How do nuclei rotate?

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

2. 3 2 1 The classical rotor

3. J K orbit Axial rotor Classical motion of J

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

5. Euler angles 5/30

6. Quantization

7. 3 Axial rotor 2 1 The molecular rotor

8. J K orbit

9. Centrifugal stretching Stiff bonds

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

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

12. Adiabatic approximation el rot vib

13. HCl Microwave absorption spectrum

14. Band Spectrum

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

17. Most nuclei have a deformed axial shape. Unified Model (Bohr and Mottelson): The nuclear rotor 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. Axial symmetry The nucleus does not have an orientation degree of freedom with respect to the symmetry axis. Nucleons are indistinguishable

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

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

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.