The conventional theory for what holds a nucleus together is based upon the assumption that all nucleons (protons and neutrons) attract each other equally. This attraction was given the name "nuclear strong force." There is no more empirical content to this name than something that holds nuclei together. It superficially explains the existence of stable nuclei, but fails to explain, among other things, why there limits to the number of protons in nuclei with various numbers of neutrons.

The nucleons in a nucleus are held together largely by their spin pairing. See Nucleus for the details on this. The material below provides estimates of the binding energy due the formation of proton-proton spin pairs and its variation with the location within the nucleus where they are formed.

Consider first the incremental binding energies of the isotopes of Tin. Tin has the greatest number of stable isotopes of any element. Those incremental binding energies are shown below.

The peaks represent the formation of a spin pair. The sharp break after 82 protons represents the filling of a shell. The difference in the sizes of the peaks before and after 82 protons shows that the binding energy due to spin pair formations is not the same at all locations in the nucleus however it could be roughly constant within a nuclear shell

The binding energy due to the formation of a spin pair can be computed as the difference in the incremental binding energy at one point and the average of the value at the two adjacent points, as shown below.

This procedure is not valid at a point where there is a change in shell.

The Nuclides with 50 Neutrons

This procedure applied to the incremental binding energies of the analogues of the Tin isotopes gives the following results.

The values are more or less constant within the 29-50 shell.

In the 29-50 shell the average increment due to proton-proton spin pair formation is 2.67 MeV with a standard deviation of 0.16 MeV. Thus the coefficient of variation is 6 percent.

The Nuclides with 82 Neutrons

The binding energy due to the formation of a proton-proton spin pair can only be estimated away from the filling of the proton shell at n=126.

The Nuclides with 26, 27 and 28 Neutrons

Conclusions

Clearly the binding energy due to the formation of a proton-proton spin pair is not independent of location. It also varies sometimes within a shell as well as between shells.

(To be contined.)