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What holds the nucleus
of an atom together?

Background

This is not the conventional explanation of what holds a nucleus together. The conventional explanation is merely a naming of what holds nuclei together; i.e., the nuclear strong force. This naming has no more empirical content than if physicists said something holds a nucleus together. The physicists at the time needed an explanation for how a nucleus composed of positively charged protons could stably hold together. They hypothesized a force which at shorter distances between protons is more attractive than the electrostatic force is repulsive, but at longer distances is weaker. The only evidence for this hypothetical nuclear strong force is that there is a multitude of stable nuclei containing multiple protons. According to the theory nuclear stability was aided by the neutrons of a nucleus being attracted to each other as well as to the protons. So the conventional theory is merely an explanation of how a nucleus containing multiple positive charges can be stable.

But even if a theory explains empirical facts that does hot mean that it is necessarily true. It only means the theory might be physically true. There might be an alternate true explanation of those empirical facts. And if a theory predicts somethings which do not occur then even it explains other things it cannot be physically correct.

According to the strong force theory of nuclear structure there should be no limit on the number of neutrons in stable nuclides. There should be ones composed entirely of neutrons. There should even be ones composed entirely of a few protons. These things do not occur physically. In fact there has to be a proper proportion between the numbers of neutrons and protons. In heavier nuclides there are fifty percent more neutrons than protons. Thus there are serious flaws with the conventional theory of nuclear structure; i.e., the nuclear strong force.

When the conventional theory of nuclear structure was formulated physicists thought that they could not be wrong, but, as will be be shown below, they were wrong, because their concept of nuclear strong force conflates two disparate phenomena: spin pairing, attractive but exclusive, and non-exclusive interaction of nucleons in which like-nucleons repel each other and unlike attract. The proof of this assertion is given below. This an abbreviated version of an alternative of what holds a nucleus together. The full version is at Nucleus.

The case of an odd number of protons is of interest. Here is the graph for the isotopes of Rubidium (proton number 37).

The addition of the 38th neutron brings the effect of the formation of a neutron-neutron pair but a neutron-proton pair is not formed, as was the case up to and including the 37th neutron. The effects almost but not exactly cancel each other out. It is notable that the binding energies involved in the formation of the two types of nucleonic pairs are almost exactly the same.

This same pattern is seen in the case for the isotopes of Bromine.

The components of the incremental binding energy of neutrons can be approximated as follows. For an even proton number look at the values of IBEn at and near n=p. Project forward the values of IBEn from n=p-3 and n=p-1 to get a value of ICEn for n=p; i.e.,

IBEn(p-1, p) + ½(IBEn(p-1, p) − IBEn(p-3, p) )

Likewise the values for IBEn can be projected back from n=p+1 and n=p+3 to get a value of IBEn for n=p without the effect of either an nn spin pairing or an np spin pairing. This procedure is shown below for the isotopes of Neon (10).

When this procedure is carried out numerically the results indicate that 42.7 percent of the incremental binding energy at n=p=10 are due to the nn spin pairing, 17.1 percent is due the np spin pair and the other 40.0 is due to the net interactive binding energy.

This domination of IBEn by spin pairing can only occur for small nuclides. For iron (p=26) the figures are16.9 percent for the nn spin pairing, 12.8 percent for np spin pairing, and 70.3 percent due to the net effect of the interactive binding energy of the nucleons.

It is not just that effects of the spin pairings goes down for the heavier nuclei; it is that those of the interactions goes up. For more on the components of IBEn see Components of IBEn.

The Interactions of Nucleons
through the Nucleonic Force

Conclusions

In a nucleus wherever possible the nucleons are linked together through exclusive spin pair formation into rings of alpha modules which rotate in four different modes at rapid rates. This rapid rotation results in each nucleon being effectively smeared uniformly throughout a spherical shell.

A nucleus is also held together by nonexclusive interactions of nucleons due to their having a nucleonic charge. If the nucleonic charge of a proton is taken to be 1 then statistical analysis of binding energies indicate that the nucleonic charge of a neutron is −2/3. This results in like nucleons being repelled from each other through nucleonic interaction and unlike nucleons being attracted. For the nucleonic interactions in a nucleus to be a net attraction there must be a proper balance between the numbers of neutrons and protons. This balance in heavier nuclei requires about fifty percent more neutrons than protons.

The nucleons are organized in spherical shells containing at most certain numbers of nucleons. These nuclear magic numbers are explained by a simple algorithm.

Dynamically a nucleus is basically composed of concentric spherical shells which repel each other. This mutual repulsion results in a stable arrangement in which the centers of the concentric spherical shells coincide. This only occurs for repulsion forces that drop off faster than inverse distance squared.

Thus a nucleus is held together partly by the linkages created by the formation of spin pairs. The rings of alpha modules rotate to create the dynamic appearance of concentric spherical shells which are held together through the repulsion of the nucleonic forces. Neutron spin pairs outside of the concentric spheres are held by their attraction to the concentric spheres. So all of the nuclear forces, repulsions as well as attractions, are involved in holding a nucleus together.

For a review and critique of the conventional theory of nuclei see A statistical test of the conventional theory of the nucleus

For more on the physics of nuclei and other things see New pages.

     Dedicated to K. Serventi
without whose medical and
people skills this would
not have been written.

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