1. 4. Rotation about a tilted axis and reflection asymmetry
How do nuclei rotate?
4. Rotation about a tilted axis and reflection asymmetry

2. discrete symmetries for
reflection symmetric shapes

3. Small E
Triaxial rotor
Classical motion of J
Uniform rotation only about
the principal axes!
Large E

4. inertial ellipsoid
molecule
nucleus

5. The nucleus is not
a simple piece of matter,
but more like a
clockwork of gyroscopes.
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6. Tilted bands contain all spins (no signature selection rule).

7. Rotational
bands in 1 1’ 2 3 4 7

8. Vacuum drives moderately toward 902 3 1’ 4 1 4 4

9. Vacuum drives strongly toward 903 1’ 2 7 1 4 7 4 7 4

10. Fixed K-approximation in CSM
Simplifying assumptions:
Comparison with calculations like for PAC.
Nice, simple, and very popular.
10/23

12. New possibility For triaxial nuclei. Principal Axis Cranking
PAC solutions
Tilted Axis Cranking
TAC or planar tilted solutions
Chiral or aplanar solutions
Doubling of states
New possibility
For triaxial nuclei.

13. Chirality It is impossible to transform one configuration
into the other by rotation.
mirror

14. mirror
mass-less particles

15. Time reversal not reflection!
15/23

17. Examples for chiral sister bands

18. Left-right tunneling
Breaking of chiral symmetry is not very strong.

19. Dynamical (Particle Rotor) calculation

20. Reflection asymmetric shapes, two reflection planes
Simplex quantum number
Parity doubling
20/23

23. Summary
The different discrete symmetries of the m.f. are manifest by different level sequences in the rotational bands.
For reflection symmetric shapes, a band has fixed parity and one has:
Rotation about a principal axis (signature selects every second I)
Rotation about an axis in a principal plane (all I)
Rotation about an axis not in a principal plane (all I, for each I a pair of states – chiral doubling)
For reflection asymmetric shapes, a band contains both parities.
If the rotational axis is normal to one of two reflection planes the bands contain all I and the levels have alternating parity.
For reflection asymmetric shapes exists 16 different symmetry types.