The common unit for cross-sections is the barn, and the vertical axis on the illustration is labeled in millibarns. The probability for absorption of an incident is expressed as an effective cross-section which is presented by the target nucleus to those incoming neutrons. The stability of those nuclei with magic numbers of neutrons makes them less likely to be excited by neutron bombardment. Part of this evidence comes from absorption cross-sections for neutrons. Part of the motivation for the shell model of nuclear structure is the existance of " magic numbers" of neutrons and protons at which the nuclei have exceptional stability, implying some kind of "closed shell". The lead-208 is doubly magic with Z=82, N=126.
The lead end products have 82 protons, a magic number, and the bismuth has 126 neutrons, also a magic number.
#The magic number series
Further evidence of the uniqueness of these numbers is the fact that the end points of all four of the natural radioactive series are nuclei which have magic numbers of either N or Z. "Magic Number" Nuclei at End of Radioactive Series It is near the peak of the binding energy curve, and therefore can be considered to be one of the end points of both nuclear fusion and fission sequences, so perhaps that is the explanation for its extraordinary abundance. It is exceeded in binding energy only by nickel-62 (the most stable nuclide) and iron-58. Iron-56 is an even-even nucleus and therefore expected to be particularly stable because of the Pauli contribution in the liquid drop model, but does not have magic numbers of either N or Z. The iron-56 is a particularly unique case, as shown by its extraordinary abundance. While the peaks in abundance for the magic number isotopes do not appear to be particularly prominent, keep in mind that the vertical scale is logaritmic. Since these nuclei are born in the maelstrom of neutrons and neutrinos in the violent outer reaches of the supernovae, one would expect a statistical advantage for those isotopes which are most stable and therefore have the smallest cross-section for the kind of scattering which would disrupt them. Our model of heavy element formation involves extraordinary processes in supernovae. The illustration examines the abundance of elements around iron and above. One indication of this stability is the enhanced abundance of isotopes which have a magic number of neutrons or protons. Shell Model of Nucleus Enhanced Abundance of Magic Number Nuclei
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