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A New Approach to Finding Magic Numbers for Heavy and Superheavy Elements

Roger A. Rydin
Year: 2011 Pages: 6
Annals of Nuclear Energy 38: 238-242 (2011).

For at least sixty years, scientists have known that certain numbers of protons or neutrons in nuclei formed closed shells of some kind, producing additional stability to nuclei that possess these properties. The most stable nuclei, or nuclei exhibiting enhanced stability, are called doubly magic. Only recently, Lucas has explained that the magic numbers are really composites of several sub shells filling, rather than being single shells. In addition, his theory leads to a conclusion that protons and neutrons fill sub shells in a different way. This is because the protons are charged particles, and by Coulomb repulsion they try to get as far away from each other as possible, hence tending to occupy the outer regions of nuclei. Neutrons, being uncharged but possibly polarizable, tend to occupy both outer and inner shells and to possibly increase the number in an outer shell when the nuclei are heavy in a similar way to electrons filling in inner shells in the Lanthanide and Actinide series.

Using these ideas, and following a simple modification of Lucas? geometrical packing scheme, individual candidates for new magic proton numbers and new magic neutron numbers have been identified. Amazingly, these new magic numbers correspond to the experimentally identified superheavy element distribution to a very large extent, and even correspond to magic numbers suggested using very sophisticated theoretical physics methods and computations. As an added bonus, the newly suggested magic numbers correspond to the long lived Thorium and Uranium isotopes, and to the Fermium isotopes, which may help explain the shape of the Peninsula of Heavy isotopes. They also suggest going back to reassess somewhat lighter isotopes to see if some magic effects have been missed.