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The Influence of Additional Neutrons on
the Incremental Structural Binding Energies
of Alpha Particles in the Fourth Shell

A previous study uncovered some interesting regularities in the incremental structural binding energies of alpha particles as a function of the number of neutron pairs in a nuclide. 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 shell are shown below.

These patterns correspond to shell structures. 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

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 the shapes to those for the first and second alpha particles of the fifth shell are obvious.

These bent line patterns indicates some sort of shell structure. If the odd-even variation, which connoted 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.

The pattern is seen more clearly in terms of the increments to the ISBE's for additional excess neutrons.

The sawtooth pattern has something to do with the formation of neutron pairs. However the magnitude of the enhancement in binding energy varies over the range so something more is involved than strictly the formation of neutron pairs.


There is a definite pattern to the influence of the number of neutrons on the incremental structural binding energies of alpha particles in the fourth shell.

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