San José State University |
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of the Addition of a Proton/Neutron Pair to Integral Alpha Particle Nuclides |
The alpha particle, He4 nuclide, and other nuclides which could contain an integral number of alpha particles have a relative large binding energy compared to nuclides having slightly fewer protons or neutrons required to form alpha particles. This phenomenon is explored quantitatively in another webpage. The results were interpreted to indicate that nuclei contain alpha particles as substructures.
This webpage investigates the binding energies of nuclides which could contain an integral number of alpha particle plus a proton/neutron pair, a deuteron. To make the presentation more concise the integral alpha particle nuclides will be referred to as α nuclides and the nuclides which are integral alpha particles plus a proton/neutron pair will be referred to as α+d nuclides. The data for this analysis are as follows.
Number of Alpha Particles | Binding Energy of α Nuclides (MeV) |
Binding Energy of α+d Nuclides (MeV) |
Effect of Proton/Neutron Pair (MeV) | Increment for α Nuclides (MeV) |
Increment for α+d Nuclides (MeV) |
0 | 0 | 2.22457 | 2.22457 | ||
1 | 28.295674 | 31.9946 | 3.698926 | 28.295674 | 29.77003 |
2 | 56.49951 | 64.7507 | 8.25119 | 28.203836 | 32.7561 |
3 | 92.161728 | 104.658625 | 12.496897 | 35.662218 | 39.907925 |
4 | 127.619336 | 137.3692 | 9.749864 | 35.457608 | 32.710575 |
5 | 160.644859 | 174.1453 | 13.500441 | 33.025523 | 36.7761 |
6 | 198.25689 | 211.89414 | 13.63725 | 37.612031 | 37.74884 |
7 | 236.53689 | 250.6049 | 14.06801 | 38.28 | 38.71076 |
8 | 271.78066 | 285.56553 | 13.78487 | 35.24377 | 34.96063 |
9 | 306.7157 | 320.6473 | 13.9316 | 34.93504 | 35.08177 |
10 | 342.052 | 354.6871 | 12.6351 | 35.3363 | 34.0398 |
11 | 375.4747 | 390.3607 | 14.886 | 33.4227 | 35.6736 |
12 | 411.462 | 426.6288 | 15.1668 | 35.9873 | 36.2681 |
13 | 447.697 | 462.7332 | 15.0362 | 36.235 | 36.1044 |
14 | 483.988 | 497.108 | 13.12 | 36.291 | 34.3748 |
15 | 514.992 | 528.17 | 13.178 | 31.004 | 31.062 |
16 | 545.95 | 558.71 | 12.76 | 30.958 | 30.54 |
17 | 576.4 | 589.2 | 12.8 | 30.45 | 30.49 |
18 | 607.1 | 620.1 | 13.0 | 30.7 | 30.9 |
19 | 638.1 | 651.7 | 13.6 | 31.0 | 31.6 |
20 | 669.8 | 682.7 | 12.9 | 31.7 | 31.0 |
21 | 700.9 | 713.7 | 12.8 | 31.1 | 31.0 |
22 | 731.4 | 744.4 | 13.0 | 30.5 | 30.7 |
23 | 762.1 | 775.2 | 13.1 | 30.7 | 30.8 |
24 | 793.4 | 806.5 | 13.1 | 31.3 | 31.3 |
The data for the difference between the α+d nuclides and the corresponding α nuclides are plotted in the following graph.
What the graph indicates is that the proton/neutron pair does not exist within nuclei as a separate particle except in a deuteron. Beyond about five alphas the proton/neutron pair adds to the binding energy about 7 MeV per nucleon.
The increase in binding energy when the nuclide includes one more alpha particle is of interest. The data are shown in the last two columns of the above table. The graphs of this data are shown below, first separately for the α nuclides and the α+d nuclides and then together to see how close they are.
Although there are some differences for the smaller nuclides the graphs nearly coincide for the larger nuclides.
(To be continued.)
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