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The Binding Energy Associated with the Addition
of a Neutron-Neutron and Proton-Proton Spin Pair to the Alpha Nuclei

In a previous study the estimate of the effect on binding energy associated with the addition of a neutron-proton spin pair to alpha nuclei was investigated. An alpha nuclei is a nuclide composed entirely of alpha modules, In this webpage the effects of adding a neutron-neutron spin pair to alpha nuclei is examined and compared with the effects of adding proton-proton spin pairs to alpha nuclei. The sum of these two effects is then compared with the effect of adding another alpha module to the alpha nuclide.

The Incremental Binding Energies
of a Neutron-Neutron Spin Pair and
a Proton-Proton Spin Pair to the Alpha Nuclides
as a Function of the Number of
Alpha Modules in the Nuclide
Number of
α Modules
IBE of nn IBE of pp IBE nn +
IBE pp
IBE of an
α Module
1 0.973426 -1.371674 -0.398248 28.203836
2 8.47769 3.82099 12.29868 35.662218
3 13.12278 6.571502 19.694282 35.457608
4 12.187664 4.534164 16.721828 33.025523
5 17.125051 7.932741 25.057792 37.612031
6 18.42374 7.78911 26.21285 38.28
7 19.08274 7.14811 26.23085 35.24377
8 20.0585 6.94034 26.99884 34.93504
9 20.627 6.4063 27.0333 35.3363
10 19.8433 4.853 24.6963 33.4227
11 22.7197 6.5003 29.22 35.9873
12 23.5821 6.238 29.8201 36.235
13 24.0617 5.453 29.5147 36.291
14 22.4658 2.972 25.4378 31.004
15 23.127 2.638 25.765 30.958
16 23.34 1.85 25.19 30.45
17 23.93 1.4 25.33 30.7
18 24.18 1.1 25.28 31
19 24.908 31.7
20 24.9 31.1
21 24.9 30.5
22 26 30.7
23 27 31.3
24 27.5 31.5

The graph below of the data reveals that the incremental binding energies of the spin pairs and alpha modules shift at points where the number of nucleons correspond to either the conventional magic numbers of {8, 20, 28} or the modified ones of {6, 14, 28}. is a function of the shell for the alpha module and the shell shifts at the neutron numbers corresponding to the convention magic numgers, {8, 20, 28}

In a sense an alpha module can be thought of as a combination of a neutron-neutron spin pair and a proton-proton spin pair. It is of interest to compare the sum of incremental binding energies of the two spin pairs with that of an alpha module.

Beyond the small nuclides it appears that the sum of the incremental binding energies of the two spin pairs is roughly 82 percent of that of an alpha module

The incremental binding energy of a nucleon combination is made up of two components. One component is the binding energy associated with the formation of the the nucleon combination and the other is the sum of the interactions through the nuclear strong force between the nucleons of the added combination and all the other nucleons of the nucleus. The binding energy associated with the formation of a nucleon combination is, in turn, composed of the binding energy due to the formation of the combination per se and the binding energy due to the adjustments in the structure of the rest of the nucleus.

In the formation of the two nucleon spin pairs there are no other structures to involve adjustment so their binding energies are entirely due to the formation of a spin pair and the interaction of the nucleon with the other nucleon of the same type through the nuclear strong force. The interaction binding energy of a nucleon with a nucleon of the same type is negative due to their repulson.

The interaction of a neutron and a neutron through the so-called strong force is on the order of −0.36 MeV which leaves the binding energy due to the formation of a neutron-neutron spin pair to be about (0.97+0.36)=1.33 MeV. The total binding energy associated with the formation of a neutron-neutron spin pair in larger nuclides is about 23 MeV. This means that the binding energy due to the adjustment in the structure of the other nucleons when a neutron-neutron spin pair is formed is about 21.7 MeV.

The interaction of a proton and a proton through the so-called strong force is on the order of −0.99 MeV which leaves the binding energy due to the formation of a neutron-neutron spin pair to be about (−1.37+0.99)=−0.38 MeV. Such a value would account for the non-formation of proton-proton spin pairs outside of a nucleus. The total binding energy associated with the formation of a proton-proton spin pair in larger nuclides is about 6 MeV. This means that the binding energy due to the adjustment in the structure of the other nucleons when a neutron-neutron spin pair is formed is about 6.4 MeV.

The total binding energy associated with the formation of an alpha module is about 31 MeV. With the two nucleon-nucleon spin pairs accounting for 82 percent of that binding energy that leaves 18 percent of the 31 MeV due strictly to the formation of the alpha module per se; about 5.6 MeV.

Conclusion

Away from the irregularities of the smaller nuclides the sum of the effects on binding energy of a neutron-neutron and proton-proton spin pair formation is slightly more than eighty percent of that of an alpha module. Most of the binding energy associated with the formation of nucleon-nucleon spin pairs in a nuclide is due to the adjustments in the structure of the other nucleons that occur as a result of the presence of those spin pairs. The binding energy of these adjustments is through the so-called nuclear strong force.

<(To be continued.)


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