1. A close up of the spinning nucleus S. Frauendorf Department of Physics University of Notre Dame, USA IKH, Forschungszentrum Rossendorf Dresden, Germany

2. How is the nucleus rotating? What is rotating? The nuclear surface Nucleons are not on fixed positions. Collective model accounts for the appearance of rotational bands E I(I+1), Alaga rules for e.m. transitions and many more phenomena. Bohr and Mottelson 2

3. HI+small arrays HI+large arrays Decay+detector Collective rotation Interplay between collective and sp. degrees of freedom Nucleonic orbitals – gyroscopes Spinning clockwork of gyroscopes Nucleonic orbitals – gyroscopes 3

4. Aspects of the close up How does orientation come about? How is angular momentum generated? Examples: magnetic rotation, band termination and recurrence Weak symmetry breaking at high spin Examples: reflection asymmetry, chirality 4

5. How does orientation come about? Orientation of the gyroscopes Deformed density / potential Deformed potential aligns the partially filled orbitals Partially filled orbitals are highly tropic Nuclus is oriented – rotational band Well deformed 5

6. How is angular momentum generated? Moving masses or currents in a liquid are not too useful concepts HCl rigid irrotational Myth: Without pairing the nucleus rotates like a rigid body. 6

7. Angular momentum is generated by alignment of the spin of the orbitals with the rotational axis Gradual – rotational band Abrupt – band crossing, no bands Microscopic cranking Calculations do well in reproducing the moments of inertia. With and without pairing. Moments of inertia for I>20 (no pairing) differ strongly from rigid body value M. A. Deleplanque et al. Phys. Rev. C69, 044309 (2004) 7

8. Magnetic Rotation Weakly deformed 8

9. TAC Long transverse magnetic dipole vectors, strong B(M1) The shears effect 9

10. Better data needed for studying interplay between shape of potential and orientation of orbitals. 10

11. Terminating bands A. Afanasjev et al. Phys. Rep. 322, 1 (99) Orientation of the gyroscopes Deformed density / potential 11

12. Instability after termination After termination, several alignments, substantial rearrangement of orbitals Coexistence of sd, hd, with wd new shape, bands instability M. Riley E. S..Paul et al. @Gammasphere Calculations: I. Ragnarsson termination 12

13. Symmetries at high spin Combination of Shape (time even) With Angular momentum (time odd) Determine the parity-spin-multiplicity sequence of the bands 13

14. Parity doubling Best case of reflection asymmetry. Must be better studied! <60keV Tilted reflection asymmetric nucleus 14

15. Good simplex Several examples in mass 230 region Substantial staggering 15

16. Weak reflection symmetry breaking Driven by rotation Staggering Parameter S Changes sign! 16

17. Condensation of non-rotating vs. rotating octupole phonons + - + - + - j=0 phonon j=3 phonon Angular momentum rotational frequency 17

18. exp n=0 n=1 n=2 n=3 n=0 n=1 n=2 n=3 harmonic (non-interacting) phonons an harmonic (interacting) phonons 0-2 1-3 Data: J.F.Smith et al.PRL 75, 1050(95) Plot :R. Jolos, Brentano PRC 60, 064317 (99) 18

19. Rotating octupole does not completely lock to the rotating quadrupole. + - + - + - 19

20. X. Wang, R.V.F. Janssens, I. Wiedenhoever et al. to be published. Preliminary 20

21. Consequence of chirality: Two identical rotational bands. Chirality 21

22. band 2 band 1 134 Pr  h 11/2 h 11/2 Come as close as 20keV Strong Transitions 2 -> 1 K. Starosta et al. Results of the GammasphereGS2K009experiment. 22

23. Soft chiral vibrations Shape Microscopic RPA calculations (D. Almehed’s talk) Decreasing energy (about 2 units of alignment) Strong transitions 2->1, weak 1->2 Tiny interaction between 0 and 1 phonon states (<20 keV) Systematic appearance of sister bands Difficult to explain otherwise. Unharmonicites Must be even, because symmetry is spontaneously broken 32

24. Triaxial Rotor with microscopic moments of inertia Rigid shape IBFFM Soft shape A. Tonev et al. PRL 96, 052501 (2006) C. Petrache et al. PRL 24

25. Transition Quadrupole moment larger smaller 25

26. Summary Close up refined our concept of how nuclei are rotating: assembly of gyroscopes Rich and unexpected response as compared to non-nuclear systems Rotation driven crossover between different discrete symmetries resolved Chirality of rotating nuclei appears as a soft an harmonic vibration 26

27. Congratulations! 27

29. Loss and onset of orientation Geometrical picture vs. TAC

30. Chiral vibrator Frozen alignmentHarmonic approximation Full triaxial rotor + particle + hole (frozen)

31. [8] K. Starosta et al., Physical Review Letters 86, 971 (2001)

32. 134Pr - a chiral vibrator, which does not make it. Experiment Calculation: Triaxial rotor with Cranking MoI +particle+hole

33. Frozen alignment Coupling to particles Additional alignment

34. Tiny interaction between states! But strong cross talk!!??

35. 4 irreducible representations of group 2 belong to even I and 2 to odd I. For each I, one is 0-phonon and one is 1-phonon. The 1-phonon goes below the 0-phonon!!!

36. vib rot Strong interband

37. Strong decay 2->1 weak decay 1->2. Cross over of the two bands (Intermediate MoI maximal) Almost no interaction between bands 1 and 2 (manifestation of D_2) Evidence for chiral vibration Problem: different inband B(E2) Coupling to deformation degrees of freedom seems important Two close bands, same dynamic MoI, 1-2 units difference in alignment

39. Do not cross

40. Conclusions So far no static chirality – look at TSD Evidence for dynamic chirality Chiral vibrators exotic: One phonon crosses zero phonon Coupling to deformation degrees

41. Deformed harmonic oscillator N=Z=4 (equilibrium shape) Moment of inertia has the rigid body value generated by the p-orbitals

42. rotational alignment Backbends K-isomers M. A. Deleplanque et al. Phys. Rev. C69, 044309 (2004) Moments of inertia for I>20 Combination of many orbitals -> classical periodic orbits Velocity field in body fixed frame of unpaired N=94 nuclides