San José State University
Thayer Watkins
Silicon Valley
& Tornado Alley

On the Basis for the Exclusivity
of the Spin Pairing of Nucleons

A model of nuclear structure has been developed elsewhere that explains the binding energy of nuclei primarily in terms of the formation of spin pairs of nucleons. Spin pairing however is exclusive in the sense that one nucleon can pair with one nucleon of the same type and with one of the opposite type. That is to say, one neutron can pair with one other neutron and with one proton and it is likewise for a proton.

There is also another force involved which is nonexclusive. This involves the interaction of nucleons. The interaction of like nucleons is a repulsion and of unlike nucleons is an attraction. This force must not be confused with the confused concept of the so-called nuclear strong force. That confused concept conflates the disparate phenomena of exclusive spin pairing (always attractive) with the nonexclusive interactive force which is a repulsion between like nucleons and an attraction between unlike nucleons. The concept of the nuclear strong force was nothing more than a giving of a name to what holds a nucleus together.

This alternative model of nuclear structure can explain 99.995 percent of the variation in the binding energies of 2931 nuclides. The signs and magnitudes of the regression coefficients are consistent with the model. Thus the model is strongly supported empirically. In contrast the conventional model of strong force nuclear structure fails almost every test of its validity.

The only thing missing for the alternate model is an explanation for the exclusivity of the spin pairing of nucleons. This webpage is an investigation of what could be the basis for the exclusivity of the formation of nucleonic spin pairs.

Spinning Elecrical Charge and Magnetism

The movement of an electric charge creates a magnetic field and the faster the movement the greater the intensity of the magnetic field created. A spinning spherically distributed electric charge creates a magnetic field with two poles on the sphere. Here is an illustration for a spinning proton.

The magnetic field of the spinning proton may be depicted by showing the magnetic lines of force; i.e.,

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

or side-by-side, as below

There is a concentration of the magnetic lines of force between the two side-by-side spinning protons.

The side-by-side arrangement requires the protons to have opposite directions of spin.

In principle another spinning proton could also be to added pole-to-pole to the first proton. In practice such linked triplets of proton never occur. Even such pairs of protons do not occur outside of a nucleus. But they do occur within nuclei although magnetism is probably not the linking force. Adding another proton to a side-by-side pair runs into the impossibility of having the direction of spin of the added proton being opposite to both directions of spin in the proton spin pair.

Thus the side-by-side arrangement enforces exclusivity. Adding a neutron to a proton spin pair has the advantage that the neutron is attracted through the interaction force to both of the protons.

The above illustration indicates why no more than two linkages can be formed with one spinning nucleon. However, before going on, it should be noted that even though a neutron is electrically neutral it has a magnetic moment because of the radial distribution of its charge, as seen below.

The outer negative charge of a neutron moves faster in a spinning neutron than its inner positive charge so the magnetic moment of neutron is opposite sign from that of a proton.

Magnetic fields may be involved in the spin pair linking of nuceons but other more powerful forces are involved as well.

The Association of a Magnetism-like
Field with any Nucleonic Force

There is a mathematical argument that the Special Theory of Relativity requires the existence of a magnetic field associated with moving electric charge. Only a slight modification of that argument shows that Special Relativity requires a magnetism-like to be associated with moving charges of any type. The force due to the interaction of nucleons can be explained by neutrons and protons possessing a nucleonic charge. If the nucleonic force of the proton is taken to be +1 then that of the neutron is found empirically to equal to −2/3.

The magnetism-like field associated with the nucleonic force is responsible for the binding energy of nucleonic spin pair formation. As in the case of magnetism no more than two linkages can be formed with one nucleon.

Energy Considerations Involved
in the Different Types of
Linkages to One Nucleon

Consider the two arrangements of linkages to one proton; i.e., P-P-P and P-P-N. The two end protons in a P-P-P arrangement repel each other whereas the end P and N attract each other. Therefore P-P-N is a lower energy state than a P-P-P and would be found to occur in preference to P-P-P.

This would provide an additiomal explanation for the prevalence of P-P-N over P-P-P in nuclei.

This however is valid only if P-P-N is an available alternative to P-P-P. In nuclides in which there are more neutrons than there are protons such would not be the case. Then the energy argument would not prevent two protons from linking to one proton.

Here is an example showing the additional binding energy due to an additional neutron.

The saw-tooth pattern is due to the effect of neutron spin pair formation. The sharp drop at 36 neutrons is due to the nonformation of neutron-proton spin pairs beyond that point. The saw-tooth pattern prevails beyond 36 neutrons indicating that neutron spin pairs occur but no neutron triplets N-N-N are formed. So it is not energy considerations that account the exclusivity of nucleon spin pair formation. The same evidence indicates that exclusivity is not merely a preference for an additional neutron to be added to a proton pair but instead an absolute prohibition of adding another proton to a proton pair. A side-by-side arrangement for nucleon spin pairs provides such a prohibition.

(To be continued.)

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