The concept of magic numbers refer to a specific properties (such as stability) for only certain representatives among a distribution of species.
The concept of magic numbers (in the field of chemistry) was first recognized by inspecting the intensity of mass-spectrometric signals of rare gas cluster ions. In case a gas condenses into clusters of atoms, the number of atoms in these clusters, that form most likely, varies between a few and hundreds. However, there are peaks at specific cluster sizes, deviating from a pure statistical distribution. Therefore, it was concluded that clusters of these specific numbers of rare gas atoms dominate due to their exceptional stability. The concept was also successfully applied to explain the monodispersed occurrence of thiolate-protected gold clusters; here the outstanding stability of specific cluster sizes is connected with their respective electronic configuration.
The term magic numbers is used also in the field of nuclear physics. In this context, magic numbers often represent three-dimensional figurate numbers such as the octahedral numbers: they count the numbers of spheres in sphere packings of Platonic solids and related polyhedra.