Deriving the Spectrum

The Structure and Transitions of Atoms and Molecules in 14 chapters — from “The exact Coulomb problem and Rydberg states” to “Polyatomic molecules: normal modes and symmetry”.

Chapters

  1. The exact Coulomb problem and Rydberg states
    • The Coulomb energy levels and their n2 degeneracy
    • Exact two-body separation and the reduced mass
    • Quantisation as the termination of the radial series
    • The radial moments ⟨rk⟩ and the contact density
    • The virial theorem for the Coulomb potential
    • The Runge-Lenz vector and the accidental degeneracy
    • Hydrogenic ions, positronium, muonium and muonic hydrogen
    • Rydberg states and the correspondence limit
    • The relativistic scale of the 1S-2S miss
    • Problems
  2. Fine structure and the Lamb shift
    • First-order perturbation theory, including a degenerate level
    • The order-α2 Hamiltonian and its three terms
    • Coupling L and S to J and the coupled basis
    • The spin-orbit interaction
    • The Darwin term and the fine-structure formula
    • The Dirac energy levels
    • The Lamb shift
    • The fine-structure formula in real spectra
    • The 1S-2S interval and the Lamb shift
    • Problems
  3. Hyperfine structure and isotope shifts
    • The nucleus as a given spin, moment and quadrupole
    • Magnetic hyperfine coupling and the F levels
    • The Fermi contact interaction
    • Orbital and spin-dipolar hyperfine coupling for l>0
    • The electric quadrupole hyperfine interaction
    • Alkali ground-state hyperfine intervals and the definition of the second
    • The normal and specific mass isotope shifts
    • The field shift and the size of the nucleus
    • The one-electron atom in one table
    • Problems
  4. Helium: exchange and the variational method
    • The two-electron Hamiltonian and atomic units
    • The electron-electron repulsion to first order
    • Variational estimates and screening
    • Identical particles and exchange symmetry
    • Direct and exchange integrals and the singlet-triplet splitting
    • Exchange written as an effective spin-spin interaction
    • The two term systems of helium and its metastable levels
    • Doubly excited states and autoionisation
    • Problems
  5. The central field and the periodic table
    • The central-field approximation
    • Core penetration and the ordering of l
    • The filling order and the periodic table
    • Ionisation energies and shell structure
    • The origin of the quantum defect
    • Alkali series and the ionisation limit
    • Penetration and the size of alkali fine and hyperfine structure
    • Inner shells, X-ray lines and Moseley's law
    • Problems
  6. Self-consistent fields and correlation
    • The Hartree method and self-consistency
    • The Hartree-Fock equations and the exchange operator
    • The exchange hole
    • Orbital energies and Koopmans' theorem
    • The Thomas-Fermi statistical atom
    • The correlation energy
    • Problems
  7. Many-electron terms, levels and Hund's rules
    • Beyond the central-field approximation
    • Residual repulsion and the spin-orbit interaction
    • The terms of a configuration
    • Term energies from Slater integrals
    • Hund's rules for the ground level
    • The spin-orbit interaction within a term
    • The Landé gJ​ factor from the projection theorem
    • jj coupling and the transition from LS
    • Intermediate coupling and intercombination lines
    • Summary
    • Problems
  8. Radiative transitions and lifetimes
    • Time-dependent perturbation theory and the golden rule
    • Einstein coefficients and detailed balance
    • The absorption rate in the electric-dipole approximation
    • The spontaneous emission rate from a matrix element
    • The electric-dipole selection rules
    • Oscillator strengths and the Thomas-Reiche-Kuhn sum rule
    • Lifetimes, branching ratios and the natural width
    • Magnetic-dipole and electric-quadrupole transitions
    • Summary
    • Problems
  9. Atoms in magnetic fields
    • The field against the spin-orbit interaction
    • The magnetic Hamiltonian of an atom
    • The weak-field Zeeman effect as first-order perturbation theory
    • The strong-field limit and its spin-orbit correction
    • The exact intermediate-field solution for a doublet
    • Polarisation and intensities of Zeeman components
    • Hyperfine levels in a field: gF​ and the Breit-Rabi formula
    • The diamagnetic term and atoms in very strong fields
    • Magnetic resonance as Zeeman spectroscopy
    • Summary
    • Problems
  10. Atoms in electric fields
    • Second-order perturbation theory
    • The quadratic Stark shift as a sum over states
    • The polarisability as a sum over oscillator strengths
    • Closure bounds and the exact hydrogen polarisability
    • The linear Stark effect of hydrogen by degenerate perturbation theory
    • Scalar and tensor polarisability
    • Field ionisation from the saddle point
    • Static polarisabilities in measurement and technology
    • Where second-order perturbation theory stops
    • Problems
  11. The Born-Oppenheimer separation and the chemical bond
    • The Born-Oppenheimer separation
    • The hydrogen molecular ion by LCAO
    • What a bond is made of: the molecular virial theorem
    • H2​: molecular orbitals, Heitler-London and the covalent bond
    • Molecular orbitals of first-row diatomics and bond order
    • Molecular term symbols and correlation with atomic limits
    • Polar and ionic bonds, and crossing curves
    • Problems
  12. Diatomic rotation-vibration spectra and nuclear spin statistics
    • Term values from an expansion about the minimum
    • The Morse oscillator and dissociation energies
    • Centrifugal distortion and vibration-rotation coupling
    • The method of combination differences
    • The dipole function, band intensities and overtones
    • Nuclear spin statistics of homonuclear molecules
    • Ortho and para hydrogen
    • Pure rotational spectroscopy and what B0​ measures
    • What the diatomic spectrum settles
    • Problems
  13. Electronic spectra of diatomic molecules
    • Reading the iodine absorption spectrum
    • Selection rules for diatomic electronic transitions
    • The Franck-Condon principle
    • Band systems, Deslandres tables and dissociation limits
    • Rotational structure of electronic bands and band heads
    • Photodissociation and predissociation
    • Fluorescence, the Stokes shift and phosphorescence
    • Raman scattering from the polarisability
    • Photoelectron spectra as Franck-Condon measurements
    • Summary
    • Problems
  14. Polyatomic molecules: normal modes and symmetry
    • Infrared and Raman bands observed
    • Point groups, characters and the reduction formula
    • Equilibrium geometry and the molecular point group
    • Normal modes of a polyatomic molecule
    • Classifying modes by symmetry
    • Infrared and Raman activity and mutual exclusion
    • Overtones, combination bands and Fermi resonance
    • Rotation of polyatomic molecules
    • Inversion doubling in ammonia
    • Why some atmospheric gases absorb thermal infrared
    • The spectrum derived
    • Problems