1. Nuclear Tidal Waves Daniel Almehed Stefan Frauendorf Yongquin Gu Yang Sun

4. Classical Quadrupole Surface Vibration

6. Tidal wave

7. Yrast line of 5D-harmonic oscillator E I In the rotating frame: small oscillations around qp. excitations Tidal waves

8. I Anharmonic oscillator E(5) like

9. I-1/2 rotor vibratortidal wave

10. I-1/2 rotor vibrator tidal wave

11. No good vibrator! N= 92 90 88 86 84

13. Theoretical methods Fix the angular momentum or rotational frequency Find the static shape – use a mean field method Cranking model: semiclassical treatment of angular momentum Angular momentum projection: Projected shell model

14. Low-spin waves

16. F. Courminboeuf et al. PRC 63 (00) 014305

17. Energy minimum (self-consistency) at: QQ model +cranking harmonic

18. Cranking model Tidal wave AMR B(E2,I->I-2)[(eb)^2] Iexpcalc tidal wave 20.090.07 40.180.17 60.240.22 antimagnetic rotor 120.150.10 140.110.10 160.120.10 Experiment:M. Piiparinen et al. NPA565 (93) 671 F. Courminboeuf et al. PRC 63 (00) 014305 R. Clark et al. private communication

19. Projected shell model

20. Monopole Pairing+Quadrupole Pairing+QQ model Zero quasiparticle version: Two quasiparticle version: Diagonalize H in the basis Minimize lowest energy

22. Projected shell model B(E2,I->I-2)[(eb)^2] Iexpcalc tidal wave 20.090.07 40.180.13 60.240.16 antimagnetic rotor 120.150.14 140.110.15 160.120.16 Tidal wave AMR

23. Antimagnetic rotor

24. Geometrical model for an antimagnetic rotor

25. A. Simons et al. Phys. Rev. Lett. 91, 162501 (2003)

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

27. yrast D. Cullen et. al

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

33. Line distance: 200 keV

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

35. 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)

36. Tidal waves Yrast mode in soft nuclei at low and high spin Angular momentum generated by shape change at nearly constant angular velocity. Shape change: Axial, triaxial quadrupole, orientation, octupole … Rotating mean field gives a reliable microscopic description No new parameters Experimental rotational frequency well defined

39. Cranking model Tidal wave AMR B(E2,I->I-2)[W.u.] Iexpcalc tidal wave 223.0 (15)18 446 (6)43 662 (20)56 antimagnetic rotor 1239 (2)25 1429 (3) 25 1625 25

40. Projected shell model Tidal wave AMR B(E2,I->I-2)[W.u.] Iexpcalc tidal wave 223.0 (15)18 446 (6)33 662 (20)41 antimagnetic rotor 1239 (2)36 1329 (3) 1625