ShuangQuan Zhang (sqzhang@pku) School of Physics, Peking University
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ShuangQuan Zhang([email protected])
School of Physics, Peking University
Static chirality and chiral vibration of atomic Static chirality and chiral vibration of atomic nucleus in particle rotor modelnucleus in particle rotor model
17th Nuclear Physics Workshop “Marie & Pierre Curie” in Kazimierz 2010-09-24
Collaborators: B. Qi, S.Y. Wang, J. Meng, S.G. Frauendof
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Content
2010-09-24 17th Nuclear Physics Workshop in Kazimierz
Introduction——Chirality in atomic nucleus
Theory——Particle Rotor Model
Results
– Quantitative description of chiral bands by PRM (126,128Cs, 135Nd, 106Rh, 103,105Rh)
– Chiral geometry from PRM(Static chirality; chiral vibration)
– An analysis of chiral doublet states with an orientation operator
Summary
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Chirality in Nature
Chirality exists commonly in nature.
Left- Right-
2010-09-24 17th Nuclear Physics Workshop in Kazimierz
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Chirality in Atomic Nucleus
The rotation of triaxial nuclei can present chiral geometry.
There are three perpendicular angular momenta: Collective triaxial rotor R , Particle-like valence proton jp , Hole-like valence neutron jn
the total angular momentum J is aplanar.
Frauendorf, Meng, Nucl. Phys. A 617,131(1997 )
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Chiral doublet bands
Expected exp. signal:Two near degenerate I =1 bands, called chiral doublet bands
S.Frauendorf and J.Meng, Nucl. Phys. A617, 131(1997)
),|(|2
|
),|(|2
1|
LR
LR
iIM
IM
R|L|
Intrinsic frame
Lab. frame: restoration of symmetry breaking
+1
-1
-1
+1
+1
+1
+1
-1
-1
-1
I+4
I+3
I+2
I+1
I
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Claimed chiral nuclei
Candidate chiral doublet bands have been claimed in many odd-odd and odd-A nuclei with different configurations in A~80, 100,130,190 mass regions.
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2010-09-24 17th Nuclear Physics Workshop in Kazimierz
Theoretical tools for nuclear chirality Tilted axis cranking – Single-j model Frauendorf and Meng NPA(1997);– Hybird Woods-Saxon and Nilsson model Dimitrov et al PRL(2000)– Skyrme Hartree-Fock model Olbratowski et al PRL(2004), PRC(2006)– Relativistic mean field (RMF) theory Madokoro et al PRC(2000); Peng et al PR
C (2008)– TAC+RPA (135Nd) S. Mukhopadhyay et al PRL2007;
Particle Core Coupling Triaxial Particle Rotor Model Frauendorf and Meng NPA(1997); Peng et al PRC(2003); Koike et al PRL(2004), SQZ et.al PRC(2007); Lawrie et al PRC (2008); Qi et al PLB(2009)– Core-quasiparticle coupling model, which follows the KKDF method Staro
sta et al PRC(2002); Koike et al PRC(2003) – Interacting Boson Fermion Fermion Model (IBFFM) S. Brant et al PRC (2004), PRC (2008), Tonev et al PRL(2006)– Pair Truncated Shell Model K. Higashiyama et al, PRC(2005)
In this talk, the particle rotor model is adopted.
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Particle Rotor Model The model Hamiltonian:
the collective part,
the intrinsic part,
We have extended such model for triaxial nuclei with 2-qp and many particle configuration based on single-j model.
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2010-09-24 17th Nuclear Physics Workshop in Kazimierz
Observation in 128Cs
h11/21h11/2
-1
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Observation in 126Cs
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h11/21h11/2
-1
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Observation in 126Cs
2010-09-24 17th Nuclear Physics Workshop in Kazimierz
Electromagnetic properties in Cs isotopes
S.Y. Wang et al. PRC 74, 017302 (2006)
h11/21h11/2
-1
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2010-09-24 17th Nuclear Physics Workshop in Kazimierz
PRM description of 126,128Cs
S.Y. Wang, SQZ, B. Qi, J. Meng. PRC75, 024309 (2007)
h11/21h11/2
-1
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2010-09-24 17th Nuclear Physics Workshop in Kazimierz
PRM description of 126,128Cs
Data From: E. Grodner, J. Srebrny et al.
h11/21h11/2
-1
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Observation in 106Rh
2010-09-24 17th Nuclear Physics Workshop in Kazimierz
g9/2-1h11/2
1
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2010-09-24 17th Nuclear Physics Workshop in Kazimierz
PRM description of 106Rh
S.Y. Wang, SQZ, B. Qi, J. Peng, J.M. Yao, J. Meng. PRC77, 034314 (2008)
g9/2-1h11/2
1
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Observation in 135Nd
S. Mukhopadhyay et al. PRL (2007)S. Zhu et al. PRL (2003)
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h11/22h11/2
-1
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PRM description of 135Nd
B(M1) & B(E2)B(M1) & B(E2)E(I)E(I)
Both energies and transition ratios are well reproduced!
β= 0.235 and γ= 22.4◦
B.Qi, SQZ, J. Meng, S.Y. Wang, S. Frauendorf. Phys. Lett. B(2009)
h11/22h11/2
-1,
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Observation in 103Rh
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h9/2-1h11/2
2
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Observation in 105Rh
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h9/2-1h11/2
2
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PRM description of 103,105Rh
2010-09-24 17th Nuclear Physics Workshop in Kazimierz
B.Qi, SQZ, S.Y. Wang, J. Meng,T. Koike . in preparation.
h9/2-1h11/2
2
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Chiral Geometry in 135Nd
Components of angular momenta
Components of angular momenta
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Chiral Geometry in 135Nd
Length and Orientation of angular momenta
Length and Orientation of angular momenta
Static chiral geometry are well developed around I~39/2 !
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Distribution of AM Projection
Chiral vibration
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Distribution of AM Projection
Static Chirality
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Chirality evolution
Chiral vibration (I=29/2) Static chirality (I=39/2) Chiral vibration (I=45/2)
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An Analysis of Chiral Doublet States with Orientation Operator
A Naive Question:For chiral doublet bands, which state is |L?
2010-09-24 17th Nuclear Physics Workshop in Kazimierz
- Not correct
Naive Question becomes:
Which state is | + ?
Which is | ?
Intrinsic frame Lab. frame
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An Analysis of Chiral Doublet States with Orientation Operator
2010-09-24 17th Nuclear Physics Workshop in Kazimierz
Possible Answer is : To judge it from the sign of Orientation parameter?
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2010-09-24 17th Nuclear Physics Workshop in Kazimierz
An Analysis of Chiral Doublet States with Orientation Operator
Before the calculation, one must constrain the phase of wave functions in lab. frame, because the sign of L||L will be changed accordingly if one change the sign of |+ or |?
Constraint of the phase of |+ or | by:
1. For same spin I with different variable :
2. For different spin I: “reduced E2 transition matrix at axial symmetry case”
“Parallel transport principle”
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2010-09-24 17th Nuclear Physics Workshop in Kazimierz
An Analysis of Chiral Doublet States with Orientation Operator
Results:1p1h PRM, hh=0.23, J=20MeV-12
– Picture of three perpendicular angular momenta can be approximately realized. (same as: K. Starosta et.al., NPA 682(2001)357c )
– In the yrast (or yrare) band of chiral doublet bands, the states are the same |+ or | state, linear combined by |L and |R.
– Such order of |+ or | state is different from the states with A quantum numbers, discussed by Koike, et al., PRL 93, 172502 (2004).
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Summary
Quantitative description have been carried out by PRM for doublet bands, in odd-odd and odd-A nuclei, in A~100 and 130 mass region, and with different quasiparticle configurations.
Static chirality and chiral vibration are shown in the framework of PRM, which have been discussed before in the framework of TAC with RPA.
An analysis of chiral doublet states with orientation operator is preformed.
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Thank you for your attention!
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PRM description of 126,128Cs
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2010-09-24 17th Nuclear Physics Workshop in Kazimierz
Static Chirality and Strong B(M1) Staggering
Static: Strong B(M1) Staggering Vibration: Weak/No B(M1) Staggering
Static: Strong B(M1) Staggering Vibration: Weak/No B(M1) Staggering
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2010-09-24 17th Nuclear Physics Workshop in Kazimierz
Chiral Vibration and Weak B(M1) Staggering
Static: Strong B(M1) Staggering Vibration: Weak B(M1) StaggeringStatic: Strong B(M1) Staggering
Vibration: Weak B(M1) Staggering
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2010-09-24 17th Nuclear Physics Workshop in Kazimierz
Selection Rules of …
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2010-09-24 17th Nuclear Physics Workshop in Kazimierz
Fingerprints
ideal chiral bands
1. nearly degenerate doublet bands
2. S(I) independent of spin
3. staggering of B(M1)/B(E2) ratios
5. identical spin alignments
4. identical B(M1), B(E2) values
6. interband B(E2)=0 at high spinKoike et al., PRL. 93, 172502 (2004)
Vaman et al., PRL.92 032501 (2004)
Petrache et al., PRL.96, 112502 (2006)