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The Interaction Binding Energy
of an Alpha Particle and Nucleon Pairs

Consider a nuclide which contains α alpha particles and q neutron pairs and nothing else. Let BE(α, q) be the binding energy of this nuclide. The incremental binding energy of the q-th neutron pair is BE(α, q)−BE(α, q-1). If the incremental binding of the q-th neutron pair for α-1 alpha particles is subtracted from the one for α alpha particles the result, called the cross difference, is, according to a lemma, equal to the interaction energy of the α-th alpha particle with the q-th neutron pair. Here is the graph of the values of the incremental excess binding energies for one neutron pair.

There is a shell structure involved. The transitions at 3, 7 and 14 alpha particles correspond to 6, 14 and 28 neutrons (and protons).

The increments with respect to unit increases in the number of alpha particles in the same shell are the cross differences that correspond to the interaction binding energies of the neutron pair with the last alpha particle. There values are shown below.

The average interaction binding energy of the neutron pair with alpha particles in the second shell (5 through 7 alpha particles) is 0.82619 MeV. For the third shell (9 through 14) it is 0.65529 MeV and the fourth shell (16 through 25) 0.45382 MeV.

The corresponding graphs for a proton pair are

Remarkably there is a close correlation between the values of the interaction binding energies for the neutron pair and the proton pair. For example, for the data in the third shells

The coefficient of correlation is 0.96.

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