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The Evidence for the Formation
of Nucleon Spin Pairs in Nuclei

A previous study investigated the formation of alpha particles and deuterons (neutron-proton pairs) in nuclei by looking for extrsaordinary increases in the binding energies of nuclides when their components were completed in a sequence of addition of neutrons and protons to nuclides. Here the same procedure is applied to identify the formation of neutron pairs and proton pairs.

Neutron-Neutron Pairs

The analysis starts with the nuclides which contain only alpha particles. Their binding energies are compared with those which contain only alpha particles and one neutron. The difference gives the increase in binding energy due to one additional neutron. This arises from the interactions of that one neutron with the alpha particles. Then another neutron is added. This neutron should have the same interactions with the alpha particle as the first neutron plus it would have a strong force interaction with the first neutron. In addition there can be the formation of a neutron pair. This would show up as a substantially larger increase in binding energy for the second neutron that occurred for the first neutron.

Here is the graph of the effect of the addition of the first neutron.

The first notable thing about the display is that one neutron enhances the binding energy of the nuclide considerably, particularly in the larger nuclides. Second, the enhancement is shell dependent. Aside from the local minima at 4 and 10 alpha particles (corresponding to 8 and 20 neutrons and 8 and 20 protons) the pattern could be explained statistically by a bent line. However the effect of a second neutron is even stronger, as can be seen below.

The difference, while not constant, is still fairly uniform. Some variation with the number of alpha particles might be explained by the interaction of the second and first neutrons. The level of the difference for larger nuclides is 2+ MeV, about the level of the binding energy of a neutron-proton pair (a deuteron).

Proton Pairs

The graphs corresponding to the previous two graphs, but for protons instead of neutron are shown below.

It is notable how much smaller the effect is for a proton than for a neutron and that the effect declines for larger nuclides.

The level of the difference varies with the number of alpha particles but for large nuclides is about 2+ MeV, the same as for a neutron-proton pair.

Comparison of the Effects

In the graph below the differences in the effects of the second nucleon compared to the effects of the first nucleon are plotted.

The difference of the differences is a remarkable pattern. First of all the difference for neutrons is always greater than that for protons. Second, except for one point at the lower end of the range and three points at the upper end the values fall nearly on a straight line and the average value is about 0.5 MeV. Thus the binding energy involved with the formation of a neutron-neutron pair is about 0.5 MeV higher than for the formation of a proton-proton pair.


The evidence is that neutron-neutron pairs and proton-proton pairs are definitely formed within nuclei. The effect of the formation of proton-proton spin pair on the binding energies in nuclides in which they are formed is about the same as the binding energy of the neutron-proton pair, the deuteron, 2.2 MeV. The effect of the formation of a neutron-neutron pairs is about 0.5 MeV higher, 2.7 MeV. The impacts of the addition of a second nucleon also includes the effect of the interactions of the two nucleons with each other, and possibly some other effects.

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