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. 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

19. Successes of Nilsson model
Nuclide Z N
Exp.
Shell
Nilsson
19F 9 10
1/2+
5/2+
21Ne 11
3/2+
21Na
23Na 12
23Mg

20. Real World Nilsson Model

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

22. 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.

23. Making the box a nucleus

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

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

26. What is the utility of all this?