may be found in Astrophysical Quantities, page 6Iff (C W Allen, 3rd edn 1973, Athlone Press) and in the references therein.
Absorption lines originating from the ground state of an atom or ion are usually very strong. Thus, for example, the H and K Fraunhofer lines in the solar spectrum originate from the ground state of ionized calcium. Such lines are known as resonance lines, and their strength is due to the very large majority of atoms or ions being in their ground state even at temperatures of several thousand degrees (see the Boltzmann formula, equation (4.5)).
Relative intensities between multiplets can also be predicted (the intensity of a multiplet is given by the sum of the individual intensities of its lines). This is relatively straightforward for multiplets arising from the same electron jump (related multiplets). Thus, the multiplets arising from one of two valence electrons jumping from a p to a d orbit have the relative intensities shown in table 4.2.
More complete tables of relative intensities between multiplets are to be found in Astrophysical Quantities, p 66ff (reference above). The relative strengths of unrelated multiplets are much more difficult to calculate; again details are given in Astrophysical Quantities.
Knowledge of such predicted relative intensities is very useful when trying to identify unknown lines in a spectrum. If one such line is tentatively identified, then the other lines in the same multiplet should be present in approximately their theoretical relative intensities. Thus if the initial identification is of a weak line in a multiplet and the stronger lines are not found, then the identification is probably wrong. Conversely, if several lines from the multiplet can be found, then the identification stands a good chance of being correct. The calculated intensities should not be relied on completely, however, since the populations of the excited levels in atoms can vary a good deal from those of thermodynamic equilibrium. Thus in low density environments such as interstellar nebulae, stellar coronae etc, metastable levels (levels from which there are only forbidden downward transitions) can become overpopulated compared with the populations in thermodynamic equilibrium, leading to forbidden lines (see later in this chapter) dominating the spectrum. In the laboratory, excitation of lines by electric sparks or arcs can lead to unusual population balances between different levels. Nonetheless, if used cautiously, the predicted relative strengths within multiplets are a useful tool to the spectroscopist.
In our discussion of selection rules, we have so far assumed that L-S coupling
(chapter 3) can be applied. This assumption is valid most of the time in astronomical spectroscopy. Nonetheless, there are occasions when j-j coupling becomes important. Since L and S no longer have any meaning under this form of interaction, the selection rules applying to them disappear. The selection rules under j-j coupling thus become
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