New magic numbers in the continent of isotopes

Abstract

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 the conclusion that protons and neutrons fill sub shells differently, because the protons tend to occupy outer shells first, while neutrons tend to occupy both outer and inner shells. Using a simple modification of Lucas’ geometrical packing scheme, new magic proton and neutron numbers were postulated for the superheavy nuclei, which matched the island of stability distribution to a large extent. These magic numbers were also tested against some nuclei in the peninsula of isotopes, and found to be relevant. Now, in consideration of a suggestion made many years ago by Linus Pauling, new magic numbers between 50 and 82 are postulated in the continent of isotopes, and compared to experimental data. These new numbers have strong support among the three elements considered by Pauling, namely Cadmium, Tin and Tellurium, and the results suggest that the range of isotopes found, their stability, and their lifetimes are strongly affected by the new magic numbers. In addition, if 58 nucleons are taken to be magic, then the double hump fission distribution for heavy isotopes may be explained semi-quantitatively.