Spectral Terms and Notation in Atomic Physics
Spectral terms provide a compact way of describing the quantum states of electrons in atoms. They summarize the total orbital angular momentum, spin, and multiplicity of a given electronic configuration.
General Form of a Spectral Term
A spectral term is written as:
$$^{2S+1}L_J$$
- S: Total electron spin quantum number.
- 2S+1: Multiplicity (singlet, doublet, triplet, etc.).
- L: Total orbital angular momentum, denoted by letters (
S, P, D, F, ...for L=0,1,2,3,...). -
J: Total angular momentum, combining
LandS, ranging from \( \lvert L+S \rvert \) to \( \lvert L-S \rvert \) in steps of 1.
Examples of Spectral Terms
(a) Hydrogen Ground State
The electron has spin \(S = \tfrac{1}{2}\) and orbital angular momentum \(L = 0\). Thus:
$$^{2}S_{1/2}$$
This represents a doublet-S state with total \(J = 1/2\).
(b) Helium \(1s2s\) Configuration
For two electrons, spins can pair to form either:
- Singlet state: \(S=0\), term \(^1S_0\)
- Triplet state: \(S=1\), term \(^3S_1\)
This splitting explains why helium exhibits both singlet and triplet spectral series.
Notes on Multiplicity
The multiplicity \(2S+1\) determines how many closely spaced energy levels appear. Higher multiplicity (like triplets) often correspond to lower energy due to electron exchange effects.
In short, spectral term notation provides a compact way to describe the structure of atomic energy levels.