2 The Hyperfine Structure.2.1 Preliminary Discussion.In establishing the characteristics of hyperfine orbitals and transitions in the resurrected theory, in order for these characteristics to be sufficient and complete, it will be necessary to answer a number of pertinent questions as follows. (i) What is the quantum number status of the hyperfine orbitals?(ii) What are the Selection Rules applicable to intra-shell hyperfine transitions? (iii) Where does the photon momentum come from in a hyperfine transition? (iv) What is the photon emission mechanism in a hyperfine transition? (v) What is the energy release in a hyperfine transition? All of these questions will be answered in the remainder of this paper. In the resurrected theory, the hyperfine orbitals in all orbit shells, are completely defined by spin magnetic dipole coupling between the electron and the proton, both of which can spin in either direction. It will be shown that hyperfine intra-shell orbital transitions, involve a spin reversal of just the electron. Now, for this to be effected in the ground state orbit shell, the electron must exist in one orbital in a spin down state with ensp = - 1/ 2 . With nf * = +1/2 in this shell, it would then mean that in the orbital concerned nj = 0, which is strictly prohibited. It is therefore proposed that in these particular ground state hyperfine orbitals, nf * must be increased by unity. This ensures that nj remains a good quantum number. Note that this condition is really no different to the relationship that exists between the ns(+) and np(-) orbitals et al via the Dead Zones as demonstrated in [2]. The fact that as a consequence in some hyperfine orbitals in the ground state orbit shell, nf * is then greater than n, is of no consequence because nj is still equal to n in these orbitals, so that they retain precisely the same geometric characteristics. Furthermore, it will be shown that it is this proposed azimuthal momentum variation that provides the momentum for the outgoing hyperfine photon emission. Also, it will be seen, when the mathematical representation is considered, that it is this variation that leads to the correct relationship. Also, it will become clear when energy levels are calculated, that the hyperfine spectra are very dependent upon dp, the proton spin magnetisation constant of proportionality. Because this factor is purported to be produced by exactly the same phenomenon as gp, the primary restriction on dp is that it must be positive and of the same order of magnitude as gp. Finally, prior to derivation of the mathematical representation of hyperfine orbital energy levels and spectral emissions, it is necessary to determine the configuration of all hyperfine orbitals and manner in which transitions between them are effected. 2.2 The Hyperfine Orbitals.With the hyperfine orbitals included, there are theoretically 4n possible orbitals in the ground state shell, and (4n - 2) in every other orbit shell. Using the results of the discussion in the previous Section, these orbitals are shown and characterised for the first three orbit shells in the following table, which is an extension of [1], Table 3.1, (listed in order of increasing energy).
From this table it is seen that for every "normal" orbital there is one
hyperfine orbital, except for the ground state orbit shell, for which there
is a hyperfine triplet. The term sequence adopted for the hyperfine orbitals
is the subscript h# with the spin designator, (+ or -), according to the
direction of electron spin. It is also clear that in the ground state orbit
shell, for hyperfine orbitals in which Note that the contents of Table 2.1 satisfactorily answers question (i) in Section 2.1.2 above.
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P.G.Bass, August 2007
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