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
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
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
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 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
Electromagnetic Transitions Emitted photon has multipolarity E1, E2, E2, ... or M1, M2, ... Multipole moments of the nucleus
Reduced transition probabilities in the Unified Model
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 motion 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.