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Nuclear mass predictions for super-heavy nuclei and drip-line nuclei

Nuclear mass predictions for super-heavy nuclei and drip-line nuclei. Ning Wang 1 , Min Liu 1 , Xi-Zhen Wu 2. 1 Guangxi Normal University, Guilin , China 2 China Institute of Atomic Energy, Beijing , China. 20th Nuclear Physics Workshop in Kazimierz, Sep. 25-29, 2013. Outline.

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Nuclear mass predictions for super-heavy nuclei and drip-line nuclei

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  1. Nuclear mass predictions for super-heavy nuclei and drip-line nuclei Ning Wang1, Min Liu1, Xi-Zhen Wu2 1 Guangxi Normal University, Guilin, China 2 China Institute of Atomic Energy, Beijing, China 20th Nuclear Physics Workshop in Kazimierz, Sep. 25-29, 2013

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

  3. Nuclear mass formulas are important for the study of super-heavy nuclei, nuclear symmetry energy and nuclear astrophysics To predict the ~5000 unknown masses based on the ~2400 measured masses SHE Isospin asymmetry Hendrik Schatz, Klaus Blaum Wang et al., PRC 82 (2010) 044304

  4. Uncertainty of mass predictions for super-heavy nuclei and drip line nuclei is large FRDM : At. Data & Nucl. Data Tables 59, 185 (1995). HFB17: Phys. Rev. Lett. 102, 152503 (2009). DZ28 : Phys. Rev. C 52, 23 (1995). WS3 : Phys. Rev. C 84, 014333 (2011). HFB24: PRC88-024308

  5. Skyrme EDF +… Liquid drop Deformation corr. Shell corr. Other corr. Duflo-Zuker WS ：PRC 81 (2010) 044322 WS*：PRC 82 (2010) 044304 WS3：PRC 84 (2011) 014333

  6. β4 β2 β=0 Shell correction Single-particle levels symmetry potential WSBETA: S. Cwiok, J. Dudek, W. Nazarewicz, J. Skalski, T. Werner, CPC 46 (1987) 379

  7. Some differences in WS formula B1 is the relative generalized surface or nuclear energy in FRDM

  8. KSO = -1 KSO = 1 Spin-orbit interaction Ni= Z for protons and Ni= N for neutrons Xu and Qi, Phys. Lett. B724 (2013) 247

  9. N=16 N=184 Emic (FRDM): ground state microscopic energy

  10. Fission barrier: Phys. Rev. C 82 (2010) 014303 M. Kowal, P. Jachimowicz, and A. Sobiczewski Nishio, el at.,40,48Ca+238U PRC86, 034608 (2012) 0

  11. Shell gaps

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

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

  14. 32 56 92 116 reduces rms error by ~10% with the same mass but withthe numbers of protons and neutrons interchanged Constraint from mirror nuclei charge-symmetry / independence of nuclear force

  15. Symmetry energy coefficient of finite nuclei I=(N-Z)/A NPA818 (2009) 36 Wang, Liu, PRC81, 067302

  16. Model errors for different region AME2003 Liu, Wang, Deng, Wu, PRC 84, 014333 (2011) Model parameters: FRDM : ~30 WS3 : ~19 DZ28 : ~28 HFB17 : ~24 HFB24 : ~30

  17. Predictive power for new masses in AME2012 HFB24: PRC88-024308

  18. Test the models with very recently measured masses 181,183Lu, 185,186Hf, 187,188Ta, 191W, and 192,193Re were measured for the first time, uncertainty of 189,190W and 195Os was improved (Storage-ring mass spectrometry GSI) HFB21: S. Goriely, N. Chamel, and J. M. Pearson, Phys. Rev. C 82, 035804 (2010)

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

  20. 178 WS* 178 Zhang, et al., Phys. Rev. C 85, 014325 (2012) N. Wang and M. Liu, arXiv:1211.2538; J. Phys: Conf. Seri. 420 (2013) 012057 162 162

  21. Radial basis function corr. Revised masses leave-one-out cross-validation Ning Wang, Min Liu, PRC 84, 051303(R) (2011)

  22. AME2012 Z. M. Niu, et al., PRC 88, 024325 (2013)

  23. RBF corrections for different mass models N. Wang and M. Liu, J. Phys: Conf. Seri. 420 (2013) 012057

  24. Summary and discussion • 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.

  25. Thanks for your attention! Codes & Nuclear mass tables：www.ImQMD.com/mass Guilin, China

  26. Shell corrections and deformations of nuclei based on the Weizsacker-Skyrme mass formula PRC88, 011301(R) (2013) RMF: Lalazissis, Raman, and Ring, At. Data Nucl. Data Tables 71, 1 (1999). Angeli and Marinova, At. Data Nucl. Data Tables 99, 69(2013)

  27. Pairing corrections J. G. Hirsch and J. Mendoza-Temis J. Phys. G: 37 (2010) 064029

  28. Linear relationship between the slope parameter L of nuclear symmetry energyand Δrch for the mirror pair 30S - 30Si Skyrme Hartree-Fock calc. 62 Skyrme parameter sets K0=210 – 280 MeV rho0=0.15 – 0.17 fm-3 Difference in the rms charge radii between mirror nuclei PRC88, 011301(R) (2013)

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