The binding energies of nuclides represent the interaction of all their nucleons with each other. There are two types of interactions; the formation of spin pairs and interaction through a distance-dependent strong force. The computation of the increments in binding energy due to a change in the number of neutrons or the number of protons provides some information about the binding energies involve in the separate types of interactions. Here are the computations for the nuclides with 10 protons (the isotopes of neon) and those with 10 neutrons.

A plot of the incremental binding energies is shown below.

The plot displays a piecewise linear character that is evivence of a shell structure. The sections of both curves beyond 10 appear to have approximately the same slope. Regression analyses for the 10 to 15 section of the data for the IBEn and the 10 to 18 section of the data for IBEp reveals that the slopes are not significantly different at the 95 percent level of confidence. The average of the two slope is 0.922 MeV. This is a very important bit of information. It is the average interaction energy of a neutron in the neutron shell including 10 to 15 neutrons with a proton in the proton shell including 10 to 15 protons. The individual slopes are two different estimates of the same quantity and therefore should be approximately equal.

The more general proposition is that the increments with respect to protons of the increments in binding energy with respect to neutrons is an estimate of the interactive binding energy of the last proton with the last neutron in the same order numbers of shells. Likewise the increments taken in the opposite order also gives an estimate of the interactive binding energy of the last neutron with the last proton. These increments in increments may be called cross differences. The above proposition is tested below.

The data for the increments in the incrementals are shown in the graph below.

While the cross differences are not always close the plot shows that the two patterns are essentially the same. This is the case for nuclides having 10 protons or 10 neutrons. It reveals the sawtooth (odd-even) pattern that indicates pair formation. The minimums in the range 10 to 15 are near zero. This might be a great significance.

Some of the other cases are shown below.

 

There are anomalies but overall the patterns where they overlap appear to coincide. The minimums in this case are not near zero as the previous case.

 

Again there are anomalies but overall the patterns nearly coincide. In this case the minimums are near zero.

 

Since it is hard to see the correspondence of the two values in the graph on the right only the overlap is displayed in the graph below.

Again the correspondence is quite close.

The strong force binding energy for the interaction of an individual neutron with an individual proton can be quite small and still be significant for the structure of nuclei. Suppose this strong force interactive energy between a neutron and a proton is 1/20 of a MeV. In a nucleus with 60 protons and 100 neutron there are 6000 interactions between neutrons and protons for a total interaction energy of 300 MeV. Suppose the binding energies involved in spin pair formations is 3 MeV. There are 30 proton pairs and 50 neutron pairs. These create altogether 240 MeV, a quantity less than that due to the strong force.