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Ning Wang 1, Min Liu 1, Xi-Zhen Wu 2 Nuclear mass predictions for super-heavy nuclei and drip-line nuclei 20th Nuclear Physics Workshop in Kazimierz, Sep , Guangxi Normal University, Guilin, China 2 China Institute of Atomic Energy, Beijing, China

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Introduction Weizsacker-Skyrme mass formula Masses of super-heavy nuclei and drip-line nuclei Summary and discussion Outline

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Hendrik Schatz, Klaus Blaum Nuclear mass formulas are important for the study of super-heavy nuclei, nuclear symmetry energy and nuclear astrophysics Wang et al., PRC 82 (2010) SHE Isospin asymmetry To predict the ~5000 unknown masses based on the ~2400 measured masses

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HFB24: PRC FRDM : At. Data & Nucl. Data Tables 59, 185 (1995). HFB17: Phys. Rev. Lett. 102, (2009). DZ28 : Phys. Rev. C 52, 23 (1995). WS3 : Phys. Rev. C 84, (2011). Uncertainty of mass predictions for super-heavy nuclei and drip line nuclei is large

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

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Single-particle levels Shell correction symmetry potential β=0 β4β4 β2β2 WSBETA: S. Cwiok, J. Dudek, W. Nazarewicz, J. Skalski, T. Werner, CPC 46 (1987) 379

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Some differences in WS formula FRDMWS3 Strength of spin-orbit potential Deformation energies of nuclei 3-6D numerical integrations Analytical expressions Mirror effectNoYes B 1 is the relative generalized surface or nuclear energy in FRDM

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Xu and Qi, Phys. Lett. B724 (2013) 247 Spin-orbit interaction K SO = -1K SO = 1 N i = Z for protons and N i = N for neutrons

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N=16 N=184 E mic (FRDM): ground state microscopic energy

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Fission barrier: Phys. Rev. C 82 (2010) M. Kowal, P. Jachimowicz, and A. Sobiczewski Nishio, el at., 4 0,48 Ca+ 238 U PRC86, (2012) 0

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Shell gaps

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

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

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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

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

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Model parameters: FRDM : ~30 WS3 : ~19 DZ28 : ~28 HFB17 : ~24 HFB24 : ~30 AME2003 Liu, Wang, Deng, Wu, PRC 84, (2011) Model errors for different region

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

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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

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

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N. Wang and M. Liu, arXiv: ; J. Phys: Conf. Seri. 420 (2013) Zhang, et al., Phys. Rev. C 85, (2012) 178 WS*

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Revised masses Radial basis function corr. Ning Wang, Min Liu, PRC 84, (R) (2011) leave-one-out cross-validation

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Z. M. Niu, et al., PRC 88, (2013) AME2012

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RBF corrections for different mass models N. Wang and M. Liu, J. Phys: Conf. Seri. 420 (2013)

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Based on the Skyrme EDF and macro-micro method, we proposed a global nuclear mass formula with which the measured masses in AME2003 and AME2012 can be well reproduced. Isospin-dependence of the strength of spin-orbit potential and of the symmetry potential significantly influence the shell corrections of super-heavy nuclei and drip line nuclei. Shell corrections and alpha-decay energies of super-heavy nuclei are investigated with the formula and the shell gap at N=178 also influences the central position of the island of SHE. Radial basis function (RBF) approach is an efficient and powerful systematic method for improving the accuracy and predictive power of global nuclear mass models. Summary and discussion

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Thanks for your attention! Codes & Nuclear mass tables Guilin, China

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RMF: Lalazissis, Raman, and Ring, At. Data Nucl. Data Tables 71, 1 (1999). Angeli and Marinova, At. Data Nucl. Data Tables 99, 69(2013) PRC88, (R) (2013) Shell corrections and deformations of nuclei based on the Weizsacker- Skyrme mass formula

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J. G. Hirsch and J. Mendoza-Temis J. Phys. G: 37 (2010) Pairing corrections

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Skyrme Hartree-Fock calc. 62 Skyrme parameter sets K 0 =210 – 280 MeV rho 0 =0.15 – 0.17 fm -3 Difference in the rms charge radii between mirror nuclei Linear relationship between the slope parameter L of nuclear symmetry energy and Δr ch for the mirror pair 30S - 30Si PRC88, (R) (2013)

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