Below are the results of applying this procedure to data arising from incrementing by proton to the incremental binding energies of neutrons.
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The Result of the Regression of Neutron-Proton Interaction Binding Energy on the Number of Protons |
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|---|---|---|
| Neutron Number N | Range of Proton Number P | t-Ratio of Coeff of P |
| 10 | 11 to 14 | -1.49 |
| 20 | 10 to 14 | -1.33 |
| 20 | 15 to 24 | -0.410 |
| 30 | 16 to 33 | 0.944 |
| 40 | 24 to 28 | -0.290 |
| 40 | 29 to 39 | -0.190 |
| 50 | 29 to 48 | -1.74 |
| 60 | 37 to 56 | 0.015 |
| 70 | 43 to 50 | -0.96 |
| 70 | 51 to 62 | -1.04 |
| 80 | 51 to70 | 0.18 |
| 90 | 53 to 77 | -1.26 |
| 100 | 60 to 81 | -0.605 |
| 110 | 70 to 82 | -0105 |
| 120 | 77 to 82 | -0.690 |
| 120 | 83 to 89 | -1.04 |
| 130 | 83 to 92 | -1.32 |
| 140 | 87 to 97 | -0.076 |
| 150 | 93 to 103 | -1.08 |
| 160 | 103 to 110 | 1.44 |
Typically the graphs of data look like the following:
However there is one case, not shown above, in which there is a definite relationship between the interaction energy and the number of protons.
The extraordinarily high value for p=10 can be ignored because it is due to the proton number being equal to the neutron number, but the values for p=5 through p=9 show a definite, more or less precise, dependence of the interactive binding energy on the proton number. The t-ratio for the coefficient of p is about 33.
Data arising from incrementing by neutron number
the incremental binding energies of protons
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The Result os the Regression of Proton-Neutron Interaction Binding Energy on the Number of Neutrons |
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|---|---|---|
| Proton Number N | Range of Neutron Number N | t-Ratio of Coeff of N |
| 10 | 11 to 20 | 1.425 |
| 20 | 16 to 28 | 0.041 |
| 20 | 29 to 36 | 0.054 |
| 30 | 29 to 50 | 0.543 |
| 40 | 41 to 50 | -1.59 |
| 40 | 51 to 67 | -0.608- |
| 50 | 52 to 82 | 0.811 |
| 60 | 68 to 82 | -1.15 |
| 60 | 83 to 100 | -2.85 |
| 70 | 83 to 110 | -0.319 |
| 80 | 97 to 126 | -2.415 |
| 90 | 122 to 126 | -0.165 |
| 90 | 127 to 147 | -0.640 |
Typically the graphs of data look like the following:
There are two cases for which the t-ratio is greater than 2. Here are the graphs forthem.
In these cases it is not so much as definite dependences of interactive binding energy on neutron numbers as unusally small standard deveiations of the estimates of the coefficients.
Conclusions
Of the cases selected only one showed a definite dependence of interactive binding energy on the number of nucleons. For all the others the interactive binding energy of two nucleons is a function just of the nucleonic shells in which they are located.
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