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An improved nuclear mass formula

An improved nuclear mass formula. Ning Wang. Guangxi Normal University, Guilin, China. KITPC 2012.6.11-29, Beijing. Introduction An improved nuclear mass formula Tests and applications Summary and discussion.

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An improved nuclear mass formula

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  1. An improved nuclear mass formula Ning Wang Guangxi Normal University, Guilin, China KITPC 2012.6.11-29, Beijing

  2. Introduction • An improved nuclear mass formula • Tests and applications • Summary and discussion

  3. Nuclear mass formulas are important for study of super-heavy nuclei and nuclear astrophysics SHE Hendrik Schatz, Klaus Blaum Wang et al., PRC 82 (2010) 044304

  4. ۞Local mass formulas： 1）Garvey-Kelson, n-p residual interaction 2）Isobaric Multiplet Mass Equation (IMME) Some nuclear mass formulas ☺ Global 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 J. Barea, et al, PRC77 041304(R) (2008) ☻ Systematic approaches： Audi、 CLEAN、RBF Y. M. Zhao,PRC82-054317; PRC84-034311

  5. Morales, NPA 828 (2009) 113 MeV 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)

  6. 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

  7. Form of asym Para. are stable for different mass region, J. Phys. Conf. Seri. 322, 012017 (2011) Symmetry energy coefficient of finite nuclei I=(N-Z)/A NPA818 (2009) 36 Wang, Liu, Phys. Rev. C 81 (2010) 067302

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

  9. Shell correction Single-particle levels

  10. 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

  11. Other residual corrections 1）Wigner effect of heavy nuclei (N,Z) N=Z K. Mazurek, J. Dudek，et al., J. Phys. Conf. Seri. 205 (2010) 012034

  12. Revised masses 2）Radial basis function corr. leave-one-out cross-validation Improve the accuracy by ~10% - 40% Ning Wang, Min Liu, PRC 84, 051303(R) (2011);

  13. Model parameters: FRDM : ~30 WS : ~15 HFB17 : ~24 DZ28 : ~28 Liu, Wang, Deng, Wu, PRC 84, 014333 (2011) keV # 2149 1988 46 2149

  14. oblate prolate Quadrupole deformation Model errors for different region

  15. Predictive power for new masses NPA 882 (2012) 71 Audi 2011: G. Audi and M. Wang (private communication)

  16. rms deviation with respect to 2149 known masses （in keV） AME95-03 test （389） Ning Wang, Min Liu, PRC 84, 051303(R) (2011)

  17. RBF corrections

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

  19. N=178 WS* N=178 N=162 N=178 WS* WS* Zhang, et al., Phys. Rev. C 85, 014325 (2012)

  20. Fission barrier: Phys. Rev. C 82 (2010) 014303 M. Kowal, P. Jachimowicz, and A. Sobiczewski

  21. Wang,Tian, Scheid, PRC84, 061601(R) (2011)

  22. Classical r-Process 被选为2012年第7期的优秀论文

  23. excitation energy of the 2+ level above 4.7 MeV PLB672（2009）17 Shell corr.

  24. Shell gaps A~190 Shell gap: Rev. Mod. Phys. 75 (2003)1021

  25. Ormand, PRC 55, 2407 rms deviation to bfit for neutron drip line nuclei Two constraints 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. 17 mass models rms deviation to 2149 masses rms deviation to GK estimates

  26. Conclusion and discussion • 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

  27. Thanks for your attention! Collaborators: Guilin：Min Liu CIAE: Xi-Zhen Wu Lanzhou: Hong-Fei Zhang Shanghai: Yu-Min Zhao Beijing: Jie Meng & Bao-Hua Sun Nuclear mass tables：www.ImQMD.com

  28. Wang,Tian, Scheid, PRC84, 061601(R) (2011)

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