San José State University

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Estimation of the Binding Energy Associated
with the Formation of a Proton Spin Pair

One major component of the binding energy of a nuclide is the binding energy associated with the formation of proton-proton spin pairs. The word associated is used for a definite reason. The observed increment in binding energy includes that due to the formation of the spin pair itself, but it also includes that due to the adjustments in the structure of the other nucleons.

An estimate of the binding energy associated with the formation of a proton-proton spin pair can be obtained for a particular nuclide by taking the difference of the incremental binding energy from the average of the two adjacent incremental binding energies.

This is for a nuclide with an even number of proton. An analogous procedure may be carried out for nuclides with an odd number of protons but what is obtained is an average of the values for the two adjacent nuclides.

A regression equation was estimated using the numbers of neutrons and protons as explanatory variables. The results were

Regression results
VariableCoefficientt-Ratio
P−0.021030229−6.9
N−0.00197109−1.0
P=N0.9694554127.7
P=N+10.7820874215.6
C03.75360628486.1

Thus the binding energy due to the formation of a proton-proton spin pair is about 3.75 MeV. This is the binding energy associated with the formation of a proton-proton spin pair which is not a function of the numbers of neutrons and protons. The standard deviation of this estimate is 0.04 MeV so the estimate may be expressed as 3.75 ±0.08 MeV as the 95 percent confidence range.

The coefficient of determination is a not-very-impressive 0.41.

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