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More Evidence for the Substructured Model of Nuclei

Nuclei are made up of protons and neutrons, but these nucleons may combine to form substructures such as proton-neutron pairs (deuterons) or alpha particles. These substructures then may be arranged to form a nucleus. One approach to finding evidence of the formation of substructures is to look at how the binding energies of nuclides change as additional nucleons are added. The data plotted below started with nuclides which could contain only alpha particles, hereafter referred to as alpha nuclides. The binding energies for nuclides which could contain only alpha particles plus one proton were compiled. Then the binding energies for alpha nuclides plus one proton and one neutron were compiled. Likewise for the alpha nuclides plus two protons and one neutron and for the alpha nuclides plus two protons and two neutrons (which is just another alpha nuclide.) The differences of the successive combinations represent the effect of the successive additions to the nuclides.

As can be seen the addition of a proton to an alpha nuclide results in a relatively small increment in binding energy, sometimes even a decrease in binding energy. When a neutron is added to the α+1p nuclides there is a much larger increase in binding energy, presumably due to the formation of a deuteron. When another proton is added there is only a small increase in binding energy. But when the remaining component of an alpha particle is added, another neutron, there is a large increase in binding energy. Another graph could be included; the case for 0 alphas. This is shown below

The pattern for the larger nuclides is more regular than the pattern for the smaller nucllides.

In the previous graphs it is difficult to observe the influence of the number of alpha particles on the effect of the final neutron required to form an alpha particle. Here is that graph.

The pattern is very regular and shows the shell structure for the alpha particles. The sharp drops occur at 3, 7 and 14 alpha particles. These numbers correspond to the modified magic numbers of 6, 14 and 28 for neutrons and protons. Within the shells the values for the increase in binding energy are upward sloping to the right; i.e., they are increasing with the number of alpha particles.

The patterns for the effects of the other additions are shown below.

Again sharp drops occur at 3 and 7, corresponding to nuclear magic numbers of 6 and 14. The conventional nuclear magic numbers of 8 and 20 show up as the minimums at 4 and 10 alpha particles.

When a neutron is added to a nuclide with a singleton proton a deuteron can be formed. The graph of the effect on binding energy shows a significantly higher increase in binding energy than when the singleton proton was added.

When another proton is added there is an increase in binding energy but not so much as when a deuteron could be formed.

When these two effects are compared and their difference computed the result is quite interesting.

The difference of the two effects displays a definite shell type pattern; i.e., a bent line in which the incremental effect is constant over a range of values of ordinate. The binding energy of the deuteron fits in nearly perfectly with the effects over the range of 1 to 3 alpha particles. The binding energy of the deuteron of 2.22457 MeV seems to have little to do with the effect of the formation of a deuteron in larger nuclides. The effect on binding energy due to the interaction of the deuteron with the other substructures of the nuclei is quite substantial, on the order of 9 to 15 MeV.


When the components for the substructures of an alpha particle or deuteron are available in a nucleus these substructures are formed. Although a large number of alpha particles can exist in a nucleus, only one deuteron can exist because two deuterons would form an alpha particle.

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