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2. The molecular view on nuclei 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
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
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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 (superfluid He droplets) “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. Nuclear flow pattern is dominated by quantal effects. Microscopic theory needed for calculating them.
3. High Spin
Coincidence measurements select rotational bands.
Stability against fission Homogenously charged droplet
fission instable fission barrier 8MeV
Rotational bands in 5/17
Semiclassics High angular momentum can be treated as a classical quantity For uniform rotation the rotational frequency (angular velocity) is given by the classical relation
Experimental rotational frequency
M1 radiation intensity also well described by classical radiation theory E2 radiation
Angular momentum, moment of inertia and routhians as functions of the frequency Long bands permit us to derive the classical functions
Includes a quantal correction Zero point fluctuation I I+1/2 10/17
M1 radiation - high spin limit K J
Rotational bands in the non-adiabatic regime How are the spectral lines arranged into bands?
Rotational bands in
band EAB band E bandcrossing
Summary Nuclei can be studied at high spin where intrinsic and rotational motion are on the same time scale. The levels still organize into rotational bands, the states of which are connected by fast electromagnetic transitions. Bands cross each other. High spin allows us to use classical concepts for the rotational degree of freedom. The angular velocity becomes a well defined concept. It is very useful to study physical quantities as functions of the angular frequency.