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!
 
Toponium is a hadron which is the bound state of a valance top quark and a valance antitop quark. Oversimplified presentations often state that top quarks don't form hadrons, because they decay to bottom quarks extremely rapidly after they are created, leaving no time to form a hadron. And, the vast majority of the time, this is true. But, the lifetime of a top quark is only an average lifetime. Sometimes it decays faster and sometimes it decays slower. In the highly improbable case that...
I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...

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