San José State University
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The Binding Energies of Nuclei
as Determined by the Energy of
Formation of their Substructures and
the Interactions Among the Nucleons

The force between two particles of strong force charges q1 and q2 is of the form


where F(x) is a positive valued function of the time averaged separation distance s between them.

This implies that the binding energy associated with the strong force interaction of the particles is of the form


where G(s) is a positive-valued function of the time averaged separation distince s.

Let the strong force charge of a proton be designated as unity and that of the neutron as q. The binding energies of neutron-neutron, neutron-proton and proton-proton interaction should be in the proportions q²: q: 1. In proton-proton interactions there is the additional effect of the electrostatic force. This effect can be represented as δ times the strong force interaction so in proton-proton interaction the effective charge of the proton is (1+δ). Thus the proportions noted above would be q²: q: (1+δ)².

It has been found that the effect of the interactions are the same for all neutronsl in the same shell and likewise for the protons.

In previous studies the measured effects for nucleons in the same shell were found to be in the proportions cited above with q equal to −2/3. But this is not the case for interactions between nucleons in different shells.

If the evidence of previous studies is taken as confirmation of the hypothesis of strong force charges then all such interactions should adhere to the cited proportions. This can be achieved by computing for the interactions between two shells, say the i-th and j-th shells, the quantities

SiSj = q²NiNj + qNiPj + q PiNj + (1+δ)²PiPj

where NiNj is the number of interactions between neutrons in the i-th shell and the neutrons in the j-th shell and likewise for the other interactions.

These variables were combined in a regression with other variables representing the effect of the formation of substructures. The computations were carried out in a way that the values of q and δ could be adjusted. The intial values used for q and δ were −2/3 and 0, respectively.

That regression had a coefficient of determination (R²) of 0.99963 and a standard error of the estimate of 9.73 million electron volts (MeV). This is not too bad but it is small potatoes compared with the value of R² of 0.9999824 and 1.86 MeV for the standard error of the estimate fould in a previous study.

An increase in the value of δ from 0 to 0.16 raises the coefficient of determination to 0.99969 and reduces the standard error of the estimate to 8.94 MeV. These are minor but worthwhile improvements. The coefficient of determination increases ever so slightly if q is reduced to −0.6. A positive value for δ indicates the strong force between two protons is of the same nature as the electrostatic force between them; i.e., repulsion. previous study developed an equation explaining the binding energies of about three thousand nuclides in terms of the nucleonic substructures they contain and the interaction of their nucleons through the nuclear strong force.

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