In an atomic nucleus, protons and neutrons, collectively called nucleons, are bound together by nuclear forces. These forces describe the interactions between nucleons, which cause them to occupy states grouped in shells, where each shell has a different energy and can host a certain number of nucleons. A nucleus is said to be magic when the neutron or protons happen to exactly fill up their respective shells up to the rim. Such magic nuclei are especially well bound and have properties that make them stand out. In fact, the variation of the properties of nuclei with nucleon number led to the formulation of the celebrated nuclear shell model some 70 years ago, with its magic numbers 2, 8, 20, 28, 50, 82 and 126, which has had spectacular success in describing many of the properties of the stable nuclei that make up the world around us.
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Source: Phys.org