Why is the nuclear shell model build around single particle motion?

  • Thread starter wuhtzu
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Hi everyone

For the past few months I have been learning about the nucleus and the nuclear shell model.

The experimental evidence for a shell structure is overwhelming and easy to understand. It is also quite straight forward to obtain the correct shell closures (magic numbers) using a 3d spherical harmonic oscillator potential plus a spin orbit coupling.

What I do not understand is the intuitive argument for modelling the nucleus as single, independent particles in an average potential. Could other models also have led to a shell structure?

It is experimentally known that the mean free path of the nucleons in the nucleus is large compared to the spacing between individual nucleons - sometimes even comparable to the radius of the nucleus. Is this the reason?

Thank you for your thoughts and inputs.
Wuhtzu
 

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  • #2
Bill_K
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Well the surprising thing is that such a simple idea works so well. It is against intuition that a system of strongly interacting particles can be modeled rather accurately by individual particles moving in a central potential. This is why it earned the Nobel prize. Although, as I'm sure you know, some nuclear features such as electric and magnetic moments are not well predicted by this model.
 
  • #3
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What the shell model uses is a version of the mean-field approximation, often used for atomic structure and condensed-matter physics. For each particle, one averages out its interactions with the other particles.

This approximation greatly simplifies the calculations, and it can be modified to include averaged-out exchange effects and the like.
 
  • #4
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Thank you for your replies.

After thinking some more about it, what my question really is, is this:

Was the "independent single particle moving a mean field" simply the first solution/model? Because it seems like the whole problem can be solved as a n-body problem nummerically using a Hartree Fock method.

But of course, the simplicity of the single particle in an harmonic oscillator can be solved analytically and then the spin-orbit coupling could can be taken into account by small enregy corrections. An appealing idea, even if it just models the shell closures and not other features.
 

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