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Weizsaecker-Skyrme mass model and the statistical errors

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1 Weizsaecker-Skyrme mass model and the statistical errors
16th International Symposium on Capture Gamma-Ray Spectroscopy and Related Topics, CGS16 Shanghai, China, Sep , 2017 Weizsaecker-Skyrme mass model and the statistical errors Ning Wang Guangxi Normal University, Guilin, China

2 Outline Introduction Nuclear mass models
Characteristics of the WS model Tests and model predictions Statistical errors in parameters and masses Conclusions

3 质量 超重 对称能 裂变 核天体 … rms error of 200 ~ 1000 keV

4 Discrepancies increase evidently approaching neutron drip line
What is the reason? How large is the model error? Y.-H. Zhang, Yu. A. Litvinov, T. Uesaka and H.-S. Xu N=82 Z=82

5 Nuclear mass models Garvey-Kelson n-p residual IMME Shell model
Global Local Systematics Garvey-Kelson n-p residual IMME Shell model … ~200keV Microscopic Macro-Micro Duflo-Zuker … ~ keV AME CLEAN RBF … ~200keV

6 Microscopic models (global)
# Relativistic energy density functional # Non-relativistic energy density functional 1. Skyrme: HFB1…HFB32; … UNEDF … 2. Gogny: Goriely…PRL102 (2009) 3. Fayans: Fayans...NPA676 (2000) 49 (m*=m) … P. Ring, J. Meng, S.-G. Zhou, W.-H. Long …

7 Macroscopic-microscopic mass models
Strutinsky type: (shell corrections) FRDM: Moller…1995, 2012, [M, β, Bf,…] Extended Thomas-Fermi+SI (ETFSI): [M, EOS, β, Bf,…] Lublin-Strasbourg Drop (LSD) model: [M, β, Bf,…] Weizsäcker-Skyrme (WS) model: [M, β, Rch,…] … … Others : Esh from valence-nucleons: Kirson, NPA798 (2008) Dieperink & Isacker, EPJA 42 (2009) 269 Wigner-Kirkwood method: Centelles, Schuck, Vinas, Anna Phys. 322 (2007) 363; Bhagwat, et al.,PRC81_044321 KUTY model: Koura, Uno, Tachibana, Yamada, NPA674(2000)47

8 Characteristics of Weizsäcker-Skyrme mass model
Liquid drop Deformation Shell Residual Residual：Mirror 、pairing 、Wigner corrections... Macro-micro concept & Skyrme energy density functional N. Wang, M. Liu, et al., PRC ；PRC ；PRC

9 Potential energy surface
are considered Liquid drop part 110Pd To obtain g.s. energy, one needs to find the minimum on the PES

10 Isospin dependence of model parameters
Symmetry energy coefficient Symmetry potential Strength of spin-orbit potential Pairing corr. term symmetry potential WS*：Phys. Rev. C 82 (2010)

11 WS* FRDM KSO = -1 KSO = 1 Xu and Qi, Phys. Lett. B724 (2013) 247
Bf : Kowal, et al., PRC82 (2010) Xu and Qi, Phys. Lett. B724 (2013) 247 N=16 N=184 WS* FRDM

12 5. Isospin dependence of surface diffuseness
Neutron-rich N. Wang, M. Liu, X. Z. Wu, and J. Meng, Phys. Lett. B 734 (2014) 215

13 D.D. Warner et al., Nature Physics 2 (2006) 311
Considering symmetries/correlations 26 25 From S. Lenzi D.D. Warner et al., Nature Physics 2 (2006) 311 Isospin Symmetry: 1932 Heisenberg SU(2)

14 Constraint from mirror nuclei
charge-symmetry / independence of nuclear force reduces rms error by ~10%

15 Wigner effect of heavy nuclei
Isospin symmetry of valence nucleons (N,Z) N=Z K. Mazurek, J. Dudek，et al., J. Phys. Conf. Seri. 205 (2010)

16 Tests and model predictions
Sobiczewski, Litvinov, Phys. Rev. C 89, (2014) WS*+RBF

17 LSD model …

18

19 Nuclear charge radii N. Wang, T. Li, PRC88, 011301(R) (2013)
Angeli, et al., JPG42 (2015)

20 Estimate of model errors from rms error to known masses?
Statistical errors keV WS* FRDM DZ28 Year 2010 1995 AME2003 441 656 360 270 new data in AME2016 589 901 763 N. Wang and M. Liu, J. Phys: Conf. Seri. 420 (2013) RBF correction

21 parameters FRDM : ~30 DZ28 : ~28 HFB17 : ~24 HFB24 : ~30 WS3 : ~16
Estimate of model errors with data in different region parameters FRDM : ~30 DZ28 : ~28 HFB17 : ~24 HFB24 : ~30 WS3 : ~16 WS* : ~13

22 Statistical errors based on variation of fit data (WS*)
Maximum likelihood estimation considering the weak correlations between parameters of macro part and those of micro part

23 M. Liu, Y. Gao, N. Wang, Chin. Phys. C 41 (2017), in press, arXiv:1709

24

25 Statistical errors Most sensitive parameter

26 4th-order symmetry energy coefficient
NW, M. Liu, H. Jiang, J. L. Tian and Y. M. Zhao, Phys. Rev. C 91 (2015) H. Jiang, NW, Lie-Wen Chen, Y. M. Zhao and A. Arima, Phys. Rev. C 91 (2015)

27 Correlations between model parameters in WS*

28 Conclusions The rms deviations of mass models with respect to known masses fall to about 200 keV (local) and keV (global) . Isospin dependence of model parameters and isospin symmetry improve the accuracy of the WS mass model. For super-heavy nuclei and neutron drip line nuclei, the statistical errors increase evidently. The symmetry energy term plays a key role to the mass predictions of nuclei approaching to neutron drip line. The large discrepancy between WS4 and HFB17 for the masses of neutron drip line nuclei could be due to the uncertainty of 4th-order symmetry energy coefficient.

29 Thank you for your attention
Nuclear mass tables & Codes ： Zhu-Xia Li (CIAE, Beijing) Xi-Zhen Wu (CIAE, Beijing) Ying-Xun Zhang (CIAE, Beijing) Kai Zhao (CIAE, Beijing) Min Liu (GXNU, Guilin) Jie Meng (Peking U, Beijing) Hui Jiang (SHMTU, Shanghai) Lu Guo (UCAS, Beijing) Yu-Min Zhao (SJTU, Shanghai) Li Ou (GXNU, Guilin) Jun-Long Tian (AYNU, Anyang) Zhi-Gang Xiao (Tsinghua U., Beijing) Shan-Gui Zhou (ITP-CAS, Beijing)

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