University13 min

Spin-orbit coupling and term symbols

Find an atom's ground term with Hund's rules, read a term symbol and understand where the yellow sodium doublet comes from.

The essentials

1

Quantised angular momenta

Orbital momentum: ∣L⃗∣=ℏℓ(ℓ+1)|\vec{L}| = \hbar\sqrt{\ell(\ell+1)} and Lz=mℓℏL_z = m_\ell \hbar. Electron spin, s=12s = \dfrac{1}{2}: ∣S⃗∣=ℏ34|\vec{S}| = \hbar\sqrt{\dfrac{3}{4}} and Sz=msℏS_z = m_s \hbar with ms=±12m_s = \pm\dfrac{1}{2}. Spin is an intrinsic property with no classical analogue.
2

The spin-orbit interaction

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3

L-S (Russell-Saunders) coupling and the term symbol

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4

Hund's rules (ground term)

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5

Fine structure and j-j coupling

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