It is in the characterisation of the Selection Rules of electron transitions, that the mechanical aspects of electron spin have another important effect. The geometry of photon emission and electron shell/orbital transitions is proposed as follows.

In a similar manner to the Compton effect, as a result of emitting a photon at the initiation of a transition, the electron will recoil in the opposite direction to the emission in accordance with the law of conservation of momentum. Fig. 4.1 below presents a pictorial representation.

The direction of photon emission can only be tangential to the orbital path, forward or backward, because they are the only directions in which the electron can impart momentum to the photon. Thus at the initiation of an electron transition, it imparts to the outgoing photon one or more quanta of kinetic energy, thereby causing the electron to fall to a lower shell. The momentum thereby imparted to the photon causes the electron to lose, (forward photon emission, backward electron recoil), /gain, (backward photon emission, forward electron recoil), that same amount of momentum such that its orbital angular momentum is reduced/increased by one quanta. Thus when the electron falls to a lower shell, the orbital it inserts into can only be one of a higher or lower orbital angular momentum by exactly one quanta, than in the emission shell. The transition to a lower shell orbital of the same angular momentum is therefore automatically excluded. i.e. Dn_f ^* = 0 is not possible. Similarly, a change of n_f ^* of greater that ± 1 quanta is also excluded. The electron transition Selection Rule governing orbital angular momentum changes is thus given simply but exactly by

The transition path of the electron from the emission shell/orbital will, in view of the tangential nature of the recoil, be tangential to the orbital path. Also, during the transition, the motion of the electron is still mostly governed by the central coulomb force, and the transition path will therefore be degenerative. Insertion of the electron into the lower shell must also be tangential to the applicable orbital, because there would be no external influence affecting this part of the transition, and it must therefore be a smooth event. As a consequence of all the above, it would be expected that electron transition geometry would be one of the two types shown in Fig. 4.2.

It is now possible to determine the manner in which electron spin enters into the Selection Rule configuration. Fig.4.3 below presents a more detailed version of Fig.4.2 in which the direction of electron spin has been added in each quadrant. This of course assumes that the nature of electron spin is as proposed in Section 2. The formal adoption of this mechanism as the cause of electron spin has been made at this point, because that mechanism incorporates a natural means by which transitional spin reversal occurs, and this feature is seen to occur in empirical data, i.e.[5].

Assume that electron transitions can occur from any quadrant on shell A to some other quadrant on shell B. The following tables and explanatory notes detail the characteristics of those transitions that are "permitted" and those that are not. It is in these tables that the inner quantum number is introduced as

The primary significance of n_j will become apparent in the next paper in which the magnetic effects of electron spin are considered.

Current theory, [6], states that these transitions are excluded because they incur a change of total angular momentum of ±2, (i.e.Dn_j = ±2). However, because the orbital and spin motions of the electron are entirely separate, there should be no quantum reason why the change in their angular momenta could not be in the same direction resulting from an electron transition. This statement is just as applicable in the theory proposed here, with the cause of electron spin as described in Section 2, as in any other theory. The reason for the exclusion of these transitions is not considered to be the Dn_j result, which is considered to be "co-incidental", but rather a result of electron transition geometry restrictions. First consider transition type 7 above in relation to Fig. 4.2. For a Dn_f ^* = -1 degenerative trajectory, it is proposed that it would not be possible for the electron to make a tangential transition from quadrants A1 or A3 into B2 or B4. The degeneracy of the transition path would be such as to allow a tangential insertion only into B3 or B1, i.e. a type 1 transition. The same comment applies to transition type 8 for a Dn_f ^* = +1 transition where for the resulting path only a type 6 is possible. Confirmation of this proposed reason for the exclusion of the Dn_j = ±2 transitions would necessitate a detailed derivation of the respective orbit and transition paths.

Transitions to a s orbital for which Dn_f ^* = +1 are excluded because this would mean a transition from a n_f ^* = 0 orbital, i.e. a pendulum orbit and these were proven in [1] to be excluded in atomic structure. Therefore, only transitions for which Dn_f ^* = -1 are possible, with one exception. Transition type 3 is also excluded because it would mean that in the receiving s orbital. n_j would be < 1, (= + 1/ 2 ), and by de Broglie's hypothesis n_j ³ 1. This has the important consequence that in the receiving s orbital only electrons with n_sp = + 1/ 2 can make a transition insertion. Because s orbitals are elliptical and therefore subject to spin induction, this raises an apparent anomaly when the inserted electron orbits to the next quadrant, and the spin changes direction. This is discussed below in (vi).

Transitions from an s orbital for which Dn_f ^* = -1 are not permitted because this would mean a transition to a n_f ^* = 0 orbital, i.e. a pendulum orbit and these were proven in [1] to be excluded in atomic structure. Therefore only transitions for which Dn_f ^* = +1 are possible with one exception. Because only electrons with n_sp = + 1/ 2 can exist in a s orbital, transition type 6 is also excluded.

There are no transitions possible from this one orbital. This is because a Dn_f ^* = -1 transition would result in a n = 1, n_f ^* = 0 pendulum orbit which were proven to be excluded in [1]. Transitions for which Dn_f ^* = +1 are also excluded because there is no orbital in the n = 1 shell for which n_f ^* = 2, and it would otherwise mean a transition from an orbital with n_f ^* = 0, a pendulum orbit. However, electrons can make a transition insertion into this orbital with n_sp = + 1/ 2 , (into a spin-up quadrant), and so it would appear that such an electron would presumably remain there until excited up through the shells again. However, in the next paper, which deals with magnetic effects, it will be shown that subsequently an electron in this orbital will quite naturally make a smooth transition into another orbital in the same shell, (with zero energy change), from which it can make a normal inter-shell transition to the ground state. This intra-shell transition occurs as the electron's spin changes as it traverses into a spin-down quadrant in this s orbital. This feature also applies in (iv) above to avoid the apparent anomaly discussed briefly there.

It is clear from the above tables and exclusion discussions that the Selection Rules stated in terms of n_j are,

However, neither (4.1) nor (4.3) are universal as both are only applicable conditionally as shown in (iii), (iv), (v) and (vi) above. The Selection Rules will be further refined when spin-orbit magnetic coupling is introduced in the next paper.