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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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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
1 4 2 3 Introduction Results and discussion Summary Theoretical framework Outline
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
Brief Review of the model 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)
Interesting topics • 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 • Spectrum ... detailed spectroscopy has been reproduced well !!
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 E(21+) B(E2) http://www.nndc.bnl.gov/
Shape evolution & coexistence in N=28 isotones http://www-phynu.cea.fr
Shape evolution & coexistence in N=28 isotones http://www-phynu.cea.fr N=28 48Ca 44S 42Si 40Mg
Shape evolution & coexistence in N=28 isotones Prolate:Δp = 5.05 MeV Oblate:Δn = 3.91 MeV
Shape evolution & coexistence in N=28 isotones C. Force et al., PRL105 • Low-lying spectrum
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
Effect of time-odd mean-field • The ATDHFB mass tensor
Effect of time-odd mean-field 128Xe MOI 128Xe Mass
Effect of time-odd mean-field • Effect of time-odd mean-field on the spectrum Z.P. Li et al. in preparation
Summary • 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
Thank You ! J. Meng & JCNP group D. Vretenar & T. Niksic P. Ring L. Prochniak G. A. Lalazissis J. M. Yao
