Nuclear Shell Model: Explaining Nucleon Occupancy

[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?

 

[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.

 

[Winga]

The pairing in an unfilled level can be complicated.

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

 

[Norman]

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

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

 

[Winga]

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.

Are these 4 states degenerate?

 

[Astronuc]

Some information on the shell model -
http://hyperphysics.phy-astr.gsu.edu/Hbase/nuclear/shell.html#c1

 

[Winga]

Some information on the shell model -
http://hyperphysics.phy-astr.gsu.edu/Hbase/nuclear/shell.html#c1

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.

 

[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)

 

[malawi_glenn]

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)

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

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

 

[Rade]

Perhaps this link will help see how nucleons fill shells:

http://www.lbl.gov/abc/wallchart/chapters/06/1.html

 

[malawi_glenn]

Perhaps this link will help see how nucleons fill shells:

http://www.lbl.gov/abc/wallchart/chapters/06/1.html

But one has to know how to cuople.