(a) The orbital angular momenta of the electrons are coupled to give a total orbital angular momentum L = Σili.The combination of a particular S value with a particular L value comprises a spectroscopic term, the notation for which is 2S+1L. The quantum number 2S + 1 is the multiplicity of the term. The S and L vectors are coupled to obtain the total angular momentum, J = S + L, for a level of the term; the level is denoted as 2S+1LJ.
(b) The spins of the electrons are coupled to give a total spin S = Σi si.
For 1snl configurations, L = l and
S = 0 or 1, i.e., the terms are singlets
(S = 0) or triplets (S = 1). As
examples of the He I structure, the ionization energy
(energy required to remove one of the 1s electrons in the
1s2 ground configuration) is 24.5874 eV, the
1s2s 3S - 1S separation is
0.7962 eV, the
1s2p 3P° - 1P°
separation is 0.2539 eV, and the
1s2p 3P°2 - 3P°0
fine-structure spread is only
1.32 × 10-4 eV.
|Quantum numbers a||Group of all|
|Polyad||(nili)Ni γS1 L1 nl S L, S L′ ...||Supermultiplet|
|Term||(nili)Ni γS L||Multiplet|
|Level||(nili)Ni γS L J||Line|
|State||(nili)Ni γS L J M||Line component|
|a The configuration may include several open subshells, as indicated by the i subscripts. The letter γ represents any additional quantum numbers, such as ancestral terms, necessary to specify a particular term.|
As an example, the Ca I 3d4p 3D°2 level belongs to the 3D° term which, in turn, belongs to the 3d4p 3(P° D° F°) triplet triad. The 3d4p configuration also has a 1(P° D° F°) singlet triad. The 3d4s configuration has only monads, one 1D and one 3D. The 3d4s 3D2 - 3d4p 3D°3 line belongs to the corresponding 3D - 3D° triplet multiplet, and this multiplet belongs to the great Ca I 3d4s 3D - 3d4p 3(P° D° F°) supermultiplet of three triplet multiplets discussed by Russell and Saunders in their classic paper on the alkaline-earth spectra . The 3d4s - 3d4p transition array includes both the singlet and triplet supermultiplets, as well as any (LS-forbidden) intercombination or intersystem lines arising from transitions between levels of the singlet system and those of the triplet system. The order of the two terms in the transitions as written above, with the lower-energy term on the left, is standard in atomic spectroscopy. Examples of notations for complex configurations are given in Notations for Different Coupling Schemes.