When a neutron pair or a neutron-proton pair is added to an alpha nuclide there is a significant increase in binding energy. The patterns of the increases are quite different, as shown below.

The effect of an additional neutron pair is shown as the red squares and that of a neutron-proton pair is given by the upper edge of the yellow area. Both curves rapidly rise from the near-zero level to a level of about 13 MeV. Thereafter the effect of the neutron-proton pair is nearly constant; if anything it declines slightly. In contrast, the effect of the neutron pair rises with the number of alpha particles (or the number of neutrons or protons). This is as it should be because the effect on binding energy comes from the interaction of the neutron pair with the other particles in the nucleus. The more other particles the greater the interaction due to the attractive nuclear force.

The neutron-proton pair is subject to the same interaction involving the nuclear force, but some of this attraction is counterbalanced by the electrostatic repulsion between the protons in the nucleus. The net force depends upon the separation distance between the protons. As shown below the potential for proton interactions is negative and the force strongly attractive over a range of small separation distances. For large separation distances the potential is positive and the force repulsive. In between there is a range in which the force is near-zero while the potential is positive.

The effects of the nucleon pairs displays a shell pattern that is essentially the same for both types. The first shell contains four alpha particles and hence eight neutrons and eight protons. The binding energy rises up to three alpha particles and then drops back as the shell is completely filled. The second shell contains the fifth through tenth alpha particle. The binding energy rises up to the ninth and drops back as the second shell is completely filled. The ten alpha particles contain 20 neutrons and 20 protons. Twenty is a nuclear magic number.

The third shell contains the eleventh through the fourteenth alpha particle. Again the effect of the nucleon pair drops as the shell is completely filled. Fourteen alpha particles contain 28 neutrons and 28 protons. Twenty eight is also a magic number. After the level of 14 alpha particles the pattern is approximately linear. There is a plateau for the nineteenth through twenty first alpha particles, which corresponds to 38 to 42 of each of the nucleons. To demonstrate that the patterns for both pair type have the same jogs it is only necessary to look at their differences, which are shown below.

The pattern for the effect of proton pairs looks quite different overall from the other two types of nucleon pairs but it has jogs at the same critical points.

The downward slope of the pattern for proton pairs indicates that the separation distances involved in the nucleus are in the range where the force between protons is definitely repulsive.

The effects of the three types of pairs is not much different for the first shell. It is only for the second and higher shells that the effects differ. This probably means that the pairs are located such that the separation distances of the pairs from the particles in the first shell are small enough that the nuclear force is dominant for the neutron-proton pair and the proton pair. This would be the case if the additional nucleon pair is located inside of the first shell. It could be that the both types of nucleon pairs are located at the otherwise empty center of mass of the nucleus. The second and higher shells are sufficiently far from the additional nucleon pairs that the repulsive electrostatic force on the protons effectively cancels the attractive nuclear force.

The pattern of the upward and downward shifts is the same for a;; three types of pairs. The patterns differ only in the slopes of the relationships. This is seen by displaying the difference in the effect for a neutron pair and a proton pair, as shown below.

Here are the results of the regression.

The goodness of fit of the regression equation can be seen in the following graphs in which the data are plotted as red squares and the regression estimate as the upper edge of the yellow area.

(To be continued.)