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

Isospin effects in nuclear mass models

Nuclear Structure and Related Topics (NSRT15), 2015.7.14-18, DUBNA

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 symmetry energy coefficients Summary

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

Super-heavy nuclei

r-process 、symmetry energy

known masses: 2438unmeasured ~ 4000

Nuclear mass models play an important role for the study of super-heavy nuclei, nuclear astrophysics, and nuclear symmetry energy. Popular mass models with rms error of ~300-600keV

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

Why is the difference so large for neutron-rich nuclei ?

Macro-micro concept & Skyrme energy density functional

Liquid drop Deformation Shell Residual

Residual ： Mirror 、 pairing 、 Wigner corrections...

PRC81-044322 ； PRC82-044304 ； PRC84-014333

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

Parabolic approx. for the deformation energies

Shell corrections

symmetry potential

Deformed Woods-Saxon potential

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

Rms (keV)

FRDM HFB24 WS WS4

To known masses 654 549 525 298

Number of model para. 31 30 13 18

9 y 13 y 4 yRm

s e

rro

r

Predictive power for new masses AME2012

rmsD (in keV) WS3 FRDM DZ28 HFB17

sigma (M)2149 336 656 360 581

sigma (M)219 424 765 673 648

M(WS3) – M(exp.)

For new masses after 2012

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

KSO = -1 KSO = 1

WS4, Phys. Lett. B 734 (2014) 215

FRDM

WS*

Wienholtz, et al., Nature 498 (2013)346

New magic numbers

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

Shell structure in heavy and super-heavy nuclei

108

142 152 162

Kowal,et al., Phys. Rev. C 82_014303

H. F. Zhang, et al., Phys. Rev. C 85_014325

178

WS*

162

Symmetry energy coefficients of nuclei

Parabolic law for drip line nuclei?

Liu, Wang, Li, Zhang, Phys. Rev. C 82_064306

Symmetry energy coefficients of finite nuclei from Skryme energy density functional + ETF

N. Wang, M. Liu, H. Jiang, J. L. Tian, Y. M. Zhao, Phys. Rev. C 91, 044308 (2015)

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.

The shell gaps from WS formula indicate that N=32 could be new magic

number in neutron-rich region, and N=142, 152, 162, 178;

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

The symmetry energy coefficients of nuclei are extracted from nuclear

masses and Skyrme energy density functional. The opposite values for the

coefficient of I^4 term used in the HFB17 and WS4 models may result in

the large difference at the predictions of the masses of neutron-rich nuclei.

Summary

Thank you for your attention

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

Guilin, China

backup

Quadrupole Deformations

Prolate

Oblate

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

原子核壳能隙可以给出子壳信息

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

Mo, Liu, Chen, Wang, Sci. China Phys. Mech. & Astron. 58 (2015) 082001

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)