Ning Wang1, Min Liu1, Xi-Zhen Wu2

Nuclear mass predictions for super-heavy nuclei and drip-line

nuclei

20th Nuclear Physics Workshop in Kazimierz, Sep. 25-29, 2013

1 Guangxi Normal University, Guilin, China

2 China Institute of Atomic Energy, Beijing, China

Introduction

Weizsacker-Skyrme mass formula

Masses of super-heavy nuclei and drip-line nuclei

Summary and discussion

Outline

Hendrik Schatz, Klaus Blaum

Nuclear mass formulas are important for the study of super-heavy nuclei, nuclear symmetry energy and nuclear astrophysics

Wang et al., PRC 82 (2010) 044304

SHE

Isospin asymmetry

To predict the ~5000 unknown masses based on the ~2400 measured masses

HFB24: PRC88-024308

FRDM : At. Data & Nucl. Data Tables 59, 185 (1995).HFB17: Phys. Rev. Lett. 102, 152503 (2009).DZ28 : Phys. Rev. C 52, 23 (1995).WS3 : Phys. Rev. C 84, 014333 (2011).

Uncertainty of mass predictions for super-heavy nuclei and drip line nuclei is large

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.

Single-particle levels

Shell correction

symmetry potential

β=0

β4

β2WSBETA: S. Cwiok, J. Dudek, W. Nazarewicz, J. Skalski, T. Werner, CPC 46 (1987) 379

Some differences in WS formula

FRDM WS3

Strength of spin-orbit potential

Deformation energies of nuclei

3-6D numerical integrations

Analytical expressions

Mirror effect No Yes

B1 is the relative generalized surface or nuclear energy in FRDM

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

Spin-orbit interaction

KSO = -1 KSO = 1

Ni = Z for protons and Ni = N for neutrons

N=16 N=184

Emic (FRDM): ground state microscopic energy

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

Nishio, el at., 40,48Ca+238UPRC86, 034608 (2012)

0

2013.6.17，桂林

Shell gaps

2013.6.17，桂林

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

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

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

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

Symmetry energy coefficient of finite nuclei

Wang, Liu, PRC81, 067302

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

Model parameters:

FRDM : ~30

WS3 : ~19

DZ28 : ~28

HFB17 : ~24

HFB24 : ~30

AME2003

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

Model errors for different region

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

Alpha decay energies of super-heavy nuclei

Alpha decay data are not used for para. fit

N. Wang and M. Liu, arXiv:1211.2538; J. Phys: Conf. Seri. 420 (2013) 012057 162

178

162

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

178WS*

Revised masses

Radial basis function corr.

Ning Wang, Min Liu, PRC 84, 051303(R) (2011)

leave-one-out cross-validation

Z. M. Niu, et al., PRC 88, 024325 (2013)AME2012

RBF corrections for different mass models

N. Wang and M. Liu, J. Phys: Conf. Seri. 420 (2013) 012057

Based on the Skyrme EDF and macro-micro method, we proposed a global nuclear mass formula with which the measured masses in AME2003 and AME2012 can be well reproduced.

Isospin-dependence of the strength of spin-orbit potential and of the symmetry potential significantly influence the shell corrections of super-heavy nuclei and drip line nuclei.

Shell corrections and alpha-decay energies of super-heavy nuclei are investigated with the formula and the shell gap at N=178 also influences the central position of the island of SHE.

Radial basis function (RBF) approach is an efficient and powerful systematic method for improving the accuracy and predictive power of global nuclear mass models.

Summary and discussion

Thanks for your attention!

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

Guilin, China

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

Angeli and Marinova, At. Data Nucl. Data Tables 99, 69(2013)

PRC88, 011301(R) (2013)

Shell corrections and deformations of nuclei based on the Weizsacker-Skyrme mass formula

J. G. Hirsch and J. Mendoza-TemisJ. Phys. G: 37 (2010) 064029

Pairing corrections

Skyrme Hartree-Fock calc.

62 Skyrme parameter sets

K0=210 – 280 MeV

rho0=0.15 – 0.17 fm-3

Difference in the rms charge radii between mirror nuclei

Linear relationship between the slope parameter L of nuclear symmetry energy and Δrch for the mirror pair 30S - 30Si

PRC88, 011301(R) (2013)