In the late19th century the first subatomic particle was identified. It was named electron after the Greek word for amber, the substance used to create static electricity when rubbed. That static electricity had been deemed negative. Physicists knew there also had to be a counterbalancing source of positive charge. At first it was believed, at least in Britain, that matter consisted of negatively charged electrons in a general background of positive charge. This was known as the plum pudding model of matter.

In the early years of the 20th century through the brilliant work of Ernest Rutherford it was established that the positive charge of an atoms is located in a tiny central portion which was called its nucleus, from the Greek word for kernel. Later it was observed that the positive charge in a nucleus was concentrated in particles, subsequently named protons. These protons should have been repelled from each other through the electrostatic force. Since most nuclei do hold together it seemed reasonable to hypothesize another force acting between protons that was stronger than the electrostatic force, at least at small distances. It required a distance dependence that had not elsewhere been observed. But basically the nuclear strong force was just giving a name to what holds nuclei together.

About 1930 it was discovered that nuclei generally contained neutral particles, neutrons, along with protons Without much justification it was further hypothesized that this strong force of attraction also acted between neutrons and between neutrons and protons. As it turns out this was wrong, a bunder, as will be shown later. There are thus two parts to the conventional nuclear strong force hypothesis; i.e., that there is an attraction between protons which is stronger at short distances than the electrostatic repulsion and weaker at large distances AND that that attractive force also prevails between neutrons and between neutrons and protons.

Then a false syllogism, all too prevalent in science, was applied

False Syllogism

Proposition A implies Proposition B
Proposition B is true
Therefore Proposition A is true

To draw that conclusion it would have to be established that Proposition B is true only if Proposition A is true, which is a much stronger proposition than what is used in the false syllogism. The usual procedure is that the truth of a Proposition B is noted then a search is carried out to find a Proposition A which implies it. When one is found the search stops and the truth of the Proposition A found is declared and cited in science books including text books for students. All that is legitimately justified is a statement that Proposition A, if true, would account for the truth of Proposition B.

The intellectual situation was made much worse by the elevation of the supposed nuclear strong force to the status of one of the four fundamental forces of the Universe. How could it not be right? So for about ninety years when physicists are asked what holds nuclei together they answer solemnly, in as deep of a voice as possible, "The nuclear strong force." But this is really only an answer to what could hold a nucleus together.

There is however an alternate explanation for the structure of nuclei and it is based upon extensive quantitative empirical evidence. In contrast the conventional theory is based upon nothing more than the qualitative evidence of the existence of stable nuclei.

The empirical evidence from which the alternate explanation arises is the binding energies of 2931 nuclides. The masses of all nuclei are less than the masses of the neutrons and protons (nucleons) that make them up. The difference for a nuclide is called its mass deficit. The mass deficit of a nuclide expressed in energy units is called its binding energy. The binding energy behaves like the loss of potential energy which occurs when the nucleons come together to form a nucleus and it is part of the energy that must be supplied to break a nucleus up into its constituent nucleons.

The incremental binding energy of a neutron for a particular nuclide is its first difference in binding energy with respect to the number of its neutrons; i.e., the binding energy of a nuclide less the binding energy of a nuclide having one less neutron. The incremental binding energy of a proton is defined similarly. These incremental binding energies reveal important aspects of nuclear structure. The second differences (the differences in the incremental differences) reveal the force between the last two nucleons added to the nuclide.

Here is an example of the relationship between incremental binding energy of neutrons (IBEn) and the number of neutrons in the nuclide.

The odd-even fluctuation is evidence of the formation of neutron spin pairs. Its regularity is evidence of the exclusivity of neutron spin pair formation. A neutron can form a spin pair with only one proton and with only one other neutron. More details are given in What holds a nucleus together? and Equations of Nuclear Structure.

The sharp drop in IBEn after 50 occurs because a neutron shell is filled at 50 neutrons and additional neutrons have to go into a higher shell. The filled-shell numbers are known as nuclear magic numbers.

The same effects on binding energy occur for proton-proton spin pair formation.

The effect of neutron-proton spin pairs is revealed by a sharp drop in incremental binding energy after the point where the numbers of neutrons and protons are equal.

Here are the graphs for the cases of the isotopes of Chromium (proton number 24) and Krypton (proton number 36).

As shown above, there is a sharp drop in incremental binding energy when the number of neutrons exceeds the proton numbers of 24 and 36. This illustrates that when a neutron is added there is a neutron-proton spin pair formed as long as there is an unpaired proton available and none after that. Furthermore this illustrates the exclusivity of neutron-proton spin pair formation. It also shows that a neutron-proton spin pair is formed at the same time that a neutron-neutron spin pair is formed.

The Nature of the Spin Pairing of Nucleons

There is some doubt that spin pairing involves anything in the nature of a force. There is no evidence of a force field being involved. Spin pairing seems to involve something more in the nature of a linkage with fixed separation distance and no distance dependence.

The alternate possibility is that the spinning nucleons create magnetic fields.

A neutron, although charge neutral, also creates a magnetic field because its negative charge is located at a greater distance from its spin axis than its positive charge.

The magnetic fields of two spinning protons can link them together. The question is whether the spatial arrangement is end-to-end, as shown below,

or side-by-side, as below

There is a concentration of the magnetic lines of force that link them together pole-to-pole either side-by-side or end-to-end. .

The Force Due to Nucleonic Interaction

There is however another force that is not exclusive and is distance dependent. It corresponds very roughly to what is called the nuclear strong force but differs from that hypothetical phenomenon in essential ways and would be more appropriately called the interactive nucleonic force, the force between nucleons.

The Interactions of Nucleons
through the Interactive Nucleonic Force

• The most important result of the analysis of incremental binding energy is that through the interactive nucleonic force like nucleons repel each other and unlike attract. It is found that the increments in the incremental binding energies are related to the interactions of the nucleons. (From here on the units of analysis are the spin pairs to eliminate the distraction of the odd-even fluctuation due to spin pair formation.)

  If the incremental binding energy of neutron pairs increases as the number of proton pairs in the nuclide increases then that is evidence that a neutron pair and a proton pair are attracted to each other.

  

  If the incremental binding energy of neutron pairs decreases as the number of neutron pairs in the nuclide increases then it is evidence that the interaction of a neutron pair and another neutron pair is due to repulsion. That is to say, neutron pairs are repelled by each other.

  

  The same effect occurs for proton pairs.

  

  The downward slope of the relationship to the right is evidence that protons are repelled from each other not only through the electrostatic force but also through the interactive nucleonic force.

  The above graphs are just illustrations but exhaustive displays are available at neutrons and protons that like-nucleons are repelled from each other and unlike attracted..

  The determination of whether nucleon type x (proton or neutron) is attracted, repelled or neutral toward nucleon type y involves the computation of the incremental binding energies of x's (IBEx) for nuclides in the same shell. Those IBEx's are then plotted versus the number of y's in the nuc‬lides. The result is a nearly straight line. If the slope of that line is positive then an x and a y are attracted to each other. If it is negative they are repelled. If they were neutral the slope would be zero. (This never happens.) The distribution of slopes is bimodal; i.e., definitely positive or definitely negative.

  There is something that is akin to a neutral effect. This is when the neutron number just exceeds the proton number. The decline in the IBEn due to the nonformation of a neutron-proton spin pair almost exactly balances the IBEn due to the formation of another neutron-neutron spin pair.

The thought occurs as to whether the force involved in spin pairing might be what conventional theory refers to as the nuclear strong force. The problem with that is that spin pairing occurs only in a special way. One neutron can pair with one proton and with one other neutron. All other forces, such as the electrostatic, magnet and gravitational forces, are not particle exclusive; i.e., they interact with all other particles having the same type of charge. This is inherent in the concept of a force; that a field is produced which the other particles interact with.

But suppose the spin pairing is called the interactive nucleonic force as an alternative nuclear strong force. Then there is the problem that another force is involved in the physics of nuclei. That force cannot be the weak force which is 10⁻¹³ times less powerful than the electrostatic force. This other force is about one fifth the magnitude of the spin pairing force and comparable in magnitude at nuclear distances to the electrostatic force between charged particles.

There is much more to the analysis but what is given here illustrates that much more is involved in nuclear structure than simply giving a name to what holds a nucleus together as the nuclear strong force, particularly since that speculative hypothesis may well be flat wrong.

The alternate hypothesis lends itself to a regression model which explains 99.995 percent of the variation in the nearly three thousand measured observations on nuclear binding energies and all of the regression coefficients are of the right sign and relative magnitude. In contrast in the regression model based upon the conventional model all but one of the regression coeficients are of the wrong sign or the relative magnitude.

As stated previously, more details are given in What holds a nucleus together? and Equations of Nuclear Structure.

Thus there is an alternate hypothesis that explains everything that the nuclear strong force correctly explains without implying the false predictions that the conventional nuclear strong force hypothesis implies. It is that the nucleons of a nucleus link together through spin pairing into chains involving modules of the form -neutron-proton-proton-neutron- or equivalently proton-neutron-neutron-proton-. These chains can close forming rings A shell in a nucleus consists of a ring of nucleon modules. Here is a schematic depiction for the third shell of Silicon 28. There are two inner shells. The first one consists of two protons and two neutrons in a closed chain module of the form -n-p-p-n- (or, equivalently -p-n-n-p-). This is equivalent to an alpha particle (He 4 nucleus). Thus such chain modules can be appropriately called alpha modules.

The second shell consists of four protons and four neutrons in the form of two alpha modules.

The third shell depicted below has red dots representing protons and the black ones neutrons. The lines between the dots represent spin pair bonds.

Such rings can rotate in four modes: 1. As a vortex ring (a smoke ring), 2. As a wheel, 3. As a flipped coin, 4. As a flipped coin about an axis perpendicular to the axis for 3.

For the above depiction of third shell rotation as a vortex ring would involve all of the proton-neutron spin pairs rotating in unison about the midpoint between the proton and the neutron.

In order to depict the other modes of rotation let the ring of spin pairs be depicted as a torus.

The above animation shows the different modes of rotation occurring sequentially but physically they occur simultaneously. (The pattern on the torus ring is just to allow the wheel-like rotation to be observed.)

Aage Bohr and Dan Mottleson found that the angular momentum of a nucleus (moment of inertia times the rate of rotation) is quantized to h(I(I+1))^½, where h is Planck's constant divided by 2π and I is a positive integer. Using this result the nuclear rates of rotation are found to be many billions of times per second. Because of the complexity of the four modes of rotation each nucleon is effectively smeared throughout a spherical shell. So, although the static structure of a nuclear shell is that of a ring, its dynamic appearance is that of a spherical shell.

Thus a ring of alpha modules turns at such fantastically high rates that it appears to be a spherical shell. --> Hence a nucleus appears to consist of concentric spherical shells. The details are at Nucleus.

Conclusions

Physicists never should have started saying

The nucleus of an atom is held together by a nuclear strong force; one that is a stronger attraction between protons than their electrostatic repulsion at short distances but weaker at longer separation distances.

Instead the most they would have been justified in saying is

If such a hypothetical nuclear strong force exists then it would explain how nuclei consisting of multiple protons could be stable.

However the conjecture that all nucleons attract each other equally would imply that arbitrary clusters of protons would exist which in fact do not exist and therefore the hypothetical nuclear strong force then cannot be true. For example, the hypothesis implies that there should exist nuclides with multiple protons and no neutrons.

The inclusion of neutrons being subject to the nuclear strong force does not help matters. It only implies the existence of more clusters of nucleons which do not in fact exist.

It is wrong to allege that because the notion of a nuclear strong force explains how nuclei with multiple protons could be stable that it is thus necessarily true. The hypothesis that the nuclear strong force attraction exists between all nucleons is contrary to the empirical evidence on nuclear binding energy. Instead this evidence shows that like-nucleons repel each other and unlike ones are attracted to each other.

Thus an alternative model based upon nucleonic spin pairing provides a better explanation of nuclear stability.