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ShuangQuan Zhang (sqzhang@pku) School of Physics, Peking University

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

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ShuangQuan Zhang (sqzhang@pku) School of Physics, Peking University

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  1. 17th Nuclear Physics Workshop “Marie & Pierre Curie” in Kazimierz2010-09-24 Static chirality and chiral vibration of atomic nucleus in particle rotor model ShuangQuan Zhang (sqzhang@pku.edu.cn) School of Physics, Peking University Collaborators: B. Qi, S.Y. Wang, J. Meng, S.G. Frauendof

  2. 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

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

  4. Chirality in Atomic Nucleus 2010-09-24 17th Nuclear Physics Workshop in Kazimierz 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.

  5. Chiral doublet bands +1 -1 I+4 -1 +1 I+3 -1 +1 I+2 +1 -1 I+1 +1 -1 I 2010-09-24 17th Nuclear Physics Workshop in Kazimierz Intrinsic frame Lab. frame: restoration of symmetry breaking Expected exp. signal：Two near degenerate DI =1 bands, called chiral doublet bands S.Frauendorf and J.Meng, Nucl. Phys. A617, 131(1997)

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

  7. Theoretical tools for nuclear chirality 2010-09-24 17th Nuclear Physics Workshop in Kazimierz • 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 (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 Starosta 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.

  8. Particle Rotor Model 2010-09-24 17th Nuclear Physics Workshop in Kazimierz 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.

  9. Observation in 128Cs 2010-09-24 17th Nuclear Physics Workshop in Kazimierz ph11/21nh11/2-1

  10. Observation in 126Cs 2010-09-24 17th Nuclear Physics Workshop in Kazimierz ph11/21nh11/2-1

  11. Observation in 126Cs 2010-09-24 17th Nuclear Physics Workshop in Kazimierz Electromagnetic properties in Cs isotopes ph11/21nh11/2-1 S.Y. Wang et al. PRC 74, 017302 (2006)

  12. PRM description of 126,128Cs 2010-09-24 17th Nuclear Physics Workshop in Kazimierz ph11/21nh11/2-1 S.Y. Wang, SQZ, B. Qi, J. Meng. PRC75, 024309 (2007)

  13. PRM description of 126,128Cs 2010-09-24 17th Nuclear Physics Workshop in Kazimierz ph11/21nh11/2-1 Data From: E. Grodner, J. Srebrny et al.

  14. Observation in 106Rh 2010-09-24 17th Nuclear Physics Workshop in Kazimierz pg9/2-1nh11/21

  15. PRM description of 106Rh 2010-09-24 17th Nuclear Physics Workshop in Kazimierz pg9/2-1nh11/21 S.Y. Wang, SQZ, B. Qi, J. Peng, J.M. Yao, J. Meng. PRC77, 034314 (2008)

  16. Observation in 135Nd 2010-09-24 17th Nuclear Physics Workshop in Kazimierz ph11/22nh11/2-1 S. Zhu et al. PRL (2003) S. Mukhopadhyay et al. PRL (2007)

  17. PRM description of 135Nd 2010-09-24 17th Nuclear Physics Workshop in Kazimierz E(I) B(M1) & B(E2) ph11/22nh11/2-1, 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)

  18. Observation in 103Rh 2010-09-24 17th Nuclear Physics Workshop in Kazimierz ph9/2-1nh11/22

  19. Observation in 105Rh 2010-09-24 17th Nuclear Physics Workshop in Kazimierz ph9/2-1nh11/22

  20. PRM description of 103,105Rh 2010-09-24 17th Nuclear Physics Workshop in Kazimierz ph9/2-1nh11/22 B.Qi,SQZ, S.Y. Wang, J. Meng,T. Koike . in preparation.

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

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

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

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

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

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

  27. 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?

  28. An Analysis of Chiral Doublet States with Orientation Operator 2010-09-24 17th Nuclear Physics Workshop in Kazimierz • 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 |-? • Constraint of the phase of |+ or |- by: 1. For same spin I with different variable g : 2. For different spin I: “reduced E2 transition matrix at axial symmetry case” “Parallel transport principle”

  29. An Analysis of Chiral Doublet States with Orientation Operator 2010-09-24 17th Nuclear Physics Workshop in Kazimierz Results:1p1h PRM, ph11/2nh11/2 , b=0.23, J=20MeV-1h2 • 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).

  30. Summary 2010-09-24 17th Nuclear Physics Workshop in Kazimierz • 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.

  31. 2010-09-24 17th Nuclear Physics Workshop in Kazimierz Thank you for your attention!

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

  33. Static Chirality and Strong B(M1) Staggering 2010-09-24 17th Nuclear Physics Workshop in Kazimierz Static: Strong B(M1) Staggering Vibration: Weak/No B(M1) Staggering

  34. Chiral Vibration and Weak B(M1) Staggering 2010-09-24 17th Nuclear Physics Workshop in Kazimierz Static: Strong B(M1) Staggering Vibration: Weak B(M1) Staggering

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

  36. Fingerprints 1. nearly degenerate doublet bands 2. S(I) independent of spin 3. staggering of B(M1)/B(E2) ratios 4. identical B(M1), B(E2) values 6. interband B(E2)=0 at high spin 2010-09-24 17th Nuclear Physics Workshop in Kazimierz ideal chiral bands Vaman et al., PRL.92 032501 (2004) 5. identical spin alignments Petrache et al., PRL.96, 112502 (2006) Koike et al., PRL. 93, 172502 (2004)

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