# Nuclear Shell Model

1. Apr 17, 2006

### Winga

I don't know how nucleons occupy each energy level, especially the one with multiple states.

For example, 1p3/2, there are 4 states in this level, that can be occupied 4 nucleons.

If there are 2 nucleons in this level, do they must be paired-up? Why?

And if there are 3 nucleons in this level, 2 nucleons are paired and 1 nucleon is unpaired? Why?

According to Pauli exclusion principle, two fermions cannot occupy the same quantum state.
For 1p3/2, how can I assign nucleons to this state without violating this principle?

#### Attached Files:

• ###### shellmod.gif
File size:
9.7 KB
Views:
253
Last edited: Apr 17, 2006
2. Apr 17, 2006

### Meir Achuz

The number of independent spin states for spin j is (2j+1), so j=3/2 has four independent spin states. There can be 4 protons and 4 neutrons in the 1p3/2 level.
The pairing in an unfilled level can be complicated.

3. Apr 17, 2006

### Winga

This is what I wonder.

Is it the 1st one is upaired,
2nd ---> paired with the 1st one
3rd ---> unpaired
4th ---> paired with the 3rd one

4. Apr 17, 2006

### Norman

In the valence nucleon model, this is usually assumed. But when you look at some nuclei and compute the nuclear spin and parity from the valence nucleon shell model, it often times gives the incorrect answers. So there must be something more going on than the shell model is able to tell us about. Krane's book, "introductory nuclear physics" gives a good (ok decent) discussion on this model and its short comings.

Cheers,
Ryan

5. Apr 18, 2006

### Winga

Are these 4 states degenerate?

6. Apr 18, 2006

### Astronuc

Staff Emeritus
7. Apr 19, 2006

### Winga

I had read it already, but it is not detail enough.

I just wonder the nuclear spin quantum number for some NMR active elements and their isotopes, but I have a difficulty in pairing up of nucleons.

Last edited: Apr 19, 2006
8. Jan 11, 2008

### tuul

i also have same problem with use of nuclear shell to predict net spin of nuclei, for example in case of 11B(3/2) and 10B(I=3)

9. Jan 12, 2008

### malawi_glenn

You mean how to find Nuclear spins of ground state for the following nuclei: ??

$$^{\text{11}}$$B and $$^{\text{10}}$$B

10. Jan 14, 2008