A close up of the spinning nucleus

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

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

3. Decay+detector Nucleonic orbitals – gyroscopes Nucleonic orbitals – gyroscopes Spinning clockwork of gyroscopes HI+small arrays HI+large arrays Collective rotation Interplay between collective and sp. degrees of freedom 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. Deformed density / potential Orientation of the gyroscopes Well deformed How does orientation come about? Deformed potential aligns the partially filled orbitals Partially filled orbitals are highly tropic Nuclus is oriented – rotational band 5

6. rigid HCl irrotational How is angular momentum generated? Moving masses or currents in a liquid are not too useful concepts 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 Moments of inertia for I>20 (no pairing) differ strongly from rigid body value Microscopic cranking Calculations do well in reproducing the moments of inertia. With and without pairing. 7 M. A. Deleplanque et al. Phys. Rev. C69, 044309 (2004)

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

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

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

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

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

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

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

18. n=3 n=3 n=2 n=2 n=1 n=1 n=0 n=0 harmonic (non-interacting) phonons Data: J.F.Smith et al.PRL 75, 1050(95) Plot :R. Jolos, Brentano PRC 60, 064317 (99) an harmonic (interacting) phonons 1-3 0-2 exp 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. Chirality Consequence of chirality: Two identical rotational bands. 21

22. Come as close as 20keV Strong Transitions 2 -> 1 K. Starosta et al. Results of the Gammasphere GS2K009 experiment. band 2 band 1 134Pr ph11/2 nh11/2 22

23. Microscopic RPA calculations (D. Almehed’s talk) Shape Soft chiral vibrations Unharmonicites Must be even, because symmetry is spontaneously broken 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. 32

24. Triaxial Rotor with microscopic moments of inertia Rigid shape IBFFM Soft shape C. Petrache et al. PRL A. Tonev et al. PRL 96, 052501 (2006) 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. Harmonic approximation Full triaxial rotor + particle + hole (frozen) Chiral vibrator Frozen alignment

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

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

33. Coupling to particles Frozen alignment 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. Strong interband vib rot vib rot

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

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

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