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Further Investigations of the Possibility that
the Nucleons of Nuclei are, Where Possible,
Organized into Alpha Particles: The Proton Data

An alpha particle, composed of two neutrons and two protons, is an amazing structure. It is relatively compact and has an extraordinary level of binding energy compared with smaller nuclides such as a deuteron or triteron. Binding energy is like, and perhaps is identical with, potential energy. Energetically it would be difficult for nucleons in a nucleus not to come together and form alpha particles wherever possible. This suggests that the binding energies of larger nuclei are composed of that due to the formation of alpha particles and that due to the arrangement of alpha particles and the extra nucleons. This latter binding energy will be called the excess binding energy. It is computed for a nuclide by subtracting from its binding energy the possible number of alpha particles it could contain times 28.29567 million electron volts (MeV), the binding energy of an alpha particle. The plot of the excess binding energies for the alpha nuclides shows a shell structure. The plot of this excess binding energy for the nuclides which could contain exactly an integral number of alpha particles is shown below.

It might appear that the graph above indicates the existence of only three shells: 1 to 2, 3 to 14 and 15 to 25. The upper limits of those shells correspond to filled shells. Fourteen alpha particles means there are 28 neutrons and 28 protons. Twenty five alpha particles correspond to 50 neutrons and 50 protons. Fifty and 28 are nuclear magic numbers.

The alpha nuclides only go up to 25 alpha particles. The range can be extended by including extra neutrons. The analysis for extra neutrons has been carried out The Neutron Data. This material covers the case of extra protons. When extra protons are included the range does not even reach 25 alpha particles, but the results are of interest anyway.

The incremental binding energy of a nuclide with a alpha particles is the excess binding energy of that nuclide less the excess binding energy of the nuclide with (a-1) alpha particles. An inspection of the graph for the incremental excess binding energies of the alpha nuclides, shown below, reveals that the 3 to 14 shell is composed of subshells. The end points of those subshells are levels of neutrons and protons that correspond with the nuclear magic numbers.

The numbers of alpha particles where there is a sharp drop; 3, 7, 10 and 14 correspond to 6, 14, 20 and 28 neutrons, all magic numbers. At points of sharp drops in the IXSBE the numbers of protons are 7, 15, 21 and 29, none of which are magic numbers. This indicates some dominance of the neutron numbers.

The graphs for the case of the two, four and six extra protons are shown below.

The sharp drops at 3, 7 and 14 alpha particles and corresponding to 6, 14 and 28 neutrons are maintained for the two and four extra protons cases.

The Second Differences in the Excess Binding Energy:
The Interaction Binding Energy of the Last Two Alpha Particles

According to the theory developed previously the increments in the incremental excess binding energies of alpha particles (the second differences in excess binding energy) should be negative, reflecting the net repulsion of alpha particles for each other, and constant within a shell. The graphs of the data for the cases considered above are shown below.

For this case there are the spike associated with a transition between shells the other values are generally near zero with some above and some below.

Except where the spikes occur for transitions from one shell to another the values are generally negative and roughly constant.

As in the previous cases the alpha-plus-four-protons and alpha-plus-six-protons nuclides give the interaction energies for the alpha particles in the same shell as negative.

The Alpha Particle and Proton Cross Differences

According to the theory the cross differences of excess binding energy is equal to the interactive binding energy of the last alpha particle with the last extra proton. According to another development the alpha particle has a nucleonic (strong force) charge that is a fraction of that of the proton. This means that protons should be repelled by alpha particles and thus the interactive binding energy should be negative when the increments are computed from the binding energy of nuclides in the same shell. The following graphs give the results of that computation.

In each case when the spikes associated with a change in shell the data points are predominantly negative. According to the conventional theory both protons and neutrons should be strongly attracted to alpha particles. Results here and a previous study indicate that alpha particles and neutrons are attracted to each other but alpha particles and protons are repelled by each other.

Conclusions

The incremental excess binding energy of alpha particles for various numbers of extra protons displays sharp drops at particular numbers of alpha particles. These drops occur at the numbers of neutrons correspond to the number of neutrons reach a level where a neutron shell is filled and additional neutrons must go to a higher shell.

The previous theoretical analysis that the increments in the incremental excess binding energies of alpha particles should be negative and roughly constant within a shell is confirmed.


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