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The Effect on Binding Energy
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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