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Shell model
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Shell model

In nuclear physics, the nuclear shell model is a model of the atomic nucleus. It is analogous to the atomic shell model that is more familiar to those who have studied basic physics. Recall that in the atomic shell model, the electrons populate shells, and once a shell is filled, there is a significant drop in the binding energy for the next electron added.

It is similar for the nuclear shell model. When adding nucleons (protons or neutrons) to a nucleus, there are certain points where the binding energy of the next nucleon is significantly less than the last one. This observation, that there are certain magic numberss of nucleons: 2, 8, 20, 28, 50, 82, 126 which are more tightly bound than the next higher number, that are the origin of the shell model.

Note that the shells exist for both protons and neutrons individually, so that we can speak of "magic nuclei" where one nucleon type is at a magic number, and "doubly magic nuclei", where both are. Due to some variations in orbital filling, the upper magic numbers are 126 and, speculatively, 184 for neutrons but only 114 for protons. This has a relevant role in the search of the so-called stability island. Besides, there have been found some semimagic numbers, noticeably Z=40.

In order to get these numbers, the nuclear shell model starts from an average potential with a shape something between the square well and the harmonic oscillator. To this potential a relativistic spin orbit term is added. Even so, the total perturbation does not coincide with experiment, and an empirical spin orbit coupling, named Nilsson Term, must be added with at least two or three different values of its coupling constant, depending of the nuclei being studied.

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