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What is an adequate way to understand this simultaneously. One has the underlying assumption that matter is saturated and has the merit of being able to come up with an accurate formula for the Binding Energy (the SEMF/Bethe-Weiszacker) and the other can explain the magic numbers by building up energy levels in a shell structure similar to atomic orbitals. However, the underlying assumptions appear to be completely contradictory. I am looking for a better perspective on how to understand these two simultaneously.

Edit: Apologies for the cheesy title.

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Although I have nothing against cheesy titles, this one winds up not being formatted all that well... not that you need to change it or anything, I'm just commenting ;-) –  David Z Apr 27 '11 at 2:21
    
@David if you have ideas feel free to edit ;) –  yayu Apr 27 '11 at 4:01
    
The right framework is called Quantum Chromodynamics, QCD. You describe a nucleus with $A$ nucleons as a bound state of $3A$ valence quarks (plus infinitely many other quarks and gluons) interacting via the strong force and creating an environment that is similar to a liquid, you take a supercomputer, and get results that may be accurate but in principle don't teach you much about the nuclei beyond the two phenomenological models. –  Luboš Motl Apr 27 '11 at 5:11
    
@Luboš Motl That clears it a lot. Thanks, as always. –  yayu Apr 28 '11 at 7:09
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Here comes an experimentalist point of view.These models are approximations of the real theoretical description of matter in aggregate,which at the moment is not a simple one.

To truly describe nuclear forces in the language of QCD , our current knowledge of the theory of strong interactions, is a formidable many body task.

In the calculational methods that exist now you would need thousands of Feynman diagrams calculated for each specific question. The models, fitted to real data, allow one to describe the behavior of nuclei and have some predictive power over it.

Qualitatively one can think of the drop model as an approximation to the continuity of force interchanges with gluon exchanges between the quarks of the nuclei within the nuclear bag. At high energies one talks of quark-gluon plasma. This is the liquid phase analogy.

The shell model works as a total approximation to a potential well, similar to the way the Bohr model worked for describing the atom. There is a collective potential well there, created by all the gluon exchanges, and it is approximated in this simplified form using data to be able to predict further data. It works.

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Thanks Anna that was insightful. –  yayu Apr 28 '11 at 7:09
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