Static chirality and chiral vibration of atomic nucleus

Static chirality and chiral vibration of atomic nucleus in particle rotor model Shuang. Quan Zhang (sqzhang@pku. edu. cn) School of Physics, Peking University Collaborators: B. Qi, S. Y. Wang, J. Meng, S. G. Frauendof 17 th Nuclear Physics Workshop “Marie & Pierre Curie” in Kazimierz 2010 -09 -24

Content l Introduction——Chirality in atomic nucleus l Theory——Particle Rotor Model l Results – Quantitative description of chiral bands by PRM (126, 128 Cs, 135 Nd, 106 Rh, 103, 105 Rh) – Chiral geometry from PRM (Static chirality; chiral vibration) – An analysis of chiral doublet states with an orientation operator l Summary 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Chirality in Nature Left- Right- Chirality exists commonly in nature. 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Chirality in Atomic Nucleus Frauendorf, Meng, Nucl. Phys. A 617, 131(1997 ) 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. 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Chiral doublet bands Intrinsic frame Lab. frame: restoration of symmetry breaking +1 -1 -1 +1 +1 -1 I+4 I+3 I+2 I+1 I Expected exp. signal： Two near degenerate DI =1 bands, called chiral doublet bands S. Frauendorf and J. Meng, Nucl. Phys. A 617, 131(1997) 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Claimed chiral nuclei Candidate chiral doublet bands have been claimed in many oddodd and odd-A nuclei with different configurations in A~80, 100, 130, 190 mass regions. 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Theoretical tools for nuclear chirality l 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 PRC (2008) – TAC+RPA (135 Nd) S. Mukhopadhyay et al PRL 2007; l 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 Starosta et al PRC(2002); Koike et al PRC(2003) – Interacting Boson 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) v In this talk, the particle rotor model is adopted. 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Particle Rotor Model The model Hamiltonian: the collective part, the intrinsic part, v We have extended such model for triaxial nuclei with 2 -qp and many particle configuration based on single-j model. 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Observation in 128 Cs ph 11/21 nh 11/2 -1 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Observation in 126 Cs ph 11/21 nh 11/2 -1 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Observation in 126 Cs Electromagnetic properties in Cs isotopes ph 11/21 nh 11/2 -1 S. Y. Wang et al. PRC 74, 017302 (2006) 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

PRM description of 126, 128 Cs ph 11/21 nh 11/2 -1 S. Y. Wang, SQZ, B. Qi, J. Meng. PRC 75, 024309 (2007) 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

PRM description of 126, 128 Cs ph 11/21 nh 11/2 -1 Data From: E. Grodner, J. Srebrny et al. 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Observation in 106 Rh pg 9/2 -1 nh 11/21 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

PRM description of 106 Rh pg 9/2 -1 nh 11/21 S. Y. Wang, SQZ, B. Qi, J. Peng, J. M. Yao, J. Meng. PRC 77, 034314 (2008) 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Observation in 135 Nd ph 11/22 nh 11/2 -1 S. Zhu et al. PRL (2003) 2010 -09 -24 S. Mukhopadhyay et al. PRL (2007) 17 th Nuclear Physics Workshop in Kazimierz

PRM description of 135 Nd E(I) B(M 1) & B(E 2) ph 11/22 nh 11/2 -1, β= 0. 235 and γ= 22. 4◦ Both energies and transition ratios are well reproduced! B. Qi, SQZ, J. Meng, S. Y. Wang, S. Frauendorf. Phys. Lett. B(2009) 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Observation in 103 Rh ph 9/2 -1 nh 11/22 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Observation in 105 Rh ph 9/2 -1 nh 11/22 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

PRM description of 103, 105 Rh ph 9/2 -1 nh 11/22 B. Qi, SQZ, S. Y. Wang, J. Meng, T. Koike. in preparation. 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Chiral Geometry in 135 Nd Components of angular momenta 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Chiral Geometry in 135 Nd Length and Orientation of angular momenta Static chiral geometry are well developed around I~39/2 ! 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Distribution of AM Projection Chiral vibration 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Distribution of AM Projection Static Chirality 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Chirality evolution Chiral vibration (I=29/2) Static chirality (I=39/2) 2010 -09 -24 Chiral vibration (I=45/2) 17 th Nuclear Physics Workshop in Kazimierz

An Analysis of Chiral Doublet States with Orientation Operator A Naive Question： For chiral doublet bands, which state is |L ? Intrinsic frame - Not correct Lab. frame Naive Question becomes: Which state is | + ? Which is | - ? 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

An Analysis of Chiral Doublet States with Orientation Operator Possible Answer is : To judge it from the sign of Orientation parameter? 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

An Analysis of Chiral Doublet States with Orientation Operator l Before the calculation, one must constrain the phase of wave functions in lab. frame, because the sign of L|s|L will be changed accordingly if one change the sign of |+ or |- ? l Constraint of the phase of |+ or |- by: 1. For same spin I with different variable g : “Parallel transport principle” 2. For different spin I: “reduced E 2 transition matrix at axial symmetry case” 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

An Analysis of Chiral Doublet States with Orientation Operator Results: 1 p 1 h PRM, ph 11/2 nh 11/2 , b=0. 23, J=20 Me. V-1 h 2 – Picture of three perpendicular angular momenta can be approximately realized. (same as: K. Starosta et. al. , NPA 682(2001)357 c ) – 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). 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Summary l 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. l Static chirality and chiral vibration are shown in the framework of PRM, which have been discussed before in the framework of TAC with RPA. l An analysis of chiral doublet states with orientation operator is preformed. 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Thank you for your attention! 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

PRM description of 126, 128 Cs 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Static Chirality and Strong B(M 1) Staggering Static: Strong B(M 1) Staggering Vibration: Weak/No B(M 1) Staggering 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Chiral Vibration and Weak B(M 1) Staggering 2010 -09 -24 Static: Strong B(M 1) Staggering Vibration: Weak B(M 1) Staggering 17 th Nuclear Physics Workshop in Kazimierz

Selection Rules of … 2010 -09 -24 17 th Nuclear Physics Workshop in Kazimierz

Fingerprints 1. nearly degenerate doublet bands 2. S(I) independent of spin 3. staggering of B(M 1)/B(E 2) ratios ideal chiral bands 4. identical B(M 1), B(E 2) values 5. identical spin alignments 6. interband B(E 2)=0 at high spin 2010 -09 -24 Vaman et al. , PRL. 92 032501 (2004) Petrache et al. , PRL. 96, 112502 (2006) Koike et al. , PRL. 93, 172502 (2004) 17 th Nuclear Physics Workshop in Kazimierz