Fine Structure

Fine Structure and External Fields

Phase 1: The Foundation

Syllabus Goal

Physical mechanisms and energy level splitting for Fine Structure, Hyperfine Structure, Zeeman Effect, and Stark Effect.

Fine Structure

Corrections to the Bohr energies:

  1. Relativistic kinetic energy correction.
  2. Spin-Orbit Coupling: Interaction between electron spin and orbital magnetic field. $$ \Delta E_{SO} \propto \mathbf{L} \cdot \mathbf{S} $$

External Fields

  • Zeeman Effect: Splitting in a magnetic field ($B$).
    • Normal (Spin 0) vs Anomalous (Spin 1/2).
  • Stark Effect: Splitting in an electric field ($E$).
    • Linear vs Quadratic Stark effect.

Hyperfine Structure

Interaction between nuclear spin ($I$) and electron angular momentum ($J$).