1. Triaxiality in nuclei: Theoretical aspects S. Frauendorf Department of Physics University of Notre Dame, USA IKH, Forschungszentrum Rossendorf Dresden, Germany

2. In collaboration with D. Almehed, UMIST V. Dimitrov, FZR, ND F. Doenau, FZR Ying-ye Zhang, UT

3. Triaxial shell gaps

4. A normal def. A large def. 165 190 134 105 80

5. Phenomena in triaxial nuclei Wobbling Chiral vibrations Static chirality Tidal waves

6. Wobbler types

7. Collective Wobbler large

8. Aligned Wobbler 1 3 High-j particle Increases with spin

9. Tilted Wobbler High-j hole

11. High-j particle, Irrotational flow MoI realignment with 2-axis

12. Irrotational exchanged Cranking moments of inertia

15. Matsuzaki, Shimizu, Matsuyanagi, PRC 65, 041303(R) (2002) RPA

16. Wobbling (A=164) No collective wobbler Transition probablities  Aligned wobbler Energies  Tilted wobbler TAC in between Constant moment of inertia ?? Lower I in other mass regions (A=105,134,190)  chirality__

17. Chirality

19. Dynamical (Particle Rotor) calculation Chiral vibration

20. chiral vibration chiral rotation

21. Chiral vibrator

22. [8] K. Starosta et al., Physical Review Letters 86, 971 (2001)

23. Transition probabilities

24. out in out in yrast  yrare 

25. yrast  yrare  out in

26. Microscopic TAC calculations

27. Consequence of chirality: Two identical rotational bands. (Static approximation)

28. Chiral sister bands Representative nucleus observed13 0.21 14 13 0.21 40 13 0.21 14 predicted 45 0.32 26 observed 23 0.20 29 observed13 0.18 26 31/37

30. Composite chiral bands

31. Types of chirality

32. Status of breaking of chiral symmetry Chiral mean field solutions do exist Chiral sister bands are seen Transition from chiral vibrations to rotations Transition matrix elements needed Sensitive to details Microscopic approach to dynamics needed

33. “I call any geometrical figure, or group of points, chiral, and say it has chirality, if its image in a plane mirror, ideally realized, cannot brought to coincide with itself.” Kelvin, 1904, Baltimore lectures on Molecular Dynamics and Wave Theory of Light

34. Chirality of molecules mirror The two enantiomers of 2-iodubutene

35. carvon

37. mirror Chirality of mass-less particles z

39. Chirality “I call a physical object, chiral, and say it has chirality, if its image, generated by space inversion or time reversal, cannot brought to coincide with itself by a rotation.” 11/37

40. Tidal wave

41. High-spin waves Combination of Angular momentum reorientation Triaxial deformation

42. yrast D. Cullen et. al

44. 25 26 27 28 29 30 Line distance: 20keV TAC

46. Line distance: 200 keV

47. Tidal wave Less favored vibrations Mixed with p-h excitations

48. s ot i m K=25 i (130 ns) s o t m K=0 0 8 14 21 24 P. Chowdhury et al NPA 484, 136 (1988)

49. First example of a triaxial tilted Tidal Wave 10 Phonons! Softness in shows up in isomer decay Large order amplitude phonons First phase transition

50. Rotating mean field: Cranking model Seek a mean field solution carrying finite angular momentum. Use the variational principle with the auxillary condition The state |> is the stationary mean field solution in the frame that rotates uniformly with the angular velocity w about the z axis. In the laboratory frame it corresponds to a uniformly rotating mean field state

51. Can calculate molecule Very different from

53.     p   n  