The Bohr/Sommerfeld theory of atomic structure, as so far re-stated in [7], [8] and [9], is herein further developed to incorporate small relativistic energy correction terms that lead to the Lamb Shift. These terms are shown to be due to primarily two causes, (i) the distributed nature of electron charge, and (ii) the dynamic distance of the nucleus from the central point of orbital rotation. The first of these, (i), is augmented by consideration of the nature of the electron spin matter wave radius.

The Lamb Shift is a very small difference in the orbital energies of the s and p(-) orbitals, primarily in the 2^nd shell although it is also apparent down to at least shell 8. In the modern quantum mechanics/quantum electrodynamics theory of atomic structure, the Lamb Shift is attributed to changes in the electron self energy resulting from its interaction with fluctuating electric and magnetic fields that contribute to the zero point energy of the vacuum. Thereby the purported potentiality of the electron to emit and re-absorb virtual photons, which contribute to electron self energy, result in the value of this parameter being different in different orbitals, [1], [2], [3], [4].

In the resurrected Bohr/Sommerfeld theory presented here, because the electron is treated as a real physical particle, albeit with a dual corpuscular/matter wave existence, recourse to quantum electrodynamic phenomena such as described above, to explain the Lamb Shift, is not necessary as other simpler physical causes become apparent.

In this resurrected theory, the development to date has treated both the nucleus and, more particularly, the electron as spinning point charges. When the electron is afforded finite dimensions, in order that it subsequently conforms to the spin angular momentum criteria, especially in circular orbits, it will be proposed that its spin matter wave radius must become a variable that is to be determined. When this is coupled with the introduction of the concept that the electron charge is distributed uniformly on its outer surface, a small additional energy term is created, of relativistic magnitude, that must be added to the fine structure orbital energy levels.

In addition to the above, the development to date, while incorporating the finite mass of the nucleus, has only partly taken account of the fact that due to this finite mass, it, together with the electron, will orbit about a central point of rotation. The ratio of the distance of the nucleus from this central point of rotation, to that of the electron, will be the inverse of the ratio of their masses. Augmenting this is the fact that, as shown in [9], the spin - orbit magnetic dipole coupled precession rate of the nucleus is significantly greater than that of the electron. When allowance for these latter factors is introduced, a further small additional energy term of relativistic magnitude results that is also to be added to the fine structure orbital energy levels.

When these extra terms are introduced the overall orbital energy levels are seen to incorporate the Lamb Shift. The resulting energy levels and emission spectra so obtained can then be compared in detail with those in [5], which is believed to be the most accurate published data on outer shell single electron atoms.

Note that in the mathematical derivations in this paper, a parameter will only be defined if it has not previously been so in earlier papers in this series, i.e. [6], [7], [8] and [9].