Nuclear Shell model, how do we know energy levels?

[UniPhysics90]

One of my 'course aims' is to be able to classify the shell model energy levels in terms of quantum numbers l and n and explain how magic numbers arise.

I'm using this to help to understand it as well as lecture notes. http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/shell.html

I know that l is the 'letter' in the energy states (s=0, p=1 etc) and n is the number (as in lowest s level is 1, second lowest 2 etc).

The energy levels are split into groups, but how are these groups actually decided? Is there some formula which predicts this? (I'm on about both the energy levels before and after spin orbit coupling)

Thanks

 

[Bloodthunder]

Quantum mechanics, solving the atom.

 

[eXorikos]

It's basically the same process as in atomic physics. In atomic physics you have all electrons moving in a central potential caused by the nucleus. This causes the different quantum levels to appear.

In nuclear physics you can do the same. It is possible to use mean field theory on all the nucleons. This means that every nucleon moves in a potential caused by all the other nucleons. Averaging this for every nucleon gives a very different, but still central, potential problem. This can be solved assuming some shapes for the potential like Woods Saxon potential or square well. Again some quantum levels appear for the nucleons. That's why it is called the nuclear shell model.

 

[UniPhysics90]

Thanks guys, I guess I'll just learn the splitting of the first few levels so I can draw the diagram if required.

 

[eXorikos]

The first levels are easily calculated using simple potential models. The larger magic number are harder, because for more nucleons the potential gets adjusted and so do the magic numbers if you use a simple harmonic oscillator for example.