During the early part of the 20^th century, investigations into the structure of the atom were primarily led by Niels Bohr and his collaborators. Niels Bohr was a Danish physicist working in Manchester. In the original Bohr theory for hydrogen like atoms with a single electron, (H, He⁺, L⁺⁺ etc), the atom was perceived with the electron as a real physical particle orbiting a central nucleus in a circular orbit. The energy levels of the orbits were specified by Niels Bohr based upon an empirical formula devised by Thomas Balmer, [3], [7], to portray the visible spectral lines of hydrogen. While such an arbitrary hypothesis is unsatisfactory as the basis for a theory of atomic structure, it was nevertheless developed to a point of considerable sophistication, e.g. to explain the fine structure of the hydrogen spectra, elliptic orbits together with relativistic mass correction effects were subsequently incorporated by the German physicist Arnold Sommerfeld. The energy levels of Niels Bohr were eventually shown to be theoretically derivable if the angular momentum of the electron in its orbit was quantised. However, there was in turn no theoretical basis for this stipulation and the entire theory, (the öld" quantum theory), was dropped. It was replaced by the newly emerging wave mechanics in which, subsequent to Planck's and de Broglie's hypotheses and Erwin Schrodinger's construction of his describing equation, the electron was represented as a wave function wherein, in a stable atomic örbit", its orbital path length was stipulated to be an integral number of its wavelength. Despite the subsequent success that this approach has had in describing atomic structure, it is considered that it suffers from similar deficiencies to those of the old quantum theory. For instance, it is acknowledged that Schrodinger's equation cannot be derived from first principles, or "proved", and is regarded as a fundamental hypothesis of the quantum mechanics theory of the atom, [4], [5]. It is believed that this is the only case in science where a second order differential equation is accepted as a basic hypothesis. Also there does not appear to be any theoretical justification for the criterion of quantisation, viz. the single valuedness of the electron matter wave wavelength in its örbit" of the nucleus.

To avoid such difficulties, this paper presents a resurrection of the Bohr/Sommerfeld old quantum theory of atomic structure into which, based upon the results contained in [1], the primary quantisation criterion of the quantum mechanics theory, subsequent to its theoretical justification in this paper, can be re-interpreted and inserted. Justification for this is that in [1] it has been shown that in the Relativistic Space-Time D₀, the characteristics of de Broglie matter waves provide a sound theoretical basis by which the spatial part of the wavelength of such waves can be expressed as a function of the relativistic physical velocity of the matter particle they represent. viz. [1], Eq.(). The resurrection of this theory will thereby provide an alternative to the unfortunate direction that quantum mechanics has taken in portraying the electron in probabilistic terms rather than physical. The former being completely foreign to the existence of real energy in a real space-time domain. Consequently, if in the resurrected Bohr/Sommerfeld theory, the electron is to be depicted as a real physical particle with finite extensions, albeit with a dual wave function existence, it will be necessary, wherever possible as the development proceeds, to provide a physical interpretation of the results.

Before the ideas in [1], as discussed above are linked into the resurrected theory, it is necessary to address some preliminary points. First, it will be useful to define the nomenclature for quantum numbers to be used in this paper for comparison with those in current practice. Next, in the derivation of the principle quantum number, the requirement that the orbit path length be an integral number of the electrons matter wave wavelength is itself an arbitrary stipulation without theoretical formalism. This must be provided. Next, this theoretical formalism should also provide a logical reasoning for which types of orbit are allowed and their basic characteristics. Also, a suitable expression for the bound energy of the electron is needed into which suitably quantised parameters can be inserted to produce a stable orbit energy level. This expression must allow for electron relativistic mass increase effects. All of the above points are addressed in the next Section.

It should be noted that this paper, particularly Section 2 should be read in conjunction with reference [1].