Term symbol

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In atomic spectroscopy, a term symbol indicates the total spin-, orbital-, and spin-orbital angular momentum of an atom in a certain quantum state (often the ground state). The simultaneous eigenfunctions of L2 and S2 labeled by a term symbol are obtained in the Russell-Saunders coupling (also known as LS coupling) scheme.

A term symbol has the following form:


  ^{2S+1}\!L_{J} .\;

Here:


S(0), \; P(1),\; D(2),\; F(3),\; G(4),\; H(5),\; I(6),\; K(7), \dots,
and further up the alphabet (excluding P and S).

J = |L-S|,\, |L-S|+1, \, \ldots,\, L+S-1, \, L+S,\quad\hbox{that is,}\quad |L-S| \le J\le L+S.
.


A term symbol is often preceded by the electronic configuration that leads to the L-S coupled functions, thus, for example,


(ns)^k \, (n'p)^{k'}\, (n''d)^{k''}\,\,\, ^{2S+1}L ,

which indicates an electron configuration with k electrons occupying an ns orbital (0 ≤ k ≤ 2), k′ electrons occupying an n′p orbital (0 ≤ k′ ≤ 6), and k′′ electrons occupying an n′′d orbital (0 ≤ k′′ ≤ 10). The k+k′+k′′ electrons are coupled to a spin state of quantum number S that has multiplicity 2S+1; and the electrons are coupled to an orbital state characterized by the letter L (where the letter is in one-correspondence with the quantum number L) that has multiplicity 2L+1. The (2S+1)(2L+1) different functions referred to by a term symbol form a term. When the quantum number J is added (as a subscript) the symbol refers to an energy level, comprising 2J+1 components.

Sometimes the parity of the state is added, as in


  ^{2S+1}L_{J}^o, \,

which indicates that the state has odd parity. This is the case when the sum of the one-electron orbital angular momentum numbers in the electronic configuration is odd.

For historical reasons, the term symbol is somewhat inconsistent in the sense that the quantum numbers L and J are indicated directly, by a letter and a number, respectively, while the spin S is indicated by its multiplicity 2S+1.


[edit] Examples

A few ground state atoms are listed.

[edit] External links

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