The original intent of this series of papers was to resurrect the old quantum theory of Niels Bohr and Arnold Sommerfeld and, together with some input from modern quantum mechanics show that a theory of atomic structure could, for single electron atoms and ions, be developed in which the electron was interpreted as a real physical particle. With the incorporation of magnetic dipole coupling, it is proposed that this objective has been largely accomplished. This is considered to be a reasonable claim at this stage because the resurrected theory can now predict all that the modern quantum mechanics theory of atomic structure can predict. Further refinement in the latter theory, i.e. the Lamb Shift, has had to make recourse to additional techniques within quantum electrodynamics. Because of the philosophical intent of the resurrected Bohr/Sommerfeld theory, it will need to introduce this variation without recourse to quantum electrodynamics or similar disciplines. This will be the subject of the next paper.

Albeit the above statement on the maturity of the resurrected theory is considered justifiable at this stage, it must still be viewed as somewhat embryonic. This is because essentially, only the hydrogen atom has been considered in detail, and only to the point of fine structure splitting. To provide further substance to the theory, not only will it be necessary to incorporate an explanation for the Lamb Shift, but also a sound mathematical model for the hyperfine structure will need to be added. Both of these additions will require a physical interpretation in keeping with the original objective. Furthermore, it would also be very desirable to extend the theory to cover at the very least simple multi-electron atoms. However, this would be, as is well known, severely restricted by the difficulties inherent in solving three body, (and more), dynamic problems. Despite the fact that in the modern quantum mechanics theory of atomic structure, the electron is viewed as a probabilistic wavefunction, it is, strangely, subject to the same difficulties.

The comparison of the two theories, as so far developed, in Section 5.0, is from the mathematical point of view, favourable, minor differences aside. However, when the comparison is extended to include physical attributes, some anomalies result. Extending the comparison is justified despite the fact that the electron is viewed so differently in the quantum mechanics theory because that theory still makes extensive reference to such physical parameters as spin, angular momentum, magnetic moment and relativistic mass increase when discussing the electron. The extended comparison centres exclusively around the quantum numbers used to characterise the electron orbital energy levels. The main consequence of this comparison is that in the quantum mechanics theory, the lack of s orbital angular momentum, results in the necessity for two separate equations to describe the orbital energy for all orbitals. One equation is required for s orbitals, in which the Darwin term is included but spin-orbit coupling excluded, and a second equation for all other orbitals with the Darwin term excluded and spin-orbit coupling included. The only terms common are those for the gross energy levels resulting from the basic central coulomb force and the "relativistic mass increase" of the electron.

In the resurrected Bohr/Sommerfeld theory only one equation is necessary incorporating the appropriate terms for the gross energy levels, the relativistic electron mass increase and all magnetic dipole coupling effects. All of these terms appearing in all orbitals. This is considered a superior aspect of the Bohr/Sommerfeld theory over the quantum mechanics.

Within the Bohr/Sommerfeld theory it has been possible to ascribe real physical meanings to all of the parameters involved and which appears free of apparent anomalies. Possible mechanisms have been identified for electron spin and photon emission, from which it has been possible to derive all except one of the so called Selection Rules. The one exception is for transitions in which Dn_j = ± 2. These have been excluded in the resurrected theory for orbit transition path geometrical reasons. In the quantum mechanics theory, exclusion is for the inner quantum number change only. However, in this regard, it is noted that the orbital angular momentum Selection Rule governing transitions, is, even with spin-orbit coupling incorporated, still n_f ^*, (or l), because only that quantum number is subject to a direct change when a photon emission occurs.

To complete the current phase of development, in addition to the incorporation of the Lamb Shift and the hyperfine structure, it will be useful to demonstrate the physical characteristics of all orbitals, the electron transition paths between them, and the strengths of the emitted spectra. These will be the subject of future papers.

Finally, as in previous papers in this series, the emission spectra as predicted by this theory are shown in Appendix C. If the Lamb Shift effect is removed from [6], the spectra of Appendix C are seen to compare very favourably provided allowance is made for the small differences in the values of the constants used.