1. Nuclear mass predictions for super-heavy nuclei and drip-line nuclei
Ning Wang1, Min Liu1, Xi-Zhen Wu2
1 Guangxi Normal University, Guilin, China
2 China Institute of Atomic Energy, Beijing, China
20th Nuclear Physics Workshop in Kazimierz, Sep , 2013

2. Outline Introduction Weizsacker-Skyrme mass formula
Masses of super-heavy nuclei and drip-line nuclei
Summary and discussion

3. Hendrik Schatz, Klaus Blaum
Nuclear mass formulas are important for the study of super-heavy nuclei, nuclear symmetry energy and nuclear astrophysics
To predict the ~5000 unknown masses based on the ~2400 measured masses
SHE
Isospin asymmetry
Hendrik Schatz, Klaus Blaum
Wang et al., PRC 82 (2010)

4. Uncertainty of mass predictions for super-heavy nuclei and drip line nuclei is large
FRDM : At. Data & Nucl. Data Tables 59, 185 (1995).
HFB17: Phys. Rev. Lett. 102, (2009).
DZ28 : Phys. Rev. C 52, 23 (1995).
WS3 : Phys. Rev. C 84, (2011).
HFB24: PRC

5. +… 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)
WS3：PRC 84 (2011)

6. Single-particle levels
Shell correction
Single-particle levels
β=0 β4 β2
symmetry potential
WSBETA: S. Cwiok, J. Dudek, W. Nazarewicz, J. Skalski, T. Werner, CPC 46 (1987) 379

7. Some differences in WS formula
FRDM
WS3
Strength of spin-orbit potential
Deformation energies of nuclei
3-6D numerical integrations
Analytical expressions
Mirror effect No
Yes
B1 is the relative generalized surface or nuclear energy in FRDM

8. Spin-orbit interaction
KSO = -1
KSO = 1
Ni = Z for protons and Ni = N for neutrons
Xu and Qi, Phys. Lett. B724 (2013) 247

10. Emic (FRDM): ground state microscopic energy

11. Fission barrier: Phys. Rev. C 82 (2010) 014303
M. Kowal, P. Jachimowicz, and A. Sobiczewski
Nishio, el at., 40,48Ca+238U
PRC86, (2012)

12. Shell gaps
，桂林

13. L. S. Geng, H. Toki, and J. Meng, Prog. Theor. Phys. 113, 785 (2005)
，桂林

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

15. Constraint from mirror nuclei
with the same mass but with the numbers of protons and neutrons interchanged
Constraint from mirror nuclei 32 56 92
116
reduces rms error by ~10%
charge-symmetry / independence of nuclear force

16. Symmetry energy coefficient of finite nuclei
I=(N-Z)/A
NPA818 (2009) 36
Wang, Liu, PRC81,

17. AME2003 Model errors for different region Model parameters: FRDM : ~30
Liu, Wang, Deng, Wu, PRC 84, (2011)
Model errors for different region
Model parameters:
FRDM : ~30
WS3 : ~19
DZ28 : ~28
HFB17 : ~24
HFB24 : ~30

18. Predictive power for new masses in AME2012 in MeV WS3 FRDM DZ28 HFB17
HFB24: PRC
in MeV
WS3
FRDM
DZ28
HFB17
HFB24
sigma (M)2353
0.335
0.654
0.394
0.576
0.549
sigma (M)219
0.424
0.765
0.673
0.648
0.580
sigma(Sn)2199
0.273
0.375
0.294
0.500
0.474

19. Test the models with very recently measured masses
181,183Lu, 185,186Hf, 187,188Ta, 191W, and 192,193Re were measured for the first time, uncertainty of 189,190W and 195Os was improved (Storage-ring mass spectrometry GSI)
HFB21: S. Goriely, N. Chamel, and J. M. Pearson, Phys. Rev. C 82, (2010)

21. Alpha decay energies of super-heavy nuclei
Alpha decay data are not used for para. fit

22. 178
WS*
178
Zhang, et al., Phys. Rev. C 85, (2012)
N. Wang and M. Liu, arXiv: ; J. Phys: Conf. Seri. 420 (2013)
162
162

23. Radial basis function corr.
leave-one-out cross-validation
Revised masses
Ning Wang, Min Liu, PRC 84, (R) (2011)

24. AME2012
Z. M. Niu, et al., PRC 88, (2013)

25. RBF corrections for different mass models
N. Wang and M. Liu, J. Phys: Conf. Seri. 420 (2013)

26. Summary and discussion
Based on the Skyrme EDF and macro-micro method, we proposed a global nuclear mass formula with which the measured masses in AME2003 and AME2012 can be well reproduced.
Isospin-dependence of the strength of spin-orbit potential and of the symmetry potential significantly influence the shell corrections of super-heavy nuclei and drip line nuclei.
Shell corrections and alpha-decay energies of super-heavy nuclei are investigated with the formula and the shell gap at N=178 also influences the central position of the island of SHE.
Radial basis function (RBF) approach is an efficient and powerful systematic method for improving the accuracy and predictive power of global nuclear mass models.

27. Thanks for your attention!
Codes & Nuclear mass tables：
Guilin, China

28. Angeli and Marinova, At. Data Nucl. Data Tables 99, 69(2013)
Shell corrections and deformations of nuclei based on the Weizsacker-Skyrme mass formula
PRC88, (R) (2013)
RMF: Lalazissis, Raman, and Ring, At. Data Nucl. Data Tables 71, 1 (1999).
Angeli and Marinova, At. Data Nucl. Data Tables 99, 69(2013)

31. Pairing corrections J. G. Hirsch and J. Mendoza-Temis
J. Phys. G: 37 (2010)

32. Linear relationship between the slope parameter L of nuclear symmetry energy and Δrch for the mirror pair 30S - 30Si
Skyrme Hartree-Fock calc.
62 Skyrme parameter sets
K0=210 – 280 MeV
rho0=0.15 – 0.17 fm-3
Difference in the rms charge radii between mirror nuclei
PRC88, (R) (2013)