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

An improved nuclear mass formula Tests and applications Introduction An improved nuclear mass formula Tests and applications Summary and discussion KITPC, 2012.6.11-29, Beijing

Nuclear mass formulas are important for study of super-heavy nuclei and nuclear astrophysics SHE Hendrik Schatz, Klaus Blaum KITPC, 2012.6.11-29, Beijing Wang et al., PRC 82 (2010) 044304

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 ۞ 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 Y. M. Zhao, PRC82-054317; PRC84-034311

Mass predictions from local mass equations by using iterations 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, ~100keV 2）predicted masses are used in new iteration KITPC, 2012.6.11-29, Beijing Zhao, PRC 84, 034311 (2011)

+… 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 KITPC, 2012.6.11-29, Beijing WS3：PRC 84 (2011) 014333

Symmetry energy coefficient of finite nuclei Para. are stable for different mass region, J. Phys. Conf. Seri. 322, 012017 (2011) Form of asym I=(N-Z)/A NPA818 (2009) 36 Wang, Liu, Phys. Rev. C 81 (2010) 067302 KITPC, 2012.6.11-29, Beijing

Influence of nuclear deformations on liquid-drop energy (parabolic approx.) Skyrme EDF plus extended Thomas-Fermi approach, significantly reduces CPU time KITPC, 2012.6.11-29, Beijing

Single-particle levels Shell correction Single-particle levels KITPC, 2012.6.11-29, Beijing

Constraint from mirror nuclei with the same mass but with the numbers of protons and neutrons interchanged Constraint from mirror nuclei reduces rms error by ~10% charge-symmetry / independence of nuclear force KITPC, 2012.6.11-29, Beijing

Other residual corrections 1）Wigner effect of heavy nuclei (N,Z) N=Z KITPC, 2012.6.11-29, Beijing K. Mazurek, J. Dudek，et al., J. Phys. Conf. Seri. 205 (2010) 012034

2）Radial basis function corr. leave-one-out cross-validation Improve the accuracy by ~10% - 40% Revised masses KITPC, 2012.6.11-29, Beijing Ning Wang, Min Liu, PRC 84, 051303(R) (2011);

Model parameters: FRDM : ~30 WS : ~15 HFB17 : ~24 DZ28 : ~28 Liu, Wang, Deng, Wu, PRC 84, 014333 (2011) keV # 2149 1988 46 KITPC, 2012.6.11-29, Beijing

Model errors for different region oblate Quadrupole deformation prolate Model errors for different region KITPC, 2012.6.11-29, Beijing

Predictive power for new masses NPA 882 (2012) 71 in keV 154 new data in Audi 2011 53 new masses in GSI FRDM / 2012 723 / 562 600 HFB17 693 582 DZ28 622 504 WS3 433 360 KITPC, 2012.6.11-29, Beijing Audi 2011: G. Audi and M. Wang (private communication)

rms deviation with respect to 2149 known masses （in keV） 154 new masses in Audi 2011 53 new masses in GSI Model with RBF FRDM 723 475 600 193 HFB17 693 596 582 250 DZ28 622 442 504 287 WS3 433 397 360 229 AME95-03 test （389） KITPC, 2012.6.11-29, Beijing Ning Wang, Min Liu, PRC 84, 051303(R) (2011)

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

N=178 WS* N=162 N=178 N=178 WS* WS* KITPC, 2012.6.11-29, Beijing Zhang, et al., Phys. Rev. C 85, 014325 (2012)

Fission barrier: Phys. Rev. C 82 (2010) 014303 KITPC, 2012.6.11-29, Beijing M. Kowal, P. Jachimowicz, and A. Sobiczewski

Wang,Tian, Scheid, PRC84, 061601(R) (2011) KITPC, 2012.6.11-29, Beijing Wang,Tian, Scheid, PRC84, 061601(R) (2011)

Classical r-Process 被选为2012年第7期的优秀论文 KITPC, 2012.6.11-29, Beijing

Shell corr. excitation energy of the 2+ level above 4.7 MeV PLB672（2009）17 KITPC, 2012.6.11-29, Beijing

Shell gaps A~190 Shell gap: Rev. Mod. Phys. 75 (2003)1021 KITPC, 2012.6.11-29, Beijing Shell gap: Rev. Mod. Phys. 75 (2003)1021

Two constraints 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. 17 mass models Ormand, PRC 55, 2407 rms deviation to GK estimates rms deviation to 2149 masses KITPC, 2012.6.11-29, Beijing

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 KITPC, 2012.6.11-29, Beijing

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 KITPC, 2012.6.11-29, Beijing

Wang,Tian, Scheid, PRC84, 061601(R) (2011) KITPC, 2012.6.11-29, Beijing Wang,Tian, Scheid, PRC84, 061601(R) (2011)

KITPC, 2012.6.11-29, Beijing