Ning Wang An improved nuclear mass formula Guangxi Normal University, Guilin, China KITPC , Beijing

KITPC, , Beijing Introduction An improved nuclear mass formula Tests and applications Summary and discussion

KITPC, , Beijing Hendrik Schatz, Klaus Blaum Nuclear mass formulas are important for study of super-heavy nuclei and nuclear astrophysics Wang et al., PRC 82 (2010) SHE

KITPC, , Beijing Some nuclear mass formulas 1 ） Macro-micro ： FRDM （ 1995 ） 656 keV FRDM （ 2012 ） 570 keV 2 ） HFB 、 RMF ： HFB17 （ 1999 ） 581 keV PC-PK1 （ 2010 ） 1400 keV 3 ） Duflo-Zuker ： DZ28 （ 1995 ） 360 keV 4 ） Weizsäcker-Skyrme ： WS3 （ 2011 ） 336 keV Y. M. Zhao, PRC ; PRC ☺ Global nuclear mass formulas ： ۞ Local mass formulas ： 1 ） Garvey-Kelson, n-p residual interaction 2 ） Isobaric Multiplet Mass Equation (IMME) J. Barea, et al, PRC (R) (2008) ☻ Systematic approaches ： Audi 、 CLEAN 、 RBF

KITPC, , Beijing Morales, NPA 828 (2009) 113 Mass predictions from local mass equations by using iterations errors increase rapidly with iterations 1 ） error of local mass equations, ~100keV 2 ） predicted masses are used in new iteration Zhao, PRC 84, (2011) MeV

KITPC, , Beijing WS ： PRC 81 (2010) WS* ： PRC 82 (2010) Skyrme EDF Duflo-Zuker Liquid drop Deformation corr. Shell corr. WS3 ： PRC 84 (2011) … Other corr.

KITPC, , Beijing Symmetry energy coefficient of finite nuclei Wang, Liu, Phys. Rev. C 81 (2010) Para. are stable for different mass region, J. Phys. Conf. Seri. 322, (2011) Form of a sym I=(N-Z)/A NPA818 (2009) 36

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

KITPC, , Beijing Single-particle levels Shell correction

KITPC, , Beijing 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

KITPC, , Beijing 1 ） Wigner effect of heavy nuclei K. Mazurek, J. Dudek ， et al., J. Phys. Conf. Seri. 205 (2010) Other residual corrections N=Z (N,Z)

KITPC, , Beijing Improve the accuracy by ~10% - 40% Revised masses 2 ） Radial basis function corr. Ning Wang, Min Liu, PRC 84, (R) (2011); leave-one-out cross-validation

KITPC, , Beijing Liu, Wang, Deng, Wu, PRC 84, (2011) keV # Model parameters: FRDM : ~30 WS : ~15 HFB17 : ~24 DZ28 : ~28

KITPC, , Beijing Model errors for different region prolate oblate Quadrupole deformation

KITPC, , Beijing Predictive power for new masses in keV 154 new data in Audi new masses in GSI FRDM / / HFB DZ WS Audi 2011: G. Audi and M. Wang (private communication) NPA 882 (2012) 71

KITPC, , Beijing rms deviation with respect to 2149 known masses （ in keV ） AME95-03 test （ 389 ） in keV 154 new masses in Audi new masses in GSI Model with RBF Model with RBF FRDM HFB DZ WS Ning Wang, Min Liu, PRC 84, (R) (2011)

KITPC, , Beijing RBF corrections

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

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

KITPC, , Beijing Fission barrier: Phys. Rev. C 82 (2010) M. Kowal, P. Jachimowicz, and A. Sobiczewski

KITPC, , Beijing Wang,Tian, Scheid, PRC84, (R) (2011)

KITPC, , Beijing 被选为 2012 年第 7 期的优秀论文 Classical r-Process

KITPC, , Beijing excitation energy of the 2+ level above 4.7 MeV PLB672 （ 2009 ） 17 Shell corr.

KITPC, , Beijing Shell gaps Shell gap: Rev. Mod. Phys. 75 (2003)1021 A~190

KITPC, , Beijing rms deviation to 2149 masses rms deviation to GK estimates rms deviation to b fit for neutron drip line nuclei Fulfilling both the Isobaric Multiplet Mass Equation and the Garvey- Kelson relations seem to be two necessary conditions for improving the quality of the model prediction. Two constraints 17 mass models Ormand, PRC 55, 2407

KITPC, , Beijing Based on the Skyrme EDF and macro-micro method, we proposed a global nuclear mass formula with high accuracy and reliability Shell effect and isospin effect, especially isospin symmetry play a crucial role for improving the nuclear mass formula The neutron separation energies, alpha-decay energies of SHN, shell gaps, Gavey-Kalson relations and IMME can also be reproduced remarkably well Radial basis function (RBF) approach is an efficient and powerful systematic method for improving the accuracy and predictive power of global nuclear mass models Conclusion and discussion

KITPC, , Beijing Thanks for your attention! Nuclear mass tables ： Collaborators: Guilin ： Min Liu CIAE: Xi-Zhen Wu Lanzhou: Hong-Fei Zhang Shanghai: Yu-Min Zhao Beijing: Jie Meng & Bao-Hua Sun

KITPC, , Beijing Wang,Tian, Scheid, PRC84, (R) (2011)

KITPC, , Beijing