San José State University
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The Incremental Binding Energy Relationships Among Nuclides
Consisting of only Alpha Modules and Proton Spin Pairs

Among the nearly three thousand nuclides whose binding energies have been determined there are 696 which consist of only alpha modules and neutron spin pairs. On the other hand there are only 42 that consist only of alpha modules and proton spin pairs. Alpha modules are on balance protonic in their nucleonic charge and therefore neutron spin pairs are attracted to them, but proton spin pairs should be repelled. Therefore it is surprising that there is even one nuclide with only alpha modules and proton spin pairs. This page is an investigation of the binding energies of those 42 nuclides.

The 42 were first sorted by their number of alpha modules and then their number of proton spin paCirs. The surprise is that there are for most numbers of alpha modules exactly three cases of different numbers of proton spin pairs; zero, one and two. The incremental binding energies of the proton spin pairs were computed and they are tabulated below.

The Incremental Binding Energy of Proton
Spin Pairs in Nuclides Consisting of only
Alpha Modules and Proton Spin Pairs
Number of Proton Spin Pairs
Number of
Alpha Modules
1 2
1 -2.142
2 -1.7715
3 -1.40823
4 2.3165 -0.02
5 3.4264 -0.604
6 3.364 -1.41
7 2.695 -0.78
8 2.639 -0.96
9 1.368 -0.29
10 2.995 0.3
11 3.215 0.31
12 2.76 -1.56
13 1.15 -2.8
14 0.05

The surprise is the relatively large positive values for the first proton spin pair and the relatively small positve and negative values for the second proton spin pair. The positive values indicate some sort of attraction between the proton spin pair and the alpha modules. The graph below shows the relationships better.

There appears to be a repulsion of a proton spin pair by the alpha modules up to and including thee and then an attraction for nuclides containing four through twelve which drops off rapidly for the nuclides with 13 and 14 alpha modules. For the second proton spin pair the effect seems to be a small repulsion up to and including the eleventh alpha module and thereafter a strong repulsion.

The phenomenon of a particle combining with a combination for which there is a net repulsion is reminiscent of negative ions. An oxygen ion with one electron, O, is able to acquire another electron and become O−−.

To put things into perspective the corresponding data for neutron spin pairs are plotted in the graph along with those for proton spin pairs.

The effect of one proton spin pair on binding energy is almost one order of magnitude smaller than the effect of one neutron spin pair. However, the incremental binding energy of a particle is due to its interactions with with all of particles in the nuclide and more over it included the binding energy associated with the formation of a composite particle. Call this the intrinsic binding energy of the particle. The cross differences of binding energy with respect to the numbers of a nucleon spin pair and the number of alpha modules provide an estimate of the interaction of a spin pair of that type with an alpha module and it eliminates the intrinsic binding energies of the the interacting particles. The estimates of the interaction binding energies are shown below.

Except where the number of nucleons is near 8, 20 or 28 (conventional magic numbers) the interaction of a neutron spin pair with an alpha module is positive, indicating an attraction, and the interaction of a proton spin pair with an alpha module is negative, indicating a repulsion.


The data is consistent with proton spin pairs being repelled from alpha modules and neutron spin pairs being attracted. If the nucleonic charge of a neutron is opposite in sign and smaller in magnitude than that of a proton then an alpha module is on balance protonic in nucleonic charge. Thus a neutron spin pair being attrracted to an alpha module and a proton spin pair being repelled is consistent with like nucleons being repelled from each other and unlike ones attracted

(To be continued.)

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