Appendix C.

Extension of the Transition Type Table to Incorporate the Hyperfine Orbitals.

In [9], all possible electron inter-shell transitions for the "normal" orbitals, were analysed for permissability and presented as a series of tables, i.e. [9], Section 4.0, Tables (i), (ii) and (iii). Here, those tables are consolidated and extended to incorporate the hyperfine orbitals. To simplify matters, the quadrant numbers are omitted in order to make way for details concerning the status of the proton.

The nomenclature adopted for the type numbers are as those in [9], Section 4.0, Tables (i), (ii) and (iii), with the bracketted sense of Dpnsp added to distinguish the hyperfine orbitals. In the "Status" column, Ö.K". means this transition is permitted by the Selection Rules. "N.P." means the transition is not.

Note 1 in Table C.1 below.

This transition is into a spin-up quadrant in which the spin induction mechanism and the external stimulus are complementary for the proton. It cannot therefore change proton spin from spin-up to spin-down. Hence the transition is "N.P", {Selection Rule (2.6)}

In the downloadable spreadsheet Hydrogen Spectra, in Appendix A, the algorithm for Selection Rule (2.6) has been truncated to omit the status of ensp in the receiving orbital, because transition type 6(-) does not occur between orbit shells 3 & 2 to 2 & 1.

Although not shown in the table below, it is noted for interest that the hyperfine transition 1sh2(-) Þ 1s(+), is a type 2 transition.

It is important to note that as a result of the Selection Rule extensions in this paper, transitions into some orbitals are more prevalent than into others. This will affect the distribution of spectral relative intensities.

Inter-Shell Transition
"From" Orbital
Inter-Shell Transition
"To" Orbital
Quantum Number Change
D(Quantum Number)
Type Status "Not
Permitted
Reason"
nf* ensp nj pnsp nf nf* ensp nj pnsp nf nf * ensp nj pnsp nf
Transition Type Group Dfn *  =  -1
nf* + 1/2 nf* + 1/2 + 1/2 nf* +1 nf * -1 + 1/2 nf* - 1/2 + 1/2 nf* -10-1 0-11O.K.  
nf* -1 + 1/2 nf* - 1/2 - 1/2 nf* -1 -1 0 -1 -1 -2 1(-) N.P. Dnf < -1
nf* -1 - 1/2 nf* -3/2 + 1/2 nf* -1 -1 -1 -2 0 -2 7 N.P. Dnj < -1
D
nf < -1
nf* -1 - 1/2 nf* - 3/2 - 1/2 nf* -2 -1 -1 -2 -1 -3 7(-) N.P. Dnj < -1
D
nf < -1
nf* + 1/2 nf* + 1/2 - 1/2 nf* nf* -1 + 1/2 nf* - 1/2 + 1/2 nf* -1 0 -1 +1 0 1(+) O.K.  
nf* -1 + 1/2 nf* - 1/2 - 1/2 nf* -1 -1 0 -1 0 -1 1 O.K.  
nf* -1 - 1/2 nf* - 3/2 + 1/2 nf* -1 -1 -1 -2 +1 -1 7(+) N.P. Dnj < -1
nf* -1 - 1/2 nf* - 3/2 - 1/2 nf* -2 -1 -1 -2 0 -2 7 N.P. Dnj < -1
D
nf < -1
nf* - 1/2 nf* - 1/2 + 1/2 nf* nf* -1 + 1/2 nf * - 1/2 + 1/2 nf * -1 +1 0 0 0 2 O.K.  
nf* -1 + 1/2 nf* - 1/2 - 1/2 nf* -1 -1 +1 0 -1 -1 2(-) N.P. See Note 1
above
nf * -1 - 1/2 nf* - 3/2 + 1/2 nf* -1 -1 0 -1 0 -1 3 O.K.  
nf* -1 - 1/2 nf* - 3/2 - 1/2 nf * -2 -1 0 -1 -1 -2 3(-) N.P. Dnf < -1
nf* - 1/2 nf* - 1/2 - 1/2 nf* nf* -1 + 1/2 nf* - 1/2 + 1/2 nf* -1 +1 0 +1 +1 2(+) O.K.  
nf* -1 + 1/2 nf* - 1/2 - 1/2 nf* -1 -1 +1 0 0 0 2 O.K.  
nf* -1 - 1/2 nf* - 3/2 + 1/2 nf* -1 -1 0 -1 +1 0 3(+) O.K.  
nf* -1 - 1/2 nf* - 3/2 - 1/2 nf* -2 -1 0 -1 0 -1 3 O.K.  
Transition Type Group Dfn * = +1
nf* + 1/2 nf* + 1/2 + 1/2 nf* +1 nf* +1 + 1/2 nf* + 3/2 + 1/2 nf* +2 +1 0 +1 0 +1 4 O.K.  
nf* +1 + 1/2 nf* + 3/2 - 1/2 nf* +1 +1 0 +1 -1 0 4(-) N.P. See Note 1
above
nf* +1 - 1/2 nf* + 1/2 + 1/2 nf* +1 +1 -1 0 0 0 5 O.K.  
nf* +1 - 1/2 nf* + 1/2 - 1/2 nf* +1 -1 0 -1 -1 5(-) O.K.  
nf* + 1/2 nf* + 1/2 - 1/2 nf* nf* +1 + 1/2 nf* + 3/2 + 1/2 nf* +2 +1 0 +1 +1 +2 4(+) N.P. Dnf > +1
nf* +1 + 1/2 nf* + 3/2 - 1/2 nf* +1 +1 0 +1 0 +1 4 O.K.  
nf* +1 - 1/2 nf* + 1/2 + 1/2 nf* +1 +1 -1 0 +1 +1 5(+) O.K.  
nf* +1 - 1/2 nf* + 1/2 - 1/2 nf* +1 -1 0 0 0 5 O.K.  
nf* - 1/2 nf* - 1/2 + 1/2 nf* nf* +1 + 1/2 nf* + 3/2 + 1/2 nf* +2 +1 +1 +2 0 +2 8 N.P. Dnj > +1
D
nf > +1
nf* +1 + 1/2 nf* + 3/2 - 1/2 nf* +1 +1 +1 +2 -1 +1 8(-) N.P. Dnj > +1
nf* +1 - 1/2 nf* + 1/2 + 1/2 nf* +1 +1 0 +1 0 +1 6 O.K.  
nf* +1 - 1/2 nf* + 1/2 - 1/2 nf* +1 0 +1 -1 0 6(-) O.K.  
nf* - 1/2 nf* - 1/2 - 1/2 nf* -1 nf* +1 + 1/2 nf* + 3/2 + 1/2 nf * +2 +1 +1 +2 +1 +3 8(+) N.P. Dnj > +1
D
nf > +1
nf* +1 + 1/2 nf* + 3/2 - 1/2 nf* +1 +1 +1 +2 0 +1 8 N.P. Dnj > +1
nf* +1 - 1/2 nf* + 1/2 + 1/2 nf* +1 +1 0 +1 +1 +2 8(+) N.P. Dnf > +1
nf* +1 - 1/2 nf* + 1/2 - 1/2 nf* +1 0 +1 0 +1 6 O.K.  

TABLE C.1. - TRANSITION TYPES INCLUDING ALL POSSIBLE NORMAL AND HYPERFINE TRANSITION COMBINATIONS.


P6 Version 1.0.0
Ó P.G.Bass, August 2007

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