1. Symmetry energy coefficients and shell gaps from nuclear masses
Ning Wang
Guangxi Normal University, Guilin, China
Introduction/motivations
Symmetry energy coefficients from nuclear masses
Properties of nuclear matter in liquid-drop models
Shell gaps in unmeasured mass region
Conclusions
SINAP-CUSTIPEN workshop, Shanghai, Dec. 13 – 18, 2015

2. Does the “island of stability” of super-heavy elements exist?
Super-heavy nuclei
To predict the ~ 4000 unknown masses based on the ~2353/2438 measured masses
Does the “island of stability” of super-heavy elements exist?
Or maybe just a shoal?

3. The masses of neutron-rich nuclei are important for the study of r-process and nuclear symmetry energy
WS4: N. Wang, M. Liu, X. Z. Wu, J. Meng, Phys. Lett. B 734, 215 (2014)

4. Parabolic law for drip line nuclei?
Normal Accelerating Decelerative
Higher-order terms of symmetry energy coefficients
Parabolic law for drip line nuclei?
From Wikipedia

5. Weizsäcker-Skyrme mass model
Liquid drop
Deformation
Shell
Residual
Residual：Mirror 、pairing 、Wigner corrections...
Macro-micro concept & Skyrme energy density functional
N. Wang, M. Liu, et al., PRC ；PRC ；PRC

6. Isospin dependence of model parameters
Symmetry energy coefficient
Symmetry potential
Strength of spin-orbit potential
Pairing corr. term
symmetry potential
WS3：Phys.Rev.C84_014333

7. Mass dependence of asym
Form of asym
Wang_Liu, Phys. Rev. C 81 (2010) S0
P. Danielewicz et al., Nucl. Phys. A 818 (2009) 36

8. M. Liu, N. Wang, Z. Li, F. Zhang, PRC82, 064306 (2010)
Wigner correction
M. Liu, N. Wang, Z. Li, F. Zhang, PRC82, (2010)
广西师范大学，王 宁

9. Symmetry energy coefficients of finite nuclei from Skryme energy density functional + ETF2
Second-order
Fourth-order
N. Wang, M. Liu, H. Jiang, J. L. Tian, Y. M. Zhao, Phys. Rev. C 91(2015)

10. asymptotic behavior of asym when

11. asymptotic behavior of the fourth-order term
ETF2
(MeV)
SkM*
-3.9
-4.4
SLy4
-4.1
-4.5
SkSC4
0.46
0.45
Binding energy per nucleon at saturation density
L. W. Chen, B. J. Cai, C. M. Ko, B. A. Li, C. Shen, J. Xu, Phys. Rev. C80 (2009)

12. The value of the fourth-order term is opposite for WS4 and HFB17
After removing Coulomb term, Wigner term, and asym
HFB17
N. Wang, M. Liu, H. Jiang, J. L. Tian, Y. M. Zhao, Phys. Rev. C 91(2015)

13. H. Jiang, N. Wang, L. W. Chen, Y. M. Zhao, A
H. Jiang, N. Wang, L. W. Chen, Y. M. Zhao, A. Arima, PRC 91 (2015)
Nbound

14. Properties of nuclear matter in Liquid-Drop models
Density dependence of binding energy & Esym
Lublin–Strasbourg drop (LSD) formula : Pomorski, Dudek, PRC67 (2003)
Through matching the liquid drop energy in LSD, one may find the best-fit Skyrme energy density functional for the LSD formula.

15. N. Wang, M. Liu, L. Ou, Y. X. Zhang, Phys. Lett. B 751 (2015) 553

16. Slope parameter LSD: Pomorski, Dudek, Phys. Rev. C 67, 044316 (2003).
Matching LSD
LSD: Pomorski, Dudek, Phys. Rev. C 67, (2003).
WS*: N. Wang, Z. Liang, M. Liu and X. Wu, Phys. Rev. C 82, (2010).

17. Splitting of neutron and proton effective masses for neutron matter
from the optical potential model
X. H. Li, W. J. Guo, B. A. Li, L. W. Chen, et al, Phys. Lett. B743 (2015) 408

18. N. Wang, M. Liu, Chin. Sci. Bull. 60, 1145 (2015)
Magic numbers in unknown region
Wienholtz, et al., Nature 498 (2013) 346
1) New magic number N=32
N. Wang, M. Liu, Chin. Sci. Bull. 60, 1145 (2015)
2) Sub-shell closure in 252Fm
Mo, Liu, Wang, PRC 90, (2014)

19. Contour plot of shell corrections
WS4
N. Wang, M. Liu, X. Z. Wu and J. Meng, to appear in Phys. Rev. C
The super-heavy nucleus with N=184 and Z=114 deviates evidently from the line

21. Conclusions
After removing the Coulomb and Wigner terms, the symmetry energy coefficients of finite nuclei can be extracted from nuclear masses.
The fourth-order term of symmetry energy coefficients might result in the big difference of model predictions.
Through matching the Liquid-drop energy and the Skyrme energy density functional, we obtain the slope parameter L ~ 42 MeV (LSD) and 52 MeV (WS*).
Many doubly-magic nuclei (N>Z) locate along the N=1.37Z+13.5, might due to the correlation between nucleons near Fermi surface, and more attentions should be paid to SHN with N=178.

22. Thank you for your attention
Codes & Nuclear mass tables：

23. Levels: H. Koura, S. Chiba, J. Phys. Soc. Jpn. 82, 014201 (2013)
Correlations between neutrons and protons near Fermi surface
Neutron
Proton Nv Zv
Core
208Pb
active nucleons
effective ratio of neutron to proton
Levels: H. Koura, S. Chiba, J. Phys. Soc. Jpn. 82, (2013)
For all doubly magic nuclei along the line, one gets almost the same value of Tv

24. For new masses after 2012

25. Rms charge radii
N. Wang, T. Li, Phys. Rev. C88, (R)