Spin-Orbit Coupling Calculator

Calculate spin-orbit coupling and fine structure splitting

Atomic Number (Z):

Principal Quantum Number (n):

Orbital Angular Momentum (L):

Spin Angular Momentum (S):

About Spin-Orbit Coupling

Spin-orbit coupling is a relativistic interaction between an electron's spin and its orbital motion. It causes fine structure splitting of spectral lines and is responsible for the sodium doublet.

Key Formulas:

J = |L - S|, |L - S| + 1, ..., L + S
ESO = (ξ/2)[J(J+1) - L(L+1) - S(S+1)]
gJ = 1 + [J(J+1) + S(S+1) - L(L+1)]/[2J(J+1)]

Examples:

Sodium D-lines: 3p → 3s with J=3/2 and J=1/2
Hydrogen fine structure: ~0.45 cm⁻¹ for n=2