1. 20/30

2. 2. The molecular view on nuclei
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)

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

4. symmetry

5. No signature selection
rule

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

7. Multipole moments of the nucleus

8. Reduced transition probabilities in the Unified Model

9. 25/30

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

11. More like a liquid, but what kind of?
Ideal (superfluid He droplets)
“irrotational flow” moment of inertia
viscous

12. rigid
irrotational

13. Breakdown of adiabatic approximation

14. 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.
Nuclear flow pattern is dominated by quantal effects.
Microscopic theory needed for calculating them.

15. 3. High Spin

16. Coincidence measurements
select rotational bands.

18. Stability against fission
Homogenously charged droplet

19. fission instable
fission barrier 8MeV

20. Rotational
bands in
5/17

21. Semiclassics High angular momentum
can be treated as a classical quantity
For uniform rotation the
rotational frequency (angular velocity)
is given by the classical relation

22. Experimental rotational frequency

23. M1 radiation
intensity
also well
described
by classical
radiation
theory
E2 radiation

24. Angular momentum, moment of inertia and routhians as functions of the frequency
Long bands permit us to derive the classical functions

25. Includes a quantal correction
Zero point fluctuation I
I+1/2
10/17

26. M1 radiation - high spin limitK J

28. Rotational bands in the non-adiabatic regime
How are the spectral lines arranged into bands?

29. Rotational
bands in

30. band EAB
band E
bandcrossing

31. Summary
Nuclei can be studied at high spin where intrinsic and rotational motion are on the same time scale.
The levels still organize into rotational bands, the states of which are connected by fast electromagnetic transitions.
Bands cross each other.
High spin allows us to use classical concepts for the rotational degree of freedom.
The angular velocity becomes a well defined concept.
It is very useful to study physical quantities as functions of the angular frequency.