The force that holds the nucleons inside the atomic nucleus, the strong nuclear force, puzzled physicists since the neutron was found, back in the 1930s. The potential of the force between nucleons relative to the distance between them is quite known and the graph looks like the figure below [1, page 97].
This kind of graph implies that there are two forces between the nucleons – attraction force whose intensity decreases faster than that of the electromagnetic force while distance increases. Furthermore, this attractive force decreases relatively slower than another force, the repulsion force between the nucleons.
But what causes the attraction force and what causes the repulsion force between the nucleons?
The search for an answer to these two questions continues until today. Let’s discuss the issue and the behavior of the physicist community that cannot provide answers and hardly admits that such a fundamental question was not solved for almost 80 years now.
The search for the foundations of the attraction force between the nucleons
The Japanese physicist Yukawa was the first to provide a theory which explains this force, back then in 1935. During the 1930s not much was known about the structure of the nucleons and Yukawa was looking for an attraction force which decreases faster than the electromagnetic forces. He assumed that the proton and the neutron are elementary spin 1/2 particles and invented a new particle, the Yukawa particle, which is an elementary particle with no electric charge which carries the strong nuclear force. He also predicted that the mass of the Yukawa particle would be nearly 100 MeV.
The particle π0 was found in 1947 and scientists thought that this is the Yukawa particle. Its mass is 135 MeV, rather close to Yukawa’s prediction. But in the 1960s, when scientists understood that the nucleons and the pions, including π0, are not elementary and actually composed of quarks, the theory of Yukawa was no longer coherent. Yukawa’s theoretical foundation assumed that π0 is elementary and the theoretical structure of Yukawa collapsed.
Comay recalls that when he was a student during the 1960s his professor was asked by the students why he taught Yukawa theory although it is known that its theoretical foundation is erroneous. The professor promised his students that soon, after we will know more about the quarks, a new and coherent nuclear theory would replace the Yukawa particle. Isn’t it amazing that today, 45 years later, we are still waiting for such a theory?
In the 1970s, after the quarks were confirmed and QCD became the dominant theory, scientists believed that the strong nuclear force is just a residual force which is implied by the strong forces between the quarks in the nucleons. They were looking for a mechanism which can produce such forces, like the van der Waals force between molecules which is produced as a residual force of the electromagnetic forces between the nucleus and the electrons inside molecules. But such mechanism was not found, and in fact, Wong even claimed that such mechanism cannot be obtained from QCD [1, page 102].
But textbooks prefer not to say that they do not have a clue regarding how this force is obtained. It is amazing and amusing to see how this issue is taught today. In Wikipedia, for example, the Yukawa theory is still alive with π0 as the force carrier, and it is claimed that this force is residual. The concept of residual force clearly contradicts Yukawa theory, but this doesn’t seem to bother the authors. The authors even put a nice animation that demonstrates how the attraction force works…
There is no hint in this Wikipedia topic that this force is still unexplained.
The repulsion force
The roots of the repulsion force between the nucleons are also not understood. Before QCD was invented and after the quarks were confirmed, physicists assumed that Pauli exclusion principle that works between the quarks is responsible to the repulsion force between two nucleons, for example the proton and the neutron in the deuteron (the nucleus of heavy hydrogen).
However, after QCD was accepted and the colors were invented, Pauli exclusion principle could not explain the repulsion force any more. The proton (uud) and the neutron (udd) have 3 u quarks and 3 d quarks together, and in a world with 3 colors they can easily live in the same space. Why they do not do that? The density of the nucleons inside atomic nuclei is almost constant, and this must be a consequence of a very strong repulsion force between the nucleons. What produces this repulsion force?
This contradiction between Pauli exclusion principle, the colors and the state of the deuteron (and other atomic nuclei) is not taught as a fundamental problem, although some physicists are aware of that problem, and sometimes they even talk about it in their forums. The comment below was taken from a discussion regarding the nuclear force in the deuteron:
“… In the end it should come from some fundamental computations in QCD. Maybe it does, but I am not aware of any published work on that. (I hope I am wrong, I will be the first to check and read it, if it exists.) Worse yet, there are no QCD calculations that I know of which explains why there are no six quark color singlet states. Of course, one might consider Deutorium a six quark color singlet, but it does not cut the muster. Because it is not really a six quark color singlet; it is a bound state of two more-or-less spatially separated three-quark color singlets…”
The existence of 6 strongly bound quarks, the dibaryon, was even predicted by Jaffe in 1977 , but the search after such particle failed to find it.
In 2007, Frank Wilczek published a paper that summarizes this problem loud and clear :
“Ironically, from the perspective of QCD, the foundations of nuclear physics appear distinctly unsound.” He continues by explaining what the contradiction is: “Yet QCD tells us that protons and neutrons are themselves built from quarks and gluons that move at very nearly the speed of light. These more basic particles carry colour charges, leading to the additional requirement that they be confined within ’bags’ whose contents are overall colour-neutral.” And he further asks: “But why don’t the separate proton and neutron bags in a complex nucleus merge into one common bag? On the face of it, the one-bag arrangement has a lot going for it. It would allow quarks and gluons free access to a larger region of space, and so save on the energetic cost of localizing their quantum-mechanical wave functions. But in such a merger, protons and neutrons would lose their individual identities, and our traditional, quite successful model of atomic nuclei would crumble. What prevents that calamity?”
Suddenly it seems that Wilczek didn’t feel too confident with QCD for more than 30 years! Why did he wait so long with this confession?
Wilczek provided this statement in the context of Ishii et al paper about the strong nuclear forces and lattice QCD. He continued and expressed the hope that the ideas in this paper would finally solve this built-in contradiction.
We already discussed one aspect of Ishii’s paper in the previous post, and here I will discuss another important flaw in Ishii et al paper. First, the attraction forces in this paper are produced by pions. The authors use again the Yukawa theory which does not have coherent theoretical ground for force carrying particles which are not elementary. Second, the repulsion forces are caused in this paper by vector mesons. Vector mesons, like pions, are not elementary and their usage as repulsive force carriers suffers from the same problem as that of the pions.
Never look back
In Comay model, the strong nuclear force can be explained in few minutes to anyone who is ready to listen.
But particle physicists, so it seems, prefer to invent new theories without coherent theoretical basis, and never look back whether they ever did something wrong. They will take contradicting theories like QCD and Yukawa and add another groundless idea like repulsion forces which are carried by vector meson. Religious people never put their beliefs under scientific examination. But scientists must do that, especially when their leading theory fails to explain so many fundamental phenomena.
 S. S. M. Wong, Introductory Nuclear Physics (Wiley, New York, 1998).
 R.L. Jaffe, Perhaps a Stable Dihyperon? Physical Review Letters 38 195, (1977)
 Frank Wilczek, Hard-core revelations, Nature, Vol 445, 156 (2007)