Energy density functional description of nuclear spectrum and shape transition
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第十四届全国核结构大会暨第十次全国核结构专题讨论会 湖州, 2012 年 4.12-16. Energy Density Functional Description of Nuclear Spectrum and Shape Transition. 李志攀 西南大学物理科学与技术学院. 1. 4. 2. 3. Introduction. Results and discussion. Summary. Theoretical framework. Outline. Nuclear Low-lying Spectrum.

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Energy density functional description of nuclear spectrum and shape transition

第十四届全国核结构大会暨第十次全国核结构专题讨论会第十四届全国核结构大会暨第十次全国核结构专题讨论会

湖州,2012年4.12-16

Energy Density Functional Description of Nuclear Spectrum and Shape Transition

李志攀

西南大学物理科学与技术学院


Outline

1第十四届全国核结构大会暨第十次全国核结构专题讨论会

4

2

3

Introduction

Results and discussion

Summary

Theoretical framework

Outline


Nuclear low lying spectrum
Nuclear Low-lying Spectrum第十四届全国核结构大会暨第十次全国核结构专题讨论会

  • Nuclear low-lying spectrum is an important physical quantity that can reveal rich structure information of atomic nuclei

    • Shape and shape transition

9-

8+

7-

5-

6+

3-

4+

1-

2+

0+


Nuclear low lying spectrum1
Nuclear Low-lying Spectrum第十四届全国核结构大会暨第十次全国核结构专题讨论会

  • Nuclear low-lying spectrum is an important physics quantity that can reveal rich structure information of atomic nuclei

    • Shape and shape transition

    • Evolution of the shell structure

T. Baumann

Nature06213(2007)

Z

N=28

N=20

N

N=16


Nuclear low lying spectrum2
Nuclear Low-lying Spectrum第十四届全国核结构大会暨第十次全国核结构专题讨论会

  • Nuclear low-lying spectrum is an important physics quantity that can reveal rich structure information of atomic nuclei

    • Shape and shape transition

    • Evolution of the shell structure

    • Evidence for pairing correlation


Covariant energy density functional cedf
Covariant Energy Density Functional (CEDF)第十四届全国核结构大会暨第十次全国核结构专题讨论会

Ring96, Vretenar2005, Meng2006

  • CEDF: nuclear structure over almost the whole nuclide chart

    • Scalar and vector fields: nuclear saturation properties

    • Spin-orbit splitting

    • Origin of the pseudo-spin symmetry

    • Spin symmetry in anti-nucleon spectrum

    • ……

  • Spectrum: beyond the mean-field approximation

    • Restoration of broken symmetry, e.g. rotational

    • Mixing of different shape configurations

AMP+GCM: Niksic2006, Yao2010

PES

5D Collective Hamiltonian based on CEDF


Energy density functional description of nuclear spectrum and shape transition

Brief Review of the model第十四届全国核结构大会暨第十次全国核结构专题讨论会

Coll. Potential

Moments of inertia

Mass parameters

Diagonalize:

Nuclear spectroscopy

T. Niksic, Z. P. Li, D. Vretenar, L. Prochniak, J. Meng, and P. Ring 79, 034303 (2009)


Energy density functional description of nuclear spectrum and shape transition

Interesting topics第十四届全国核结构大会暨第十次全国核结构专题讨论会

  • Microscopic Analysis of nuclear QPT

  • Fission barrier and SD band

  • Shape evolution in N=28 isotones

  • Effect of the time-odd mean-field


Nuclear quantum phase transition qpt 1 st order
Nuclear Quantum Phase Transition(QPT) - 1第十四届全国核结构大会暨第十次全国核结构专题讨论会st order

Critical

E

  • Nuclear QPT

  • Two approaches to study

    QPT

Spherical

Potential

Order par.

β

Iachello, PRL2004

  • Method of Landau based on PES

  • Computation of order parameters

Deformed


First order qpt
First order QPT 第十四届全国核结构大会暨第十次全国核结构专题讨论会

  • Spectrum

... detailed spectroscopy has been reproduced well !!


First order qpt1
First order QPT 第十四届全国核结构大会暨第十次全国核结构专题讨论会

  • Characteristic features:

Sharp increase of R42=E(41)/E(21) and B(E2; 21→01) in the yrast band

X(5)

Li, Niksic, Vretenar, Meng. Lalazissis & Ring, PRC79,054301(2009)

Li, Niksic, Vretenar, &Meng. PRC80,061301(R) (2009)

Li, Niksic, Vretenar, & Meng. PRC81,034316 (2010)


Fission barrier and sd band
Fission barrier and SD band 第十四届全国核结构大会暨第十次全国核结构专题讨论会

  • Extended 3DRMF+BCS to 3DRHB

Li, Niksic, Vretenar, Ring & Meng. PRC81,064321(2010)


Energy density functional description of nuclear spectrum and shape transition

Shape evolution & coexistence in 第十四届全国核结构大会暨第十次全国核结构专题讨论会N=28 isotones

E(21+)

B(E2)

http://www.nndc.bnl.gov/


Shape evolution coexistence in n 28 isotones
Shape evolution & coexistence in 第十四届全国核结构大会暨第十次全国核结构专题讨论会N=28 isotones

http://www-phynu.cea.fr


Shape evolution coexistence in n 28 isotones1
Shape evolution & coexistence in 第十四届全国核结构大会暨第十次全国核结构专题讨论会N=28 isotones

http://www-phynu.cea.fr

N=28

48Ca

44S

42Si

40Mg


Shape evolution coexistence in n 28 isotones2
Shape evolution & coexistence in 第十四届全国核结构大会暨第十次全国核结构专题讨论会N=28 isotones


Shape evolution coexistence in n 28 isotones3
Shape evolution & coexistence in 第十四届全国核结构大会暨第十次全国核结构专题讨论会N=28 isotones

Prolate:Δp = 5.05 MeV

Oblate:Δn = 3.91 MeV


Shape evolution coexistence in n 28 isotones4
Shape evolution & coexistence in 第十四届全国核结构大会暨第十次全国核结构专题讨论会N=28 isotones


Shape evolution coexistence in n 28 isotones5
Shape evolution & coexistence in 第十四届全国核结构大会暨第十次全国核结构专题讨论会N=28 isotones

C. Force et al., PRL105

  • Low-lying spectrum


Shape evolution coexistence in n 28 isotones6
Shape evolution & coexistence in 第十四届全国核结构大会暨第十次全国核结构专题讨论会N=28 isotones

  • Low-lying spectrum

Li, Yao, Vretenar, Niksic, Chen & Meng, PRC84, 054304 (2011)


Effect of time odd mean field
Effect of time-odd mean-field第十四届全国核结构大会暨第十次全国核结构专题讨论会

P. Ring and P. Schuck, “The Nuclear Many-Body Problem”

  • The ATDHFB mass tensor


Energy density functional description of nuclear spectrum and shape transition

Effect of time-odd mean-field第十四届全国核结构大会暨第十次全国核结构专题讨论会

  • The ATDHFB mass tensor


Energy density functional description of nuclear spectrum and shape transition

Effect of time-odd mean-field第十四届全国核结构大会暨第十次全国核结构专题讨论会

128Xe MOI

128Xe Mass


Energy density functional description of nuclear spectrum and shape transition

Effect of time-odd mean-field第十四届全国核结构大会暨第十次全国核结构专题讨论会

  • Effect of time-odd mean-field on the spectrum

Z.P. Li et al. in preparation


Energy density functional description of nuclear spectrum and shape transition

Summary第十四届全国核结构大会暨第十次全国核结构专题讨论会

  • Microscopic Collective Hamiltonian based on

  • CEDF has been developed

  • Application to the interesting topics

    • Nuclear QPT

    • Fission barrier and SD band in 240Pu

    • Shape evolution & coexistence in N=28 isotones

    • Effect of time-odd mean-field


Energy density functional description of nuclear spectrum and shape transition

Thank You !第十四届全国核结构大会暨第十次全国核结构专题讨论会

J. Meng & JCNP group

D. Vretenar & T. Niksic

P. Ring

L. Prochniak

G. A. Lalazissis

J. M. Yao


Energy density functional description of nuclear spectrum and shape transition

Collective Hamiltonian第十四届全国核结构大会暨第十次全国核结构专题讨论会


Energy density functional description of nuclear spectrum and shape transition

Collective Parameter第十四届全国核结构大会暨第十次全国核结构专题讨论会


Energy density functional description of nuclear spectrum and shape transition

Collective Parameter第十四届全国核结构大会暨第十次全国核结构专题讨论会


Energy density functional description of nuclear spectrum and shape transition

Collective Parameter第十四届全国核结构大会暨第十次全国核结构专题讨论会