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The Interaction of Alpha Particles and
Proton Pairs Within Nuclei

This is an examination of the binding energies of nuclides which could contain an integral number of alpha particles plus a fixed number of proton pairs. It is based upon the presumption that within a nucleus the protons and neutrons form alpha particles whenever possible. The formation of an alpha particle entails a binding energy of 28.295 million electron volts (MeV). The binding energy from the formation of alpha particles accounts for most of the binding energies of nuclides. If BE is the binding energy of a nuclide and α is the number of alpha particles it contains then the excess binding energy XSBE is given by

XSBE = BE − 28.295*α

Below is shown the plot of the XSBE for the nuclides which could contain an integral number of alpha particles, hereafter referred to as the alpha nuclides.

A bent line in which the bends come at the points where the number of protons (and the number of neutrons) is equal to the magic numbers of {2, 6, 14, 28}. The statistical fit is near perfect, as shown by the coefficient of determination (R²) for the regression of 0.999169.

The plot of the excess binding energies of the nuclides which could contain an integral number of alpha particles plus an additional proton pair is shown below.

The bends in this case are not so sharp as in the case of the alpha nuclides. This may be because the effects of transitions to a new proton shell and a new neutron shell is spread over two changes in the number of alpha particles.

At this point it is important to note that there is a question of which is the crucial variable, the number of protons or the number of alpha particles?

A larger picture of the differences is useful at this point.

The difference is a sequence of nearly linear functions. This is described as a piecewise linear function. Note that the jumps in the level occur after 3, 7 and 14 alpha particles, which correspond to the magic numbers of protons and neutrons of 6, 14 and 28. The nature of the relationship can be more easily seen in the graph below.

Now a comparison can be made between the XSBE of the alpha+2proton nuclides and that of the alpha+4proton nuclides.

The relationship is also piecewise linear. The differences are plotted versus the number of the alpha particles of the nuclides because this makes the transitions occur at 3, 7, and 14 alpha particles which correspond to the magic numbers of 6, 14, and 28.

The differences between the excess binding energies for the alpha+6proton nuclides and those for the alpha+4proton nuclides show a similar pattern.

There are no more cases to consider.

Conclusions

At this point in the analysis one can only say that the operative variable determining the effect of additional proton pairs is either the number of alpha particles or the number of neutrons. But a similar analysis concerning the effect of additional neutron pairs concludes that the operative variable is either the number of alpha particles or the number of protons. Thus the joint conclusion is that the operative variable is the number of alpha particles in the nuclide.

It is not plausible that the operative variable would be the number of alpha particles that could be but are not formed. It would have to be the number that are actually formed. Thus the analysis provides definite evidence for the alpha particle structure of nuclides; i.e., whenever possible the nucleons of a nucleus form alpha particles. In other words, a nucleus is composed of alpha particles along with possisbly either proton pairs or neutron pairs and a singleton nucleon of the other type.


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