shuangquan zhang (sqzhang@pku) school of physics, peking university

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

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

Chirality in Nature

Chirality exists commonly in nature.

Left- Right-


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 )


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


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.



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.

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.



Observation in 128Cs

h11/21h11/2

-1



h11/21h11/2

-1



Electromagnetic properties in Cs isotopes

S.Y. Wang et al. PRC 74, 017302 (2006)

h11/21h11/2

-1


PRM description of 126,128Cs

S.Y. Wang, SQZ, B. Qi, J. Meng. PRC75, 024309 (2007)

h11/21h11/2

-1



Data From: E. Grodner, J. Srebrny et al.

h11/21h11/2

-1

Observation in 106Rh


g9/2-1h11/2

1


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

Observation in 135Nd

S. Mukhopadhyay et al. PRL (2007)S. Zhu et al. PRL (2003)


h11/22h11/2

-1


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,



h9/2-1h11/2

2

PRM description of 103,105Rh


B.Qi, SQZ, S.Y. Wang, J. Meng,T. Koike . in preparation.

h9/2-1h11/2

2


Chiral Geometry in 135Nd

Components of angular momenta

Components of angular momenta


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 !


Distribution of AM Projection

Chiral vibration


Distribution of AM Projection

Static Chirality

Chirality evolution

Chiral vibration (I=29/2) Static chirality (I=39/2) Chiral vibration (I=45/2)


An Analysis of Chiral Doublet States with Orientation Operator

A Naive Question：For chiral doublet bands, which state is |L?


- Not correct

Naive Question becomes:

Which state is | + ?

Which is | ?

Intrinsic frame Lab. frame



Possible Answer is : To judge it from the sign of Orientation parameter?



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”



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).

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.


Thank you for your attention!



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


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


Selection Rules of …


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)

shuangquan zhang (sqzhang@pku) school of physics, peking university

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