Ning Wang 1, Min Liu 1, Xi-Zhen Wu 2, Jie Meng 3 Isospin effect in Weizsaecker-Skyrme mass formula ISPUN14, , Ho Chi Minh City 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 charge radii of nuclei  Summary

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

Nasirov, et al., Phys. Rev. C 84, (2011) Different mass tables lead to quite different survival probability of Compound nucleus 2. Survival probability of SHE ？ Fission barriers of super-heavy nuclei ：

FRDM : At. Data Nucl. Data Tables59, 185 (1995) HFB17: Phys. Rev. Lett. 102, (2009) PC-PK1:Phys. Rev. C82, (2010) DZ28: Phys. Rev. C 52, 23 (1995) WS3 : Phys. Rev. C 84, (2011)

Semi-empirical mass formula ‘semi-empirical mass formula’ of von Weizsäcker in 1935

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

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

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

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

Symmetry energy coefficient: J = 29.1 MeV (WS3), J = 30.2 MeV (WS4) 2353 measured masses in AME2012

N=16 N=184 E mic (FRDM): ground state microscopic energy FRDM WS* Shell corrections of super-heavy nuclei

Kowal,et al., PRC82_

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

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)

 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.  Based on the shell gaps and alpha-decay energies from the Weizsaecker-Skyrme mass formula, N=142, 152, 162, 178; Z=92, 100, 108, 120 could be sub-shell in super-heavy region.  Nuclear rms charge radii can be well reproduced with the deformations and shell corrections from the WS formula. Summary

Rms (keV) FRDMHFB24WSWS4 To 2353 masses Number of model para y9 y 13 y 4 y4 y Rms error

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

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

Spin-orbit term Xu and Qi, Phys. Lett. B724 (2013) 247 K SO = -1K SO = 1

Predictive power for new masses in AME2012 in MeVWS3FRDMDZ28HFB17HFB24 sigma (M) sigma (M) sigma(S n ) HFB24: PRC

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

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

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

Wigner effect of heavy nuclei K. Mazurek, J. Dudek ， et al., J. Phys. Conf. Seri. 205 (2010) N=Z (N,Z)

H. F. Zhang, et al., Phys. Rev. C 85, (2012) N=178 WS* N=178 WS* N=162N=178 WS*

原子核壳能隙可以给出子壳信息

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

Deformation energies

Hendrik Schatz, Klaus Blaum Nuclear mass formulas are also important for the study of nuclear astrophysics Beta-decay energies and neutron separation energies

To predict the ~5000 unmeasured masses based on the ~2400 measured masses, Not an easy task! Bao-Hua Sun WS4: Wang, Liu, Wu, Meng, Phys. Lett. B 734, 215 (2014)