The conventional theory of what holds a nucleus together is based upon the assumption that all nucleons (neutrons and protons) 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 neutrons in nuclei with various numbers of protons.

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 neutron-neutron 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 neutrons represents the filling of a shell. The difference in the sizes of the peaks before and after 82 neutrons 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.

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

The values are more or less constant within the 51-82 shell, but definitely drop for the 83-126 shell.

In the 51-82 shell the average increment due to neutron-neutron spin pair formation is 2.63 MeV with a standard deviation of 0.161 MeV. Thus the coefficient of variation is 6.1 percent.

To see how the binding energy increments due to neutron-neutron spin pair formation are affected by the number of protons in the nucleus the values were calculated also for p=49 and p=51.

Here are the data plotted.

Clearly there is something special about the case of p=50. Its values are higher than those for p=49 and p=51.

Lead

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

Gold

The Magnetic Metals
Iron, Cobalt and Nick

The binding energy due to spin pair formation is roughly constant within shells but if affected by the proton number.

Conclusions

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

The relationships are "continuous" in the sense that the changess from one step to the next are relatively small.

(To be contined.)