Quantal rotation Molecules The molecular view on nuclei (Bohr-Mottelson) High spin The rotating mean field – spontaneous symmetry breaking Exotic modes of nuclear rotation Emergence of orientation Rotation in abstract spaces

Rotating objects classic Spitzer M81 quantal molecule nucleus

1. Molecules

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

HCl Microwave absorption spectrum

Centrifugal stretching Stiff bonds

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

Experimental spectrum of water

Born-Oppenheimer Approximation . Electronic motion Vibrations Rotations CO

Adiabatic approximation el rot vib

II I n=4 n=3 I 10 n=2 n=1 5 n=0 P Q R n=4 I n=3 10 P n=2 I 5 R 10 n=1 P Q R n=4 I n=3 10 P n=2 I 5 R 10 n=1 I 5 n=0

Band Spectrum

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