2.3.1  Pre-Amble.

Prior to determination of the Selection Rule extensions to include hyperfine transitions, it is necessary to ascertain what phenomena affect such transitions and the order of precedence in which they take effect.

Because the ground state set of orbitals are inherently stable, any electron transition between them can only be initiated by some external stimulus extant within the inter-stellar environment. Consequently this increases to three, the number of phenomena affecting transitions. They are:-

(i) The spin angular momentum criteria.

(ii) The spin induction mechanism.

(iii) The external stimulus.

Now, the order of precedence with which these phenomena take effect can only be determined by analysing the spectral signature for each of their six possible order combinations, and comparing the results with the known correct signature. Having performed this analysis for hydrogen, the correct order is in fact as shown above. Any other order does not produce the correct spectral signature.

The application of these phenomena in the order listed to set the Selection Rules, and thus govern the manner of electron transitions, is to some extent orbit shell and orbital quadrant dependent.
In all orbit shells other than the ground state and the 2^nd, the spin angular momentum criteria governs exclusively the manner in which all electron transitions are initiated. Then, subsequent to such an electron transition, the spin induction mechanism and the external stimulus act in a secondary capacity to re-align particle spins according to the orbital quadrant into which the electron makes the transition. In quandrants where the spin induction mechanism and the external stimulus are complementary, both particle spins can be re-aligned. In quadrants where they are in opposition, only the electron's spin is certain to be re-aligned. The spin direction of the proton, because of its much higher mass, may not be changed before the electron spin angular momentum criteria causes a further electron inter-shell transition.
In the 2^nd orbit shell, the 2s(+) and the 2s_h(+) orbitals are meta-stable, i.e. the spin angular momentum criteria has been met, and therefore the second of the above phenomena becomes predominantly effective in re-aligning both electron and proton spins as the electron passes through the Dead Zones into the 2p(-) orbital. In this latter orbital the spin angular momentum criteria once again takes precedence and initiates an inter-shell electron transition to the ground state as has been previously described in [1].
In the ground state orbit shell the situation is again different because not only has the spin angular momentum criteria been met in all orbitals, but they are all circular orbitals and so spin induction is not present. Therefore the only phenomenon affecting electron transitions is the external stimulus.

The above dissertation now permits the determination of the Selection Rules for both intra and inter-orbit transitions, and the permitted transitions themselves.

2.3.2  Intra-Orbit Shell Hyperfine Transitions.

However, it will be seen that out of this total number of combinations, there is only one intra-orbit hyperfine transition possible.

The Selection Rules that govern inter-shell transitions do not apply here and it is necessary to develop a new set, which is effected taking into account the dissertation of the previous Section, and by using empirical results as follows.

The external stimulus governing the ground state hyperfine transitions must be such that it only causes the single transition resulting in the 21cm line. Furthermore, to cause this emission its effect must be to result in a spin reversal of either the electron or proton, but not both, (because of their opposite polarity charge). Lastly, of course the outgoing photon must take one quanta of momentum with it. From Table 2.1, it is clear that the only transition that satisfies all of these conditions is a 1s_h2(-) Þ 1s(+) transition. Note that this transition incurs a spin reversal of just the electron, and a reduction in n_f ^* of unity.This latter effect obviously answers question (iii) in Section 2.1.2 above.

The above conditions define the Selection Rules which govern hyperfine transitions, and which may be stated as follows

These Rules answer question (ii) in Section 2.1.2 above.

Note that these results are sufficient in themselves to govern all intra-shell transitions without the necessity of considering n_f.

As a result of these Rules, the following tables list all intra-orbit transition combinations for the first two orbit shells together with all pertinent characteristics governing permissibility or otherwise. Note that these include the transitions of electrons through the Dead Zones between spin-up and spin-down elliptic orbitals as delineated in [1].

1. Orbit shell 2 is ünstable" and electrons in all orbitals of this shell will make an inter-shell transition to the ground state. The only exceptions to this are transition numbers 2 and 3. The 2s(+) and 2s_h(+) orbitals are meta-stable and electrons in these orbitals must make a Dead Zone transition into the 2p(-) orbital before making the inter-orbit transition to the ground state. Also, allowed transition #1, incurring no emission line, but just a minor orbit change, may not occur before an inter-orbit shell transition to the ground state is initiated by the electron spin angular momentum criteria.

Analysis of the intra-orbital transition combinations in all other orbit shells produces results identical to those of the 2^nd. These orbitals are also ünstable" and a similar note to that above for Table 2.3 applies, (apart from the reference to the meta-stable orbitals).

From the above tables it is clear that the only hyperfine transition that exists for hydrogen, is in the ground state orbit shell to produce the 21.1 cm emission line.

2.3.3  Intra-Orbital Hyperfine Transition Mechanisms.

Once an electron is captured in the 1s_h2(-) orbital, it would be in a stable orbit and could only make the 21.1cm hyperfine transition via the influence of the external stimulus. In order to cause the electron in this orbital to release a photon emission and make the transition, it is proposed that the external stimulus would have to be such as to cause the magnitude of the electron spin rate to increase. Its matter wave radius, G_e, would consequently reduce so as to maintain the spin angular momentum quantum criteria. In this way |_ew_sp| G_e would track up line 2 in [2], Fig. 5.1 until it reached the point at which |_ew_sp| G_e = c and, subsequently, via exactly the same mechanism as in an inter-orbit transition, a photon emission would be initiated and the hyperfine transition effected.

This proposed mechanism provides the answer to question (iv) in Section 2.1.2 above.

Electrons that enter the other two ground state hyperfine orbitals, 1s_h1(-) and 1s_h3(+), are also affected by the external stimulus. In the same way that it causes the spin-down magnitude of electron spin to increase, it would also cause the spin-up spin rate of the proton to increase. For the 1s_h3(+) orbital, if the spin of the proton was reversed due to this effect the electron would thereby move into the 1s(+) ground state orbital with no photon emission, (n_f ^* is the same in both orbitals), and the small energy difference would be accommodated by a minor orbital geometry change.

In the case of the electron in the 1s_h1(-) orbital, exactly the same effect as above would cause it to move into the 1s_h2(-) orbital, again with no photon emission. From there it would immediately make the 21.1cm hyperfine transition to the 1s(+) ground state. Note however, that this particular "transition", 1s_h1(-) Þ 1s_h2(-), would involve a very small energy absorption from the external stimulus.

Accepting this scenario results in additions, and the modification of appropriate entries, in Table 2.2.

2.3.4  Inter-Orbit Shell Transitions.

The number of theoretical transition combinations between any two orbit shells, including the hyperfine orbitals, is given by

n_(m) and n_(n) are the principle quantum numbers for the orbit shells in question.

This latter rule simply states that the maximum angular momentum quanta lost or gained by the atom in any transition cannot be greater than unity.

In the receiving quadrant if

the transition is "Not Permitted".

Appendix C contains the complete transition combination complex, in generalised form for inter-shell transitions, and shows in detail the reasons for permissability or otherwise.

All the above rules, for both intra and inter-orbit transitions, are utilised in Appendix A to generate the final spectral signature of hydrogen.