Why would I need to redo what has already been done. Electron scattering treats electrons as point particles, even though they have spin, and at low energies around 25 MeV their scattering shows that electrons are relatively evenly distributed around the atom. At higher energies the scattering of electrons is inconsistent with the idea of a uniformly distribution of nucleons, which is evidence for nuclear shell structure.. At even higher energies this type of penetration is used to show that protons and neutrons are not point particles, but must have structure.
In my model, nuclear H forms a shell around a central neutron core. Periodically speaking it takes time for this shell to develope, so naturally there will be a departure from the norm in the earlier elements He-B, where by time I mean the number of protons.
The model not only predicts the magic numbers mathematically, but also shows which nuclei are stable even though they don't fit into that numerology. In other words there are nuclei that show the same stability, actually more than all the rest that are not a part of that number scheme.
By mathematical , I am referring to geometry, in electromagnetic terms, and the completion of both neutron core and protonic shells. In this model, the most symmetrically complete structures are by coincidence ' magic'.
In other words, nuclear stability is a structural phenomenon, and the equations I use are structural.