San José State University
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Further Confirmation that the Nucleonic
(Strong Force) Charge of a Neutron is
Opposite in Sign and Two Thirds of the
Magnitude of that of a Proton

There are three types of interactions between nucleons in nuclei which affect the binding energy. First there is the interaction of spin pair formation. There are the three types of spin pairs; neutron-neutron, proton-proton and neutron-proton. These all involve an attraction. The second type is the strong force interactions. This is a repulsion between like type nucleons and an attraction between unlike type nucleons. The third type is the electrostatic repulsion between protons.

For now in the analysis the electrostatic repulsion between protons is ignored. Below is a tabulation of the number of interactions of the first two types for a nucleus with n neutrons and p protons.

n-p spin
n-n spin
p-p spin

The symbols [n/2] and [p/2] denote the integer parts of n/2 and p/2.

Let the strong force charge of a proton be taken as 1 and that of a neutron denoted as −dddddddddddq. The force between particle of charges q1 and q2 is proportional to q1q2. The potential energy is also proportional to q1q2 and therefore also the binding energy. Then the binding energy associated with the strong force interaction of a neutron and a proton is proportional to 1*q, between two protons is proportional to 1*1 and between two neutrons is proportional to q*q=q².

The equation for the binding energy BE should be

BE = c1min(n,p) + c2[n/2] + c3[p/2] + Hq*np − Hq²*n(n-1)/2 − H*p(p-1)/2

where H is a constant that depends upon the parameters of the strong force and the separation distance between nucleons.

The regression coefficients obtained by regressing the binding energies of the 2931 nuclides on the above variables are

BE = 10.31173861min(n,p) + 13.83460453[n/2] + 4.310005984[p/2] + 0.278037752n*p − 0.192544389n(n-1)/2 − 0.489577522p(p-1)/2
[34.7]   [76.9]   [8.3]  
[35.9] [-37.3] [-40.8]

where the numbers in the brackets below the coefficients is the coefficient's t-ratio, the ratio of the coefficient to its standard deviation. The t-ratio for a coefficient must be two or greater in magnitude for the coefficient to be statistically significantly different from zero at the 95 percent level of confidence. The coefficient of determination (R²) for the regression is 0.999882068.

The ratio of the coefficient of p(p-1)/2 to that of n*p should be q. The value of that ratio is 0.6925. The ratio of the coefficient of n(n-1)/2 to that of n*p also should be q. That ratio is 0.5679. The ratio of the coefficient of n(n-1)/2 to that of p(p-1)/2 should be q². That ratio is 0.393289 and its square root is 0.62713. Other studies concluded that the value of q is 2/3. These results confirm that estimate.

The electrostatic repulsion of protons would give a coefficient that is −(H+Δ) where Δ is some positive amount. Thus the ratio of the negative of the coefficient of n*p to that of p(p-1)/2 would be smaller than q. Likewise the ratio of the the coefficient of n(n-1)/2 to that of p(p-1)/2 would be smaller than q².

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