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A Comparison of the Incremental Binding Energies of
Alpha Modules in Alpha Nuclides and Nuclides Which Are
Made Up of Alpha Modules and One or Two Neutron Spin Pairs

Background

The details of the alpha module model of nuclear structure are given elsewhere. Briefly the basis for it is that whenever possible a nucleon (neutron or proton) forms a spin pair with one other nucleon of the same type and with one nucleon of the opposite type. This leads to chains composed of modules of the form -n-p-p-n- (or equivalently -p-n-n-p-). These chains form rings which rotate in four modes; as a vortex ring, rotation about an axis through the center of the ring and perpendicular to its plane and flipping rotation about two diameters of the ring. These rotations take place so rapidly that the alpha module ring dynamically appears as a sphere with the nucleons smeared uniformly throughout a spherical shell.

The occupancies of the spherical shells are basically what were found by Maria Goeppert Mayer and Hans Jensen and labeled nuclear magic numbers. The Goeppert Mayer and Jensen magic numbers were based upon the numbers of stable isotopes and isotones. Their values were (2, 8, 20, 28, 50, 82, 126). The patterns of incremental binding energies justify a modified sequence of (2, 6, 14, 28, 50, 82, 126). The numbers 8 and 20 instead represent the filling of subshells within shells.

The Incremental Binding Energies of Alpha Modules

If the binding energy BE is given as a function of the number of alpha modules #α then the incremental binding energy IBEα of an alpha module is given by

IBEα(#α) = BEα(#α) − BEα(#α−1)

The Incremental Binding Energies
of Alpha Modules in Two Groups of Nuclides

 

There are similarities and differences.

These graph reveals that there are changes in the level of the incremental bindind energies at critical values of #α. One critical value is #α equal to 14, which corresponds to 28 neutrons and 28 protons. Twenty eight is a magic number corresponding to the filling of a shell. Another critical number is at #α equal to 4, which corresponds to 8 neutrons and 8 protons. Another is for #α equal to 7 which corresponds to 14 neutrons and 14 protons. The changes in slope are not so sharp as is the case with the alpha nuclides.

When the relationships of IBE to #α are plotted together the correspondence is more easily seen.

The Comparison with the Results for Alpha+2nn Nuclides

 

The results for the three cases plotted in the same graph are:

Conclusions

There is a close correspondences in the range from 15 to 25 alpha modules which is for the nucleon shells containing 30 to 50 nucleons. There is also a reasonably close correspondence in the range from 8 to 14 which corresponds to the nucleon shell containing 16 to 28 nucleons. There is no correspondence for the lower shells. This is perhaps because the addition of one or two alpha modules too greatly alters the balance between neutrons and protons at those lower levels but is not of much significance for the higher level shells.


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