Previous studies established that the relationships between the incremental increases in binding energy and the total number of neutrons in a nuclide changes form at a definite set of values; i.e., 6, 8, 14, 20, 28, 50 and 82. The numbers 8, 20, 50 and 82 are traditional magic numbers for nuclides, established by examining the number of stable nuclids. The numbers 6 and 14 should undoubtably be included among those magic numbers. The traditional magic numbers also include 2 and 126. The previous studies did not reach levels of 126 neutrons because they involved the alpha nuclides, the nuclides which could contain an integral number of alpha particles. Such nuclides extend only up to the element tin which is of atomic number 50.

There is no need to limit the analysis to the alpha nuclides. Consider the case of the element polonium.

Polonium of atomic number 84 has no nuclide stable enough to have its mass measured which has fewer than 106 neutrons. At 126 neutrons the incremental increase in binding energy falls significantly. This is most likely to there being some arrangement of neutrons which can accommodate 126 neutrons and no more. Thereafter the neutrons are accommodated in a different structure which involves smaller levels of energy differences.

The data for the element Mercury confirms the special significance of 126 in terms of neutron number.

The data for Lead also confirms the magicalness of 126 as a neutron number.

There are some nuclides whose range of possible neutron numbers do not encompass 126 neutrons. Gold and Uranium are at the limits of the set of such elements.

Although this is not an exhaustive survey the evidence is clear that 126 is as much of a magic number in terms of neutron numbers as 50 and 28.