Term symbol: Difference between revisions
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In [[atomic spectroscopy]], a '''term symbol''' gives the total spin-, orbital-, and spin-orbital [[angular momentum (quantum)|angular momentum]] of the | In [[atomic spectroscopy]], a '''term symbol''' gives the total spin-, orbital-, and spin-orbital [[angular momentum (quantum)|angular momentum]] of an [[atom]] in a certain quantum state (often the ground state). The simultaneous eigenfunctions of '''L'''<sup>2</sup> and '''S'''<sup>2</sup> labeled by a term symbol are obtained in the [[Russell-Saunders coupling]] (also known as ''LS'' coupling) scheme. | ||
:<math> | |||
^{2S+1} | A term symbol has the following form: | ||
::<math> | |||
^{2S+1}\!L_{J} .\; | |||
</math> | |||
Here: | |||
*The symbol ''S'' is the total spin angular momentum of the state and 2''S''+1 is the spin multiplicity. | |||
*The symbol ''L'' represents the total orbital angular momentum of the state. For historical reasons ''L'' is coded by a letter as follows (between brackets the ''L'' quantum number): | |||
::<math> | |||
S(0), \; P(1),\; D(2),\; F(3),\; G(4),\; H(5),\; I(6),\; K(7), \dots, | |||
</math> | </math> | ||
:and further up the alphabet (excluding ''P'' and ''S''). | |||
*The subscript ''J'' in the term symbol is the quantum number of the spin-orbital angular momentum: '''J''' ≡ '''L''' + '''S'''. The value ''J'' satisfies the [[Angular momentum coupling#Triangular conditions|triangular conditions]]: | |||
::<math> | |||
J = |L-S|,\, |L-S|+1, \, \ldots, L+S, | |||
</math>. | |||
A term symbol is often preceded by the [[Atomic electron configuration|electronic configuration]] that leads to the ''L''-''S'' coupled functions, thus, for example, | |||
:<math> | :<math> | ||
(ns)^k \, (n'p)^{k'}\, (n''d)^{k''}\,\,\, ^{2S+1}L . | |||
</math> | </math> | ||
The (2''S''+1)(2''L''+1) different functions referred to by this symbol form a ''term''. When the quantum number ''J'' is added (as a subscript) the symbol refers to an ''energy level'', comprising 2''J''+1 components. | |||
Sometimes the [[parity]] of the state is added, as in | Sometimes the [[parity]] of the state is added, as in | ||
:<math> | :<math> | ||
^{2S+1} | ^{2S+1}L_{J}^o, \, | ||
</math> | </math> | ||
which indicates that the state has odd parity. This is the case | which indicates that the state has odd parity. This is the case when the sum of the one-electron | ||
orbital angular | 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 2''S''+1 | 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 2''S''+1. | ||
{{editintro}} | {{editintro}} | ||
==Examples== | ==Examples== | ||
A few ground state atoms are listed. | A few ground state atoms are listed. | ||
* [[Hydrogen]] atom: <math> ^2S_{\frac{1}{2}}</math>. Spin angular momentum: ''S'' = 1/2. Orbital angular momentum: ''L'' = 0. Spin-orbital angular momentum: ''J'' = 1/2. | * [[Hydrogen]] atom: <math>\scriptstyle 1s\,\,\, ^2S_{\frac{1}{2}}</math>. Spin angular momentum: ''S'' = 1/2. Orbital angular momentum: ''L'' = 0. Spin-orbital angular momentum: ''J'' = 1/2. Parity: even. | ||
* [[Carbon]] atom: <math>\scriptstyle (1s)^2\,(2s)^2\, (2p)^2\,\,\, ^3P_{0}\,</math>. Spin angular momentum: ''S'' = 1. Orbital angular momentum: ''L'' = 1. Spin-orbital angular momentum: ''J'' = 0. Parity even. | |||
* [[ | * [[Aluminium]] atom: <math>\scriptstyle (1s)^2\,(2s)^2\,(2p)^6\,(3s)^2\,3p\,\,\, ^2P_{\frac{1}{2}}^o\,</math>. Spin angular momentum: ''S'' = 1/2. Orbital angular momentum: ''L'' = 1. Spin-orbital angular momentum: ''J'' = 1/2. Parity odd. | ||
* [[ | * [[Scandium]] atom: <math>\scriptstyle (1s)^2\,(2s)^2\,(2p)^6\,(3s)^2\, (3p)^6\, 3d\, (4s)^2 \,\,\, ^2D_{\frac{3}{2}}\,</math>. Spin angular momentum: ''S'' = 1/2. Orbital angular momentum: ''L'' = 2. Spin-orbital angular momentum: ''J'' = 3/2. Parity even. | ||
* [ | ==External links== | ||
* [http://physics.nist.gov/Pubs/AtSpec/node09.html NIST Atomic Sectroscopy] | |||
* [http://physics.nist.gov/PhysRefData/IonEnergy/tblNew.html A list of term symbols for ground state atoms] | |||
[[Category: | [[Category:Suggestion Bot Tag]] | ||
Latest revision as of 17:01, 25 October 2024
In atomic spectroscopy, a term symbol gives 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:
Here:
- The symbol S is the total spin angular momentum of the state and 2S+1 is the spin multiplicity.
- The symbol L represents the total orbital angular momentum of the state. For historical reasons L is coded by a letter as follows (between brackets the L quantum number):
- and further up the alphabet (excluding P and S).
- The subscript J in the term symbol is the quantum number of the spin-orbital angular momentum: J ≡ L + S. The value J satisfies the triangular conditions:
- .
A term symbol is often preceded by the electronic configuration that leads to the L-S coupled functions, thus, for example,
The (2S+1)(2L+1) different functions referred to by this 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
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.
Examples
A few ground state atoms are listed.
- Hydrogen atom: . Spin angular momentum: S = 1/2. Orbital angular momentum: L = 0. Spin-orbital angular momentum: J = 1/2. Parity: even.
- Carbon atom: . Spin angular momentum: S = 1. Orbital angular momentum: L = 1. Spin-orbital angular momentum: J = 0. Parity even.
- Aluminium atom: . Spin angular momentum: S = 1/2. Orbital angular momentum: L = 1. Spin-orbital angular momentum: J = 1/2. Parity odd.
- Scandium atom: . Spin angular momentum: S = 1/2. Orbital angular momentum: L = 2. Spin-orbital angular momentum: J = 3/2. Parity even.