Nuclear Structure and Spin

To demonstrate the importance of the golden ratio it is assumed that protons and neutrons occur in the nucleus on three-dimensional spirals of opposite chirality, and balanced in the ratio Z/N = r, about a central point. The overall ratio for all nuclides, invariably bigger than r, means that a number of protons, equal to Z — Nt, will be left over when all neutrons are in place on the neutron spiral. These excess protons form a sheath around the central spiral region, analogous to the valence-electron mantle around the atomic core. The neutron spiral is sufficient to moderate the coulomb repulsion while the surface layer of protons enhances the attraction on the extranuclear electrons. 

By fixing the scale of mass number to proton excess at 8 1, the latter quantity is mapped on a 44 x 44 square lattice, gauged on atomic number. The isotopes of any element map on to straight lines perpendicular to OZ, with Ru on the diagonal. The relative proton excess, 1 — tN/Z, varies 

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