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
In the rotating frame:
small oscillations around E I
qp. excitations
Tidal waves

8. Anharmonic oscillator
E(5) like I
Anharmonic oscillator

9. I-1/2
rotor
tidal wave
vibrator

10. N=
No good vibrator!

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

13. Low-spin waves

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

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

16. Cranking model B(E2,I->I-2)[(eb)^2] I exp calc tidal wave 0.09 0.07
AMR
B(E2,I->I-2)[(eb)^2]
I exp calc
tidal wave
antimagnetic rotor
Experiment: M. Piiparinen et al. NPA565 (93) 671
F. Courminboeuf et al. PRC 63 (00)
R. Clark et al. private communication

17. Projected shell model

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

20. Projected shell model B(E2,I->I-2)[(eb)^2] I exp calc tidal wave
antimagnetic rotor
AMR
Tidal wave

21. Antimagnetic rotor

22. Geometrical model for an antimagnetic rotor

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

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

25. yrast
D. Cullen et. al

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

31. Line distance:
200 keV

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

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

34. 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

37. Cranking model B(E2,I->I-2)[W.u.] I exp calc tidal wave
AMR
B(E2,I->I-2)[W.u.]
I exp calc
tidal wave
23.0 (15) 18
(6) 43
(20) 56
antimagnetic rotor
39 (2) 25
29 (3) 25

38. Projected shell model B(E2,I->I-2)[W.u.] I exp calc tidal wave
23.0 (15) 18
(6) 33
(20) 41
antimagnetic rotor
39 (2) 36
29 (3)
16 25
AMR
Tidal wave