Atomic and Molecular Physics

6.

Multi-Electron Atoms

6.1.

The Many-Electron Problem

6.1.1.

Schrödinger Equation for N Electrons

6.1.2.

Electron-Electron Repulsion

6.1.3.

Complexity of Exact Solutions

6.2.

The Helium Atom

6.2.1.

Two-Electron System

6.2.2.

Electron-Electron Interaction Term

6.2.3.

Indistinguishable Particles

6.2.4.

Exchange Symmetry Requirements

6.2.5.

Symmetric and Antisymmetric Wavefunctions

6.2.6.

6.2.7.

Singlet States (Parahelium)

6.2.8.

Triplet States (Orthohelium)

6.2.9.

Exchange Energy

6.3.

Approximation Methods

6.3.1.

The Variational Principle

6.3.2.

Variational Method

6.3.3.

Trial Wavefunctions

6.3.4.

Application to Helium Ground State

6.3.5.

Perturbation Theory

6.3.6.

First-Order Perturbation Theory

6.3.7.

Second-Order Perturbation Theory

6.3.8.

Application to Helium

6.3.9.

The Hartree Method

6.3.10.

Self-Consistent Field Approach

6.3.11.

The Hartree-Fock Method

6.3.12.

Exchange Interactions

6.3.13.

Slater Determinants

6.3.14.

The Central Field Approximation

6.3.15.

Effective Nuclear Charge

6.3.16.

Screening Effects

6.3.17.

6.4.

The Pauli Exclusion Principle

6.4.1.

Statement of the Principle

6.4.2.

Antisymmetrization Requirement

6.4.3.

Consequences for Atomic Structure

6.4.4.

Fermi Statistics

6.5.

Electronic Structure of Atoms

6.5.1.

Electron Configurations

6.5.2.

Aufbau Principle

6.5.3.

Order of Orbital Filling

6.5.4.

Electron Shells and Subshells

6.5.5.

Shell Notation (K, L, M, N)

6.5.6.

Subshell Notation (s, p, d, f)

6.5.7.

6.5.8.

Maximum Multiplicity Rule

6.5.9.

Parallel Spin Preference

6.5.10.

The Periodic Table

6.5.11.

Periodic Trends

6.5.12.

Ionization Energy

6.5.13.

Electron Affinity

6.5.14.

6.6.

Atomic Term Symbols

6.6.1.

Russell-Saunders (LS) Coupling

6.6.2.

Total Orbital Angular Momentum L

6.6.3.

Total Spin Angular Momentum S

6.6.4.

Total Angular Momentum J

6.6.5.

Term Symbol Notation ²ˢ⁺¹Lⱼ

6.6.6.

Ground State Terms

6.6.7.

Hund's Rules for Ground States

6.6.8.

6.6.9.

6.6.10.

Intermediate Coupling

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7. Interaction of Atoms with Electromagnetic Radiation