How do nuclei rotate? 1. The molecular picture

The classical rotor 1 2 3

Axial rotor Classical motion of J K J orbit

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

Euler angles 5/30

Quantization

The molecular rotor Axial rotor 1 2 3

K J orbit

Centrifugal stretching Stiff bonds

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

Born-Oppenheimer Approximation . Electronic motion Vibrations Rotations CO

Adiabatic approximation el rot vib

HCl Microwave absorption spectrum

Band Spectrum

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

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)

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

symmetry

20/30

No signature selection rule

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

Multipole moments of the nucleus

Reduced transition probabilities in the Unified Model

25/30

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

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

rigid irrotational

Breakdown of adiabatic approximation

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.