Many-Electron Atoms

Many-Electron Atoms

Phase 2: Building Complexity

Syllabus Goal

Coupling schemes: LS coupling (Russell-Saunders) and jj coupling. X-ray spectra.

Central Field Approximation

Electrons move in an effective potential $V_{eff}(r)$ created by nucleus and other electrons.

Coupling Schemes

  • LS Coupling (Light atoms):
    • $\mathbf{L} = \sum \mathbf{l}_i$
    • $\mathbf{S} = \sum \mathbf{s}_i$
    • $\mathbf{J} = \mathbf{L} + \mathbf{S}$
  • jj Coupling (Heavy atoms):
    • $\mathbf{j}_i = \mathbf{l}_i + \mathbf{s}_i$
    • $\mathbf{J} = \sum \mathbf{j}_i$

Hund’s Rules

Determine the ground state configuration term.

  1. Maximize $S$.
  2. Maximize $L$.
  3. Smallest $J$ (if shell < half full) or largest $J$ (if > half).