Background

Nuclei are held together largely by the spin pairing of the nucleons (protons and neutrons) Such spin pairins are exclusive; meaning one proton can pair wit0h one other proton and with one neutron and no more. The same applies for neutrons.

There are other nonexclusivee interactions between nucleons but each each such interaction is generally an order of magnitude smaller than that of a spin pairing.

It is worth while to estimate the increments in binding energy due to the formation of proton spin pairs and explain their variation in terms of the makeup of the nuclei.

The binding energy due to the formation of a spin pair can be computed as the difference in the incremental binding energy at one point and the average of the value at the two adjacent points, as shown below.

This procedure is not valid near where the incremental binding energy makes a big drop.

The results from applying the procedure to the incremental binding energies of protons are given below. They include 2405 cases with an average effect of 2.365 million electron volts (MeV) and a standard deviation of 0.835 MeV.

The frquency distribution of the effect of the formation of a proton-proton spin pair is shown below.

The database compiled can be used to test the dependence of the increment of binding energy due to the formation of a proton-proton spin pair (BEppSP)

BEppSP = 3.59267 − 0.01004p −0.0077n
[104.6] [-4.3] [-5.0]

The coeffient of determination (R²) for this equation is an unimpressive 0.451 but the t-ratios, shown in square brackets [ ] below the coeffient, show that BEppSP is definitely a function of n and p. However the dependence is likely a complicated nonlinear binary function. A comparison of cases in which the values of n and p are interchanged shows that the binary function has a degree of symmetry with respect to n and p. See Comparisons for examples.