Fundamentals of Inelastic Electron Scattering

1. Classical Scattering Theory.- 1.1 Elastic Cross Sections.- 1.2 The Deflection Function.- 1.3 Scattering on a Hard Sphere.- 1.4 The General Case.- 1.5 Rutherford Scattering.- 1.6 Singularities.- 1.7 Inelastic Cross Sections.- 1.8 The Ramsauer-Townsend Effect.- 1.9 On the Validity of the Classical Description.- 2. Quantum Mechanical Scattering Theory.- 2.1 Absorption Edges.- 2.2 The Differential Cross Section.- 2.3 The Dynamic Form Factor.- 2.4 The Generalized Oscillator Strength ..- 2.5 Rutherford Scattering.- 2.6 The Bethe Differential Cross Section.- 2.7 The Hydrogenic Approach.- 2.8 The Bethe Approximation.- 2.9 Zonal Harmonics Expansion.- 2.10 Qualitative Interpretation.- 2.11 The Total Elastic Cross Section.- 2.12 The Ramsauer-Townsend Effect.- 3. Practical Aspects of Absorption Edge Spectroscopy.- 3.1 A Survey of Applications.- 3.2 Microanalysis.- 3.3 Electron Compton Scattering.- 3.4 Site-specific Excitations.- 3.5 Extended Energy Loss Fine Structure (EXELFS).- 4. Electrodynamics in Homogeneous, Isotropic Media.- 4.1 Fourier Transform.- 4.2 Linear Response of a Medium.- 4.3 The Maxwell Equations.- 4.4 The Dielectric Function.- 4.5 The Drude Model.- 4.6 Charge Oscillations in a Metal.- 5. Some Details on Charge Oscillations.- 5.1 Screening.- 5.2 Plasmons.- 5.3 Plasmon Dispersion.- 5.4 Boundaries.- 5.5 Surface Oscillations.- 5.6 The ATR-Method.- 5.7 On the Restricted Validity of the Fresnel Equations.- 5.8 The Differential Cross Section.- 5.9 Energy Loss Function.- 6. Quantum Mechanical Preliminaries.- 6.1 Summary of Important Facts.- 6.2 The Lippman-Schwinger Equation.- 6.3 The Green Operator.- 6.4 The Dyson Equation.- 6.5 Green Operators in the Time Domain.- 6.6 Relation of G0 to the Time Evolution Operator.- 6.7 Second Quantization.- 6.8 Operators in Second Quantization.- 6.9 The Perturbation Series in Graphical Representation.- 6.10 An Example.- 6.11 The Coulomb Interaction.- 7. Quantum Mechanical Description of the Electron Gas.- 7.1 The Jellium Hamiltonian.- 7.2 Sommerfeld Non-interacting e--Gas.- 7.3 Hartree Approximation (HA).- 7.4 Hartree-Fock Approximation (HFA).- 7.5 Why Higher Order Perturbation Theory Does not Work.- 7.6 The Random Phase Approximation (RPA).- 7.7 Electron Scattering.- 7.8 Polarization Diagrams.- 8. Beyond Simple Models.- 8.1 Solid State Effects.- 8.2 Ion-Electron Interactions.- 8.3 Multiple Scattering.- References.- Author Index.