Ning Wang
An improved nuclear mass formula
Guangxi Normal University, Guilin, China
KITPC
2012.6.11-29, Beijing
KITPC, 2012.6.11-29, Beijing
Introduction
An improved nuclear mass formula
Tests and applications
Summary and discussion
KITPC, 2012.6.11-29, Beijing
Hendrik Schatz, Klaus Blaum
Nuclear mass formulas are important for study of super-heavy nuclei and nuclear astrophysics
Wang et al., PRC 82 (2010) 044304
SHE
KITPC, 2012.6.11-29, Beijing
Some nuclear mass formulas
1 ) Macro-micro : FRDM ( 1995 ) 656 keV FRDM ( 2012 ) 570 keV
2 ) HFB 、 RMF : HFB17 ( 1999 ) 581 keV PC-PK1 ( 2010 ) 1400 keV
3 ) Duflo-Zuker : DZ28 ( 1995 ) 360 keV
4 ) Weizsäcker-Skyrme : WS3 ( 2011 ) 336 keV
Y. M. Zhao, PRC82-054317; PRC84-034311
☺ Global nuclear mass formulas :
۞ Local mass formulas : 1 ) Garvey-Kelson, n-p residual interaction 2 ) Isobaric Multiplet Mass Equation (IMME)
J. Barea, et al, PRC77 041304(R) (2008)
☻ Systematic approaches : Audi 、 CLEAN 、 RBF
KITPC, 2012.6.11-29, Beijing
Morales, NPA 828 (2009) 113
Mass predictions from local mass equations by using iterations
errors increase rapidly with iterations
1 ) error of local mass equations, ~100keV2 ) predicted masses are used in new iteration
Zhao, PRC 84, 034311 (2011)
MeV
KITPC, 2012.6.11-29, Beijing
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.
KITPC, 2012.6.11-29, Beijing
Symmetry energy coefficient of finite nuclei
Wang, Liu, Phys. Rev. C 81 (2010) 067302
Para. are stable for different mass region, J. Phys. Conf. Seri. 322, 012017 (2011)
Form of asym
I=(N-Z)/ANPA818 (2009) 36
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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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Single-particle levels
Shell correction
KITPC, 2012.6.11-29, Beijing
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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1 ) Wigner effect of heavy nuclei
K. Mazurek, J. Dudek , et al., J. Phys. Conf. Seri. 205 (2010) 012034
Other residual corrections
N=Z
(N,Z)
KITPC, 2012.6.11-29, Beijing
Improve the accuracy by ~10% - 40%
Revised masses
2 ) Radial basis function corr.
Ning Wang, Min Liu, PRC 84, 051303(R) (2011);
leave-one-out cross-validation
KITPC, 2012.6.11-29, Beijing
Liu, Wang, Deng, Wu, PRC 84, 014333 (2011)
keV #
2149
1988
46
2149
Model parameters:
FRDM : ~30
WS : ~15
HFB17 : ~24
DZ28 : ~28
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Model errors for different region
prolate
oblateQuadrupole deformation
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Predictive power for new masses
in keV154 new data in Audi 2011
53 new masses in GSI
FRDM / 2012
723 / 562 600
HFB17 693 582
DZ28 622 504
WS3 433 360
Audi 2011: G. Audi and M. Wang (private communication)
NPA 882 (2012) 71
KITPC, 2012.6.11-29, Beijing
rms deviation with respect to 2149 known masses ( in keV )
AME95-03 test ( 389 )in keV
154 new masses in Audi 2011
53 new masses in GSI
Modelwith RBF
Modelwith RBF
FRDM 723 475 600 193
HFB17 693 596 582 250
DZ28 622 442 504 287
WS3 433 397 360 229
Ning Wang, Min Liu, PRC 84, 051303(R) (2011)
KITPC, 2012.6.11-29, Beijing
RBF corrections
KITPC, 2012.6.11-29, Beijing
Alpha decay energies of super-heavy nuclei
Alpha decay data are not used for para. fit
KITPC, 2012.6.11-29, Beijing
Zhang, et al., Phys. Rev. C 85, 014325 (2012)
N=178
WS*
N=178
WS*
N=162 N=178
WS*
KITPC, 2012.6.11-29, Beijing
Fission barrier: Phys. Rev. C 82 (2010) 014303M. Kowal, P. Jachimowicz, and A. Sobiczewski
KITPC, 2012.6.11-29, Beijing
Wang,Tian, Scheid, PRC84, 061601(R) (2011)
KITPC, 2012.6.11-29, Beijing
被选为 2012 年第 7 期的优秀论文
Classical r-Process
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excitation energy of the 2+ level above 4.7 MeV
PLB672 ( 2009 ) 17
Shell corr.
KITPC, 2012.6.11-29, Beijing
Shell gaps
Shell gap: Rev. Mod. Phys. 75 (2003)1021
A~190
KITPC, 2012.6.11-29, Beijing
rms deviation to 2149 masses
rms deviation to GK estimates
rms deviation to bfit for neutron drip line nuclei
Fulfilling both the Isobaric Multiplet Mass Equation and the Garvey-Kelson relations seem to be two necessary conditions for improving the quality of the model prediction.
Two constraints
17 mass models
Ormand, PRC 55, 2407
KITPC, 2012.6.11-29, Beijing
Based on the Skyrme EDF and macro-micro method, we proposed a global nuclear mass formula with high accuracy and reliability
Shell effect and isospin effect, especially isospin symmetry play a crucial role for improving the nuclear mass formula
The neutron separation energies, alpha-decay energies of SHN, shell gaps, Gavey-Kalson relations and IMME can also be reproduced remarkably well
Radial basis function (RBF) approach is an efficient and powerful systematic method for improving the accuracy and predictive power of global nuclear mass models
Conclusion and discussion
KITPC, 2012.6.11-29, Beijing
Thanks for your attention!
Nuclear mass tables :www.ImQMD.com
Collaborators:
Guilin : Min Liu
CIAE: Xi-Zhen Wu
Lanzhou: Hong-Fei Zhang
Shanghai: Yu-Min Zhao
Beijing: Jie Meng & Bao-Hua Sun
KITPC, 2012.6.11-29, Beijing
Wang,Tian, Scheid, PRC84, 061601(R) (2011)
KITPC, 2012.6.11-29, Beijing