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Energies of Nucleons in Various Shells Based upon Increments in the Incremental Binding Energies |
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A previous study established that, generally, the binding energy due the interaction of the n-th neutron with the p-th proton depends only upon the even-or-oddness of n and p and the shells that n and p are in. The interaction binding energies IE come from the cross differences in binding energies, the increments in the incremental binding energies.
The proposition is that the interaction binding energy between a neutron and a proton depends only upon which nucleonic shells the neutron and proton are located in. It is tested by tabulating the estimated interaction binding energies in terms of the shell-to-shell cells, as shown below.
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The Interaction Binding Energy Between a Neutron and a Proton Based Upon the Shells They are Located in (MeV) |
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|---|---|---|---|---|---|---|
| Neutron shell | ||||||
| 4th | 5th | 6th | 7th | 8th | ||
| Proton shell | ≤28 | 29 to 50 | 51 to 82 | 83 to 126 | ≥127 | |
| 4th | ≤28 | 1.19 | 0.68 0.53 | |||
| 5th | 29 to 50 | 0.59 0.48 | 0.36 0.40 | |||
| 6th | 51 to 82 | 0.31 0.28 | 0.31 0.28 0.35 0.33 | |||
| 7th | 83 to 126 | 0.18 | 0.32 0.24 0.25 0.28 | |||
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The Interaction Binding Energy Between a Neutron and a Proton Based Upon the Shells They are Located in (MeV) |
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|---|---|---|---|---|---|---|
| Neutron shell | ||||||
| 4th | 5th | 6th | 7th | 8th | ||
| Proton shell | ≤28 | 29 to 50 | 51 to 82 | 83 to 126 | ≥127 | |
| 4th | ≤28 | 1.07 | ||||
| 5th | 29-50 | 0.69 0.41 | 0.47 0.41 | |||
| 6th | 51 to 82 | 0.30 | 0.30 0.26 0.25 | |||
| 7th | 83 to 126 | 0.27 | 0.22 | |||
If the proposition were exactly correct the numbers for the alternate estimates of the various shell-to-shell interactions would be precisely the same. And the values in the corresponding cells of the two tables would be the same. That would be too much to expect from empirical estimates. What is found is that the alternate estimates are of the same order of magnitude, as are the values in the the corresponding cells of the two tables; i.e., approximately the same.
(To be continued.)
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