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

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

Hendrik Schatz, Klaus Blaum 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

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

+… Liquid drop Deformation corr. Shell corr. Other corr. 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

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

Some differences in WS formula FRDM WS3 Strength of spin-orbit potential Deformation energies of nuclei 3-6D numerical integrations Analytical expressions Mirror effect No Yes B1 is the relative generalized surface or nuclear energy in FRDM

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

Emic (FRDM): ground state microscopic energy

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

Shell gaps 2013.6.17，桂林

L. S. Geng, H. Toki, and J. Meng, Prog. Theor. Phys. 113, 785 (2005) 2013.6.17，桂林

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

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

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

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

Predictive power for new masses in AME2012 in MeV WS3 FRDM DZ28 HFB17 HFB24: PRC88-024308 in MeV WS3 FRDM DZ28 HFB17 HFB24 sigma (M)2353 0.335 0.654 0.394 0.576 0.549 sigma (M)219 0.424 0.765 0.673 0.648 0.580 sigma(Sn)2199 0.273 0.375 0.294 0.500 0.474

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)

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

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

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

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

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

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.

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

Angeli and Marinova, At. Data Nucl. Data Tables 99, 69(2013) 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)

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

Linear relationship between the slope parameter L of nuclear symmetry energy and 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)