En física nuclear, un número mágico es un número de nucleones (ya sean protones o neutrones) de un núcleo atómico que otorgan mayor estabilidad al mismo frente a la desintegración nuclear. Los siete números mágicos más reconocidos al año 2007 son 2, 8, 20, 28, 50, 82, y 126 (sequencia A018226 en OEIS). Los núcleos atómicos que contienen tales números mágicos de nucleones tienen una media más alta de energía de enlace por nucleón comparado con lo que se había predicho, como la fórmula de la masa de Bethe-Weizsäcker y son por lo tanto más estables frente a la desintegración nuclear. En cierta medida, los números mágicos de protones se corresponden al máximo de la abundancia solar de elementos.

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In nuclear physics, a magic number is a number of nucleons (either protons or neutrons) such that they are arranged into complete shells within the atomic nucleus. The seven most widely recognized magic numbers as of 2007 are 2, 8, 20, 28, 50, 82, and 126 (sequence A018226 in the OEIS). Atomic nuclei consisting of such a magic number of nucleons have a higher average binding energy per nucleon than one would expect based upon predictions such as the semi-empirical mass formula and are hence more stable against nuclear decay. The unusual stability of isotopes having magic numbers means that transuranium elements can be created with extremely large nuclei and yet not be subject to the extremely rapid radioactive decay normally associated with high atomic numbers. Large isotopes with magic numbers of nucleons are said to exist in an island of stability. Unlike the magic numbers 2–126, which are realized in spherical nuclei, theoretical calculations predict that nuclei in the island of stability are deformed. Before this was realized, higher magic numbers, such as 184, 258, 350, and 462 (sequence A033547 in the OEIS), were predicted based on simple calculations that assumed spherical shapes: these are generated by the formula (see binomial coefficient). It is now believed that the sequence of spherical magic numbers cannot be extended in this way. Further predicted magic numbers are 114, 122, 124, and 164 for protons as well as 184, 196, 236, and 318 for neutrons.

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