Now pure j-j coupling occurs relatively seldom, and within a single atom some terms may remain determined by L-S coupling while others are influenced by j-j coupling. Thus, in practice, the importance of j-j coupling is in modifying the L-S coupling selection rules, rather than having a widespread application in its own right. The commonest such modification results in the relaxation of the L-S selection rule, AS = 0, so that transitions in which the multiplicity changes can occur. Thus for example in the spectrum of neutral silicon, we may find lines arising from the transition
where S changes from 1 to 0. Lines arising from such transitions are forbidden by the strict L-S coupling selection rules, and so are often called Forbidden Lines. This particular breakdown of L-S coupling due to the onset of j-j coupling is a relatively mild and quite prevalent transgression against the L-5 selection rules. Lines resulting from it are often regarded as not 'really' forbidden, and are called Intercombination Lines. Intercombination lines can often be found in normal stellar spectra, though their intensities will usually be much less than those of comparable allowed lines and multiplets. The presence of intercombination lines in the spectrum of an atom indicates that strict L-S coupling is starting to break down. When writing down transitions and their resulting lines, a system of square-bracket notation is used to indicate the nature of the transitions (the positioning of the brackets can vary): No brackets: allowed line, e.g. H I 656.3 or O I 630.0 One bracket: intercombination line, e.g. Mg I] 457.1 or K III 348.1] Two brackets: forbidden line, e.g. [N III] 386.9 or [O II 732.0]. What we may now call 'true' forbidden lines arise from other modes in which L-S coupling fails. This may occur in several ways. The selection rule itself may only be a first approximation, the transition may occur through magnetic dipole or electric quadrupole interactions, or the presence of electric or magnetic fields from nearby atoms and ions may disturb the L-S coupling sufficiently for the transition to take place. These variations allow changes such as A 7 = ±2, AL = ±2, AM = ±2 to occur during transitions, or for the parity not to change. In the laboratory or in stellar spectra, lines arising from such forbidden transitions may be expected to be from 10"5 to 10"12 times fainter than the allowed lines in the same atom.
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