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20/30. Most nuclei have a deformed axial shape. Unified Model (Bohr and Mottelson):. 2. The molecular view on nuclei. The nucleus rotates as a whole. (collective degrees of freedom). The nucleons move independently inside the deformed potential (intrinsic degrees of freedom).

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20/30

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  1. 20/30

  2. Most nuclei have a deformed axial shape. Unified Model (Bohr and Mottelson): 2. The molecular view on nuclei 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)

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

  4. symmetry

  5. No signature selection rule

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

  7. Multipole moments of the nucleus

  8. Reduced transition probabilities in the Unified Model

  9. 25/30

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

  11. Ideal (superfluid He droplets) “irrotational flow” moment of inertia viscous More like a liquid, but what kind of?

  12. rigid irrotational

  13. Breakdown of adiabatic approximation

  14. 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.

  15. 3. High Spin

  16. Coincidence measurements select rotational bands.

  17. Homogenously charged droplet Stability against fission

  18. fission instable fission barrier 8MeV

  19. Rotational bands in 5/17

  20. High angular momentum can be treated as a classical quantity Semiclassics For uniform rotation the rotational frequency (angular velocity) is given by the classical relation

  21. Experimental rotational frequency

  22. E2 radiation M1 radiation intensity also well described by classical radiation theory

  23. Angular momentum, moment of inertia and routhians as functions of the frequency Long bands permit us to derive the classical functions

  24. Includes a quantal correction I+1/2 Zero point fluctuation I 10/17

  25. M1 radiation - high spin limit K J

  26. Rotational bands in the non-adiabatic regime How are the spectral lines arranged into bands?

  27. Rotational bands in

  28. band EAB band E bandcrossing

  29. Summary • Nuclei can be studied at high spinwhere 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.

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