After I developed rigorous empirical proof that the strong force between neutrons is repulsion and likewise for protons I wanted to find the basis, if any, for the conventional view that both protons and neutrons are subject to an attractionl for all combinations.

Howard Georgi's comments in his book Lie Algebras in Particle Physics are typical

A lot of physics can be explained by the simple assumption that the strong force between nucleons is independent of particle type -- that it is the same for PP, PN and NN.

Suppose we could turn off the EM and the weak interaction and at the same time eliminate the small mass difference between P and N, then look at any nucleus. If we could take out any N and replace it with a P, all the forces are the same so we ought to get a state with the same energy. Right? Almost but not quite, because the N's are identical particles, so we have to sum over all possible replacements, N→P.

First note that the strong force attractions between all nucleons is an assumption. Second, it is an assumption that is not expected to be exactly verified. Therefore it cannot be falsified by any comparison of the energies of nuclides differing by only a change of one proton into a neutron.

The nuclear binding energies can be taken to be the negative of potential energy. Suppose a graph is constructeds giving binding energy of all nuclides having a fixed sum for the numberof neutrons and protons plotted versus the number of neutrons. What Georgi is conjecturing is that the graph would look the one below.

What such a graph using empirical data actually looks like is:

A portion of the graph is essentially flat as Georgi conjectures. It is near the maximum. For comparisons near the maximum it would be true that the replacement of a proton with a neutron would not effect the value of the binding energy. But this flat place at the maximum is achieved even for the case that neutrons repel other neutrons and protons repel other protons while neutrons attract protons.

The nuclides with the maximum binding energy are the most stable and the also the most common. Thus the nuclides near the maximum are most likely to be the ones investigated andl give a false confirmation of the conjecture of Georgi.

(To be continued.)