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The Incremental Structural Binding Energies
of Alpha Particles in Nuclides With Varying
Numbers of Additional Neutron Pairs

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 four neutron pairs. Since in each case the number of additional neutron pairs is held constant the ISBE's are independent of the value of the binding energy for a neutron pair.

The graph of these ISBE values is shown below.

The pattern up to 14 alpha particles is pretty much a jumble. For the range of 15 to 25 alpha particles there is a definite pattern for all five cases. Likewise for 26 and beyond there is a close correspondence among the five cases.

These correspondences involve a shell structure. There are four alpha particles shells for the range from one to 14 alpha particles. Fifteen to 25 is the fifth alpha particle shell and 26 to 41 is the sixth.

The graph of the ISBE for the nuclides which contain only alpha particles and one deuteron displays the same sort of pattern.

Is the Shell Structure in Terms of Alpha Particles or Neutrons?

The pattern displayed previously for the nuclides containing zero to four neutron pairs might just be a pattern based upon the number of neutron pairs and the number of alpha particles serves only as an approximation for that quantity. To test this possibility the ISBE's were replotted in terms of the number of neutron pairs. Here is the results.

The pattern for the higher level shells is less regular in this case than when the number of alpha particles is used the determining variable. The values of the lower level shells are a jumble, as is the case when the number of alpha particles is used as the determining variable.

The Incremental Structural Binding Energies of Alpha Particles
as a Function of the Number of Neutron Pairs in the Nuclide

The increase in the incremental structural binding energy of an alpha particle with the number of neutron pairs represents the energy of the interaction of the additional alpha particle with the additional neutron pair.

For the first alpha particle in the fifth shell there is about 0.66 MeV increased structural binding energy per additional neutron pair.

Conclusion

The incremental structural binding energies of nuclides are a function of the number of alpha particles in the nuclide.


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