an improved nuclear mass formula

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


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


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


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


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.


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


Skyrme EDF plus extended Thomas-Fermi approach,significantly reduces CPU time

Influence of nuclear deformations on liquid-drop energy (parabolic approx.)


Single-particle levels

Shell correction


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


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)


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


Liu, Wang, Deng, Wu, PRC 84, 014333 (2011)

keV #

2149

1988

46

2149

Model parameters:

FRDM : ~30

WS : ~15

HFB17 : ~24

DZ28 : ~28


Model errors for different region

prolate

oblateQuadrupole deformation


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


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)


RBF corrections


Alpha decay energies of super-heavy nuclei

Alpha decay data are not used for para. fit


Zhang, et al., Phys. Rev. C 85, 014325 (2012)

N=178

WS*

N=178

WS*

N=162 N=178

WS*


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


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


被选为 2012 年第 7 期的优秀论文

Classical r-Process


excitation energy of the 2+ level above 4.7 MeV

PLB672 （ 2009 ） 17

Shell corr.


Shell gaps

Shell gap: Rev. Mod. Phys. 75 (2003)1021

A~190


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


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


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


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

an improved nuclear mass formula

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