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Exploring Nuclear Collective Behavior: Deformed Nuclei and Fermi Gas Model

Learn about collective excitations in nuclei, deformed shapes, rotational vibrations, Fermi gas model, and Fermi level in a thermodynamic context. Discover the dynamics of highly excited nuclei.

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Exploring Nuclear Collective Behavior: Deformed Nuclei and Fermi Gas Model

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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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