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* |
-1 | 0 | -1 |
0 | -1 | 1 | O.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 Dnf < -1 |
| nf* -1 |
- 1/2 |
nf* - 3/2 |
- 1/2 |
nf* -2 |
-1 |
-1 |
-2 |
-1 |
-3 |
7(-) |
N.P. |
Dnj < -1 Dnf < -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 Dnf < -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 Dnf > +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 Dnf > +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
|