Ning Wang1, Min Liu1, Xi-Zhen Wu2, Jie Meng3

Isospin effect in Weizsaecker-Skyrme mass formula

ISPUN14, 2014.11.3-8, Ho Chi Minh City

1 Guangxi Normal University, Guilin, China2 China Institute of Atomic Energy, Beijing, China3 Peking University, Beijing, China

Introduction Weizsaecker-Skyrme mass formula Shell gaps and charge radii of nuclei Summary

Yu. Oganessian. SKLTP/CAS - BLTP/JINR July 16, 2014, Dubna

neutrons →

1. Central position of the island for SHE ？

N. Wang, M. Liu, X. Wu, PRC 82 (2010) 044304

Courtesy of Qiu-Hong Mo

Nasirov, et al., Phys. Rev. C 84, 044612 (2011)

Different mass tables lead to quite different survival probability of Compound nucleus

2. Survival probability of SHE ？

Fission barriers of super-heavy nuclei ：

FRDM : At. Data Nucl. Data Tables59, 185 (1995)HFB17: Phys. Rev. Lett. 102, 152503 (2009)PC-PK1:Phys. Rev. C82, 054319 (2010)DZ28: Phys. Rev. C 52, 23 (1995)WS3 : Phys. Rev. C 84, 014333 (2011)

www.nupecc.org

Semi-empirical mass formula

‘semi-empirical mass formula’ of von Weizsäcker in 1935

Volume term

Surface energy term

Coulomb energy term

Symmetry energy term

Nuclear surface diffuseness results in the deformation energies being complicated

Isospin dependence of the surface diffuseness Deformation dependence of the symmetry energy coefficients of nuclei

Skyrme energy density functional + ETF2

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

Parabolic approx. for the deformation energies

Macro-micro concept & Skyrme energy density functional

Liquid drop Deformation Shell Residual

Residual ： Mirror 、 pairing 、 Wigner corrections...

PRC81-044322 ； PRC82-044304 ； PRC84-014333

Isospin dependence of model parameters

1. Symmetry energy coefficient

2. Symmetry potential

3. Strength of spin-orbit potential

4. Pairing corr. term

symmetry potential

WS3 ： Phys.Rev.C84_014333

5. Isospin dependence of surface diffuseness

N. Wang, M. Liu, X. Z. Wu, and J. Meng, Phys. Lett. B 734 (2014) 215

Symmetry energy coefficient: J = 29.1 MeV (WS3), J = 30.2 MeV (WS4)

2353 measured masses in AME2012

N=16 N=184

Emic (FRDM): ground state microscopic energy

FRDM WS*

Shell corrections of super-heavy nuclei

162

178

162

Kowal,et al., PRC82_014303

152

Mo, Liu, Wang, Phys. Rev. C 90, 024320 (2014)

Nuclear deformations

Prolate

Oblate

N. Wang, T. Li, Phys. Rev. C88, 011301(R)

Rms charge radii

RMF: Lalazissis, Raman, and Ring, At. Data Nucl. Data Tables 71, 1 (1999)

Inspired by the Skyrme energy-density functional, we propose a

new macro-micro mass formula with an rms error of 298 keV,

considering the isospin dependence of model parameters.

Based on the shell gaps and alpha-decay energies from the

Weizsaecker-Skyrme mass formula, N=142, 152, 162, 178;

Z=92, 100, 108, 120 could be sub-shell in super-heavy region.

Nuclear rms charge radii can be well reproduced with the

deformations and shell corrections from the WS formula.

Summary

Rms (keV)

FRDM HFB24 WS WS4

To 2353 masses 654 549 525 298

Number of model para. 31 30 13 18

9 y 13 y 4 yRm

s e

rro

r

Thank you for your attention

Codes & Nuclear mass tables ：www.ImQMD.com/mass

Guilin, China

Symmetry energy coefficient of finite nuclei

Wang, Liu, PRC81, 067302

I=(N-Z)/ANPA818 (2009) 36

Spin-orbit term

Xu and Qi, Phys. Lett. B724 (2013) 247

KSO = -1 KSO = 1

Predictive power for new masses in AME2012

in MeV WS3 FRDM DZ28 HFB17 HFB24

sigma (M)2353 0.335 0.654 0.394 0.576 0.549

sigma (M)219 0.424 0.765 0.673 0.648 0.580

sigma(Sn)2199 0.273 0.375 0.294 0.500 0.474

HFB24: PRC88-024308

181,183Lu, 185,186Hf, 187,188Ta, 191W, and 192,193Re were measured for the first time, uncertainty of 189,190W and 195Os was improved (Storage-ring mass spectrometry GSI)

HFB21: S. Goriely, N. Chamel, and J. M. Pearson, Phys. Rev. C 82, 035804 (2010)

Test the models with very recently measured masses

Mo, Liu, Wang ， Phys. Rev. C 90, 024320 (2014)

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

32 56 92 116

Wigner effect of heavy nuclei

K. Mazurek, J. Dudek ， et al., J. Phys. Conf. Seri. 205 (2010) 012034

N=Z

(N,Z)

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

N=178

WS*

N=178

WS*

N=162 N=178

WS*

原子核壳能隙可以给出子壳信息

2013.6.17，桂林

L. S. Geng, H. Toki, and J. Meng, Prog. Theor. Phys. 113, 785 (2005)

Deformation energies

Hendrik Schatz, Klaus Blaum

Nuclear mass formulas are also important for the study of nuclear astrophysics

Beta-decay energies and neutron separation energies

www.nupecc.org

To predict the ~5000 unmeasured masses based on the ~2400 measured masses, Not an easy task!

Bao-Hua Sun

WS4: Wang, Liu, Wu, Meng, Phys. Lett. B 734, 215 (2014)