Fine Structure of Sodium D Lines

Spectrum of Neutral Sodium and the D-Line Doublet

1. Electronic Structure of Sodium

• The neutral sodium atom (Na) has 11 electrons.
• 10 electrons are tightly bound in closed inner shells (core electrons).
• These contribute no net angular momentum to the atom.
• The 11^th (valence) electron determines the optical properties and spectrum.

2. Principal Series and the D-Line

The D-line doublet (5890 Å and 5896 Å) belongs to the principal series, arising from transitions between:

• Upper state: P-orbital (L = 1)
• Lower state: S-orbital (L = 0)

Fine Structure Terms:

P-state (L = 1): Spin-orbit coupling splits it into two fine-structure levels:

• ²P_3/2 (J = 3/2)
• ²P_1/2 (J = 1/2)

S-state (L = 0): Only one term:

• ²S_1/2 (J = 1/2)

3. Allowed Transitions

The D-line doublet consists of two allowed transitions:

• D₁ line (5896 Å): ²P_1/2 → ²S_1/2
• D₂ line (5890 Å): ²P_3/2 → ²S_1/2

Selection Rules:

• ΔL = ±1
• ΔJ = 0, ±1 (but J = 0 → J = 0 is forbidden)

4. Origin of the Doublet

The energy splitting between ²P_3/2 and ²P_1/2 is due to spin-orbit coupling. This fine-structure splitting explains the two closely spaced D-line wavelengths.