Anyway, we are optimistic because it is known that the elliptical functions are double-periodic functions so that the possibility to “discover” even more quantum numbers in addition to the already introduced principal quantum number definitely does not seem to be hopeless – no, on the contrary, it must even be expected. Indeed, from the double periodicity inevitably follows that not two new secondary quantum numbers independent of each other can be found but only one; the other one must inevitably satisfy a simple ratio of a principal and an independent secondary quantum number. Of course, we assess this “strange coincidence” as an indication in terms of our hypothesis. But soon after writing down the determination equation for the semi-axes ratio this optimism is considerably dampened.

This would mean solving an equation as a determination equation for the semi-axes, which already becomes totally confusing when writing it down. Even the formulation of the functions in such an equation is so complex and leads to elliptical integrals with very complicated integrands that an elementary solution is no longer imaginable, particularly, if one keeps in mind the tools required (which of course are not available to the author). Thus, this proof must be postponed. (In the final comments we will revert to this problem.).

Now we turn our attention to the principles of atomic structure and ask if our model also here provides clear results in accordance with nature. Therefore, we imagine – according to the already known procedure – a naked nucleus that catches electrons one after the other. We do not have to discuss hydrogen and helium because we have found by explanation of the Pauli principle that these two cases are in accordance with the real conditions. The question about lithium is much more interesting.

Initially we observe that the two electrons travelling on the 1s orbit do not realize the 2s valence electron revolving outside because they are always inside the spherical shell generated by the 2s orbit and, thus, within the range of “magnetic calm”. Now we ask: Doesn’t the 2s electron “take notice” of the 1s electron? Here two options are possible: first we will discuss the possibility that the 2s electron can interact with the spin rosette in direction e-f.