This theory is truly not just a resurrection of the old quantum theory of atomic structure, because it recognises and uses throughout the development, the duality of the existence of matter. That combined with the old quantum theory enabled this entire development to be derived from just two basic postulates, those of Planck's quantum energy and de Broglie's matter wave quantum momentum. From the inception of these in [6] through to this paper, the mathematical development, with the exception of the subject discussed below, has been rigorous, with no unsound assumptions, and in which the only approximations taken have been to discard third and higher relativistic terms, that have a negligible impact on the results to the accuracy and precision targeted.

The one exception to the above statement is the manner in which the spin matter wave radius has been determined. In a theory of atomic structure in which the electron is treated as a real physical particle, albeit with a dual corpuscular/wave function existence, and spin is a real parameter, it is necessary to know with great precision all of the contributing attributes of that particle. One of the critical requirements in this, and in fact also in the quantum mechanics version, is that the electron conform to the spin angular momentum quantum criteria, howsoever the concept of electron spin is defined. To do that with the electron as treated here, it is first necessary to know accurately and precisely the value of electron spin angular rate. Secondly, bearing in mind the manner in which electron transitions have been defined, the only manner in which the above criteria can be met is, in conjunction with its spin rate, for the electron spin matter wave radius to be a variable. Consequently, it is further necessary to know accurately and with adequate precision the value of this parameter. With the electron as an integral part of an atom, there is no known method with which either of these two parameters can be measured experimentally. Similarly, there is no known way in which they can be determined to the accuracy and precision required purely theoretically, even given the manner of spin inducement proposed in this series of papers. Accordingly, it is therefore necessary to resort to the semi-empirical method of determination adopted here. In doing so it is therefore not unreasonable to tailor the determination process to provide results that match experimentally derived data. This of course is only acceptable, provided that the determination process follows a logical procedure, that integrates smoothly with the rest of the development. It is proposed that this is indeed the case here, as exemplified with particularly the discussion of the initiation of the transition process in Section 5.4 above.

That point accepted, the results obtained here are in excellent agreement with those in the literature. A detailed examination of them, and their numerical calculations, may be obtained from the spreadsheets in which they are computed. See Appendix A.

Finally, any theory of atomic structure does not end with the development to the fine structure level and, in future papers, this theory will be further developed to the level of the hyperfine structure, and to cover the concepts of transition probabilities and spectral intensities, as well as investigation of the potential additions highlighted in the previous Section.