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The Effect of a
Neutron Pair on
the Excess Binding
Energy of Nuclides

The masses of nuclei are less than the masses of the protons and neutrons that they are composed of. These mass deficits expressed in energy units are called the binding energies for the nuclides. The binding energy for a nuclide is often represented as the energy required to disassemble the nuclide. This is a bit misleading. The nucleus may be composed of substructures, such as alpha particles. Some of the binding energy for a nuclide would then represent the binding energy involved in the creation of the substructures. The energy required to disassemble a nuclide would be only the binding energy in excess of that involved in the creation of the substructures.

Some nuclides could contain an integral number of alpha particles. Their excess binding energy is binding energy in excess of that involved in assembling the protons and neutrons into alpha particles. When the excess binding energy of these integral alpha particle nuclides is plotted versus their atomic number (number of protons) the result is as shown below.

This graph indicates that alpha particles are formed within the nucleus and they are arrayed in shells. The graph indicates that the first shell can contain only two alpha particles. The second shell can contain twelve alphas. The third can contain at least eleven alphas and work elsewhere indicates that eleven is the capacity of the third shell.

When the same sort of analysis is carried out for nuclides that could contain an integral number of alpha particle plus one neutron pair the resulting graph of the excess binding energies as a function of the atomic number is essentially the same as the previous one.

The question dealt with here is how much does the additional neutron pair enhance the binding energy of the nuclide. The graph shown below has a few interesting characteristics.

There has to be a few alpha particles before the neutron pair has a substantial effect on binding energy. The fact that the enhancement due to the neutron pair changes with the number of alpha particles indicates that the way the neutron pair fits into the arrangement of alpha particles is at the end. If the neutron pair fit into the first shell there would be no change in its effect as more alpha particles are added. The graph indicates that the effect of the neutron pair is slightly larger when the second shell is not completely full. When the third shell is being filled the enhancement for the neutron pair is less. For both the second and third shells there is a slight upward trend as the effective charge on the particles in the shells increases with the filling of the shell.

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