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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. Nuclear Vibrations Types of vibrations

  9. Levels resulting from these motions

  10. You can build rotational levels on these vibrational levels

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

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

  13. 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 The highest occupied level Fermi level.

  14. Making the box a nucleus

  15. Thermodynamics of a Fermi gas • Start with the Boltzmann equation S=kBln • Applying it to nuclei • The evaluation of this expression requires some detailed considerations of the • statistical thermodynamics of the system, which are outlined in the book.

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

  17. What is the utility of all this?

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