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

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Presentation transcript:

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

discrete symmetries for reflection symmetric shapes

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

molecule inertial ellipsoid nucleus

The nucleus is not a simple piece of matter, but more like a clockwork of gyroscopes. 5/23

Tilted bands contain all spins (no signature selection rule).

Rotational bands in 11’2347

Vacuum drives moderately toward 90

1’ Vacuum drives strongly toward 90

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

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.

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

mirror mass-less particles

Time reversal not reflection! 15/23

Examples for chiral sister bands

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

Dynamical (Particle Rotor) calculation

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

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.