Term symbol

In atomic spectroscopy, a term symbol gives the total spin-, orbital-, and spin-orbital angular momentum of the atom. The term symbol has the following form:

$^{2S+1}X_{J},\,$

where S is the total spin angular momentum and 2S+1 is the spin multiplicity. The symbol X represents the total orbital angular momentum. For historical reasons it is coded by a letter as follows (between brackets the L quantum number designated by the letter):

$S(0),\,P(1),\,D(2),\,F(3),\,G(4),\,H(5),\,I(6),\,K(7),\dots ,$

and further up the alphabet (excluding P and S). The value J is the quantum number of the spin-orbital angular momentum: J ≡ L + S. The value J satisfies the triangular conditions:

$J=|L-S|,\,|L-S|+1,\,\ldots ,L+S,$.

Sometimes the parity of the state is added, as in

$^{2S+1}X_{J}^{o},\,$

which indicates that the state has odd parity. This is the case if the sum of the one-electron orbital angular momenta 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. The eigenstates labeled by a term symbol are obtained in the Russell-Saunders coupling scheme.

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Examples

A few ground state atoms are listed.

• Hydrogen atom: $^{2}S_{\frac {1}{2}}$. Spin angular momentum: S = 1/2. Orbital angular momentum: L = 0. Spin-orbital angular momentum: J = 1/2. Electronic configuration: 1s. Parity: even.

• Carbon atom: $^{3}P_{0}\,$. Spin angular momentum: S = 1. Orbital angular momentum: L = 1. Spin-orbital angular momentum: J = 0. Electronic configuration: [He]2s²2p². Parity even.

• Aluminium atom: $^{2}P_{\frac {1}{2}}^{o}\,$. Spin angular momentum: S = 1/2. Orbital angular momentum: L = 1. Spin-orbital angular momentum: J = 1/2. Electronic configuration: [Ne]3s²3p¹. Parity odd.

• Scandium atom: $^{2}D_{\frac {3}{2}}\,$. Spin angular momentum: S = 1/2. Orbital angular momentum: L = 2. Spin-orbital angular momentum: J = 3/2. Electronic configuration: [Ne]3s²3p⁶3d¹4s². Parity even.