Nuclei are thought of as being composed of protons and neutrons. Their binding energies are computed in terms of the deficit of their masses compared to the masses of the constituent protons and neutrons. However there is a good deal of evidence that the protons and neutrons form alpha particles whenever possible.l (The nuclides which could and probably do contain an integral number of alpha particles are here called alpha nuclides.) Any additional neutrons beyond those tied up in alpha particles form pairs where possible. Therefore the binding energy of a nuclide is largely a matter of the binding energies of the subparticles (alpha particles and nucleon pairs) of which it is composed. There is an additional component of binding energy for a nuclide which comes from the arrangement of those subparticles in the nuclide. This binding energy will be referred to as excess binding energy.

When the excess binding energies are computed for the alpha nuclides and the values plotted versus the number of alpha particles in the nuclide the result is as shown below.

For the data and further detail of the alpha particle substructure of nuclides see Alpha Particle Substructure of Nuclides.

The above graph indicates a shell structure for the alpha nuclides. There is a shell of two alpha particles, then a shell of twelve and then a shell of at least eleven.

If the excess binding energies are computed for the nuclides which could contain an integral number of alpha particles plus four additional neutrons the result also shows a shell structure.

This indicates that the capacity of the third shell of alpha particles is indeed eleven.

The excess binding energy computed above took into account only the binding energy of the alpha particle substructures. The four neutrons would have binding energy of at least two neutron pairs. There is the possibility that four neutrons might form a structure of greater binding energy than that of two neutrons pairs just as the binding energy of an alpha particle is much greater than the binding energy of two proton-neutron pairs (deuterons). To investigate this possibility and others the binding energies of the alpha-plus-four-neutrons nuclides are complied along with those which contain a proton-neutron pair and another neutron pair. For comparison the effect of the addition of another alpha particle is included. These are shown below.

For a small number of alpha particles the addition of four neutrons or a p-n pair and n-n pair does not have much of an effect on binding energy. For a large number of alpha particles the case is much different.

The relevant information is the excess binding energy; the binding energy above what is accounted for by the alpha particles. This information is shown below.

The above data are shown in the following display. The red profile is for an added alpha particle. The effect of this four nucleon combination is immediately about 35 MeV and stays at that level until an alpha nuclide of 14 is reached. The effect then falls to about 31 MeV.

The yellow profile is for the effect of four additional neutrons. This effect is small for the small alpha nuclides but it quickly rises and then increases linearly with the number of alphas. The sharp rise and then smaller rise is a shell phenomenon. The linear rise indicates that the four neutron combination is interacting with each alpha particle in a shell.

The green profile is for the effect of a combination of a p-n pair and n-n pair on binding energy. The effect is small for small alpha nuclides but rises quickly to a level of 25 MeV and then increases linearly toward a level of about 40 MeV. Again the linear increase with the number of alpha particles in a shell indicates that the p-n and n-n pair combination is interacting with each of the alpha particles in a shell.

The absence of a linear rise for the effect of an additional alpha particle indicates that the alpha particles are not all interacting with each other.

The is a hump that appears in each of the profiles indicating that it is a structural feature of the nuclides.

(To be continued.)