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Evidence Concerning Alpha Particle Substructures
in Nuclei from Changes in the Number of Protons

These is considerable evidence that at least some of the neutrons and protons in a nucleus form alpha particles. A relatively large amount of energy is involved in the formation of an alpha particle, about 28.3 million electron volts (MeV). If a nuclide consists entirely of alpha particles then the removal of one of the constituents of an alpha particles should result in a relatively large effect on binding energy.

There are twenty five nuclides which could consist entirely of alpha particles. They will be referred to as alpha nuclides. The removal of a neutron from each of the alpha nuclide should result in a relatively large decrease in binding energy compared to that resulting from the addition of one neutron to each of the alpha nuclides. The evidence supports this proposition for the smaller nuclides.

The material below tests the proposition using data on the effect on binding energy of the subtraction of one proton from each alpha nuclide in comparison with the effect of adding one proton to such nuclides. kc

Number
of alphas
Binding
Energy
of alphas
Binding
Energy
of alphas
Less one
Proton
Binding
Energy
of alphas
Plus one
Proton
Decrease
in Binding
Energy
Due to One
Less Proton
Increase
in Binding
Energy
Due to One
More Proton
Incremental
Binding
Energy
of an Alpha
1 28.295674 8.481821 26.33 19.813853 -1.965674 28.295674
2 56.49951 39.2445 56.3144 17.25501 -0.18511 28.203836
3 92.161728 76.2048 94.1053 15.956928 1.943572 35.662218
4 127.619336 115.49193 128.21961 12.127406 0.600274 35.457608
5 160.644859 147.80136 163.0762 12.843499 2.431341 33.025523
6 198.25689 186.56402 200.5282 11.69287 2.27131 37.612031
7 236.53689 224.95195 239.285 11.58494 2.74811 38.28
8 271.78066 262.91669 274.0572 8.86397 2.27654 35.24377
9 306.7157 298.20981 308.5735 8.50589 1.8578 34.93504
10 342.052 333.7237 343.137 8.3283 1.085 35.3363
11 375.4747 366.8251 377.089 8.6496 1.6143 33.4227
12 411.462 403.362 413.547 8.1 2.085 35.9873
13 447.697 440.3156 449.296 7.3814 1.599 36.235
14 483.988 476.8229 484.682 7.1651 0.694 36.291
15 514.992 509.8713 515.45 5.1207 0.458 31.004
16 545.95 540.93 545.9 5.02 -0.05 30.958
17 576.4 571.6 575.9 4.8 -0.5 30.45
18 607.1 602.3 606.5 4.8 -0.6 30.7
19 638.1 633.625 637.9 4.475 -0.2 31
20 669.8 665.5 669.2 4.3 -0.6 31.7
21 700.9 696.8 700 4.1 -0.9 31.1
22 731.4 727.7 730.3 3.7 -1.1 30.5
23 762.1 758.4 3.7 30.7
24 793.4 790.1 3.3 31.3
25 824.9 821.6 3.3 31.5

Because the results for the subtraction and addition of protons are irregular and a bit puzzling the following graph on the incremental binding energies of alpha particles is presented first to show that regularities exist.

Here is the graph of the effect of removing one proton from each of the alpha nuclides.

Again shell phenomena is evidenced by the relatively sharp drop at the nuclear magic numbers of 6, 20 and 28.

The effect of adding one proton is much different from that for subtracting one proton.

Now the two previous graphs can be combined to show a comparison.

The two curves appear to be becoming approximately parallel. The more precise nature of the difference is shown below.l

This is remarkably similar to the corresponding graph for neutrons, as can be seen in the graph below.


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