE: Xi-Zhen Wu Lanzhou: Hong-Fei Zhang Shanghai: Yu-Min Zhao Beijing: Jie Meng & Bao-Hua Sun

28. KITPC, 2012.6.11-29, Beijing Wang,Tian, Scheid, PRC84, 061601(R) (2011)

29. KITPC, 2012.6.11-29, Beijing