San José State University
Thayer Watkins
Silicon Valley
& Tornado Alley

An Estimation of the Nucleonic Charge
of a Neutron Relative to that of a Proton
Using the Ratios of Second Differences
to Cross Differences

What is conventionally called the nuclear strong force is here called the nucleonic force. The reason for this change in terminology is that this force is not so strong in comparison with another type of force involved in the structure of nuclei. That other type of force is the force involved in the formation of spin pairs. That force, although strong, is exclusive in the sense that one neutron can form a spin pair with one and only one other neutron and with one and only one proton. The same holds true for a proton.

Each nucleon has a charge with respect to the nucleonic force. The force between two nucleons or aggregates of nucleons is of the form

F = Hq1q2f(s)/s²

where H is a constant, q1 and q2 are the nucleonic charges, s is the distance between the particles and f(s) is a declining function of distance. Since f(s) is a declining function this means the nucleonic force drops off with distance faster than inverse distance-squared.

For now the repulsion between two protons is ignored.

The loss in potential energy involved in the formation of the system is then proportional q1q2U(s), where U(s) is an integral of f(z)/z² from ∞ down to s.

Let the nucleonic charge of the proton be taken to be 1 and denote the nucleonic charge of the neutron as q, where q can be a negative or positive number. The binding energy of a nucleus is closely related to the loss of potential energy involved. The three types of interactions through the nucleonic force are then

neutron-neutron: Inn = Hq²U(snn)
neutron-proton: Inp = HqU(snp)
proton-proton: Ipp = HU(s)

Thus, among other relationship, there is

Inn/Inp = q[U(snn)/U(snp)]

If snn is equal to snp then the ratio R=Inn/Inp gives an estimate of q.

The second differences in the binding energies of neutron spin pairs and the cross differences of the binding energies of neutron and proton spin pairs were computed and used as estimates of InnT and Inp, respectively. Their ratios were computed and taken as estimates of q. There were 586 separate values for √R computed. The average of these 586 values is −0.7294, only about 2.8 percent lower in magnitude than thevalue of −0.75=−3/4, but 9.4 percent larger in magnitude than −2/3. However the most important thing is that q is negative and different from unity in magnitude.

For each number of proton spin pairs the estimates of q were averaged. The plot of those averages is shown below.

(To be continued.)

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