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), , 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

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 ~ keV

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) Courtesy of Qiu-Hong Mo

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

Macro-micro concept & Skyrme energy density functional Liquid drop Deformation Shell Residual Residual ： Mirror 、 pairing 、 Wigner corrections... PRC ； PRC ； PRC

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

Shell corrections symmetry potential Deformed Woods-Saxon potential

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

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

Rms (keV) FRDMHFB24WSWS4 To known masses Number of model para y9 y 13 y 4 y4 y Rms error

Predictive power for new masses AME2012 rmsD (in keV) WS3FRDMDZ28HFB17 sigma (M) sigma (M) M(WS3) – M(exp.)

For new masses after 2012

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

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

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

Kowal,et al., Phys. Rev. C 82_ H. F. Zhang, et al., Phys. Rev. C 85_ WS* 162

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

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

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

 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

Thank you for your attention Codes & Nuclear mass tables ： Guilin, China

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Quadrupole Deformations Prolate Oblate

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

原子核壳能隙可以给出子壳信息

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

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)

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

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