Background

The data on binding energies of nuclides indicate that when a nucleon is added to a nuclide there is an increase in binding energy due to the interaction of the new nucleon with the nucleons which are already there. The enhancement of binding energy is substanially more if the new nucleon can form a spin pair with one or two of the nucleons already there. This results in a sawtooth pattern for the incremental binding energy of neutrons as a function of the number of neutrons in the nuclide.

The sawtooth pattern is a result of the enhancement of incremental binding energy due to the formation of neutron-neutron spin pairs. The regularity of the sawtooth pattern demonstrates that one and only one neutron-neutron spin pair is formed when a neutron is added to a nuclide.

The same effects occur for proton-proton spin pair formation on binding energy

The spin pairing results in chains of nucleons containg modules of the form -n-p-p-n-, or equivalently -p-n-n-p-. These modules can appropriately be called alpha modules because the smallest one is the alpha particle.

The binding energy due to spin pairing includes the effect of the formation of the spin pair itself, but also includes the change in interaction energies among the other nucleons resulting from adjustment in their positions due to the introduction of the new nucleon.

Nucleonic Shells

As new nucleons of the same type are added to a nuclide the incremental binding energy changes in a regular pattern until a limit is reached and the value drops sharply. This is displayed in the patterns of incremental binding energies shown above. This is interpreted as the existence of shells for the nucleons.

The regularity of the sawtooth pattern demonstrates that one and only one neutron-neutron spin pair is formed when a neutron is added to a nuclide. These cases also illustrate that the enhancement due to spin pair formation is roughly constant within a shell but varies between shells.

Structure of Shells

There are a couple of signicant possibilities concerning the structure of the partially filled shells. One possibility is that a partially filled shell consists unclosed chains. The other is that the nucleon chains, where possible, are closed into rings.

The significant diference is that for the first possibility when a nucleon is added there is a single spin pair formed until the shell is filled. When the shell is filled the filling nucleon closes the the chain into a ring by forming a spin pair wih each end of the chain.

In contrast, where shells consist of rings a set of nucleons can be added to a ring only if they constitute an alpha module. That addition breaks on spin pair and adds two for a net addition of one spin pair. This holds for all additions including the one that fills the shell.

The Empirical Evidence

The incremental binding energies, both for neutrons and protons, show no special enhancement for the nucleons that fills a shell. Thus the nucleons in partially filled shells are, where possible organized into rings. This means alpha module rings and possibly an isolated neutron and/or proton. When the extra nucleons constitute an alpha module the ring is broken and the module is inserted.

(To be continued.)

Conclusions

The partially filled shells of nuclides consist of alpha module rings and nucleons which do not quite constitue an alpha module.