1. Meng, J,Toki, H, Zhou, SG, Zhang, SQ, Long, WH, Geng, LS, Relativistic continuum Hartree Bogoliubov theory for ground-state properties of exotic nuclei, PROGRESS IN PARTICLE AND NUCLEAR PHYSICS, VOL 57, NO 2, 57 (2): 470-563 2006

2. Meng, J; Toki, H; Zeng, JY; Zhang, SQ; Zhou, SG, Giant halo at the neutron drip line in Ca isotopes in relativistic continuum Hartree-Bogoliubov theory, PHYSICAL REVIEW C, 65 (4): Art. No. 041302 APR 2002

3. Zhang, W; Meng, J; Zhang, SQ; Geng, LS; Toki, H, Magic numbers for superheavy nuclei in relativistic continuum Hartree-Bogoliubov theory, NUCLEAR PHYSICS A, 753 (1-2): 106-135 MAY 2 2005

4. Geng, LS; Toki, H; Sugimoto, S; Meng, J, Relativistic mean field theory for deformed nuclei with pairing correlations, PROGRESS OF THEORETICAL PHYSICS, 110 (5): 921-936 NOV 2003

5. Geng, LS; Toki, H; Meng, J, alpha-decay chains of (288)(173)115 and (287)(172)115 in the relativistic mean field theory, PHYSICAL REVIEW C, 68 (6): Art. No. 061303 DEC 2003

6. Meng, J; Zhang, W; Zhou, SG; Toki, H; Geng, LS, Shape evolution for Sm isotopes in relativistic mean-field theory, EUROPEAN PHYSICAL JOURNAL A, 25 (1): 23-27 JUL 2005

7. Geng, LS; Toki, H; Meng, J, Masses, deformations and charge radii - Nuclear ground-state properties in the relativistic mean field model,PROGRESS OF THEORETICAL PHYSICS, 113 (4): 785-800 APR 2005

8. Geng, LS; Toki, H; Ozawa, A; Meng, J, Proton and neutron skins of light nuclei within the relativistic mean field theory, NUCLEAR PHYSICS A, 730 (1-2): 80-94 JAN 12 2004

9. Geng, LS; Toki, H; Meng, J, Proton-rich nuclei at and beyond the proton drip line in the relativistic mean field theory, PROGRESS OF THEORETICAL PHYSICS, 112 (4): 603-617 OCT 2004

10. Geng, LS; Toki, H; Meng, J, A systematic study of Zr and Sn isotopes in the relativistic mean field theory, MODERN PHYSICS LETTERS A, 19 (29): 2171-2190 SEP 21 2004

11. Geng, LS; Toki, H; Meng, J, A systematic study of neutron magic nuclei with N=8, 20, 28, 50, 82 and 126 in the relativistic mean-field theory, JOURNAL OF PHYSICS G-NUCLEAR AND PARTICLE PHYSICS, 30 (12): 1915-1928 DEC 2004

手性原子核：手性原子核： 20072007Chiral symmetry in atomic nuclei: 2007Chiral symmetry in atomic nuclei: 2007

孟 杰 孟 杰 Jie MengJie Meng北京大学物理学院 北京大学物理学院 School of Physics/Peking UniversitySchool of Physics/Peking University

Chiral07Chiral Symmetry in Hadron and Nuclear PhysicsNovember 13-16, 2007, Convention Center, Suita campus, Osaka University, Japan

Introduction

The concept of the chirality in atomic nuclei

Recent theoretical and experimental

progress

Future efforts and perspectives to

understand nuclear chirality

Summary

手征对称性在自然界中普遍存在手征对称性在自然界中普遍存在Chiral symmetries exist commonly in Chiral symmetries exist commonly in

naturenatureMacroscopic spirals of snail shells and the Human hands, etc.In geometry, a figure is chiral if it is not identical to its mirror image, or it cannot be mapped onto its mirror image by rotations and translations aloneParticle physics, chirality is a dynamic property distinguishing between the parallel and anti-parallel orientations of the intrinsic spin with respect to the momentum of the massless particle.Chemistry, the study of chirality is a very active in inorganic, organic, physical, biochemistry and supramolecular chemistry.Nobel Prize in Chemistry for 2001: the development of catalytic asymmetric synthesis Chiral symmetry in atomic nuclei ?Chiral symmetry in atomic nuclei ?

Fingerprints for Chirality in atomic nucleus

3 2

1

1, 30

2o

i

i i

H R

2 2 23

1 ( 1) sincos

2 3 2 3sp

j jH C j j j

2 2 23

1 ( 1) sincos

2 3 2 3sp

j jH C j j j

1. H. Toki and A. Faessler; Nucl. Phys. A253 (1975) 231-252 Asymmetric rotor model for decoupled bands in transitional odd mass nuclei

2. H. Toki and A. Faessler; Z. Physik A276 (1976) 35-43 Extended VMI model for asymmetric deformed nuclei

3. H. Toki and A. Faessler; Phys. Lett. 63B (1976) 121-124 Asymmetric rotor model for positive parity states of 71As, 73As and 81Rb

4. H. Toki, H.L. Yadav and A. Faessler; Phys. Lett. 66B (1977) 310-314 Strong and decoupling structure in transitional odd-odd mass nuclei

5. H. Toki, H.L. Yadav and A. Faessler; Phys. Lett. 71B (1977) 1-4 Decoupled and strongly coupled particle system in odd-odd mass nuclei

原子核手征对称性的提出

手征对称性破缺：三轴变形的实验信号

推转模型

空穴 + 粒子 + 三轴转子：非平面转动

Orientations of the A.M. 3D Cranking model

两个空穴 + 三轴转子 = 磁转动

空穴 + 粒子 + 三轴转子 = 手征双重态

两条简并的磁转动带，由于量子PRM 模型导致分裂从而可以从实验上进行观测。

Neutron and proton coupled with triaxial rotor

I=2 rotational bands

I= １ magnetic rotational bands

Shears bands

1. J lies along a principal axis

2. J lies in a principal plane

Chiral doublets bands, Why ?Chiral doublets bands, Why ?

Chiral bandsExperimental signature:

Degenerate pairs of I=1 bands

= y()

3. J does not lie in any of principal plane

Frauendorf, Meng, Nucl. Phys. A 617, 131(1997 )

Chiral doublets bands, Why ?Chiral doublets bands, Why ?

原子核手征对称性的实验验证

Good agreement between the experimental

and the PRM calculated results

Near energy degeneracy: Near energy degeneracy: easy !easy !

Peng, Meng, Zhang,Phys. Rev.C68, 044324 (2003 )

原子核手征对称性的实验验证

原子核手征对称性的理论文章

A~130 region

A~100 regionChiral bands candidates Chiral bands candidates in odd-odd nucleiin odd-odd nuclei

手征原子核 -- 实验进展

A~130Odd-Odd (h11/2h11/2): (g9/2h11/2)132Cs,130Cs,128Cs,126Cs,124Cs,122Cs 118I134La, 132La,130La 134Pr, 132Pr 136Pm 138EuOdd-A ((h11/2)2h11/2):

135NdEven-Even ((h11/2d5/2)(h11/2)2): 136Nd

A~100Odd-Odd (g9/2h11/2)106Ag, 106Rh, 104RhOdd-A (g9/2h11/2)2)105Rh

A~190Odd-Odd (h9/2i13/2)188Ir

手征原子核 -- 实验进展

原子核手征对称性的的研究进展的研究进展

至少有来自 21 国家（地区）的 123 研究组的 356 人参与原子核手征对称性的研究

Near energy degeneracy - 手征原子核？

134 Pr - 手征原子核 ？？？

End of the story ?

手征原子核 : best example ！？

Level scheme in 128Cs

The calculated spectra agree with the data.

B(E2) in 128Cs

data Koike et al Our work

E. Grodner et al., PRL 97, 172501 (2006)

B(M1) B(M1) in 128Cs

data Koike et al Our work

手征原子核 : another in A=100 mass region

手征原子核 : another best example in 2007

chiral bands

1. nearly degenerate doublet bands

2. S(I) independent of spin

3. identical spin alignments

4. identical B(M1), B(E2) values

6. interband B(E2)=0 at high spin

5. staggering of B(M1)/B(E2) ratios

Chiral nucleusChiral nucleus ：： Based on the geometry for one Based on the geometry for one particle and one hole coupled to a triaxial rotor particle and one hole coupled to a triaxial rotor

with gamma=30with gamma=3000

1. Triaxial rotor

2. many-particles plus many-holes!

S.Y. Wang, S.Q. Zhang, B. Qi, and J. Meng, Examining the Chiral Geometry in 104Rh and 106Rh, Chinese Physics Letters 2007 24 (3): 664-667

在兰州重离子国家实验室观测到的首例手征双重带

Question: Chiral bands ?Question: Chiral bands ?

Reproduction of Spectra & transition in 2qp coupled with triaxial rotor ! Examine the orientation of the AM

Pairing correlation can imitate the many-particles Pairing correlation can imitate the many-particles plus many-holes coupled with triaxial rotorplus many-holes coupled with triaxial rotor

S.Y. Wang, S.Q. Zhang, B. Qi, and J. Meng, Doublet bands in 126Cs in the triaxial rotor model coupled with two quasiparticles, Physical Review C 75, 024309 (2007)

electromagnetic electromagnetic properties of properties of 126126CsCs

Pairing correlation can imitate the many-particles Pairing correlation can imitate the many-particles plus many-holes coupled with triaxial rotorplus many-holes coupled with triaxial rotor

S.Y. Wang, S.Q. Zhang, B. Qi, and J. Meng, Doublet bands in 126Cs in the triaxial rotor model coupled with two quasiparticles, Physical Review C 75, 024309 (2007)

Subject: 126Cs DATA Date: Fri, 09 Mar 2007 17:48:49 +0000 From: Julian Srebrny <js@zfja-gate.fuw.edu.pl> To: mengj@pku.edu.cn Dear ProfesSor Meng, I hope you remember me and Ernest Grodner from Trento 2003 workshopand later on from Kazimierz conference the same year. I am writing to You in connection to your very interesting paper from February 23, 2007 in the Physical Review C75. Our team has published the results on the 128Cs lifetime measurements and comparison with CQPC calculations for chiral bands in that nucleus in PRL 97, 172501(2006). The present mail is written to you in behalf of authors of this paper. Just after evaluation ofthe absolute M1 and E2 transition probabilities in 128Cs we have performed experiment on 126Cs. Now, we have nearly finished our analysis and should like to publish our results on chirality in 126Cs. We should like to propose you to take a look into our data for 128Cs and 126Cs and to publish together our experimental results and your interpretation in the frame of your Particle Rotor Model with pairing included. It seems to us that we can submit such a paper to Physical Review Letter as a confirmation of chirality in odd-odd Cesium isotopes.

Dear Professor Meng, Would you mind considering our proposition and writing to us your opinion?

With the best regards, Julian Srebrny.

Exotic shape: triaxial deformationExotic shape: triaxial deformation

Conventional constraints

: i() +: j( +)

: i() +: j( +)

Configuration fixed constraints

Chirality in atomic nucleus – Microscopics RMF investigation

MD

SP level for 106Rh

手征原子核—微观研究进展

手征原子核—微观研究进展

Recent theoretical and experimental

progress on chirality in atomic nuclei

are briefly reviewed

Possible signal for chirality in atomic

nuclei are summarized

Future efforts to understand nuclear

chirality are suggested

总结与展望