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Energy Density Functional Description of Nuclear Spectrum and Shape Transition

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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

李志攀

西南大学物理科学与技术学院

Nuclear Low-lying Spectrum

- 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 Spectrum

- 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 Spectrum

- 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)

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

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)

- 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) - 1st 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

- 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

- Extended 3DRMF+BCS to 3DRHB

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

Shape evolution & coexistence in N=28 isotones

http://www-phynu.cea.fr

Shape evolution & coexistence in N=28 isotones

- Low-lying spectrum

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

Effect of time-odd mean-field

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

- The ATDHFB mass tensor

- The ATDHFB mass tensor

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

Z.P. Li et al. in preparation

- 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

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