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Ning Wang1, Min Liu1, Xi-Zhen Wu2
Nuclear mass predictions for super-heavy nuclei and drip-line
nuclei
20th Nuclear Physics Workshop in Kazimierz, Sep. 25-29, 2013
1 Guangxi Normal University, Guilin, China
2 China Institute of Atomic Energy, Beijing, China
Introduction
Weizsacker-Skyrme mass formula
Masses of super-heavy nuclei and drip-line nuclei
Summary and discussion
Outline
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) 044304
SHE
Isospin asymmetry
To predict the ~5000 unknown masses based on the ~2400 measured masses
HFB24: PRC88-024308
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).
Uncertainty of mass predictions for super-heavy nuclei and drip line nuclei is large
WS : PRC 81 (2010) 044322 WS* : PRC 82 (2010)
044304
Skyrme EDF
Duflo-Zuker
Liquid drop Deformation corr. Shell corr.
WS3 : PRC 84 (2011) 014333
+…
Other corr.
Single-particle levels
Shell correction
symmetry potential
β=0
β4
β2WSBETA: 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
Xu and Qi, Phys. Lett. B724 (2013) 247
Spin-orbit interaction
KSO = -1 KSO = 1
Ni = Z for protons and Ni = N for neutrons
N=16 N=184
Emic (FRDM): ground state microscopic energy
Fission barrier: Phys. Rev. C 82 (2010) 014303M. Kowal, P. Jachimowicz, and A. Sobiczewski
Nishio, el at., 40,48Ca+238UPRC86, 034608 (2012)
0
2013.6.17,桂林
Shell gaps
2013.6.17,桂林
L. S. Geng, H. Toki, and J. Meng, Prog. Theor. Phys. 113, 785 (2005)
Skyrme EDF plus extended Thomas-Fermi approach,significantly reduces CPU time
Influence of nuclear deformations on liquid-drop energy (parabolic approx.)
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
32 56 92 116
Symmetry energy coefficient of finite nuclei
Wang, Liu, PRC81, 067302
I=(N-Z)/ANPA818 (2009) 36
Model parameters:
FRDM : ~30
WS3 : ~19
DZ28 : ~28
HFB17 : ~24
HFB24 : ~30
AME2003
Liu, Wang, Deng, Wu, PRC 84, 014333 (2011)
Model errors for different region
Predictive power for new masses in AME2012
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
HFB24: PRC88-024308
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)
Test the models with very recently measured masses
Alpha decay energies of super-heavy nuclei
Alpha decay data are not used for para. fit
N. Wang and M. Liu, arXiv:1211.2538; J. Phys: Conf. Seri. 420 (2013) 012057 162
178
162
Zhang, et al., Phys. Rev. C 85, 014325 (2012)
178WS*
Revised masses
Radial basis function corr.
Ning Wang, Min Liu, PRC 84, 051303(R) (2011)
leave-one-out cross-validation
Z. M. Niu, et al., PRC 88, 024325 (2013)AME2012
RBF corrections for different mass models
N. Wang and M. Liu, J. Phys: Conf. Seri. 420 (2013) 012057
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
Thanks for your attention!
Codes & Nuclear mass tables :www.ImQMD.com/mass
Guilin, China
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, 011301(R) (2013)
Shell corrections and deformations of nuclei based on the Weizsacker-Skyrme mass formula
J. G. Hirsch and J. Mendoza-TemisJ. Phys. G: 37 (2010) 064029
Pairing corrections
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
Linear relationship between the slope parameter L of nuclear symmetry energy and Δrch for the mirror pair 30S - 30Si
PRC88, 011301(R) (2013)