1. How do nuclei rotate?
1. The molecular picture

2. The classical rotor 1 2 3

3. Axial rotor
Classical motion of J K J
orbit

4. Small E
Triaxial rotor
Classical motion of J
wobbling
motion
Intermediate E
Large E

5. Euler angles
5/30

6. Quantization

7. The molecular rotor
Axial rotor 1 2 3

8. K J
orbit

9. Centrifugal stretching
Stiff bonds

10. 1 2 3
Triaxial rotor
Small E
wobbling
motion
10/30

11. Born-Oppenheimer Approximation.
Electronic motion
Vibrations
Rotations CO

12. Adiabatic approximationel
rot
vib

13. HCl
Microwave absorption
spectrum

14. Band Spectrum

15. Indistinguishable Particles.
Upper particles
Lower particles 2
Restriction of orientation
15/30

17. The nuclear rotor Most nuclei have a deformed axial shape.
Unified Model (Bohr and Mottelson):
The nucleus rotates as a whole.
(collective degrees of freedom)
The nucleons move independently
inside the deformed potential (intrinsic degrees of freedom)
The nucleonic motion is much faster
than the rotation (adiabatic approximation)

18. Nucleons are indistinguishable
The nucleus does not have an orientation degree of freedom
with respect to the symmetry axis.
Axial symmetry

19. symmetry

20. 20/30

21. No signature selection
rule

23. Electromagnetic Transitions
Emitted photon with multipolarity E1, E2, E2, ... or M1, M2, ...
Reduced transition probability
contains the information about nuclear structure.

24. Multipole moments of the nucleus

25. Reduced transition probabilities in the Unified Model

26. 25/30

27. Limitations of the molecular picture
rigid rotor
HCl
Nucleons are not on fixed positions.
The nuclear surface
What is rotating?

28. More like a liquid, but what kind of?
Ideal
“irrotational flow” moment of inertia
viscous

29. rigid
irrotational

30. Breakdown of adiabatic approximation

31. Summary Molecules are the protoype of quantal rotors.
Electronic and vibrational motions are much faster than rotation.
Rotational bands consist of states with different angular momentum and the same intrinsic state (elec., vib.).
Indistiguishability leads to restrictions in the possible values of the angular momentum.
Nuclei at low spin are are similar to molecules. The nuclear surface is rotating.
Unified model: intrinsic states correspond to the motion of nucleons in the deformed potential.
Nuclei are liquid-like. The flow pattern is dominated by quantal effects.
Microscopic theory needed for calculating them.