1. The Collective Model and the Fermi Gas Model
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= , 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

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

14. 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.

15. Making the box a nucleus

16. 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.

17. Relation between Temperature and Level Density
Lang and LeCouteur
Ericson

18. What is the utility of all this?