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Lesson 6

Lesson 6. The Collective Model and the Fermi Gas Model. Evidence for Nuclear Collective Behavior. Existence of permanently deformed nuclei, giving rise to “collective excitations”, such as rotation and vibration Systematics of low lying 2+ states in many nuclei

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Lesson 6

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  1. Lesson 6 The Collective Model and the Fermi Gas Model

  2. Evidence for Nuclear Collective Behavior • Existence of permanently deformed nuclei, giving rise to “collective excitations”, such as rotation and vibration • Systematics of low lying 2+ states in many nuclei • Large transition probabilities for 2+0+ transitions in deformed nuclei • Existence of giant multipole excitations in nuclei

  3. Deformed Nuclei • Which nuclei? A=150-190, A>220 • What shapes?

  4. How do we describe these shapes?

  5. Rotational Excitations • Basic picture is that of a rigid rotor

  6. Are nuclei rigid rotors? • No, irrotational rigid

  7. Backbending

  8. Rotations in Odd A nuclei • The formula on the previous slide dealt with rotational excitations in e-e nuclei. • What about odd A nuclei? • Here one has the complication of coupling the angular momentum of the rotational motion and the angular momentum of the odd nucleon.

  9. Rotations in Odd A nuclei (cont.) For K  1/2 I=K, K+1, K+2, ... For K=1/2 I=1/2, 3/2, 5/2, ...

  10. Nuclear Vibrations • In analogy to molecules, if we have rotations, then we should also consider vibrational states • How do we describe them? • Most nuclei are spherical, so we base our description on vibrations of a sphere.

  11. Shapes of nuclei shaded areas are deformed nuclei Types of vibrations of spherical nuclei

  12. Formal description of vibrations Suppose =0 Suppose =1 Suppose =2

  13. Nuclear Vibrations

  14. Levels resulting from these motions

  15. You can build rotational levels on these vibrational levels

  16. Net Result

  17. Nilsson model • Build a shell model on a deformed h.o. potential instead of a spherical potential Superdeformed nuclei Hyperdeformed nuclei

  18. Successes of Nilsson model

  19. Real World Nilsson Model

  20. Fermi Gas Model • Treat the nucleus as a gas of non-interacting fermions • Suitable for predicting the properties of highly excited nuclei

  21. Details Consider a box with dimensions Lx,Ly,Lz in which particle states are characterized by their quantum numbers, nx,ny,nz. Change our descriptive coordinates to px,py,pz, or their wavenumbers kx,ky,kz where ki=ni/Li=pi/ The highest occupied level Fermi level.

  22. Making the box a nucleus

  23. Thermodynamics of a Fermi gas • Start with the Boltzmann equation S=kBln • Applying it to nuclei

  24. Relation between Temperature and Level Density • Lang and LeCouteur • Ericson

  25. What is the utility of all this?

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