1. Ning Wang 1, Min Liu 1, Xi-Zhen Wu 2, Jie Meng 3 Isospin effects in nuclear mass models Nuclear Structure and Related Topics (NSRT15), 2015.7.14-18, DUBNA 1 Guangxi Normal University, Guilin, China 2 China Institute of Atomic Energy, Beijing, China 3 Peking University, Beijing, China  Introduction  Weizsaecker-Skyrme mass formula  Shell gaps and symmetry energy coefficients  Summary

2. N. Wang, M. Liu, X. Z. Wu, J. Meng, Phys. Lett. B 734, 215 (2014) Super-heavy nuclei r-process 、 symmetry energy known masses: 2438 unmeasured ~ 4000 Nuclear mass models play an important role for the study of super-heavy nuclei, nuclear astrophysics, and nuclear symmetry energy. Popular mass models with rms error of ~300-600keV

3. Yu. Oganessian. SKLTP/CAS - BLTP/JINR July 16, 2014, Dubna neutrons → 1.Central position of the island for SHE ？ N. Wang, M. Liu, X. Wu, PRC 82 (2010) 044304 Courtesy of Qiu-Hong Mo

4. Why is the difference so large for neutron-rich nuclei ?

5. Macro-micro concept & Skyrme energy density functional Liquid drop Deformation Shell Residual Residual ： Mirror 、 pairing 、 Wigner corrections... PRC81-044322 ； PRC82-044304 ； PRC84-014333

6. Skyrme EDF plus extended Thomas-Fermi approach, significantly reduces CPU time Parabolic approx. for the deformation energies

7. Shell corrections symmetry potential Deformed Woods-Saxon potential

8. Isospin dependence of model parameters 1.Symmetry energy coefficient 2.Symmetry potential 3.Strength of spin-orbit potential 4.Pairing corr. term symmetry potential WS3 ： Phys.Rev.C84_014333

9. 5. Isospin dependence of surface diffuseness N. Wang, M. Liu, X. Z. Wu, and J. Meng, Phys. Lett. B 734 (2014) 215

10. Rms (keV) FRDMHFB24WSWS4 To known masses 654549525298 Number of model para. 31301318 9 y9 y 13 y 4 y4 y Rms error

11. Predictive power for new masses AME2012 rmsD (in keV) WS3FRDMDZ28HFB17 sigma (M) 2149 336656360581 sigma (M) 219 424765673648 M(WS3) – M(exp.)

12. For new masses after 2012

13. Xu and Qi, Phys. Lett. B724 (2013) 247 K SO = -1K SO = 1 WS4, Phys. Lett. B 734 (2014) 215 FRDM WS*

14. Wienholtz, et al., Nature 498 (2013)346 New magic numbers

15. Mo, Liu, Wang, Phys. Rev. C 90, 024320 (2014 ) Shell structure in heavy and super-heavy nuclei 108

16. 142 152 162

17. Kowal,et al., Phys. Rev. C 82_014303 H. F. Zhang, et al., Phys. Rev. C 85_014325 178 WS* 162

18. Symmetry energy coefficients of nuclei Parabolic law for drip line nuclei? Liu, Wang, Li, Zhang, Phys. Rev. C 82_064306

19. Symmetry energy coefficients of finite nuclei from Skryme energy density functional + ETF

20. N. Wang, M. Liu, H. Jiang, J. L. Tian, Y. M. Zhao, Phys. Rev. C 91, 044308 (2015)

21.  Inspired by the Skyrme energy-density functional, we propose a new macro-micro mass formula with an rms error of 298 keV, considering the isospin dependence of model parameters.  The shell gaps from WS formula indicate that N=32 could be new magic number in neutron-rich region, and N=142, 152, 162, 178; Z=92, 100, 108, 120 could be sub-shell closure in super-heavy region.  The symmetry energy coefficients of nuclei are extracted from nuclear masses and Skyrme energy density functional. The opposite values for the coefficient of I^4 term used in the HFB17 and WS4 models may result in the large difference at the predictions of the masses of neutron-rich nuclei. Summary

22. Thank you for your attention Codes & Nuclear mass tables ： www.ImQMD.com/mass www.ImQMD.com/mass Guilin, China

23. backup

25. Quadrupole Deformations Prolate Oblate

26. Mo, Liu, Wang ， Phys. Rev. C 90, 024320 (2014)

27. 原子核壳能隙可以给出子壳信息

28. Volume term Surface energy term Coulomb energy term Symmetry energy term Nuclear surface diffuseness results in the deformation energies being complicated

29. Isospin dependence of the surface diffuseness  Deformation dependence of the symmetry energy coefficients of nuclei Skyrme energy density functional + ETF2 Mo, Liu, Chen, Wang, Sci. China Phys. Mech. & Astron. 58 (2015) 082001

30. Nuclear deformations Prolate Oblate N. Wang, T. Li, Phys. Rev. C88, 011301(R) Rms charge radii

31. RMF: Lalazissis, Raman, and Ring, At. Data Nucl. Data Tables 71, 1 (1999)