A When to use collective and when shell model?

Malamala
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I am sorry if this is a silly question, but I am confused about it. When do I use a model over the other? I understand how they work separately, but I didn't understand from my readings when I should use one over the other and why. And when I look at an actual level scheme of a nucleus (for example this one, but any other would do just fine), how do I know what kind of excitation is it? Is it a nucleon jumping in a different shell, is it a rotational/vibrational excitation? Are the rotational/vibrational excitations built on top of shell model energies (similar to vibrational/rotational states on top of electronic ones in a molecule) or they are completely different (i.e. different pictures)? I am really lost and any help would be greatly appreciated. Thank you!
 
Thread 'Why is there such a difference between the total cross-section data? (simulation vs. experiment)'
Well, I'm simulating a neutron-proton scattering phase shift. The equation that I solve numerically is the Phase function method and is $$ \frac{d}{dr}[\delta_{i+1}] = \frac{2\mu}{\hbar^2}\frac{V(r)}{k^2}\sin(kr + \delta_i)$$ ##\delta_i## is the phase shift for triplet and singlet state, ##\mu## is the reduced mass for neutron-proton, ##k=\sqrt{2\mu E_{cm}/\hbar^2}## is the wave number and ##V(r)## is the potential of interaction like Yukawa, Wood-Saxon, Square well potential, etc. I first...

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