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

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

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

4. Some nuclear mass formulas
☺ Global 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
۞ Local mass formulas：
1）Garvey-Kelson, n-p residual interaction
2）Isobaric Multiplet Mass Equation (IMME)
J. Barea, et al, PRC (R) (2008)
☻ Systematic approaches：
Audi、 CLEAN、RBF
KITPC, , Beijing
Y. M. Zhao, PRC ; PRC

5. Mass predictions from local mass equations by using iterations
Morales, NPA 828 (2009) 113
MeV
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
KITPC, , Beijing
Zhao, PRC 84, (2011)

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

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

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

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

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

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

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

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

15. Predictive power for new masses
NPA 882 (2012) 71
in keV
154 new data in Audi 2011
53 new masses in GSI
FRDM / 2012
723 / 562
600
HFB17
693
582
DZ28
622
504
WS3
433
360
KITPC, , Beijing
Audi 2011: G. Audi and M. Wang (private communication)

16. rms deviation with respect to 2149 known masses （in keV）
154 new masses in Audi 2011
53 new masses in GSI
Model
with RBF
FRDM
723
475
600
193
HFB17
693
596
582
250
DZ28
622
442
504
287
WS3
433
397
360
229
AME95-03 test （389）
KITPC, , Beijing
Ning Wang, Min Liu, PRC 84, (R) (2011)

17. RBF corrections
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18. Alpha decay energies of super-heavy nuclei
Alpha decay data are not used for para. fit
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19. N=178
WS*
N=162
N=178
N=178
WS*
WS*
KITPC, , Beijing
Zhang, et al., Phys. Rev. C 85, (2012)

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

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

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

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

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

25. Two constraints
rms deviation to bfit 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.
17 mass models
Ormand, PRC 55, 2407
rms deviation to GK estimates
rms deviation to 2149 masses
KITPC, , Beijing

26. Conclusion and discussion
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
KITPC, , Beijing

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

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

29. KITPC, , Beijing