This is a continued analysis of nuclear binding energies based the alpha particle substructure model of nuclei. This means that in a nucleus the neutrons and protons form alpha particles whenever possible. Thus the binding energy of a nuclide is made up of one part due to the formation of the alpha particles and another, called the structural binding energy, which is due to the arrangement of those alpha particles in the nucleus. The structural binding energy for a nuclide can be computed by deducting from its binding energy the binding energy due to the formation of alpha particle, which is simply the number of alpha particles times 28.29457 million electron volts (MeV), the binding energy of one alpha particle. This computed structural binding energy is positive for all 2931 nuclides except for four: Carbon 8, Boron 7, Berylium 6 and Berylium 5. Berylium 5 is the one nuclide out of 2931 which has negative binding energy.

The nuclides which could contain an integral number of alpha particles are an interesting starting point. The graph of the structural binding energies of these nuclides as a function of the number of alpha particles in the nuclide displays an interesting shape.

This form indicates a shell structure for the alpha particles of the nuclei. The graph for those nuclides which could contain an integral number of alpha particles plus one neutron or plus one proton have similar shapes. The data for the alpha nuclides plus one neutronand the alpha plus one proton nuclides are shown below.

The fact that the two relationships are diverging with increasing numbers of alpha particles indicates that the excess neutron and the excess proton are interacting with the alpha particles in the nuclei. The difference in the structural binding energies, shown below, reflects the affect of the positive charge on the potential energies of the arrangements of alpha particles.

The pattern of the differences is remarkably regular, appearing to be some quadratic function of the number of alpha particles. However the regularity is a bit deceptive. The increments in the differences show fluctuations.

The fluctuations are related to the nuclear magic numbers. The sharp drops come at 3, 9, 14, and 18 alpha particles which correspond to 6, 18, 28 and 36 in neutron/proton numbers. Six and 28 are magic numbers. The low points with subsequent large jumps are at 4, 10, 15 and 21 alpha particles, which correspond to 8, 20, 30 and 42 in terms of neutrons and protons. Eight and 20 and perhaps 42 are magic numbers, but in a different category than the main line of magic numbers.

The differences in structural binding energies for the alpha+1neutron and the alpha+1proton are due not only to the electrostatic repulsion of the one proton and the other protons in the nucleus but there is also a difference in the interactions of excess neutron and the excess proton with the other nucleons.

The increments do not appear to be asymptotically tending toward zero. Instead they appear to approach a value of about 0.4 MeV.

(To be continued.)