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The Influence of Additional Neutrons on the
Incremental Structural Binding Energies of
Alpha Particles in the Third and Second Shells

Previous studies (1 and 2) uncovered interesting regularities in the incremental structural binding energies of alpha particles as a function of the number of neutrons in a nuclide. Those studies dealt with the alpha particles in the fifth and fourth shells. The investigation was carried out first for the higher shells because the patterns tend to be more regular and simple for the higher shells than for the lower shells.

The Structural Binding Energy (ISBE) of a nuclide is its binding energy (BE) less the binding energy that is accounted for by the formation of substructures. The substructures are alpha particles and nucleon pairs. There are accepted values for the binding energies of an alpha particle and a neutron-proton pair (deuteron) but none for a neutron-neutron pair or a proton-proton pair. The value of the structural binding energies of nuclides were computed by deducting 28.29567 million electron volts (MeV) for every alpha particle they could contain and 2.22457 MeV if they contain a separate deuteron. (They can contain only one deuteron; two would form an alpha particle.)

The structural binding energies were compiled for sets of nuclides. First these values were compiled for the 25 nuclides which could contain only alpha particles. These nuclides are hereafter called alpha nuclides. From this compilation the incremental structural binding energies were computed. This same procedure was carried out for nuclides containing only alpha particle plus one through however many neutrons could be added to the alpha nuclides.

The graphs of these ISBE values for the first two alpha particles in the fifth and fourth shells are shown below.

These patterns correspond to shell structures.

These bent line patterns indicates some sort of shell structure. If the odd-even variation, which connotes the formation of neutron pairs, is ignored then the patterns are straight line segments. A range of values over which the slope of the relationship is nearly constant indicates a shell. When a shell is filled a different slope prevails.

There are four alpha particles shells for the range from one to 14 alpha particles. The first shell contains only one alpha particle; the second, two alpha particles. The third shell can contain four and the fourth seven.

The Incremental Structural Binding Energies of Alpha Particles
as a Function of the Number of Excess Neutrons in the Nuclide

Excess neutrons here means the neutrons in excess of those contained in the alpha particles of the nuclides. The increase in the incremental structural binding energy of an alpha particle with the number of neutrons represents the energy of the interaction of the additional alpha particle with the additional neutrons.

Here are the graphs of the relationships. In the displays the term Number of Neutrons refers to the number of neutrons in the nuclide in excess of those contained in the alpha particles.

The similarities of these shapes to portions of those for the first and second alpha particles of the fifth and fourth shells are clear. The graphs for the third and fourth alpha particles of the third shell are shown below.

The patterns for the third and fourth alpha particles in the fourth shell are more complex.

A similarity can be discerned of the pattern for the third alpha particle in the third shell to a portion of the pattern for the third alpha particle in the fourth shell, but none for the fourth alpha particles in the third and fourth shells.

The Relationships for the Second Shell

The second shell can contain only two alpha particles and the numbers of excess neutrons are severely limited. Here are the graphs for the case of the alpha particles in the second shell.

There are regularities and similarities to the third shell cases. However the range of the number of excess neutrons is about three times as much for the third and fourth shells as for this case. Thus only a small portion of any pattern is observable.

Conclusions

There is a definite pattern to the influence of the number of neutrons on the incremental structural binding energies of first, second and third alpha particles in the third shell similar to those found for the fifth and fourth shells, but the similarity disappears for the fourth alpha particles. For the second shell alpha particles the range of variation in the number of excess neutrons means that only a small part of the patterns found for the higher shells can be observed.


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